Oat sheaves lean in a corner of the front window.
|
|
Yellow and black spots appeared on the leaves and sheaves of wheat.
|
|
A little later, dancers huddle together in three groups like tall sheaves of wheat.
|
|
The pianists filed out, carefully arranging their sheaves of photographs on each gleaming black instrument.
|
|
Teiji Ito's sparse music employs Asian instruments; the décor features three vast sheaves of rushes or hemp.
|
|
Chinese buyers brandish sheaves of permits when they import logs of taun, pencil cedar or kwila from the country.
|
|
For expats in Cairo, buying spirits required a trip to a distant state outlet and pharaonic sheaves of paperwork.
|
|
The levitating skyline of Constantinople pricked its sheaves of thin cylinders and its hemispheres out of the sea-mist.
|
|
Our group of five traveled by Jeep past rice fields full of golden sheaves in the process of being harvested.
|
|
The sun has risen a handsbreadth above the horizon, crowning the eastern hills, sheaves of light slanting through the stunted trees.
|
|
The small Japanese paper lanterns, tiny beside the vast sheaves, that dancers used to hold are now glass-like bulbs illuminated by electricity.
|
|
Stuff too many sheaves of paper into a staple gun and it will struggle to fasten them together, however thin each page may be.
|
|
From Epiphanies past, I've saved fèves shaped like macarons (one was black — so chic and so unusual), sheaves of wheat, hearts and stylized beans.
|
|
In sheaves of legal appeals, she begged a long list of Russian military officials — the defense minister himself, finally — to restore her husband's pension.
|
|
People scratched them into desks, scrawled them across the bathroom stalls, handed sheaves of workings-out over to the teachers instead of their math homework.
|
|
Ms. Gordon-Reed said sheaves of wheat had also appeared on American pennies and did not have the visceral associations of a Confederate or Nazi flag.
|
|
And right now, to an unusual degree, the market itself is giving each side of the the bull-bear debate sheaves of evidence supporting its case.
|
|
Pictures showed no notes on the table in front of Davis and his two advisers, in contrast to sheaves of paperwork brought by Barnier and his team.
|
|
But the aesthetics are more important: We see Clinton carrying weighty sheaves of government papers, descending from Air Force One, hugging children, and walking around her Senate office.
|
|
As a boy, Ivan Albright modeled for some of his father's paintings featuring young lads in straw hats gazing into the shimmering water or clutching sheaves of wheat.
|
|
He worked PVC into coats of crumpled rosettes and layered sheaves of petals made of polyester organdy until the women wearing them seemed part human, part landscape, entirely elemental.
|
|
He drove them around in his blue convertible (sometimes without a car seat), took them swimming at the pool outside his apartment and gave them sheaves of $20 bills.
|
|
Observing the trash heap of tissues on my desk and floor, the sheaves of rumpled printouts beside my keyboard, scrawled with addendums in rainbow colors, she grabbed my wrists.
|
|
While we talked, white guys in pickups parked in the driveway and came to the front door, where they conferred with Nasrin over sheaves of documents—constituent service on a rainy Saturday afternoon.
|
|
FRIEDMAN There's a Chanel dress in the Cloisters, with sheaves of wheat and flowers made of gold thread, that had very similar embroideries to one of the papal vestments in the Costume Institute.
|
|
I didn't have to share it with my brother; I didn't have to use the treacle-slow dial-up internet to print of sheaves of badly-written game guides to figure out how to play.
|
|
Designed in 1936, the shield displays three sheaves of wheat taken from the Royalls family coat of arms, with the university's motto, "Veritas," the Latin word for truth, scrolled on three panels across the top.
|
|
Think of a diamond-encrusted oak-leaf ring, brushed-gold earrings in the shape of wheat sheaves that gently sweep along the ear or a between-the-finger ring that looks like a laurel leaf.
|
|
And we should do that in a way that shows the inherently entwined nature of the good and bad of our past, using written text and symbols like the sheaves and, even, buildings like Monticello.
|
|
Though dwarfed by nearby sheaves of bladed flax, or harakeke, the woolly stems can hold their ground like hooves; the individual petioles try to overtake one another, competing harmlessly, like teams in the fairest of sports.
|
|
It was, in the end, the classic pieces that showcased the art of the ateliers that made the biggest statement: a beautiful sheer cape embroidered with sequined gold wheat sheaves, for example, or feather covered cocktail dresses.
|
|
During an 18-month excavation, the archaeologists unearthed objects such as a gold ring engraved with two bulls surrounded by sheaves of grain, as well as a gold pendant depicting an Egyptian goddess who protected the dead.
|
|
Among the bound sheaves is an uprooted tussock, yanked from the earth by King Leopold III himself in 250 — three years before Belgium relinquished its claim to Congo — squashed flat and taped to a sheet of paper.
|
|
His achievements in the job included computerizing jury selection and overseeing the microfilming of sheaves of historical documents, including records from Alexander Hamilton's law office, plagiarism suits by Mark Twain and the divorce papers of Aaron Burr.
|
|
Those caught (their sheaves of papers, including court documents and letters of complaint, give them away) are often whisked to "black jails" where they are held until officials arrange to have them escorted back to their home towns.
|
|
Mr. Hartnell and the queen chose motifs from across the United Kingdom and the Commonwealth: maple leaves for Canada, wheat sheaves for Pakistan, lotus flowers for South Africa, the English Rose, Welsh leeks, Scottish thistles and Irish shamrocks.
|
|
Although speaking of foodstuffs, a little more puzzling were the sheaves of dried spaghetti and free-floating penne pasta prints on black silk; the ice cream cones on slouchy pajama suiting; and the fish swimming across a white pencil skirt.
|
|
It shows three sheaves of wheat, a symbol that is derived from the family crest of an 18th-century slave owner, Isaac Royall Jr., who endowed the first law professorship at Harvard, though the gift did not by itself create the law school.
|
|
Jordan gets away with these infelicities, paradoxically, because he's a good writer and knows how to pace a story — an uncommon gift these days — and because (also rare) his earnest curiosity about the emotional pulses of his characters isn't buried in sheaves of novelistic analysis or digression.
|
|
Against this tumultuous backdrop, David Davis, the British secretary of state for exiting the European Union, was photographed with colleagues in Brussels on Monday sitting at the negotiating table without any documents or notes, while their European Union counterparts had sheaves of position papers before them.
|
|
It turns out gamebooks are making something of a comeback in the Kindle age, thanks to this essential efficiency: tapping on a "go to page X" option on your ebook is just a hell of a lot faster than flicking back and forth through sheaves of dead wood.
|
|
The exploits of Mr. Hoare, who was called "Mad Mike" for his recklessness under fire, were recounted in books by him and others, in a film starring Richard Burton, and in sheaves of foreign correspondents' dispatches, now faded yellow in old newspaper morgues with datelines from far-off places.
|
|
The meeting between Davis and Barnier featured just two aides each; the absence of notes in front of the British trio, compared to sheaves of papers on the EU side, sparked scathing jibes from critics in Britain who see Prime Minister Theresa's May's government as divided and badly unprepared.
|
|
The art of that time was made to be photographed — happenings, kinetic sculpture, dance, performance, Arman stuffing his gallery full of trash, Jacques Villeglé tearing sheaves of stuck-together posters off walls to take them home and frame them, Yayoi Kusama covering nudes with polka dots on the Brooklyn Bridge.
|
|
There's the chorus, which slides an excited shout of "stand in the kitchen and whip out the work" into a couple sheaves of melody, and which, once you've heard it, becomes impossible to not think about any time you're in a kitchen, busy tossing together your latest fricassee or what have you.
|
|
A Kodachrome color transparency of sheaves of wheat in a field, taken by J.C.A. Redhead during World War II. Kodachrome film was imported from the US and was in very short supply during World War II. As head of Kodak's photo-finishing laboratory in Harrow, England, Redhead had access to supplies of this scarce color film.
|
|
In tribute to the designer's former apartment, there were ears of wheat from the gilded sheaves that Chanel kept for good luck; embroidery on cardigans worn with sleek jogging pants; Chinese lacquered Coromandel screens that appeared as pocket flaps; and strands of her infamous pearls that covered little black dresses — definitely Coco's codes, and a bit of Karl's, too.
|
|
" The Book of Ruth in the Old Testament tells the story of literature's most famous gleaner, a pauper and an alien in Judah who so enchanted the landowner, Boaz, that he instructed his reapers actively to help her: "Let her glean even among the sheaves, and reproach her not: And let fall also some of the handfuls of purpose for her, and leave them.
|
|
The category of perverse sheaves is an abelian subcategory of the (non-abelian) derived category of sheaves, equal to the core of a suitable t-structure, and is preserved by Verdier duality. The bounded derived category of perverse l-adic sheaves on a scheme X is equivalent to the derived category of constructible sheaves and similarly for sheaves on the complex analytic space associated to a scheme X/C.
|
|
The quasi-coherent sheaves are a generalization of coherent sheaves and include the locally free sheaves of infinite rank. Coherent sheaf cohomology is a powerful technique, in particular for studying the sections of a given coherent sheaf.
|
|
The Riemann–Hilbert correspondence establishes a link between certain D-modules and constructible sheaves. As such, it provided a motivation for introducing perverse sheaves.
|
|
They are variously defined, for example, as sheaves of sets or sheaves of rings, depending on the type of data assigned to open sets. There are also maps (or morphisms) from one sheaf to another; sheaves (of a specific type, such as sheaves of abelian groups) with their morphisms on a fixed topological space form a category. On the other hand, to each continuous map there is associated both a direct image functor, taking sheaves and their morphisms on the domain to sheaves and morphisms on the codomain, and an inverse image functor operating in the opposite direction. These functors, and certain variants of them, are essential parts of sheaf theory.
|
|
The decomposition theorem, a far- reaching extension of the hard Lefschetz theorem decomposition, requires the usage of perverse sheaves. Hodge modules are, roughly speaking, a Hodge- theoretic refinement of perverse sheaves. The geometric Satake equivalence identifies equivariant perverse sheaves on the affine Grassmannian Gr_G with representations of the Langlands dual group of a reductive group G - see . A proof of the Weil conjectures using perverse sheaves is given in .
|
|
This gives an upper bound on the absolute values of the eigenvalues of Frobenius, and Poincaré duality then shows that this is also a lower bound. In general Rif! does not take pure sheaves to pure sheaves. However it does when a suitable form of Poincaré duality holds, for example if f is smooth and proper, or if one works with perverse sheaves rather than sheaves as in .
|
|
In mathematics, in the theory of sheaves the direct image with compact (or proper) support is an image functor for sheaves. It is one of Grothendieck's six operations.
|
|
In mathematics, specifically in algebraic topology and algebraic geometry, an inverse image functor is a contravariant construction of sheaves; here “contravariant” in the sense given a map f : X \to Y, the inverse image functor is a functor from the category of sheaves on Y to the category of sheaves on X. The direct image functor is the primary operation on sheaves, with the simplest definition. The inverse image exhibits some relatively subtle features.
|
|
Most examples of constructible sheaves come from intersection cohomology sheaves or from the derived pushforward of a local system on a family of topological spaces parameterized by a base space.
|
|
A similar definition applies to sheaves on topoi, such as étale sheaves. Instead of the above preimage f−1(U) the fiber product of U and X over Y is used.
|
|
Accessed 13 February 2012 The wheat sheaves and blue background are incorporated into the logo for Cheshire West and Chester Council and the wheat sheaves are incorporated into the logo for Cheshire East Council. Additionally, the logo of Stockport County F.C. features the three golden sheaves of wheat and golden blade on a blue background as its escutcheon.
|
|
In algebraic geometry, Graded manifolds are extensions of the concept of manifolds based on ideas coming from supersymmetry and supercommutative algebra. Both graded manifolds and supermanifolds are phrased in terms of sheaves of graded commutative algebras. However, graded manifolds are characterized by sheaves on smooth manifolds, while supermanifolds are constructed by gluing of sheaves of supervector spaces.
|
|
In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a class of sheaves closely linked to the geometric properties of the underlying space. The definition of coherent sheaves is made with reference to a sheaf of rings that codifies this geometric information. Coherent sheaves can be seen as a generalization of vector bundles. Unlike vector bundles, they form an abelian category, and so they are closed under operations such as taking kernels, images, and cokernels.
|
|
In algebraic geometry and complex analytic geometry, coherent sheaves are a class of sheaves of particular geometric importance. For example, an algebraic vector bundle (on a locally Noetherian scheme) or a holomorphic vector bundle (on a complex analytic space) can be viewed as a coherent sheaf, but coherent sheaves have the advantage over vector bundles that they form an abelian category. On a scheme, it is also useful to consider the quasi-coherent sheaves, which include the locally free sheaves of infinite rank. A great deal is known about the cohomology groups of a scheme or complex analytic space with coefficients in a coherent sheaf.
|
|
Purchase cables or tapes run through sheaves in the flight deck or alongside of the runway to the arresting engines. Damper sheaves act as hydraulic shock absorbers that provide for the increased landing speeds.
|
|
Every torsion sheaf is a filtered inductive limit of constructible sheaves.
|
|
This phenomenon is studied and used in the theory of perverse sheaves.
|
|
In terms of localization of modules, one can define quasi-coherent sheaves and coherent sheaves on locally ringed spaces. In algebraic geometry, the quasi-coherent OX-modules for schemes X are those that are locally modelled on sheaves on Spec(R) of localizations of any R-module M. A coherent OX-module is such a sheaf, locally modelled on a finitely-presented module over R.
|
|
Effective Cartier divisors are those which correspond to ideal sheaves. In fact, the theory of effective Cartier divisors can be developed without any reference to sheaves of rational functions or fractional ideal sheaves. Let X be a scheme. An effective Cartier divisor on X is an ideal sheaf I which is invertible and such that for every point x in X, the stalk Ix is principal.
|
|
In contrast, sheaves of smooth functions tend not to carry much topological information.
|
|
The abstract framework for defining cohomology and derived functors does not need them. However, in most concrete situations, resolutions by acyclic sheaves are often easier to construct. Acyclic sheaves therefore serve for computational purposes, for example the Leray spectral sequence.
|
|
Wheat sheaves near King's Somborne, England arranged into a stook. Stooking maize in Kenya. A stook /stʊk/, also referred to as a shock or stack,Oxford Dictionary definition of shock is an arrangement of sheaves of cut grain- stalks placed so as to keep the grain-heads off the ground while still in the field and prior to collection for threshing. Stooked grain sheaves are typically wheat, barley and oats.
|
|
Bundles may also be described by their sheaves of sections. The pullback of bundles then corresponds to the inverse image of sheaves, which is a contravariant functor. A sheaf, however, is more naturally a covariant object, since it has a pushforward, called the direct image of a sheaf. The tension and interplay between bundles and sheaves, or inverse and direct image, can be advantageous in many areas of geometry.
|
|
A "topos" is a category behaving like the category of sheaves of sets on a topological space. In analogy, Lurie's definition and characterization theorem of an ∞-topos says that an ∞-topos is an ∞-category behaving like the category of sheaves of spaces.
|
|
He has several tattoos, including one of sheaves of wheat representing the province of Saskatchewan.
|
|
Quasi-coherent sheaves on any scheme form an abelian category. Gabber showed that, in fact, the quasi-coherent sheaves on any scheme form a particularly well-behaved abelian category, a Grothendieck category.. A quasi-compact quasi-separated scheme X (such as an algebraic variety over a field) is determined up to isomorphism by the abelian category of quasi-coherent sheaves on X, by Rosenberg, generalizing a result of Gabriel.Antieau (2016), Corollary 4.2.
|
|
The purpose of a stook [or 'stooking'] is to dry the unthreshed grain while protecting it from vermin until it is brought into long-term storage. The unthreshed grain also cures while in a stook. In England, sheaves were commonly stacked in stooks of twelve and may therefore refer to twelve sheaves. Stook may also have a general meaning of 'bundle' or 'heap' and applicable to items other than sheaves or bales.
|
|
Huybrechts does research on K3 surfaces and their higher- dimensional analogues (compact hyperkähler manifolds) and moduli spaces of sheaves on varieties. In 2010 he was an invited speaker at the International Congress of Mathematicians in Hyderabad and gave a talk Hyperkähler Manifolds and Sheaves.
|
|
Perverse sheaves are a fundamental tool for the geometry of singular spaces. Therefore, they are applied in a variety of mathematical areas. In the Riemann-Hilbert correspondence, perverse sheaves correspond to regular holonomic D-modules. This application establishes the notion of perverse sheaf as occurring 'in nature'.
|
|
The school badge depicts crossed corn sheaves in gold on a white and red shield, representing growth and a rich educational harvest while linking to Lincolnshire's rural and agricultural heritage. Above the corn sheaves are the words King Edward VI and below is the word Spilsby.
|
|
Photos of show the change in bow sheaves after a modernization. In that case the entire ship was essentially rebuilt. The Monarch (4) page at History of the Atlantic Cable & Undersea Communications has a painting of Monarch anchored off Sesimbra during 1969 operations showing the drastic change in the ship's bow after the 1968 modernization. After a 1968 modification Monarch had three bow sheaves, a flat surface sheave and two "V" sheaves, and one "V" stern sheave.
|
|
Much of algebraic geometry and complex analytic geometry is formulated in terms of coherent sheaves and their cohomology.
|
|
For specific classes of spaces or sheaves, there are many tools for computing sheaf cohomology, some discussed below.
|
|
In mathematics, the Andreotti–Vesentini separation theorem, introduced by states that certain cohomology groups of coherent sheaves are separated.
|
|
The fundamental technical tool in algebraic geometry is the cohomology theory of coherent sheaves. Although it was introduced only in the 1950s, many earlier techniques of algebraic geometry are clarified by the language of sheaf cohomology applied to coherent sheaves. Broadly speaking, coherent sheaf cohomology can be viewed as a tool for producing functions with specified properties; sections of line bundles or of more general sheaves can be viewed as generalized functions. In complex analytic geometry, coherent sheaf cohomology also plays a foundational role.
|
|
Differentiable stacks and topological stacks are defined in a way similar to algebraic stacks, except that the underlying category of affine schemes is replaced by the category of smooth manifolds or topological spaces. More generally one can define the notion of an n-sheaf or n–1 stack, which is roughly a sort of sheaf taking values in n–1 categories. There are several inequivalent ways of doing this. 1-sheaves are the same as sheaves, and 2-sheaves are the same as stacks.
|
|
However, coherent sheaves are richer; for example, a vector bundle on a closed subscheme Y of X can be viewed as a coherent sheaf on X which is zero outside Y (by the direct image construction). In this way, coherent sheaves on a scheme X include information about all closed subschemes of X. Moreover, sheaf cohomology has good properties for coherent (and quasi-coherent) sheaves. The resulting theory of coherent sheaf cohomology is perhaps the main technical tool in algebraic geometry.Dieudonné (1985), sections VIII.
|
|
In mathematics, an ∞-topos is, roughly, an ∞-category such that its objects behave like sheaves of spaces with some choice of Grothendieck topology; in other words, it gives an intrinsic notion of sheaves without reference to an external space. The prototypical example of an ∞-topos is the ∞-category of sheaves of spaces on some topological space. But the notion is more flexible; for example, the ∞-category of étale sheaves on some scheme is not the ∞-category of sheaves on any topological space but it is still an ∞-topos. Precisely, in Lurie's Higher Topos Theory, an ∞-topos is defined as an ∞-category X such that there is a small ∞-category C and a left exact localization functor from the ∞-category of presheaves of spaces on C to X. A theorem of Lurie states that an ∞-category is an ∞-topos if and only if it satisfies an ∞-categorical version of Giraud’s axioms in ordinary topos theory.
|
|
In the 1960s, a typical use of triangulated categories was to extend properties of sheaves on a space X to complexes of sheaves, viewed as objects of the derived category of sheaves on X. More recently, triangulated categories have become objects of interest in their own right. Many equivalences between triangulated categories of different origins have been proved or conjectured. For example, the homological mirror symmetry conjecture predicts that the derived category of a Calabi–Yau manifold is equivalent to the Fukaya category of its "mirror" symplectic manifold.
|
|
In mathematics, injective sheaves of abelian groups are used to construct the resolutions needed to define sheaf cohomology (and other derived functors, such as sheaf Ext). There is a further group of related concepts applied to sheaves: flabby (flasque in French), fine, soft (mou in French), acyclic. In the history of the subject they were introduced before the 1957 "Tohoku paper" of Alexander Grothendieck, which showed that the abelian category notion of injective object sufficed to found the theory. The other classes of sheaves are historically older notions.
|
|
Due to their general nature and versatility, sheaves have several applications in topology and especially in algebraic and differential geometry. First, geometric structures such as that of a differentiable manifold or a scheme can be expressed in terms of a sheaf of rings on the space. In such contexts several geometric constructions such as vector bundles or divisors are naturally specified in terms of sheaves. Second, sheaves provide the framework for a very general cohomology theory, which encompasses also the "usual" topological cohomology theories such as singular cohomology.
|
|
In algebraic geometry, Horrocks bundles are certain indecomposable rank 3 vector bundles (locally free sheaves) on 5-dimensional projective space, found by .
|
|
Neptune before substantial modifications. Note almost original bow sheaves and absence of helicopter deck. Cable drums from foredeck. Cable drums from below.
|
|
The properties characterizing perverse sheaves already appeared in the 75's paper of Kashiwara on the constructibility of solutions of holonomic D-modules.
|
|
Several sheaves are then leant against each other with the ears off the ground to dry out, forming a stook. After drying, the sheaves are gathered from the field and stacked, being placed with the ears inwards, then covered with thatch or a tarpaulin; this is called a stack or rick. In the British Isles a rick of sheaves is traditionally called a corn rick, to distinguish it from a hay rick ("corn" in British English retains its older sense of "grain" generally, not "maize"). Ricks are made in an area inaccessible to livestock, called a rick-yard or stack-yard.
|
|
Foundations for the many relations between the two theories were put in place during the early part of the 1950s, as part of the business of laying the foundations of algebraic geometry to include, for example, techniques from Hodge theory. The major paper consolidating the theory was Géometrie Algébrique et Géométrie Analytique by Jean-Pierre Serre, now usually referred to as GAGA. It proves general results that relate classes of algebraic varieties, regular morphisms and sheaves with classes of analytic spaces, holomorphic mappings and sheaves. It reduces all of these to the comparison of categories of sheaves.
|
|
Most of the harvesting is still done by hand. As soon as the grains reach maturity, usually in July or August, men cut the fonio with sickles while women and children gather it into sheaves. A motor-driven mower may be used to assist in this. The sheaves must be stored in a dry and well ventilated area to prevent mould formation.
|
|
The barley, kernels and sheaves, were then winnowed-(of the sheaves) with pitchforks and laid on sticks to make clean. The writer of the Sumerian Farmer's Almanac said that the agricultural instructions were not his, however those of the god Ninurta, the son and "true farmer" of the leading Sumerian deity, Enlil. This translation of the complete text is by Kramer.Kramer, pp.
|
|
Since the data of a (pre-)sheaf depends on the open subsets of the base space, sheaves on different topological spaces are unrelated to each other in the sense that there are no morphisms between them. However, given a continuous map f : X → Y between two topological spaces, pushforward and pullback relate sheaves on X to those on Y and vice versa.
|
|
The name derives from the use of the term garb to describe sheaves of grain depicted on a heraldic shield or coat of arms. Thus the name of garbure, which is eaten with a fork, is a reference to the use of pitchforks to pick up sheaves of grain. It originated in Gascony in southwest France. It is similar to potée.
|
|
There are, a bit weaker, reconstruction theorems from the derived categories of (quasi)coherent sheaves motivating the derived noncommutative algebraic geometry (see just below).
|
|
In commutative algebra, Grothendieck local duality is a duality theorem for cohomology of modules over local rings, analogous to Serre duality of coherent sheaves.
|
|
Grothendieck sites are categories with additional data axiomatizing whether a family of arrows covers an object. Sites are a general setting for defining sheaves.
|
|
Castings made by this method are used extensively to make machine tools, gears, sheaves, cylinder heads, valve bodies, rollers and other highly engineered applications.
|
|
The model at the Telegraph Museum Porthcurno shows an original configuration in which a "V" sheave was in the center flanked by two flat sheaves.
|
|
The procession proceeds along the Estrada de Santos Passos which joins to Rua de Novidade. This 1 km long route is traditionally decorated with 24 arches of bamboo shoots. After a short prayer, the Parish priest blesses the sheaves by sprinkling holy water and burning incense. Then the feast President cuts the sheaves with a silver sickle and carries them in a silver tray to the church.
|
|
The motivation behind Artin and Grothendieck's proof for constructible sheaves was to give a proof that could be adapted to the setting of étale and \ell-adic cohomology. Up to some restrictions on the constructible sheaf, the Lefschetz theorem remains true for constructible sheaves in positive characteristic. The theorem can also be generalized to intersection homology. In this setting, the theorem holds for highly singular spaces.
|
|
Since topological spaces are constructed from points, which are themselves a kind of local data, the category of sheaves can therefore be used as a replacement for the original space. Grothendieck consequently defined a topos to be a category of sheaves and studied topoi as objects of interest in their own right. These are now called Grothendieck topoi. Every topological space determines a topos, and vice versa.
|
|
Giraud's theorem already gives "sheaves on sites" as a complete list of examples. Note, however, that nonequivalent sites often give rise to equivalent topoi. As indicated in the introduction, sheaves on ordinary topological spaces motivate many of the basic definitions and results of topos theory. The category of sets is an important special case: it plays the role of a point in topos theory.
|
|
An abelian étale sheaf F on X is called finite locally constant if it is a representable functor which can be represented by an étale cover of X. It is called constructible if X can be covered by a finite family of subschemes on each of which the restriction of F is finite locally constant. It is called torsion if F(U) is a torsion group for all étale covers U of X. Finite locally constant sheaves are constructible, and constructible sheaves are torsion. Every torsion sheaf is a filtered inductive limit of constructible sheaves. Grothendieck originally introduced the machinery of Grothendieck topologies and topoi to define the étale topology.
|
|
In mathematics, the Andreotti–Grauert theorem, introduced by , gives conditions for cohomology groups of coherent sheaves over complex manifolds to vanish or to be finite-dimensional.
|
|
The ship was radically changed during the 1968 refit with removal of the center mast, a new deck house forward and major change to the bow sheaves.
|
|
The six operations formalism has since been shown to apply to contexts such as D-modules on algebraic varieties, sheaves on locally compact topological spaces, and motives.
|
|
The Geometric Satake equivalence establishes an equivalence between representations of the Langlands dual group {}^L G of a reductive group G and certain equivariant perverse sheaves on the affine Grassmannian associated to G. This equivalence provides a non-combinatorial construction of the Langlands dual group. It is proved by showing that the mentioned category of perverse sheaves is a Tannakian category and identifying its Tannaka dual group with {}^L G.
|
|
Grothendieck's definition of sheaf cohomology, now standard, uses the language of homological algebra. The essential point is to fix a topological space X and think of cohomology as a functor from sheaves of abelian groups on X to abelian groups. In more detail, start with the functor E ↦ E(X) from sheaves of abelian groups on X to abelian groups. This is left exact, but in general not right exact.
|
|
Especially in algebraic geometry and the theory of complex manifolds, sheaf cohomology provides a powerful link between topological and geometric properties of spaces. Sheaves also provide the basis for the theory of D-modules, which provide applications to the theory of differential equations. In addition, generalisations of sheaves to more general settings than topological spaces, such as Grothendieck topology, have provided applications to mathematical logic and number theory.
|
|
This segment includes do-it-yourself, agriculture and forestry products like wires and ropes, rings and swivels, shackles and links, hooks, sheaves, belt brackets, nails, and cattle chains.
|
|
A central part of scheme theory is the notion of coherent sheaves, generalizing the notion of (algebraic) vector bundles. For a scheme X, one starts by considering the abelian category of OX-modules, which are sheaves of abelian groups on X that form a module over the sheaf of regular functions OX. In particular, a module M over a commutative ring R determines an associated OX-module on X = Spec(R). A quasi-coherent sheaf on a scheme X means an OX-module that is the sheaf associated to a module on each affine open subset of X. Finally, a coherent sheaf (on a Noetherian scheme X, say) is an OX-module that is the sheaf associated to a finitely generated module on each affine open subset of X. Coherent sheaves include the important class of vector bundles, which are the sheaves that locally come from finitely generated free modules. An example is the tangent bundle of a smooth variety over a field.
|
|
These two different statements are not however contradictory insomuch that, as indicated by the Five Aggregates model, name-form includes mental fabrications (see the "Five Aggregates" diagram above). In the "Sheaves of Reeds Discourse" (Nalakalapiyo Sutta, SN 12.67), Ven. Sariputta uses this famous analogy to explain the interdependency of consciousness and name-form: :"It is as if two sheaves of reeds were to stand leaning against one another. In the same way, from name-form as a requisite condition comes consciousness, from consciousness as a requisite condition comes name-form.... :"If one were to pull away one of those sheaves of reeds, the other would fall; if one were to pull away the other, the first one would fall.
|
|
It was a possible question to ask, around 1957, for a purely category-theoretic characterisation of categories of sheaves of sets, the case of sheaves of abelian groups having been subsumed by Grothendieck's work (the Tôhoku paper). Such a definition of a topos was eventually given five years later, around 1962, by Grothendieck and Verdier (see Verdier's Nicolas Bourbaki seminar Analysis Situs). The characterisation was by means of categories 'with enough colimits', and applied to what is now called a Grothendieck topos. The theory was rounded out by establishing that a Grothendieck topos was a category of sheaves, where now the word sheaf had acquired an extended meaning, since it involved a Grothendieck topology.
|
|
The setup, especially the Nisnevich topology, is chosen as to make algebraic K-theory representable by a spectrum, and in some aspects to make a proof of the Bloch-Kato conjecture possible. After the Morel-Voevodsky construction there have been several different approaches to homotopy theory by using other model category structures or by using other sheaves than Nisnevich sheaves (for example, Zariski sheaves or just all presheaves). Each of these constructions yields the same homotopy category. There are two kinds of spheres in the theory: those coming from the multiplicative group playing the role of the -sphere in topology, and those coming from the simplicial sphere (considered as constant simplicial sheaf).
|
|
A constructible sheaf on a variety over a finite field is called pure of weight β if for all points x the eigenvalues of the Frobenius at x all have absolute value N(x)β/2, and is called mixed of weight ≤β if it can be written as repeated extensions by pure sheaves with weights ≤β. Deligne's theorem states that if f is a morphism of schemes of finite type over a finite field, then Rif! takes mixed sheaves of weight ≤β to mixed sheaves of weight ≤β+i. The original Weil conjectures follow by taking f to be a morphism from a smooth projective variety to a point and considering the constant sheaf Ql on the variety.
|
|
Image:Sheaves Cove NFLD.JPG Image:Sheaves Cove NFLD3.JPG Image:Sheaves Cove Falls2 NFLD.JPG Sheaves Cove is also known for a family feud between the Rowe and Jesso family from 2007 - 2015.
|
|
A special mass is celebrated on the occasion which is also attended by devotees residing around Old Goa. The blessed sheaves are then distributed by the priest during the mass. After the mass, fov are also distributed by the President of the feast to the congregation and the resident priests. Later, the group presents fov and sheaves to the Archbishop at Paço Patriarcal and to the Governor of Goa at Raj Bhavan.
|
|
The first reference in any census was in 1891, when "Charley Sheaves Cove" was listed with 21 residents. It was named for one of the first settlers, Charles Sheaves, who arrived in the mid-19th century. Longtime resident Isaac Jesso says the very first settler was his grandfather, Peter "Pierre Jesseau" Jesso. a Mi'kmaw who was married to Elizabeth Barry, and he doesn't know why the town wasn't named for him instead of Charley.
|
|
In 1978, Beilinson published a paper on coherent sheaves and several problems in linear algebra. His two-page note in the journal Functional Analysis and Its Applications was one of the papers on the study of derived categories of coherent sheaves. In 1981 Beilinson announced a proof of the Kazhdan–Lusztig conjectures and Jantzen conjectures with Joseph Bernstein. Independent of Beilinson and Bernstein, Brylinski and Kashiwara obtained a proof of the Kazhdan–Lusztig conjectures.
|
|
In mathematics, the étale topos of a scheme X is the category of all étale sheaves on X. An étale sheaf is a sheaf on the étale site of X.
|
|
It was particularly useful for binding sheaves of grain because mice do not gnaw on it.Kržan, Vanja. 2010. "Mi pa oznanjamo Kristusa, križanega (1 Kor 1,23)." Zaveza 42 (25 February).
|
|
A sense of distance is conveyed by the workers carrying sheaves of wheat through the clearing, the people bathing in the pond, the children playing and the ships far away.
|
|
Unbind the Sheaves: A Prairie Memoir is thought to describe a world which the people (people from the 1960s ) find relevant and yet as if it's from a different era.
|
|
If X and Y are topological spaces and u is a continuous map between them, then the pullback and pushforward operations on sheaves yield a geometric morphism between the associated topoi.
|
|
G-theory had been defined early in the development of the subject by Grothendieck. Grothendieck defined G0(X) for a variety X to be the free abelian group on isomorphism classes of coherent sheaves on X, modulo relations coming from exact sequences of coherent sheaves. In the categorical framework adopted by later authors, the K-theory of a variety is the K-theory of its category of vector bundles, while its G-theory is the K-theory of its category of coherent sheaves. Not only could Quillen prove the existence of a localization exact sequence for G-theory, he could prove that for a regular ring or variety, K-theory equaled G-theory, and therefore K-theory of regular varieties had a localization exact sequence.
|
|
Grid-mount upright loft blocks Under-hung loft & mule blocks A block is a pulley used to support and direct lift and operating lines. A block consists of a grooved wheel, known as a sheave (pronounced "shiv"), steel side plates, spacers, shaft, flange bearings, mounting angles and clips, etc. Blocks are sized based on anticipated live loads, operating speeds, line type and other factors. Sheaves were traditionally fabricated of cast iron, but steel and nylon sheaves are now common.
|
|
Blocks are either upright, when mounted atop a support structure, or under-hung, when mounted to the underside of a support structure. The side plates of blocks preferably fully cover the profile of (fully enclose) the sheaves to lend the block greater stability and limit the sheave's (and crew's) potential for damage from foreign objects. Nevertheless, blocks are available with exposed sheaves. ;Loft block A Loft block is an overhead block that supports a single lift line.
|
|
When he visited his mother Philemena Perrier's home in St. George's, he was called Tom. By 1901, 38 people in nine Roman Catholic families lived in Sheaves Cove where they were fishermen-farmers. Residents processed 46 cases of lobster, and caught 144 quintals of cod and four tierces of sair in a fishery worth $1,135. The large beach at Sheaves Cove was considered exceptional, and until recently as many as 10 fishermen used it on a regular basis.
|
|
For the derived category of constructible sheaves, see a section in ℓ-adic sheaf. The finiteness theorem in étale cohomology states that the higher direct images of a constructible sheaf are constructible.
|
|
In later Western art, Abundantia is often portrayed holding her cornucopia and sheaves of corn or wheat.Jürg Meyer zur Capellen, Raphael: The Roman Religious Paintings, ca. 1508-1520 (Arcos, 2005), p. 264.
|
|
In mathematics, the Grauert–Riemenschneider vanishing theorem is an extension of the Kodaira vanishing theorem on the vanishing of higher cohomology groups of coherent sheaves on a compact complex manifold, due to .
|
|
Other important research achievements of Deligne include the notion of cohomological descent, motivic L-functions, mixed sheaves, nearby vanishing cycles, central extensions of reductive groups, geometry and topology of braid groups, etc.
|
|
"Bringing in the Sheaves" is a popular American Gospel song used almost exclusively by Protestant Christians (though the content is not specifically Protestant in nature). The lyrics were written in 1874 by Knowles Shaw, who was inspired by Psalm 126:6, "He that goeth forth and weepeth, bearing precious seed, shall doubtless come again with rejoicing, bringing his sheaves with him." Shaw also wrote music for these words, but they are now usually set to a tune by George Minor, written in 1880.
|
|
Unlike a regular manifold, a supermanifold is not entirely composed of a set of points. Instead, one takes the dual point of view that the structure of a supermanifold M is contained in its sheaf OM of "smooth functions". In the dual point of view, an injective map corresponds to a surjection of sheaves, and a surjective map corresponds to an injection of sheaves. An alternative approach to the dual point of view is to use the functor of points.
|
|
Unlike rice granaries in Java, which hold sheaves of rice, rice granaries in Aceh hold unhusked rice. Wealthier Acehnese may build a wooden gateway entrance (Acehnese: keupaleh) at the entrance of the house area.
|
|
Weyburn is located astride the Williston geological Basin which contains oil deposits, and several wells operate in the vicinity. Weyburn features roadside attractions of a large lighthouse water tower, wheat sheaves and prairie lily.
|
|
New cross deck pendants are coiled and ready for quick installation. The major systems that make up typical arresting gear are the hook cable or pendants, purchase cables or tapes, sheaves and arresting engines.
|
|
Hans Rugh remplace Yves Laszlo à la Fondation mathématique Jacques Hadamard , Press release, November 20, 2012. The Beauville–Laszlo theorem on gluing sheaves together is named after Laszlo and Beauville, who published it in 1995..
|
|
Liturgical elements of the service include a chalice with water from a local river, a box or chest containing earth from sacred ground, candles, a copy of the Maha Vira, wheat- sheaves, herbs and flowers.
|
|
Calendar Documents Scotland, vol.5, Scottish Record Office (n.d.) p.303 no.1100 Equipped with 2,000 sheaves of arrows and ordnance brought from Newcastle upon Tyne by 120 cart horses, Gloucester and Albany recaptured Berwick.
|
|
Then F(X)G consists of equivariant sheaves on X; thus, the descent in this case says that to give an equivariant sheaf on X is to give a sheaf on the quotient X/G.
|
|
Later Voevodsky proved the general Bloch–Kato conjecture.Voevodsky (2010) The starting point for the proof is a series of conjectures due to and . They conjectured the existence of motivic complexes, complexes of sheaves whose cohomology was related to motivic cohomology. Among the conjectural properties of these complexes were three properties: one connecting their Zariski cohomology to Milnor's K-theory, one connecting their etale cohomology to cohomology with coefficients in the sheaves of roots of unity and one connecting their Zariski cohomology to their etale cohomology.
|
|
Alumot fields Alumot (, lit. "Sheaves") is a kibbutz in northern Israel. Located to the south of the Sea of Galilee, it falls under the jurisdiction of Emek HaYarden Regional Council. In it had a population of .
|
|
One consequence of the lemma is the Krull intersection theorem. The result is also used to prove the exactness property of completion . The lemma also plays a key role in the study of ℓ-adic sheaves.
|
|
It has revolutionized the subject of homological algebra, a purely algebraic aspect of algebraic topology. It removed the need to distinguish the cases of modules over a ring and sheaves of abelian groups over a topological space.
|
|
The sheaves were not replaced at Deep Navigation until 1961 (No.2 South), and 1963 (No.1 North). On 11 November 1902, five men lost their lives and two others were injured in No.2 South pit.
|
|
In mathematics, the Beauville–Laszlo theorem is a result in commutative algebra and algebraic geometry that allows one to "glue" two sheaves over an infinitesimal neighborhood of a point on an algebraic curve. It was proved by .
|
|
For the theory of reflexive sheaves, one works over an integral noetherian scheme. A reflexive sheaf is torsion-free. The dual of a coherent sheaf is reflexive. Usually, the product of reflexive sheaves is defined as the reflexive hull of their tensor products (so the result is reflexive.) A coherent sheaf F is said to be "normal" in the sense of Barth if the restriction F(U) \to F(U - Y) is bijective for every open subset U and a closed subset Y of U of codimension at least 2.
|
|
One of the basic constructions in commutative algebraic geometry is the Proj construction of a graded commutative ring. This construction builds a projective algebraic variety together with a very ample line bundle whose homogeneous coordinate ring is the original ring. Building the underlying topological space of the variety requires localizing the ring, but building sheaves on that space does not. By a theorem of Jean-Pierre Serre, quasi-coherent sheaves on Proj of a graded ring are the same as graded modules over the ring up to finite dimensional factors.
|
|
In algebraic geometry, dévissage is a technique introduced by Alexander Grothendieck for proving statements about coherent sheaves on noetherian schemes. Dévissage is an adaptation of a certain kind of noetherian induction. It has many applications, including the proof of generic flatness and the proof that higher direct images of coherent sheaves under proper morphisms are coherent. Laurent Gruson and Michel Raynaud extended this concept to the relative situation, that is, to the situation where the scheme under consideration is not necessarily noetherian, but instead admits a finitely presented morphism to another scheme.
|
|
About one-quarter mile from Sheaves Cove there was a second beach in the community called Red Cove because of the ochre which could be found there, it was there for more than 30 years that Isaac, his father and two brothers fished together in just two dories. None of the 10 children was in school in 1901 although a school was built early in the community history and later became the church. The current church seats about 80. By 1911, 50 lived in Sheaves Cove, and by 1935, 92.
|
|
Grothendieck unified the two theories: they both arise as derived functors on abelian categories; the abelian category of sheaves of abelian groups on a topological space, and the abelian category of G-modules for a given group G.
|
|
For any locally compact space X, Borel–Moore homology with integral coefficients is defined as the cohomology of the dual of the chain complex which computes sheaf cohomology with compact support.Birger Iversen. Cohomology of sheaves. Section IX.1.
|
|
In algebraic geometry and other areas of mathematics, an ideal sheaf (or sheaf of ideals) is the global analogue of an ideal in a ring. The ideal sheaves on a geometric object are closely connected to its subspaces.
|
|
The two drums were too large to fit in the usual position beneath the boiler and so were moved to a horizontal axle behind the engine's scuttle, with a pair of sheaves beneath the boiler to guide the cables.
|
|
This arrangement eliminates the need for sheaves and v-belts, allowing for simplified operation and maintenance. A variable speed drive package is included to optimize the speed of the machine to the given liner profile, feed and production conditions.
|
|
66 (1982), 57-71. More recently, a series of papers by Kawamata related the derived category of coherent sheaves on an algebraic variety to geometric properties in the spirit of minimal model theory.Y. Kawamata. D-equivalence and K-equivalence.
|
|
Two galleries allow the visitor to overlook the main power house, and also to descend below the junction of Washington and Mason Streets and see the large cavern where the haulage cables are routed out to the street via huge sheaves.
|
|
In some places, the Fellahs, men and women, were at work, reaping and binding the sheaves."Taylor, 1855, p. 108 Solamon Malan described the village houses in 1857: "Each house, whether separate or attached to another, consisted of one room only.
|
|
Sheaves Cove is a small Port au Port Peninsula community along the shore of St. George's Bay. There is a small tourist alcove just off the highway (Route 460) where views of the waterfalls and the ocean are visited often.
|
|
In 2008 Iovita received the Ribenboim Prize. In 2018 he was an invited speaker, with Vincent Pilloni and Fabrizio Andreatta, with talk p-adic variation of automorphic sheaves (given by Pilloni) at the International Congress of Mathematicians in Rio de Janeiro.
|
|
Translated by Jacob Neusner, page 21. Reading , the Gemara noted that a Baraita (Tosefta Peah 1:5) taught that the optimal way to fulfill the commandment is for the owner to separate the portion for the poor from grain that has not been harvested. If the owner did not separate it from the standing grain, the owner separates it from the sheaves of grain that have been harvested. If the owner did not separate it from the sheaves, the owner separates it from the pile of grain, as long as the owner has not yet smoothed the pile.
|
|
In the first reading (, aliyah), Jacob lived in the land of Canaan, and this is his family's story. When Joseph was 17, he fed the flock with his brothers, and he brought Jacob an evil report about his brothers. Because Joseph was the son of Jacob's old age, Jacob loved him more than his other children, and Jacob made him a coat of many colors, which caused Joseph's brothers to hate him. And Joseph made his brothers hate him more when he told them that he dreamed that they were binding sheaves in the field, and their sheaves bowed down to his sheaf.
|
|
Let X be a complex Kähler manifold. Then every Hodge class on X is a linear combination with rational coefficients of the cohomology classes of complex subvarieties of X. This is too optimistic, because there are not enough subvarieties to make this work. A possible substitute is to ask instead one of the two following questions: ::Hodge conjecture for Kähler varieties, vector bundle version. Let X be a complex Kähler manifold. Then every Hodge class on X is a linear combination with rational coefficients of Chern classes of vector bundles on X. ::Hodge conjecture for Kähler varieties, coherent sheaf version. Let X be a complex Kähler manifold. Then every Hodge class on X is a linear combination with rational coefficients of Chern classes of coherent sheaves on X. proved that the Chern classes of coherent sheaves give strictly more Hodge classes than the Chern classes of vector bundles and that the Chern classes of coherent sheaves are insufficient to generate all the Hodge classes.
|
|
It is tradition to sing "Bringing in the Sheaves" (by Shaw and Minor) every Thanksgiving assembly, and for students and teachers to recite poems at the Winter Holiday assembly. Other assemblies highlight students' work on independent projects, fiction writing, music, and theater.
|
|
In 1930 the Vasylivska Village Council consisted of v. Vasylivka (the collective farm named Petrovsky) and v. Brats'ke (the collective farm named Stalin). The land was cultivated by horses and oxen, sheaves were driven on wagons, grain was threshed with Garman (hewn stone).
|
|
According to a general splitting principle this can determine the rest of the theory (if not explicitly). There are theories of holomorphic line bundles on complex manifolds, and invertible sheaves in algebraic geometry, that work out a line bundle theory in those areas.
|
|
In algebraic geometry, the Ramanujam vanishing theorem is an extension of the Kodaira vanishing theorem due to , that in particular gives conditions for the vanishing of first cohomology groups of coherent sheaves on a surface. The Kawamata–Viehweg vanishing theorem generalizes it.
|
|
Conversely, Alexander Beilinson proved that the existence of a category of motives implies the standard conjectures. Additionally, cycles are connected to algebraic K-theory by Bloch's formula, which expresses groups of cycles modulo rational equivalence as the cohomology of K-theory sheaves.
|
|
There are two common ways to define algebraic spaces: they can be defined as either quotients of schemes by etale equivalence relations, or as sheaves on a big etale site that are locally isomorphic to schemes. These two definitions are essentially equivalent.
|
|
In mathematics, more specifically sheaf theory, a branch of topology and algebraic geometry, the exceptional inverse image functor is the fourth and most sophisticated in a series of image functors for sheaves. It is needed to express Verdier duality in its most general form.
|
|
Essentially they are a smooth version of abelian gerbes belonging more to the hierarchy starting with principal bundles than sheaves. Bundle gerbes have been used in gauge theory and also string theory. Current work by others is developing a theory of non-abelian bundle gerbes.
|
|
During the dry season, sheaves are piled to large stacks in the sun to completely dry them. Threshing is done manually as well. Tractor- driven threshers are rarely used due to higher costs and a higher loss of the small grains. Grains are stored loosely.
|
|
Vermont has both a state seal and a state coat of arms that are independent of one another (though both contain a pine tree, a cow and sheaves of grain); the seal is used to authenticate documents, whilst the heraldic device represents the state itself.
|
|
Behind the portico, the rectangular hall is topped with a prang spire, and the four pediments below it are decorated with floral designs. The carved doors and windows of the shrine depict sheaves of rice, fish and shrimp to represent the fecundity of the nation.
|
|
The most common type of CVT uses a V-belt which runs between two variable diameter pulleys. The pulleys consist of two cone-shaped halves which move together and apart. The V-belt runs between these two halves, so the effective diameter of the pulley is dependent on the distance between the two halves of the pulley. The V-shaped cross section of the belt causes it to ride higher on one pulley and lower on the other, therefore the gear ratio is adjusted by moving the two sheaves of one pulley closer together and the two sheaves of the other pulley farther apart.
|
|
In algebraic geometry, a Fourier–Mukai transform ΦK is a functor between derived categories of coherent sheaves D(X) → D(Y) for schemes X and Y, which is, in a sense, an integral transform along a kernel object K ∈ D(X×Y). Most natural functors, including basic ones like pushforwards and pullbacks, are of this type. These kinds of functors were introduced by in order to prove an equivalence between the derived categories of coherent sheaves on an abelian variety and its dual. That equivalence is analogous to the classical Fourier transform that gives an isomorphism between tempered distributions on a finite-dimensional real vector space and its dual.
|
|
The novel arrangement allowed electric motors to stall yet still exert holding effect similar to that of steam driven cable machinery. The system also allowed regenerative power so that energy developed by cable being paid out can be used to provide electrical power to the ship's lighting and other systems. The anchor windlass and capstan motors were electrically powered. The most prominent external feature of cable ships until some recently designed were the bow sheaves and often stern sheaves that are included in length overall and are subject to change as cable machinery and needs change, thus will be a factor in length overall measurement as ships are modified.
|
|
In the context of schemes, the importance of ideal sheaves lies mainly in the correspondence between closed subschemes and quasi-coherent ideal sheaves. Consider a scheme X and a quasi-coherent ideal sheaf J in OX. Then, the support Z of OX/J is a closed subspace of X, and (Z, OX/J) is a scheme (both assertions can be checked locally). It is called the closed subscheme of X defined by J. Conversely, let i: Z → X be a closed immersion, i.e., a morphism which is a homeomorphism onto a closed subspace such that the associated map : i#: OX → i⋆OZ is surjective on the stalks.
|
|
In the special case when Y is the spectrum of an algebraically closed field (a point), Rqf∗(F ) is the same as Hq(F ). Suppose that X is a Noetherian scheme. An abelian étale sheaf F over X is called finite locally constant if it is represented by an étale cover of X. It is called constructible if X can be covered by a finite family of subschemes on each of which the restriction of F is finite locally constant. It is called torsion if F(U) is a torsion group for all étale covers U of X. Finite locally constant sheaves are constructible, and constructible sheaves are torsion.
|
|
Given a locally ringed space (X, OX), certain sheaves of modules on X occur in the applications, the OX-modules. To define them, consider a sheaf F of abelian groups on X. If F(U) is a module over the ring OX(U) for every open set U in X, and the restriction maps are compatible with the module structure, then we call F an OX-module. In this case, the stalk of F at x will be a module over the local ring (stalk) Rx, for every x∈X. A morphism between two such OX-modules is a morphism of sheaves which is compatible with the given module structures.
|
|
Print the pine tree in the middle of the coat of arms represents the Vermont forests. The cow and three sheaves of wheat represent the dairy and agriculture industries. The deer head on top represents Vermont's wildlife. The Green Mountains are in the background as well.
|
|
Grothendieck originally introduced stacks as a tool for the theory of descent. In that formulation, stacks are (informally speaking) sheaves of categories.Vistoli (2005), Definition 4.6. From this general notion, Artin defined the narrower class of algebraic stacks (or "Artin stacks"), which can be considered geometric objects.
|
|
Steel wires for wire ropes are normally made of non-alloy carbon steel with a carbon content of 0.4 to 0.95%. The very high strength of the rope wires enables wire ropes to support large tensile forces and to run over sheaves with relatively small diameters.
|
|
This is a resolution, i.e. an exact complex of sheaves by the Poincaré lemma. The cohomology of X with values in \R can thus be computed as the cohomology of the complex of globally defined differential forms: :H^i(X,\R) = H^i(C^\bullet_X(X)).
|
|
Publicationes Mathematicae Debrecen, vol. 5 (1957), p. 128 In 2011, a strengthened version of the conjecture (see below) was proved independently by Joel FriedmanJoel Friedman, "Sheaves on Graphs, Their Homological Invariants, and a Proof of the Hanna Neumann Conjecture" American Mathematical Soc., 2014 and by Igor Mineyev.
|
|
Cable Laying Ship.Presented at the April 18, 1979, meeting of Chesapeake Section of The Society of Naval Architects and marine Engineers. CS Cable Innovator at anchor in Astoria, Oregon, showing a modern design without bow sheaves. The most common laying engine in use is the Linear Cable Engine (LCE).
|
|
Grothendieck & Raynaud, SGA 1, Exposé XII. (The first group here is defined using the Zariski topology, and the second using the classical (Euclidean) topology.) For example, the equivalence between algebraic and analytic coherent sheaves on projective space implies Chow's theorem that every closed analytic subspace of CPn is algebraic.
|
|
In mathematics, Verdier duality is a duality in sheaf theory that generalizes Poincaré duality for manifolds. Verdier duality was introduced by as an analog for locally compact spaces of the coherent duality for schemes due to Alexander Grothendieck. It is commonly encountered when studying constructible or perverse sheaves.
|
|
The obverse depicts the city seal of Norfolk. A sailing ship is shown, sailing on stylized waves; below is a plow and three sheaves of wheat. Underneath that is the Latin word , translated as "may you prosper". Above the ship is , meaning "both land and sea are your riches".
|
|
In this painting, the whole countryside is marked out in blue squares that seems like a chessboard. All of the activities are picturesquely grouped around a golden blaze such as men doubled over, women hurrying along the narrow paths, and people stooking sheaves of corn and loading carts.
|
|
It leads into a wooden vestibule with carved rosettes and triglyphs, which opens onto the main lobby. There, terrazzo flooring is complemented by panelled wainscoting and plaster walls, ceiling and Gothic cornice. The door to the postmaster's office is framed with carved rosettes, sheaves of wheat and dentils.
|
|
The company sells Baldor-Reliance and ABB branded industrial electric motors. Products are available in both IEC and NEMA configurations and range from fractional to 100,000 horsepower. The company also sells the Dodge brand of mechanical power transmission products, including mounted bearings, enclosed gearing, couplings, sheaves, and bushings.
|
|
They are medium in height. The ploidy level for the species range from diploid (2n), tetraploid (4n), to hexaploid (6n). Fonio is labor intensive to harvest and process. Men and boys use sickles to cut down the fonio, which women then gather into sheaves and set out to dry.
|
|
Typical K values are 1.04 for roller bearing sheaves and 1.09 for plain bearing sheaves (with wire rope). The increased force produced by a tackle is offset by both the increased length of rope needed and the friction in the system. In order to raise a block and tackle with a mechanical advantage of 6 a distance of 1 metre, it is necessary to pull 6 metres of rope through the blocks. Frictional losses also mean there is a practical point at which the benefit of adding a further sheave is offset by the incremental increase in friction which would require additional force to be applied in order to lift the load.
|
|
The University of Saskatchewan Students' Union is the students' union representing full-time undergraduate students at the University of Saskatchewan. Since 1992, the graduate students are represented by the University of Saskatchewan Graduate Student's Association (GSA-uSask), a not-for-profit student organization that provides services, events, student clubs and advocacy work to the graduate students of the U of S. Since 2007, the GSA-uSask is located in the Emmanuel and St. Chad Chapel, also called GSA Commons. The University of Saskatchewan has adopted as its logo the book of knowledge and three wheat sheaves set inside of a green heraldic shield. The wheat sheaves and book of knowledge are yellow.
|
|
The adjective abstract has often been applied to differential geometry before, but the abstract differential geometry (ADG) of this article is a form of differential geometry without the calculus notion of smoothness, developed by Anastasios Mallios and Ioannis Raptis from 1998 onwards."Geometry of Vector Sheaves: An Axiomatic Approach to Differential Geometry", Anastasios Mallios, Springer, 1998, Instead of calculus, an axiomatic treatment of differential geometry is built via sheaf theory and sheaf cohomology using vector sheaves in place of bundles based on arbitrary topological spaces."Modern Differential Geometry in Gauge Theories: Maxwell fields", Anastasios Mallios, Springer, 2005, Mallios says noncommutative geometry can be considered a special case of ADG, and that ADG is similar to synthetic differential geometry.
|
|
Kuznetsov is known for his research in algebraic geometry, mostly concerning derived categories of coherent sheaves and their semiorthogonal decompositions. Kuznetsov received an August Möbius fellowship in 1997. He was awarded a European Mathematical Society prize in 2008. He was an invited speaker at the International Mathematical Congress in Seoul (2014).
|
|
Much of Schreyer's research deals with syzygy theory and the development of algorithms for the calculation of syzygies. In 2010 he was an invited speaker (jointly with David Eisenbud) at the International Congress of Mathematicians in Hyderabad.Schreyer, F. O., & Eisenbud, D. (2011). Betti numbers of syzygies and cohomology of coherent sheaves.
|
|
In mathematics, a Lawvere–Tierney topology is an analog of a Grothendieck topology for an arbitrary topos, used to construct a topos of sheaves. A Lawvere–Tierney topology is also sometimes also called a local operator or coverage or topology or geometric modality. They were introduced by and Myles Tierney.
|
|
Back splicing uses a stranded rope's own fibres to prevent fraying. A back splice adds extra thickness to the rope end, preventing it from running through blocks and sheaves. It can also be of benefit when a user needs to feel the end of the rope, as on a bucket lanyard.
|
|
There is a welded anodized aluminum bow fitting with two cunningham sheaves, and three removable pins for two separate jib tack positions. The boat has bow and stern pulpits made of stainless steel, with double life lines and gates. Two goiot hatches and a spray shield are designed into the deck.
|
|
175 The category having these branes as its objects is called the Fukaya category.Aspinwal et al. 2009, p. 575 The derived category of coherent sheaves is constructed using tools from complex geometry, a branch of mathematics that describes geometric curves in algebraic terms and solves geometric problems using algebraic equations.
|
|
The threshing was done by means of a sledge for a period of five days. This was a device drawn back and forth over the heaped-up grain stalks. The barley was then "opened" with an "opener". A team of oxen drove this primitive machine to crush the barley-(sheaves).
|
|
Psalm 102 is one of 15 psalms recited as additional hymns during the Yom Kippur service by Sephardi Jews. Verse 1 is recited by the sheaves of barley in Perek Shirah. Verse 14 is said in Selichot. Sephardi Jews recite verse 14 after the prayer of Ein Keloheinu in the morning service.
|
|
According to the richness and character of the architectural composition, this is not only an image of a hotel – it is a monument of the greatness of the Stalin era architect Oltarzhevsky According to Oltarzhevsky, even the steps that led from the embankment to the river pier were monumental. Most of the building outside is lined with ceramic blocks, the first two floors are limestone, and the basement and the main entrance are granite. Corner towers adorn wheat sheaves and flowerpots stylized as sheaves. The interiors were decorated with paintings by Soviet artists; a total of 1,200 canvases. On the ceiling in the central hall a picturesque ceiling “The Feast of Labor and Harvest in the Hospitable Ukraine” was created.
|
|
Kazhdan and Lusztig found a topological construction of Springer representations using the Steinberg variety and, allegedly, discovered Kazhdan–Lusztig polynomials in the process. Generalized Springer correspondence has been studied by Lusztig-Spaltenstein (1985) and by Lusztig in his work on character sheaves. Borho and MacPherson (1983) gave yet another construction of the Springer correspondence.
|
|
In mathematics, Artin–Verdier duality is a duality theorem for constructible abelian sheaves over the spectrum of a ring of algebraic numbers, introduced by , that generalizes Tate duality. It shows that, as far as etale (or flat) cohomology is concerned, the ring of integers in a number field behaves like a 3-dimensional mathematical object.
|
|
Chang did her undergraduate studies in Taiwan and received a BS from National Taiwan University. She did her doctoral work at University of California, Berkeley, under the supervision of Robin Hartshorne and was awarded her PhD in 1982. Her dissertation was on Some Results on Stable Rank 2 Vector Bundles and Reflexive Sheaves on P3.
|
|
Among the core results of coherent sheaf cohomology are results on finite-dimensionality of cohomology, results on the vanishing of cohomology in various cases, duality theorems such as Serre duality, relations between topology and algebraic geometry such as Hodge theory, and formulas for Euler characteristics of coherent sheaves such as the Riemann–Roch theorem.
|
|
In mathematics, the Grothendieck–Ogg–Shafarevich formula describes the Euler characteristic of a complete curve with coefficients in an abelian variety or constructible sheaf, in terms of local data involving the Swan conductor. and proved the formula for abelian varieties with tame ramification over curves, and extended the formula to constructible sheaves over a curve .
|
|
In mathematics, a Grothendieck category is a certain kind of abelian category, introduced in Alexander Grothendieck's Tôhoku paper of 1957. English translation. in order to develop the machinery of homological algebra for modules and for sheaves in a unified manner. The theory of these categories was further developed in Pierre Gabriel's seminal thesis in 1962.
|
|
The decomposition theorem was first proved by Beilinson, Bernstein, and Deligne. Their proof is based on the usage of weights on l-adic sheaves in positive characteristic. A different proof using mixed Hodge modules was given by Saito. A more geometric proof, based on the notion of semismall maps was given by de Cataldo and Migliorini.
|
|
The town for some time was known as "Mazo Manie," and recalls in its spelling the name of a pair of Wahpeton Dakota chiefs of that era named Maz-zo-ma-nee.Robert O. Dodsworth, “Whence Mazomanie?” Local Sheaves (the Mazomanie Historical Society), Volume I, number 1 (January 1995). Robert O. Dodsworth, "The Naming of Mazomanie, Wisconsin".
|
|
Work in the spirit of Riemann was carried out by the Italian school of algebraic geometry in the early 1900s. Contemporary treatment of complex geometry began with the work of Jean-Pierre Serre, who introduced the concept of sheaves to the subject, and illuminated the relations between complex geometry and algebraic geometry.Serre, J. P. (1955). Faisceaux algébriques cohérents.
|
|
This is a very ancient tradition. Sundar mundarye ho by Assa Singh Ghuman Waris Shah Foundation ISBN B1-7856-043-7 Gurh, solidified and unrefined sugarcane juice is a traditional festive sweet. In Punjab, the harvest festival Lohri is marked by eating sheaves of roasted corn from the new harvest.Albala, Ken (2011) Food Cultures of the World Encyclopedia.
|
|
In 1979 a Chern Symposium offered him a honorary song in tribute: > Hail to Chern! Mathematics Greatest! He made Gauss-Bonnet a household word, > Intrinsic proofs he found, Throughout the World his truths abound, Chern > classes he gave us, and Secondary Invariants, Fibre Bundles and Sheaves, > Distributions and Foliated Leaves! All Hail All Hail to CHERN.
|
|
The yellowish marble pylons resemble stylized sheaves of wheat in keeping with the station's original name, Kolkhoznaya or "Collective Farm." The walls are faced with white marble and decorated with plaques by R. Pogrebnoy (who was also the architect), Ye. Kolyupanova, and S. Kolyupanov. Lighting comes from rows of inset lamps running along the base of the ceiling.
|
|
536 Intuitively, one can think of a submanifold as a surface embedded inside of a Calabi–Yau manifold, although submanifolds can also exist in dimensions different from two.Yau and Nadis 2010, p. 165 In mathematical language, the category having these branes as its objects is known as the derived category of coherent sheaves on the Calabi–Yau.
|
|
The lower gate sections of lyre-like panels with leaf and spearhead motifs are topped with Jacobean-style arched panels. The ornate gate overthrows include shields and emblems capped with crowns, sheaves and sickles. The inner gates bear the inscription Quid retribuam domino ("What can I render to the Lord?"), while the outer gates bear the date.
|
|
Paddock Flight, Richard Pearse's Farm, Waitohi Alexander Amos Martin, born 1887, was sure in his accounts of the flight he'd seen. He recalled that he was about 16.5 years old when he saw one of Pearse's flight. Martin and his father had finished chaff cutting a stack of sheaves on Dick Connell's farm about 2:00 pm.
|
|
The Mishnah taught that if a wife foreswore all benefit from other people, her husband could not annul his wife's vow, but she could still benefit from the gleanings, forgotten sheaves, and the corner of the field that and , and commanded farmers to leave for the poor.Mishnah Nedarim 11:3, in, e.g., The Mishnah: A New Translation.
|
|
Each of these guideline tensioners consists of a hydraulic cylinder with sheaves at both sides. The cylinder is connected to one or more high pressure gas bottles via a medium separator. A wire rope is rigged in the cylinder; one end is connected to the fixed part of the tensioner, the other end to the template.
|
|
The best parts are used to create an outer sheaf and the other parts are placed within. These outer sheaves are joined to each other and overlap slightly to create a standard length stick or rod known as a quill. The sticks are then rolled daily as they dry and are tied into bundles for trading and transport.
|
|
Since the introduction of sheaves into mathematics in the 1940s, a major theme has been to study a space by studying sheaves on a space. This idea was expounded by Alexander Grothendieck by introducing the notion of a "topos". The main utility of this notion is in the abundance of situations in mathematics where topological heuristics are very effective, but an honest topological space is lacking; it is sometimes possible to find a topos formalizing the heuristic. An important example of this programmatic idea is the étale topos of a scheme. Another illustration of the capability of Grothendieck toposes to incarnate the “essence” of different mathematical situations is given by their use as bridges for connecting theories which, albeit written in possibly very different languages, share a common mathematical content .
|
|
Abelian categories were introduced by (under the name of "exact category") and in order to unify various cohomology theories. At the time, there was a cohomology theory for sheaves, and a cohomology theory for groups. The two were defined differently, but they had similar properties. In fact, much of category theory was developed as a language to study these similarities.
|
|
A wide variety of arrows were shot from the English longbow. Variations in length, fletchings and heads are all recorded. Perhaps the greatest diversity lies in hunting arrows, with varieties like broad-arrow, wolf-arrow, dog-arrow, Welsh arrow and Scottish arrow being recorded. War arrows were ordered in the thousands for medieval armies and navies, supplied in sheaves normally of 24 arrows.
|
|
Generally speaking, the term "local to global" refers to the idea that a global problem is first done at a local level, which tends to simplify the questions. Then, of course, the information gained in the local analysis has to be put together to get back to some global statement. For example, the notion of sheaves reifies that idea in topology and geometry.
|
|
So all the farmer's work was familiar to him: to mow, make hay, bind the sheaves, thresh, winnow, spread manure, plow, sow, etc. All these motifs would return in his later art. In 1833 his father sent him to Cherbourg to study with a portrait painter named Bon Du Mouchel. By 1835 he was studying with Théophile Langlois de Chèvreville,McPherson, H. (2003).
|
|
In front of the Independence Tower, there is a statue group of three women in Turkish national costumes. The two women at the sides are holding a large wreath reaching to the ground. This wreath, made up of grain sheaves, represents the abundant country. The woman on the left with a cup in her stretched-out hand is asking for God's compassion.
|
|
Super Oilite is an iron based material that is harder, stronger, and cheaper than Oilite. It is rated for slower speeds, but it can handle higher loads. Common applications include farm equipment, winches, sheaves, conveyors, and pulleys. Applicable standards are: ASTM B-439-95 Grade 4, MIL-B-5687D Type 2 Grade 4, SAE 863, and old SAE standard Type 3.
|
|
The ship then went to the Bethlehem Steel Co. in Baltimore, Maryland for a number of modifications: e.g., electric cable machinery (in place of steam), precision navigation instrumentation, and a helicopter platform over the fantail. Cable drums in diameter and bow sheaves spanning were among the more visible modifications. On 1 June 1953 the ship was commissioned USS Neptune (ARC-2), with Cdr.
|
|
A placard indicating this requirement is located on the CAT indicator and in the Pilot's Operating Handbook (POH). Power is transmitted from the engine to the drive system through drive belts. Originally, the R22 used four separate v-belts running on multi-groove sheaves. This system proved problematic, as individual belts would sometimes roll over in their groove and fail.
|
|
531 The homological mirror symmetry conjecture of Maxim Kontsevich states that the derived category of coherent sheaves on one Calabi–Yau manifold is equivalent in a certain sense to the Fukaya category of a completely different Calabi–Yau manifold.Aspinwall et al. 2009, p. 616 This equivalence provides an unexpected bridge between two branches of geometry, namely complex and symplectic geometry.
|
|
So at each point, an element of a fixed vector space is assigned. However, sheaves can "continuously change" the vector space (or more generally abelian group). This entire process is really the global section functor, which assigns to each sheaf its global section. Then sheaf cohomology enables us to consider a similar extension problem while "continuously varying" the abelian group.
|
|
In most rice-producing countries, they are used for threshing and for transporting the sheaves during the rice harvest. They provide power for oilseed mills, sugarcane presses, and devices for raising water. They are widely used as pack animals, and in India and Pakistan, for heavy haulage, also. In their invasions of Europe, the Turks used water buffaloes for hauling heavy battering rams.
|
|
THE CAPITAL Bright are the city walls of the capital; Red-robed officials shout on broad streets. There is a white-headed destitute scholar; Hanging from his mule's saddle, sheaves of poems. Clasping his calling card, he knocks on doors for work; The gate keepers smirk at one another. Ten try and ten fail; Walk the streets, his face is haggard.
|
|
Occasionally, one needs to use the tools of topology but a "set of points" is not available. In pointless topology one considers instead the lattice of open sets as the basic notion of the theory, while Grothendieck topologies are structures defined on arbitrary categories that allow the definition of sheaves on those categories, and with that the definition of general cohomology theories.
|
|
Optimal speed range is . V-belts need larger pulleys for their thicker cross- section than flat belts. For high-power requirements, two or more V-belts can be joined side-by-side in an arrangement called a multi-V, running on matching multi-groove sheaves. This is known as a multiple-V-belt drive (or sometimes a "classical V-belt drive").
|
|
In 2019 he was appointed Honorary Chaplain to the Worshipful Company of Leathersellers. In 2014, the first volume of his memoirs, Fathomless Riches, was published by Weidenfeld & Nicolson. In 2016 a follow-up volume, Bringing In The Sheaves, was published. In July 2017, Coles was elected a Fellow of King's College London and, separately, Chancellor of the University of Northampton.
|
|
Basil O. Lenoir.Col. William A. Glassford was a career Army Signal Corps officer, father of Vice Admiral William A. Glassford. The two barges were completed as vessels suited to shallow water work in Alaska with triple screws, two cable tanks capable of holding 400 tons of cable, three bow sheaves, and a Sundfelt combined paying out-picking up cable machine.
|
|
The Bishop Pall Y was used by the early Earls of Glencairn, and by the Cunninghams of Barns. This argues against the theory that the Cunninghams were great allies of the Clan Comyn, whose shield bore sheaves of corn and that when the great Comyn dynasty was overthrown by the Clan Bruce, and the Cunninghams subsequently adopted the shake-fork that was used to fork over sheaves of corn as a reference to their former allies. (Note: maize, also called corn, was introduced to Europe from the Americas by the Spanish after the year 1492.) The Cunninghams were certainly well settled in the parish of Kilmaurs by the end of the thirteenth century. The son of the Laird of Kilmaurs was Hervy de Cunningham who fought for Alexander III of Scotland at the Battle of Largs in 1263 against the Norse invaders.
|
|
The mathematical term perverse sheaves refers to a certain abelian category associated to a topological space X, which may be a real or complex manifold, or a more general topologically stratified space, usually singular. This concept was introduced in the thesis of Zoghman Mebkhout, gaining more popularity after the (independent) work of Joseph Bernstein, Alexander Beilinson, and Pierre Deligne (1982) as a formalisation of the Riemann-Hilbert correspondence, which related the topology of singular spaces (intersection homology of Mark Goresky and Robert MacPherson) and the algebraic theory of differential equations (microlocal calculus and holonomic D-modules of Joseph Bernstein, Masaki Kashiwara and Takahiro Kawai). It was clear from the outset that perverse sheaves are fundamental mathematical objects at the crossroads of algebraic geometry, topology, analysis and differential equations. They also play an important role in number theory, algebra, and representation theory.
|
|
About 1957 Foy began a series of related still lifes that involve leaves or branches wrapped by human hands into clusters or sheaves, or assembled by birds into nests. With its inner pinkish radiance and veined leaf surfaces, Cluster of Leaves (ca. 1957), for example, quivers with the power of an incubating egg. These drawings are metaphors for efforts to control the untamed sprawl of natural vegetation.
|
|
One meaning of the Cohen–Macaulay condition can be seen in coherent duality theory. A variety or scheme X is Cohen–Macaulay if the "dualizing complex", which a priori lies in the derived category of sheaves on X, is represented by a single sheaf. The stronger property of being Gorenstein means that this sheaf is a line bundle. In particular, every regular scheme is Gorenstein.
|
|
Modern barley field. Modern day wheat sheaves. The omer a ("sheaf") is an old Biblical measure of volume of unthreshed stalks of grain. The Sunday after the start of each farmer's barley grain harvest, a sheaf of barley from each farm was waved by a Priest in the Temple in Jerusalem, signalling the allowance of the consumption of chadash (grains from the new harvest).
|
|
The seal, depicts a 14-branched pine tree rising from the forest, with two grain sheaves above. The 14 branches symbolize the Thirteen Colonies and Vermont as the 14th state admitted to the union. A cow on the right, representing Vermont's history of dairy farming, also appears. On the top of the seal are wavy lines, possibly suggesting clouds; on the bottom wavy lines suggest water.
|
|
Let C be a category and let J be a Grothendieck topology on C. The pair (C, J) is called a site. A presheaf on a category is a contravariant functor from C to the category of all sets. Note that for this definition C is not required to have a topology. A sheaf on a site, however, should allow gluing, just like sheaves in classical topology.
|
|
It was a curved, knife with the edge on its concave side. The knife was fastened to a bowed oval copper plate, while the plate was fastened to a thick leather bangle. Its agricultural purpose was to enable field workers to cut wheat sheaves open before threshing them. The knife was fixed on the glove plate to prevent injuries and to increase work speed.
|
|
Arval Brethren formed a college of twelve priests, although archaeologists have found only up to nine names at a time in the inscriptions. They were appointed for life and did not lose their status even in exile. According to Pliny the Elder, their sign was a white band with the chaplet of sheaves of grain (Naturalis Historia 18.2). The Brethren assembled in the Regia.
|
|
A flexible steel wire rope is wound on the winding drum. It passes over the roller and is connected to the ladder through suitable sheaves. Steel angle sections with holes drilled to take a cross bar are fixed to the shafts for securing the ladder in a vertical position. The ladder can only be mounted when the rungs of each section are in opposition to one another.
|
|
The Coat of arms of Saskatchewan features three gold sheaves of wheat, or garbs, represent the province's agriculture; the heraldic sheaf of wheat has become a generalized symbol of the province. The gold lower half of the Flag of Saskatchewan symbolizes the southern, prairie wheat-fields. The provincial symbol is a sheaf of wheat and is generally used to identify government programs and organizations.
|
|
Bharat Mata is a work painted by the Indian painter Abanindranath Tagore in 1905. The work depicts a saffron clad woman, dressed like a sadhvi, holding a book, sheaves of paddy, a piece of white cloth and a garland (mala) in her four hands. The painting was the first illustrated depiction of the concept, and was painted during with Swadesh ideals during the larger Indian Independence movement.
|
|
The memorial consists of an enclosure of bronze railings and panels on a sandstone base, which stretch on four sides around the Earl's grave, with three bronze figures at the head of the grave. The railings are long, wide, and high. The figures are respectively , , and high. The panels are decorated with heraldic symbols of the Grosvenor family, and include portcullises, wheat sheaves, coronets, and roses.
|
|
Kopa was also used to count grain sheaves or quantities of other products (for example, nails, eggs, cabbages). Kopa's original meaning was the number of Prague groschens that could be minted from a grzywna of silver. In the Grand Duchy of Lithuania that number was 60. In Poland, during the reign of Casimir the Great (1333–1370), the weight of grzywna was reduced by about 20%.
|
|
That is, the condition of a tensor inverse then implies, locally on X, that S is the sheaf form of a free rank 1 module over a commutative ring. Examples come from fractional ideals in algebraic number theory, so that the definition captures that theory. More generally, when X is an affine scheme Spec(R), the invertible sheaves come from projective modules over R, of rank 1.
|
|
AAR Type "E" coupler serving as a tow hitch on a mobile crane. Pulling up on the link at the rear releases the knuckle allowing uncoupling. Mobile cranes generally operate a boom from the end of which a hook is suspended by wire rope and sheaves. The wire ropes are operated by whatever prime movers the designers have available, operating through a variety of transmissions.
|
|
The quotient of the Cartier divisors by the principal divisors is a subgroup of the divisor class group, isomorphic to the Picard group of invertible sheaves on Spec(A). Example: in the ring k[x,y,z]/(xy–z2) the divisor class group has order 2, generated by the divisor y=z, but the Picard subgroup is the trivial group.Hartshorne, GTM52, Example 6.5.2, p.
|
|
The shell of Neocomites is fairly involute and compressed with flattish sides; covered with flexeous ribs that branch in small sheaves from faint umbilical tubercles, in some branching again or intercaled further out on the whorls, ending in small oblique bullae in either side of a smooth flat venter. Ribs may cross the venter transversely on later whorls. Sutures have deep 1st lateral lobes.
|
|
Generalizations to the most common situations can be found in . Exterior algebras of vector bundles are frequently considered in geometry and topology. There are no essential differences between the algebraic properties of the exterior algebra of finite-dimensional vector bundles and those of the exterior algebra of finitely generated projective modules, by the Serre–Swan theorem. More general exterior algebras can be defined for sheaves of modules.
|
|
He concealed his expertise on differential equations, fearing that its connections with applied mathematics could lead him to be asked to do war work. Leray's work of this period proved seminal to the development of spectral sequences and sheaves. These were subsequently developed by many others, each separately becoming an important tool in homological algebra. He returned to work on partial differential equations from about 1950.
|
|
When dense cirrus is formed by means other than by cumulonimbus blow-off or dissipating cumulonimbus clouds, it will frequently be seen as many dense patches at different levels (cirrus spissatus duplicatus), often mixed with thin cirrus filaments. Another variety, cirrus spissatus intortus, is sometimes described as looking like "entangled sheaves" of cirrus clouds. When viewed toward the sun, the denser patches often have gray bases.
|
|
United dropped the thin red vertical stripes that had been introduced the previous season, reverting to a plain white shirt along with blue shorts and socks. This season saw the introduction of a club crest (or badge) on the shirts for the first time, utilising a red heraldic shield emblazoned with three sheaves of wheat and a lions head, along with the letters SUFC.
|
|
Cable Driving Plant, Designed and Constructed by Poole & Hunt, Baltimore, MD. Drawing by P.F. Goist, circa 1882. The powerhouse has two horizontal single- cylinder engines. The lithograph shows a hypothetical prototype of a cable powerhouse, rather than any actual built structure. Poole & Hunt, machinists and engineers, was a major cable industry designer and contractor and manufacturer of gearing, sheaves, shafting and wire rope drums.
|
|
Coonagh men used sickles to cut reed that grows along the shore of the Shannon estuary to sell as thatch, which was gathered into sheaves. After the dredging of Meelick and Cratloe Creeks in the 1960s, the sheaves were transported by gandelow to nearby Lansdowne Bridge or Sandy Bridge, where it was then loaded onto lorries for distribution. Prior to this, local farmers originally bought the reed as they were the only ones with access to the river through their own lands, either via horse and cart or later tractor and trailer. The reeds were typically used as roofing for "story and a half" thatched cottages in Coonagh and further afield, which usually consisted of a downstairs living room/kitchen with one or sometimes two rooms located off it, and a single room upstairs, similar to those that can be found in Adare and Bunratty Folk Park.
|
|
Robert Boyle later wrote of magnetism that “the ingenious Kircher hath so largely prosecuted it in his voluminous Ars Magnetica (sic), yet he has not reaped his field so clean, but that a careful gleaner, may still find ears enough to make some sheaves.” Kircher returned to the subject of magnetism several times in his later studies, publishing Magnes sive de Arte Magnetica (1641) and Magneticum naturae regnum (1667).
|
|
He was an avid art collector, and during his life acquired over 50,000 books and sheaves of official correspondence. The Kenya National Archives established a library containing some of the 8000 rare books (published before 1900) entrusted to them upon the death of Murumbi. The Kenya National Archives also created the 'Murumbi Gallery' within the same building, displaying the different African artifacts that were collected by him through his lifelife.
|
|
Harriet Converse became increasingly involved in learning about the Seneca, with Parker's help. She became inspired to defend the rights of the Iroquois by aiding them politically with her wealth and support, and helped to preserve their culture. In 1885 Converse was formally adopted by the Snipe Clan ia Seneca family. In 1883 she published her first volume of poems, Sheaves (New York City, 1883), which passed through several editions.
|
|
The so-called geometric Langlands program, suggested by Gérard Laumon following ideas of Vladimir Drinfeld, arises from a geometric reformulation of the usual Langlands program that attempts to relate more than just irreducible representations. In simple cases, it relates -adic representations of the étale fundamental group of an algebraic curve to objects of the derived category of -adic sheaves on the moduli stack of vector bundles over the curve.
|
|
The Stülcken is secured between two V-shaped, unstayed Samson-posts. This makes it possible to let the derrick swing through the posts to reach another hatch. For each post is a hoisting winch, a span winch and a lever that is run by one man only. Bearings, swivels, sheaves and the gooseneck can be unattended for up to four years and create only a friction of about 2%.
|
|
In algebraic geometry, the Gabriel–Rosenberg reconstruction theorem, introduced in , states that a quasi-separated scheme can be recovered from the category of quasi-coherent sheaves on it. The theorem is taken as a starting point for noncommutative algebraic geometry as the theorem says (in a sense) working with stuff on a space is equivalent to working with the space itself. It is named after Pierre Gabriel and Alexander L. Rosenberg.
|
|
Three sheaves rise up in the landscape behind him. A fourth sheaf appears in the foreground to the right, where a man kneels with a bushel of corn ears, ready to add to the harvest bounty. Finally, a paddle steamer navigates the calm river in the background, another example of how the river is tamed.The significance of the steamboat is noted in the Smithsonian's Educational Insights feature on the mural.
|
|
Apart from using h-principle to study the flexibility of local geometric models, Murphy's work uses cut-and-paste/surgery techniques from smooth topology. She also works on exploring the interaction of symplectic/contact topology with geometric invariants, such as those coming from pseudo-holomorphic curves or constructible sheaves. Murphy received the grants from National Science Foundation for the period 2019-2022 on the topic "Flexible Stein Manifolds and Fukaya Categories".
|
|
Eyton, volume 4, p.137. In 1256 William de Ercall, and Prioress Agnes engaged in a complicated series of lawsuits, including a fine of lands, to transfer to the convent a very small rent (a ninth of the sheaves on three carucates of land) and small piece of land for a weir.Eyton, volume 9, p. 85-6. This involved settling any competing claim that might come from Wombridge Priory.
|
|
More generally, the restriction (or domain restriction or left-restriction) of a binary relation between and may be defined as a relation having domain , codomain and graph . Similarly, one can define a right-restriction or range restriction . Indeed, one could define a restriction to -ary relations, as well as to subsets understood as relations, such as ones of for binary relations. These cases do not fit into the scheme of sheaves.
|
|
Haigh, pp. 204, 206, 211 The cable laying equipment of Monarch was a major step forward compared to the unspecialised ships that had previously been used for cable laying, with sheaves to run the cable out of the hold and a powerful dedicated brake to control the cable running out. However, Monarch did not store the cable in water-filled tanks as was done on future cable ships.
|
|
Within days of her brother's graduation, Anna and Ida C. Haskell, boarded a ship in New York and sailed for Rotterdam. Anna remained in Rijsoord for five months, and there she produced The Sand Sifter, Harvest [10], The Windmill and Girl Carrying Sheaves. This would be her last trip to the Netherlands. When Anna returned to New York that November, Willard, (as noted in his memoir) missed meeting her ship.
|
|
In algebraic geometry, the Fourier–Deligne transform, or ℓ-adic Fourier transform, or geometric Fourier transform, is an operation on objects of the derived category of ℓ-adic sheaves over the affine line. It was introduced by Pierre Deligne on November 29, 1976 in a letter to David Kazhdan as an analogue of the usual Fourier transform. It was used by Gérard Laumon to simplify Deligne's proof of the Weil conjectures.
|
|
It contains the western part of the town of Stephenville, as well as the communities of Abraham's Cove, Aguathuna, Berry Head, Black Duck Brook, Boswarlos, Campbell's Creek, Cape St. George, De Grau, Felix Cove, Fox Island River, Jerry's Nose, Kippens, Lourdes, Lower Cove, Mainland, Marches Point, Piccadilly, Point au Mal, Port au Port, Red Brook, Sheaves Cove, Ship Cove, Three Rock Cove, West Bay, West Bay Centre and Winterhouse.
|
|
These sheaves admit algebraic operations which are associative and commutative only up to an equivalence relation. Taking the quotient by this equivalence relation yields the structure sheaf of an ordinary scheme. Not taking the quotient, however, leads to a theory which can remember higher information, in the same way that derived functors in homological algebra yield higher information about operations such as tensor product and the Hom functor on modules.
|
|
London and Blackwall cable-operated railway, 1840 Cable Driving Plant, Designed and Constructed by Poole & Hunt, Baltimore, MD. Drawing by P.F. Goist, circa 1882. The powerhouse has two horizontal single-cylinder engines. The lithograph shows a hypothetical prototype of a cable powerhouse, rather than any actual built structure. Poole & Hunt, machinists and engineers, was a major cable industry designer and contractor and manufacturer of gearing, sheaves, shafting and wire rope drums.
|
|
It postulated the existence of a natural one-to-one correspondence between Galois representations and some automorphic forms. The "naturalness" is guaranteed by the essential coincidence of L-functions. However, this condition is purely arithmetic and cannot be considered for a general one-dimensional function field in a straightforward way. Drinfeld pointed out that instead of automorphic forms one can consider automorphic perverse sheaves or automorphic D-modules.
|
|
However, the direct image of a sheaf of sections of a bundle is not in general the sheaf of sections of some direct image bundle, so that although the notion of a 'pushforward of a bundle' is defined in some contexts (for example, the pushforward by a diffeomorphism), in general it is better understood in the category of sheaves, because the objects it creates cannot in general be bundles.
|
|
Joe, whose mother, Maggie Jesso, was Peter Jesso's daughter, later gave the business to his son Clifton and wife Bertha Bruce from Abraham's Cove. It was closed when they retired. In 1971, 240 people lived in Sheaves Cove, with little growth since, with just 36 families year round in the community. Among them are the Jessos, descended from the first settler, along with Felix, Rowe and Young families.
|
|
The knight's Vogt came by horse right onto the field and set aside the ten best sheaves for the lord. All other obligations had been laid down long before in the municipality's Weistum. These were read out yearly on New Year's Day, the day when the thing was held. The lordship needed everything, from hay for horse fodder to honey for their dining tables to beeswax for their candles.
|
|
Yum-Tong Siu (; born May 6, 1943 in Guangzhou, China) is the William Elwood Byerly Professor of Mathematics at Harvard University. Siu is a prominent figure in the mathematics of several complex variables. His research interests involve the intersection of complex variables, differential geometry, and algebraic geometry. He has resolved various conjectures by applying estimates of the complex Neumann problem and the theory of multiplier ideal sheaves to algebraic geometry.
|
|
They were formerly in the chapel of St. Xaviers Convent of Mercy in Ennis, and were moved to Ruan in the 1990s when the convent was closed. The window on the left shows the Nativity. That in the center is the Sacred Heart, and includes sheaves of wheat, grapes and a chalice, symbols of the consecration. The window on the right depicts life in the house of the Holy Family.
|
|
The locomotive's trailing wheels were positioned below the firebox. The cylinders were arranged outside the frames, with flat Murdoch's D slide valves arranged at an incline above the cylinders and actuated by Allan straight link valve gear, driven by eccentric sheaves which were mounted on a return crank. The brakes were actuated by hand screw from the cab. The engine had thick wooden buffer beams and was equipped with cowcatchers.
|
|
In mathematics, a topos (, ; plural topoi or , or toposes) is a category that behaves like the category of sheaves of sets on a topological space (or more generally: on a site). Topoi behave much like the category of sets and possess a notion of localization; they are a direct generalization of point-set topology. The Grothendieck topoi find applications in algebraic geometry; the more general elementary topoi are used in logic.
|
|
Crystals are prismatic, elongated along the b axis, or wedge-shaped. They occur in radiating sheaves and spherulites, and as fibrous crusts or earthy and powdery material. Cleavage is good perpendicular to the c axis, and twinning is common. Tsumcorite is yellow-brown, red-brown or orange in color, and it is one of the few minerals that have a yellow streak (orpiment and crocoite are two others).
|
|
Archaeological finds indicate that the belt continued to be used in Anglo-Saxon male costume in the seventh to the ninth centuries. Knives were often suspended from belts and in the early seventh century, leather sheaves started to appear with knives. Leather and fabric pouches make their initial appearance during this time period. Many of the buckles were simple and small, although more elaborate and opulent buckles have been discovered.
|
|
Ellerman was born 14 March 1943. He received an undergraduate degree in philosophy from Massachusetts Institute of Technology in 1965. He went on to Boston University for his graduate work, receiving an MA in philosophy of science in 1967, an MA in economics in 1968, and a doctorate in mathematics in 1972. His PhD thesis was titled Sheaves Of Relational Structures And Ultraproducts, and was advised by Rohit Jivanlal Parikh.
|
|
As it turned out, starting from, say, primitive spectra, it was not easy to develop a workable sheaf theory. One might imagine this difficulty is because of a sort of quantum phenomenon: points in a space can influence points far away (and in fact, it is not appropriate to treat points individually and view a space as a mere collection of the points). Due to the above, one accepts a paradigm implicit in Pierre Gabriel's thesis and partly justified by the Gabriel–Rosenberg reconstruction theorem (after Pierre Gabriel and Alexander L. Rosenberg) that a commutative scheme can be reconstructed, up to isomorphism of schemes, solely from the abelian category of quasicoherent sheaves on the scheme. Alexander Grothendieck taught that to do geometry one does not need a space, it is enough to have a category of sheaves on that would be space; this idea has been transmitted to noncommutative algebra by Yuri Manin.
|
|
Bridgeland's research interest is in algebraic geometry, focusing on properties of derived categories of coherent sheaves on algebraic varieties. His most-cited papers are on stability conditions, on triangulated categories and K3 surfaces; in the first he defines the idea of a stability condition on a triangulated category, and demonstrates that the set of all stability conditions on a fixed category form a manifold, whilst in the second he describes one connected component of the space of stability conditions on the bounded derived category of coherent sheaves on a complex algebraic K3 surface. Bridgeland's work helped to establish the coherent derived category as a key invariant of algebraic varieties and stimulated world-wide enthusiasm for what had previously been a technical backwater. His results on Fourier- Mukai transforms solve many problems within algebraic geometry, and have been influential in homological and commutative algebra, the theory of moduli spaces, representation theory and combinatorics.
|
|
This is a model for all kinds of local-vs.-global questions in geometry. Sheaf cohomology gives a satisfactory general answer. Namely, let A be the kernel of the surjection B → C, giving a short exact sequence : 0\to A\to B\to C\to 0 of sheaves on X. Then there is a long exact sequence of abelian groups, called sheaf cohomology groups: : 0\to H^0(X,A) \to H^0(X,B) \to H^0(X,C) \to H^1(X,A) \to \cdots, where H0(X,A) is the group A(X) of global sections of A on X. For example, if the group H1(X,A) is zero, then this exact sequence implies that every global section of C lifts to a global section of B. More broadly, the exact sequence makes knowledge of higher cohomology groups a fundamental tool in aiming to understand sections of sheaves.
|
|
From 2002 to 2009 he headed the department of mathematics at the International Centre for Theoretical Physics(ICTP), in Trieste, Italy. He was a frequent guest scientist at Harvard University (with Phillip Griffiths) and Northeastern University (with Terence Gaffney, David B. Massey). He is particularly concerned with singularity theory in the complex domain (Milnor fibrations, perverse sheaves). In 2000 he was involved in promoting scientific exchange between the United States and Vietnam.
|
|
There is a crest and shield version of the flag of Vernon that is used occasionally; it was adopted shortly after the city was incorporated. The flag of Vernon represents the city itself and its region, the Okanagan, containing a "V" to note Vernon, an elk to represent the wildlife of the area, sheaves to suggest the importance of agriculture in the city, while its horn of plenty notes its fruit industry.
|
|
He took with him a flask of wine and some bread. When he arrived at two fields, called Marone and Maturavolo, he offered the farmers the bread and wine. A furious storm rose up, risking destruction of the harvest, but through John's prayer the storm held off until the wheat be harvested and gathered in sheaves. Thus he helped to miraculously harvest a large crop ahead of destructive weather, saving the locals from starvation.
|
|
The coat of arms of the Sheffield Faculty of Medicine was granted by the College of Arms on 12 December 2003. It features elements from the coat of arms of the University of Sheffield: the Crown of Success, two sheaves of arrows and the open books, as well as the azure background colour. The rod of Asclepius is centred on the shield. It can be seen throughout the Medical School on its buildings.
|
|
On some operations, they had to be towed from astern by a tug in order to lay cable over the bow sheaves using cable machinery forward. They even had dual sets of running lights installed so the stern could be the bow and show proper lights. Kingsport was still with the project. The Navy was requesting four fully functional cable ships, the modernized Albert J. Myer and Neptune and two large new ships.
|
|
At arbor low trim, the compensating chain is fully supported by the wall. At arbor high trim, the chain is fully supported by the arbor. Paying out at half the speed of arbor travel, a compensating chain effectively eliminates imbalance along the full path of travel. A compensating wire rope line is attached to the top and to the underside of an arbor and runs through sheaves near those for the operating line.
|
|
The M9 had tandem rear axles and a single front axle on a rotating dolly. Ramps hinged down at the rear end of the trailer. Cable rollers and sheaves let the winch from the M20 truck pull tanks onto the trailer, chocks and chains were used to secure the load. The front axle suspension system was trailing beam assemblies on coil springs, with a dual tire wheel on each side of the beam.
|
|
In theoretical physics, the Penrose transform, introduced by , is a complex analogue of the Radon transform that relates massless fields on spacetime to cohomology of sheaves on complex projective space. The projective space in question is the twistor space, a geometrical space naturally associated to the original spacetime, and the twistor transform is also geometrically natural in the sense of integral geometry. The Penrose transform is a major component of classical twistor theory.
|
|
One also talks about injective objects in categories more general than module categories, for instance in functor categories or in categories of sheaves of OX-modules over some ringed space (X,OX). The following general definition is used: an object Q of the category C is injective if for any monomorphism f : X → Y in C and any morphism g : X → Q there exists a morphism h : Y → Q with hf = g.
|
|
Aeolus viewed from bow sheaves. Aeolus worked in the Atlantic and Caribbean during 1955–56; in the Pacific during 1956–59; and returned to the Atlantic and Caribbean during 1959–62. During 1962–73 she worked principally in the Atlantic, with occasional temporary assignments to the Pacific. In early 1973 the ship underwent a ten month refit at the Boston Naval Shipyard in anticipation of transfer to the Military Sealift Command (MSC) later that year.
|
|
The bride's father places the right hand of the bride on that of the groom as a symbolic gesture of handing over the bride to the groom. The groom's brother hands over a tray with seven sheaves of betel leaves with a coin placed in each. The groom holds the tray while the bride takes one leaf at a time and drops it on the Poruwa. The groom then repeats this process.
|
|
The current coat of arms consists of numerous traditional heraldic attributes. The shield is party per fess argent and gules; that is, split horizontally in two with a red lower half and silver upper half. Its lower half contains two golden sheaves of wheat on a red background; this design represents Albany's agricultural past. The upper half, which has a silver background, depicts a beaver gnawing at the stump of a fallen tree.
|
|
The Insignia was designed for the use of the national organization or local chapters. Parts of the Insignia are the equilateral triangle with the words Physical, Intellectual, and Spiritual making up the three sides, an ATA bond of fellowship that ties the sides together, the open book and the lamp of knowledge, supported by two sheaves of wheat. The Insignia is protected by copyright. The official colors of Alpha Tau Alpha are orange and brown.
|
|
Vogel, pp. 23–24. Otis were confident they would eventually be given the contract and had already started creating designs. The car was divided into two superimposed compartments, each holding 25 passengers, with the lift operator occupying an exterior platform on the first level. Motive power was provided by an inclined hydraulic ram long and in diameter in the tower leg with a stroke of : this moved a carriage carrying six sheaves.
|
|
Hori et al. 2003, p. xviii In an address at the International Congress of Mathematicians in 1994, mathematician Maxim Kontsevich presented a new mathematical conjecture based on the physical idea of mirror symmetry in topological string theory. Known as homological mirror symmetry, this conjecture formalizes mirror symmetry as an equivalence of two mathematical structures: the derived category of coherent sheaves on a Calabi–Yau manifold and the Fukaya category of its mirror.
|
|
This means among other things that they have half the dimension of the space in which they sit, and they are length-, area-, or volume-minimizing.Yau and Nadis 2010, p. 175 The category having these branes as its objects is called the Fukaya category. The derived category of coherent sheaves is constructed using tools from complex geometry, a branch of mathematics that describes geometric curves in algebraic terms and solves geometric problems using algebraic equations.
|
|
The category of small dg- categories can be endowed with a model category structure such that weak equivalences are those functors that induce an equivalence of derived categories. Given a dg-category C over some ring R, there is a notion of smoothness and properness of C that reduces to the usual notions of smooth and proper morphisms in case C is the category of quasi-coherent sheaves on some scheme X over R.
|
|
The locomotives were equipped with Clarke's chain brakes. The braking system proved to be unsatisfactory, since breaking of the chain was not uncommon. In one instance this resulted in a bad accident with loss of life while a train was descending the Hex River rail pass. The chain brake was operated by a link chain, which was carried on sheaves underneath the train along the centre, connected by coupling hooks between carriages or trucks.
|
|
The name is first documented in the 15th and 16th centuries as 'Gorbaldis', and its etymology is unclear. It may be related to the Latin word garbale (sheaf), found in the Scottish term garbal teind (tenth sheaf), a tithe of corn given to a parish rector. The taking of garbal teind was a right given to George Elphinstone in 1616 as part of his 19-year tack (lease). The placename would therefore mean "the Sheaves".
|
|
Then the Queen commands that she herself be dressed in peasant's clothes so that she may realise her own intention, having conceived the idea of giving the princess a poisoned apple. The Princess's maid dresses her. The Vision disappears. Scene 9 – Huts and a cave on rocky hills Gnomes come out of the cave and down from the hills: some are carrying sheaves of brushwood; others are digging out passageways in the crags.
|
|
Throughout the church's physical changes the altar has remained as the original centerpiece for worship. Canon Hope was instrumental in procuring a donation from England of three beautifully carved panels for the altar. The altar itself was constructed as a gift by Mr. James Massiah for the church's consecration in 1926. The three carved panels display both grapevines (representing communion wine and the blood of Christ) and sheaves of wheat (communion bread and the body of Christ).
|
|
Sculptor Dov Feigin produced "Wheat Sheaves" in 1956, and Dadaist Janco painted "Soldiers", "Air raid Alarms" and "Maabarot" (jerry-built communities housing new Jewish immigrants in the 1950s). Some of the New Horizons artists belonged to the "Center for Advanced Culture" run by the Socialist-Zionist youth movement "Hashomer Hatzair".See: Gila Blass, New Horizons, p. 29. This activity culminated in the founding of the artists' village Ein Harod by a group of artists headed by Janco.
|
|
Subspecies smitinandii is a slender rattan, clustering and growing up to 10m, rarely to 20m, it often flowers and fruits at 2-3m. Its stems without sheaves are 4-8mm in diameter. The leaf sheath is densely covered in solitary spines, 1-13mm long. The bracts on the smitinandii rachis are elongate, split for at least half their length, opening out and becoming flattened and tattering; first order branches are inserted about half way along length of the bracts.
|
|
It is a unique technique, developed by Rubin, that uses various and different materials. With this technique she expresses, in a sensitive plastic forms, her feelings towards her surroundings. The contrasts between the artist and her human milieu create conflicts that, being stormy, hard and unsolved has a lot of influence on the forming of the work. In Soft Painting - sheaves of colored fibers laid on a felt sheet replaces the brush and palette of the painter.
|
|
The bale hoist was used to load bales of wool onto transports and is located on the rear eastern side of the woolshed, adjacent to the powerhouse. The hoist is made from steel and consists of a vertical upright with a horizontal arm at the top. The arm is supported by decorative steel bracing. Part of the hydraulic power network, the hoist had a single cable that operated through a series of sheaves; the lower sheave is now missing.
|
|
Schultz was a popular architect of manor houses in Estonia, who also designed the baroque extension of Toompea Castle, Tallinn. Some very fine and comprehensive interiors from this time are still preserved complete with the original colour scheme, notably the hall and the "blue salon". The rich stucco decorations were made by Bohemian stucco master Karl Kalopka, and include typical details in rococo style such as putti, trophies and sheaves, and the owners' coat of arms.
|
|
In category theory, a branch of mathematics, a Grothendieck topology is a structure on a category C that makes the objects of C act like the open sets of a topological space. A category together with a choice of Grothendieck topology is called a site. Grothendieck topologies axiomatize the notion of an open cover. Using the notion of covering provided by a Grothendieck topology, it becomes possible to define sheaves on a category and their cohomology.
|
|
For a separated presheaf, the first arrow need only be injective. Similarly, one can define presheaves and sheaves of abelian groups, rings, modules, and so on. One can require either that a presheaf F is a contravariant functor to the category of abelian groups (or rings, or modules, etc.), or that F be an abelian group (ring, module, etc.) object in the category of all contravariant functors from C to the category of sets. These two definitions are equivalent.
|
|
In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaf cohomology is a technique for producing functions with specified properties. Many geometric questions can be formulated as questions about the existence of sections of line bundles or of more general coherent sheaves; such sections can be viewed as generalized functions. Cohomology provides computable tools for producing sections, or explaining why they do not exist. It also provides invariants to distinguish one algebraic variety from another.
|
|
Upon mine closure and mine reclamation a steel headframe is easier to demolish and may have value as scrap metal. A recently erected steel headgear in the Zambian copper belt town of Chililabombwe at the Konkola number 4 shaft has a total height of 81 metres to the top of the maintenance crane rail, with the centre-line of the head sheaves at 71 metres above the collar, making it the highest steel headgear in Africa.
|
|
Construction of Detroit began in January 1813, however delays began almost immediately as William Bell complained that he did not have enough shipwrights. The construction placed further burdens on British supply lines, with the vessel requiring of oak timber, 200 oak knees and over of pine timber and boards. Furthermore, there was shortages of fabric for sails, bolts, sheaves and deadeyes. Reinforced by shipwrights sent from Kingston, Upper Canada, planking of the sloop began in April.
|
|
Camarda has its origins during the High Middle Ages, when a raid by Lombards pushed many inhabitants of Forcona (an archaeological site located in the area of Bagno) to take refuge in the neighboring areas. According to legend, the name Camarda derives from the cry "Cama ardet!", shouted by the peasants who saw their sheaves burning, which some Lombard soldiers had set on fire. Afterwards, Camarda was one of the villages that contributed to the foundation of L'Aquila.
|
|
In Greek mythology, Lityerses (Ancient Greek: Λιτυέρσης) was an illegitimate son of Midas (or of Comis) dwelling in Celaenae, Phrygia, and of Demeter, the ancient Greek goddess of plants, wheat and harvesting. Lityerses was a talented swordsman, and was bloodthirsty and aggressive. He challenged people to harvesting contests and beheaded those he beat, putting the rest of their bodies in the sheaves. Heracles won the contest and killed him, then threw his body into the river Maeander.
|
|
The combine separates out the husk and the cob, keeping only the kernels. When maize is a silage crop, the entire plant is usually chopped at once with a forage harvester (chopper) and ensiled in silos or polymer wrappers. Ensiling of sheaves cut by a corn binder was formerly common in some regions but has become uncommon. Worldwide maize production For storing grain in bins, the moisture of the grain must be sufficiently low to avoid spoiling.
|
|
Dennis Gaitsgory is a professor of mathematics at Harvard University known for his research on the geometric Langlands program. Born in what is now Moldova, he grew up in Tajikistan, before studying at Tel Aviv University under Joseph Bernstein (1990–1996). He received his doctorate in 1997 for a thesis entitled "Automorphic Sheaves and Eisenstein Series". He has been awarded a Harvard Junior Fellowship, a Clay Research Fellowship, and the prize of the European Mathematical Society for his work.
|
|
They are p-adic analogues of Ql-adic étale sheaves, introduced by and (though the definition of isocrystal only appears in part II of this paper by ). Convergent isocrystals are a variation of isocrystals that work better over non-perfect fields, and overconvergent isocrystals are another variation related to overconvergent cohomology theories. A Dieudonné crystal is a crystal with Verschiebung and Frobenius maps. An F-crystal is a structure in semilinear algebra somewhat related to crystals.
|
|
The keel level opening was reduced to one of long and wide. A flush mounted, water tight hydraulic door or two parts, one fore and one aft, closed the well at the main deck level. Three diameter cable sheaves installed in a carriage, within which towed devices would be contained for lowering and raising, and extending below the keel allowed towing of heavy equipment without exposure on open decks. The system had a capacity of 12 tons.
|
|
In mathematics, sheaf cohomology is the application of homological algebra to analyze the global sections of a sheaf on a topological space. Broadly speaking, sheaf cohomology describes the obstructions to solving a geometric problem globally when it can be solved locally. The central work for the study of sheaf cohomology is Grothendieck's 1957 Tôhoku paper. Sheaves, sheaf cohomology, and spectral sequences were invented by Jean Leray at the prisoner-of-war camp Oflag XVII-A in Austria.
|
|
To be more precise, one must add additional data to the Lagrangian – a grading and a spin structure. A Lagrangian with a choice of these structures is often called a brane in homage to the underlying physics. The Homological Mirror Symmetry conjecture states there is a type of derived Morita equivalence between the Fukaya category of the Calabi–Yau X and a dg category underlying the bounded derived category of coherent sheaves of the mirror, and vice versa.
|
|
The brickwork masonry is articulated by pillars in form of corn sheaves which evoke Egyptian architecture. Through this building Bílek, who was a deeply religious artist, tried to express his view on substance of life. Villa Bílek has been maintained by Gallery of the Capital City of Prague () since 1963. It houses a public exposition that introduces many works by Bílek, as well as original interior fittings and furniture collection which was made according to his design.
|
|
In general, as with flat belts, rope drives were used for connections from stationary engines to the jack shafts and line shafts of mills, and sometimes from line shafts to driven machinery. Unlike leather belts, however, rope drives were sometimes used to transmit power over relatively long distances. Over long distances, intermediate sheaves were used to support the "flying rope", and in the late 19th century, this was considered quite efficient.Robert Grimshaw, Drive for Power Transmission Cassier's Magazine Vol.
|
|
Built by C. Mitchell and Co., Newcastle, 1873, . Sold 1881 to India Rubber, Gutta Percha and Telegraph Works Company and renamed Silvertown which was active in cable work through 1913. Silvertown began the trans Pacific cable at San Francisco for the Commercial Pacific Cable Company in 1902. was built for the company as tender to Silvertown with two cable tanks but no cable laying machinery until a later refit when that machinery and bow sheaves were fitted.
|
|
Charles A. Weibel, Robert W. Thomason (1952–1995). Specifically, he proved equivariant analogs of fundamental theorems such as the localization theorem. Equivalently, K_i^G(X) may be defined as the K_i of the category of coherent sheaves on the quotient stack [X/G]. (Hence, the equivariant K-theory is a specific case of the K-theory of a stack.) A version of the Lefschetz fixed point theorem holds in the setting of equivariant (algebraic) K-theory.
|
|
The étale cohomology groups Hi(F) of the sheaf F of abelian groups are defined as the right derived functors of the functor of sections, :F \to \Gamma(F) (where the space of sections Γ(F) of F is F(X)). The sections of a sheaf can be thought of as Hom(Z, F) where Z is the sheaf that returns the integers as an abelian group. The idea of derived functor here is that the functor of sections doesn't respect exact sequences as it is not right exact; according to general principles of homological algebra there will be a sequence of functors H 0, H 1, ... that represent the 'compensations' that must be made in order to restore some measure of exactness (long exact sequences arising from short ones). The H 0 functor coincides with the section functor Γ. More generally, a morphism of schemes f : X → Y induces a map f∗ from étale sheaves over X to étale sheaves over Y, and its right derived functors are denoted by Rqf∗, for q a non-negative integer.
|
|
Historically the most popular construction of a gerbe is a category-theoretic model featured in Giraud's theory of gerbes, which are roughly sheaves of groupoids over M. In 1994 Murray introduced bundle gerbes, which are geometric realizations of 1-gerbes. For many purposes these are more suitable for calculations than Giraud's realization, because their construction is entirely within the framework of classical geometry. In fact, as their name suggests, they are fiber bundles. This notion was extended to higher gerbes the following year.
|
|
According to the inscription on two of the pillars of the drawbridge on the west side, the building was finished in 1770. The production of snuff was heavy work: enormous sheaves of tobacco were hauled around manually, and horses turned the grinding mills. For centuries, Seville remained Spain's only manufacturer of snuff. The rising popularity of cigars resulted in part of the factory being adapted for that purpose; cigars were also made in several other Spanish cities: Cádiz, Alicante, La Coruña, and Madrid.
|
|
Growing up at Terras, Hocking was surrounded by the china clay mining and tin mining industries, the latter appears regularly in her work. Her father turned to farming because of a decline in the mining industry and, one day in her teens, while helping out pitching corn sheaves, she seriously injured her spine. Her shoulder and hip where twisted in opposite directions resulting in a double curvature. Hocking did not seek treatment at the time, hiding the injury under her long hair.
|
|
He is known for his work on representation theory, in particular for the objects closely related to algebraic groups, such as finite reductive groups, Hecke algebras, p-adic groups, quantum groups, and Weyl groups. He essentially paved the way for modern representation theory. This has included fundamental new concepts, including the character sheaves, the Deligne–Lusztig varieties, and the Kazhdan–Lusztig polynomials.Carter, Roger W., A survey of the work of George Lusztig, Nagoya Mathematical Journal 182 (2006), pp. 1–45.
|
|
In June 2020, the Navy released a draft request for proposals for companies to compete to build a replacement for USNS Zeus known as the T-ARC(X), to be outfitted with cable handling equipment including cable tanks, cable transporters, cable tension machines, over-boarding sheaves and dynamometer cable fairleader. It will also be equipped with a moonpool and a variety of hull mounted sonar systems to support the primary and secondary missions. The government intends to award the contract by October 2020.
|
|
He saved the lives of many of his fellow villagers of Hiro, Kii Province (current Hirogawa, Wakayama), when a massive tsunami struck the Kii Peninsula in 1854. He set fire to stacks of rice sheaves as landmarks to guide villagers to safety. Lafcadio Hearn wrote a story about him in Gleanings in Buddha-Fields: Studies of Hand and Soul in the Far East (1897), called "Inamura no Hi: The burning rice fields".First published in 1897 by Houghton, Mifflin (Boston).
|
|
A Massey-Harris reaper-binder pulled by a tractor (Rutland, England, 2008) A modern compact binder for rice (2006) The reaper-binder, or binder, is a farm implement that improved upon the simple reaper. The binder was invented in 1872 by Charles Baxter Withington, a jeweler from Janesville, Wisconsin.Charles B. Withington, "Improvement in grain-binders," U.S. Patent no. 123,967 (issued: February 20, 1872) In addition to cutting the small-grain crop, a binder also 'binds' the stems into bundles or sheaves.
|
|
Theocritus described one of Demeter's earlier roles as that of a goddess of poppies: :For the Greeks Demeter was still a poppy goddess :Bearing sheaves and poppies in both hands. — Idyll vii.157 Karl Kerenyi asserted that poppies were connected with a Cretan cult which was eventually carried to the Eleusinian mysteries in Classical Greece. In a clay statuette from Gazi (Heraklion Museum, Kereny 1976 fig 15), the Minoan poppy goddess wears the seed capsules, sources of nourishment and narcosis, in her diadem.
|
|
The sculpture was commissioned by the City of Winnipeg and was the winning proposal in a national competition by artist Catherine Widgery. The sculpture is made of stone, stainless steel, aluminum, gold leaf, and concrete, and includes an arch and two 40ft columns, each topped with golden sheaves of wheat. The arch bears a pixellated image from a photograph of a harvested field. Each column bears a sculpture of the head of a bison on each side of the base.
|
|
Wheat Fields is a series of dozens of paintings by Dutch Post-Impressionist artist Vincent van Gogh, borne out of his religious studies and sermons, connection to nature, appreciation of manual laborers and desire to provide a means of offering comfort to others. The wheat field works demonstrate his progression as an artist from the drab Wheat Sheaves made in 1885 in the Netherlands to the colorful, dramatic paintings from Arles, Saint-Rémy and Auvers-sur-Oise of rural France.
|
|
She wrote in all veins, but her particular liking was for sacred songs. She also adapted words to music for composers. In 1891 a Chicago house published a children's day service of hers, entitled "Gems for His Crown," over eighteen-thousand copies of which were readily sold. In 1892 the same firm accepted three services of hers, "Grateful Offerings to Our King," a children's day service, "Harvest Sheaves," for Thanksgiving or harvest home exercises, and "The Prince of Peace," a Christmas service.
|
|
By definition, the Proj of a graded ring R is the quotient category of the category of finitely generated graded modules over R by the subcategory of torsion modules. If R is a commutative Noetherian graded ring generated by degree-one elements, then the Proj of R in this sense is equivalent to the category of coherent sheaves on the usual Proj of R. Hence, the construction can be thought of as a generalization of the Proj construction for a commutative graded ring.
|
|
The Annotated wizard of Oz. p 173 Robert Graves believed that a second meaning of the depiction and use of poppies in the Greco-Roman myths is the symbolism of the bright scarlet colour as signifying the promise of resurrection after death Robert Graves. The Greek myths. 24.15, p 96 and that the poppy was the emblem of the goddess Demeter. According to Theocritus for the Greeks Demeter was a poppy goddess bearing sheaves and poppies in both hands (Idyll vii 157).
|
|
The stalks were bound into sheaves, and stacked in ricks for the rice to cure. The stalks were cut away, and the cured rice boiled in vats, dried, and threshed to separate the kernels from the chaff. The kernels then were pounded using wooden mortar and pestles to loosen the hulls, the hard outer coating of each grain. The pounded kernels then were carried in tightly-woven baskets up a ladder into the winnowing barn, a small building atop tall stilts.
|
|
Parama Dhamma Chetiya Pirivena Website. and the artwork was by S. M. Seneviratne. The emblem features a gold lion passant, holding a sword in its right fore paw (the same lion from the flag of Sri Lanka) in the centre on a maroon background surrounded by golden petals of a Blue Lotus the national flower of the country. This is placed on top of a traditional grain vase that sprouts sheaves of rice grains that circle the border reflecting prosperity.
|
|
These oracles include casting various forms of horoscope, looking for shapes in the clouds, and examining which nostril the breath is passing most easily. Khun Phaen is also schooled in mantras or formulas with supernatural power. They are used for such purposes as stunning enemies, transforming his body into other forms, opening locks and chains, putting everyone else to sleep, and converting sheaves of grass into invulnerable spirit warriors. Khun Phaen also uses love formulas to captivate women, and to allay the wrath of the king.
|
|
Its primary decorative feature is an inscribed harvest motif on the east and west elevations that are mirror images of each other, oriented to the north. The motif features a male nude holding a wagon wheel and a scythe, with sheaves of wheat and a dog. The bank changed its name to State Bank & Trust in 1967, and continued to operated from here until 1978. The building sat empty for five years when it was renovated for use by State Investment Company and other offices.
|
|
Hereford: EG Wright, 1812. Page 49, Broxash Hundred, Amongst the Collections of St. George, Clarencieux King at Arms His brother and son, Walter Devereux, both probably participated in Edward III's wars in Scotland and France. By 1340, Stephen had gained enough royal trust to be assigned on 20 April the task of collecting the ninth of lambs, fleeces, and sheaves in Herefordshire granted by Parliament to pay for the King's military actions on the continent.Calendar of Patent Rolls, Edward III, Volume IV, 1321-1324.
|
|
Generally, research has determined that there is limited gender division of labor among peasant men and women. Rural historian Jane Whittle described this gender division of labor thus: "Labor was divided according to the workers' gender. Some activities were restricted to either men or women; other activities were preferred to be performed by one gender over the other:" e.g. men ploughed, mowed, and threshed and women gleaned, cleared weeds, bound sheaves, made hay, and collected wood; and yet others were performed by both, such as harvesting.
|
|
A gearwheel stands for industrialization, sheaves around the perimeter stand for the farming class, and the top featured a red star with the socialist version of the Soyombo. Along the bottom, a blue-red ribbon is placed in front of the gearwheel, with the letters ', the abbreviation for ', (Mongolian People's Republic). Before 1961, the emblem did not bear most of the socialist symbols. The horseman carried a long lasso pole and the heads of four types of herd animals were shown on the sides.
|
|
In both cases the third class of morphisms is given by a lifting condition (see below). In some cases, when the category C is a Reedy category, there is a third model structure lying in between the projective and injective. The process of forcing certain maps to become weak equivalences in a new model category structure on the same underlying category is known as Bousfield localization. For example, the category of simplicial sheaves can be obtained as a Bousfield localization of the model category of simplicial presheaves.
|
|
Rabbi Judah said that a single-grape cluster was a cluster, but the Sages said that it was a defective cluster (and thus belonged to the poor).Mishnah Peah 7:4, in, e.g., Jacob Neusner, translator, Mishnah, page 31. The Mishnah taught that if a wife foreswore all benefit from other people, her husband could not annul his wife's vow, but she could still benefit from the gleanings, forgotten sheaves, and the corner of the field that and , and commanded farmers to leave for the poor.
|
|
" #"A fire, when it is kindled, burns many sheaves" (James 3:5) #"An old woman in the house is a good omen in the house" #"Even a good surety has to be applied to for a hundred morrows; a bad one for a hundred thousand." #"Rise quickly from the table and thou wilt avoid disputes." #"In thy business deal only with the upright." #"If the goods are near at hand, the owner consumes them; but if they are at a distance, they consume him.
|
|
Bnei Akiva emblem The "Semel", Bnei Akiva's emblem, shows farming utensils and wheat sheaves symbolizing the agricultural perspective of the ideology, and two tablets of stone in the center symbolizing the Torah. The two perspectives of Torah and Avoda are united together by the ribbon which says Bnei Akiva on it - symbolizing that the two aspects can only and must work hand in hand. The letters on the two tablets are the Hebrew letters 'Tav' and 'Ayin' standing for Torah veAvoda ("Torah and work").
|
|
38) At the time of the flax harvest, the Sages have even defined how many stalks of flax that were forgotten in the field by their owner can be esteemed as "forgotten sheaves," enabling their finder to possess them, without him being guilty of theft.Mishnah (Peah 6:5, p. 17) What constitutes a violation of Sabbath-day laws is also discussed with regard to flax, as bundles of freshly retted flaxOn retting, see The Mishnah (ed. Herbert Danby), Oxford University Press: Oxford 1977, s.v.
|
|
Hugh Cameron (1835–1918), The Harvest, shows a bandwin at work A bandwin was a team of agricultural workers in the Scottish Lowlands before the agricultural revolution, who carried out the harvest. The term was first recorded in 1642. The bandwin was characteristically made up of two teams of two women and a man who acted as reapers and a bandster who gathered and bound the sheaves. The work of women in the bandwin was unusually almost as valued as that of the men.
|
|
On any topological space, the skyscraper sheaf associated to a closed point x and a group or ring G has the stalks 0 off x and G in x--hence the name skyscraper. The same property holds for any point x if the topological space in question is a T1 space, since every point of a T1 space is closed. This feature is the basis of the construction of Godement resolutions, used for example in algebraic geometry to get functorial injective resolutions of sheaves.
|
|
Prior to Lawrence County's creation, it was organized as "Leatherwood Township." On March 11, 1818, the county commissioners Ambrose Carlton, Thomas Beagley, and James Stotts, met at the home of James Gregory. On the third day of this session, the commissioners proceeded to divide the county into two civil townships: Shawswick and Spice Valley. Early in 1819, the board adopted a seal for Lawrence County, which was designed with a harp, a plow, three sheaves of weat, a pair of scales, and a weathercock on top.
|
|
In 1990, development of a successor to the YJ began in Chrysler's "Jeep-Truck Engineering Pre-Program" department under Bob Sheaves and TJ program director, Craig Winn. Mules based on the YJ were built from 1990 to 1993, when formal approval was given for the TJ development program at a $260 million budget. From 1991 to 1992, designers worked at the new Chrysler Technical Center, building on various design proposals. In late 1992, Michael Santoro's TJ proposal was chosen by Tom Gale, Lee Iacocca, and executive management.
|
|
Obstructions to extending local sections may be generalized in the following manner: take a topological space and form a category whose objects are open subsets, and morphisms are inclusions. Thus we use a category to generalize a topological space. We generalize the notion of a "local section" using sheaves of abelian groups, which assigns to each object an abelian group (analogous to local sections). There is an important distinction here: intuitively, local sections are like "vector fields" on an open subset of a topological space.
|
|
The bride is in front of the green textile wall-hanging, with a paper-crown hung above her head. She is also wearing a crown on her head, and she is sitting passively, not participating in the eating or drinking taking place around her. The Bridegroom is not in attendance of the wedding feast in accordance to Flemish custom. The feast is in a barn in the summertime; two sheaves of grain with a rake recalls the work that harvesting involves, and the hard life peasants have.
|
|
Vincent van Gogh - Peasant woman binding sheaves (after Millet) The "peasant genre" that greatly influenced Van Gogh began in the 1840s with the works of Jean-François Millet, Jules Breton, and others. In 1885 Van Gogh described the painting of peasants as the most essential contribution to modern art. He described the works of Millet and Breton of religious significance, "something on high," and described them as the "voices of the wheat." Throughout Van Gogh's adulthood he had an interest in serving others, especially manual workers.
|
|
Zaslow 2008, p. 536 In the B-model of topological string theory, the D-branes are complex submanifolds of a Calabi–Yau together with additional data that arise physically from having charges at the endpoints of strings. Intuitively, one can think of a submanifold as a surface embedded inside the Calabi–Yau, although submanifolds can also exist in dimensions different from two. In mathematical language, the category having these branes as its objects is known as the derived category of coherent sheaves on the Calabi–Yau.
|
|
Yau and Nadis 2010, pp. 180–1 On the other hand, the Fukaya category is constructed using symplectic geometry, a branch of mathematics that arose from studies of classical physics. Symplectic geometry studies spaces equipped with a symplectic form, a mathematical tool that can be used to compute area in two-dimensional examples. The homological mirror symmetry conjecture of Maxim Kontsevich states that the derived category of coherent sheaves on one Calabi–Yau manifold is equivalent in a certain sense to the Fukaya category of its mirror.
|
|
Let X be a topological space and A a sheaf of rings on X. (In other words, (X, A) is a ringed space.) An ideal sheaf J in A is a subobject of A in the category of sheaves of A-modules, i.e., a subsheaf of A viewed as a sheaf of abelian groups such that : Γ(U, A) · Γ(U, J) ⊆ Γ(U, J) for all open subsets U of X. In other words, J is a sheaf of A-submodules of A.
|
|
However, in practice étale cohomology is used mainly in the case of constructible sheaves over schemes of finite type over the integers, and this needs no deep axioms of set theory: with care the necessary objects can be constructed without using any uncountable sets, and this can be done in ZFC, and even in much weaker theories. Étale cohomology quickly found other applications, for example Deligne and George Lusztig used it to construct representations of finite groups of Lie type; see Deligne–Lusztig theory.
|
|
R M Urquhart, Scottish Civic Heraldry, London, 1979R M Urquhart, Scottish Civic Heraldry 2, Hamilton, 2001 As such, the arms are today the corporate property of the City Council. No crest has ever accompanied the arms, but they may be displayed with a mural coronet, in right of Aberdeen's city status. Prior to the formation of the current council in 1996, a district council's coronet was used, representing Aberdeen's status as a district. This was made of gold, and was decorated with spikes and sheaves of wheat.
|
|
References to the term connected with harvest customs seem to emerge in the 16th century. Archbishop Parker’s rhyming translation of Psalm 126, published in 1560, ends with the reassurance that ::Who goeth from home all heavily, ::Wyth his seede leape his land to try, ::He home returnes wyth hocky cry, ::Wyth sheaves full lade abundantly.Matthew Parker, The whole Psalter translated into English metre, London 1560 p.376 Further literary evidence points to a number of customs established around the final gathering of the harvest at this period.
|
|
Bishop Władysław Oporowski organized a fundraiser to rescue St. Vitalis's Church, at the same time appointing a special indulgence for donors. However, it is not known whether the intended renovation was actually carried out. Sources say that about 100 years later, in the years 1534-1544, canon Tobiasz Janikowski renovated the whole church at his own expense and replaced the existing wooden Gothic ceiling with a brick one, which has been preserved until today. It is a kind of ribbed vault, where the sheaves of ribs fall on large supports.
|
|
In general linear systems became a basic tool of birational geometry as practised by the Italian school of algebraic geometry. The technical demands became quite stringent; later developments clarified a number of issues. The computation of the relevant dimensions -- the Riemann–Roch problem as it can be called -- can be better phrased in terms of homological algebra. The effect of working on varieties with singular points is to show up a difference between Weil divisors (in the free abelian group generated by codimension-one subvarieties), and Cartier divisors coming from sections of invertible sheaves.
|
|
War arrows were often described as being a "clothyard" in length - the clothyard being the slightly longer physical measure from the fingertips to the nose, but with the head turned away from the fingertips. At the time of the Hundred Years' War archers drew the arrow back to the ear rather than to the chin. For example, between 1341 and 1359 the English crown is known to have obtained 51,350 sheaves (1,232,400 arrows). Only one significant group of arrows, found at the wreck of the Mary Rose, has survived.
|
|
While returning to the church, prayers and sheaves are also offered at the São Miguel Arcanjo chapel en route. High mass is celebrated at the church at 10:00 am. After the mass, the parishioners participate in the Quermés (games) organised by the parish youth, with the background music of brass band. In the afternoon, coconut breaking competitions are held at every nook and corner of the village and the football finals of Säo Miguel trophy is organised at Dr. Alvaro Remigio Pinto ground by the Clube de Säo Miguel de Taleigão.
|
|
At the time of Leray's work, neither of the two concepts involved (spectral sequence, sheaf cohomology) had reached anything like a definitive state. Therefore it is rarely the case that Leray's result is quoted in its original form. After much work, in the seminar of Henri Cartan in particular, the modern statement was obtained, though not the general Grothendieck spectral sequence. Earlier (1948/9) the implications for fiber bundles were extracted in a form formally identical to that of the Serre spectral sequence, which makes no use of sheaves.
|
|
Neil Levin, "The Book of Psalms and Its Musical Interpretations," booklet notes to "Psalms of Joy and Sorrow," Naxos CD 8.55945 The psalm is also sung to secular melodies such as "Waltzing Matilda", "The Longest Time","It's a Small World", Beethoven's Ninth, and college football songs, among many others. Sons of Korah included a setting of Psalm 126 on their 2000 album, "Redemption Songs." The psalm inspired the hymn Bringing in the Sheaves, the lyrics were written in 1874 by Knowles Shaw, now usually set to a tune by George Minor, written in 1880.
|
|
" The ship has flags ("flagged") on its masts and these are red ("gules".) The ship is placed between two "garbs" or wheat- sheaves and these are coloured "Or" which is gold. Invercargill Water Tower The crest is a "Mural Crown" which is a crown made from masonry or bricks and represents city walls or towers. This crown is often found on city coats of arms. The Supporters are the creatures on either side of the shield and in this case are Takahe birds depicted in their natural colours ("proper.
|
|
In the ungraded situation described above, r0 is irrelevant, but in practice most spectral sequences occur in the category of doubly graded modules over a ring R (or doubly graded sheaves of modules over a sheaf of rings). In this case, each sheet is a doubly graded module, so it decomposes as a direct sum of terms with one term for each possible bidegree. The boundary map is defined as the direct sum of boundary maps on each of the terms of the sheet. Their degree depends on r and is fixed by convention.
|
|
Dimca competed in the International Mathematical Olympiad in 1970, 1971, and 1972, earning two bronze medals and one silver medal.. He obtained his PhD in 1981 from the University of Bucharest; his thesis "Stable mappings and singularities", was written under the direction of Gheorghe Galbură. His Google Scholar h-index is 24. Dimca is a distinguished mathematician in algebra, geometry and topology.Bridging Algebra, Geometry, and Topology He has written three important books in this field: Sheaves in Topology, Singularities and Topology of Hypersurfaces and Topics on real and complex singularities.
|
|
Graphic depiction of a single lineset and the parts of a counterweight system. (A) Hoisting cables, (B) Turnbuckles, (C) Purchase line, (D) Arbor rod, (E) Spreader plates, (F) Cut steel counterweight, (G) Rope stop/lock (brake)/Lock rail, (H) Locking safety ring, (I) Tension sheave (block). Not shown: head sheave, loft sheaves, and batten. Counterweight fly system at FirstOntario Concert Hall in Hamilton, Ontario Locking rail and arbors First introduced in Austria in 1888, counterweight rigging systems are the most common fly systems in performing arts facilities today.
|
|
The straw of certain varieties of wheat cultivated in that region is, in favourable seasons, possessed of a fine bright color and due to tenacity and strength. The straw is cut as in ordinary harvesting, but is allowed to dry in the sun, before binding. Subsequently straws are selected from the sheaves, and of these the pipes of the two upper joints are taken for plaiting. The pipes are assorted into sizes by passing them through graduated openings in a grilled wire frame, and those of good color are bleached by the fumes of sulphur.
|
|
The methods of noncommutative algebraic geometry are analogs of the methods of commutative algebraic geometry, but frequently the foundations are different. Local behavior in commutative algebraic geometry is captured by commutative algebra and especially the study of local rings. These do not have a ring-theoretic analogue in the noncommutative setting; though in a categorical setup one can talk about stacks of local categories of quasicoherent sheaves over noncommutative spectra. Global properties such as those arising from homological algebra and K-theory more frequently carry over to the noncommutative setting.
|
|
Prior to the discovery of the 1807 banknotes, the earliest representation of the coat of arms of Vermont was found on an engraved 1821 state military commissions. The exact designer is not known, but it is likely that then Secretary of State Robert Temple worked with an engraver in developing the arms. Considerable liberties were taken in early depictions of the coat of arms. The location of the cow and the sheaves (bundles of cereal grains) moved about the foreground, and the height of the pine tree and size of the buck's head also varied.
|
|
From near the base, and reaching nearly to the top of the shield, arises a pine- tree of the natural color, and between three erect sheaves, yellow, placed bendwise on the dexter side, and a red cow standing on the sinister side of the field. The Crest: A buck's head, of the natural color, cut off and placed on a scroll, blue and yellow. The Motto and Badge: On a scroll beneath the shield, the motto: Vermont: Freedom and Unity. The Vermonter's Badge: two pine branches of natural color, crossed between the shield and scroll.
|
|
A cross deck pendant milliseconds after an aircraft nose-wheel passes over it. The arched supports are leaf springs that raise the pendant above the flight deck. A normal arrestment is accomplished when the arresting hook of an incoming aircraft engages one of the deck pendants. When a landing aircraft engages a deck pendant, the force of the forward motion of the landing aircraft is transferred to a purchase cable which is routed via sheaves to the arresting engine, located in a machinery room below the flight deck or on either side of the runway.
|
|
When the vector spaces involved are over the real numbers, a slightly less general form of homogeneity is often used, requiring only that () hold for all α > 0\. Homogeneous functions can also be defined for vector spaces with the origin deleted, a fact that is used in the definition of sheaves on projective space in algebraic geometry. More generally, if S ⊂ V is any subset that is invariant under scalar multiplication by elements of the field (a "cone"), then a homogeneous function from S to W can still be defined by ().
|
|
A Table of Desserts Of the one hundred or more of his pictures seen in European galleries, only 18 are dated. An early work shows a chased tankard with a bottle, a silver cup and a lemon on a marble table, dated 1640, in the Rijksmuseum in Amsterdam. A similar work of 1645, with the addition of fruit, flowers and a distant landscape, is at Longford Castle. A chalice in a wreath, with a radiant bouquet among wheat sheaves, grapes and flowers, is a masterpiece of 1648 in the Belvedere of Vienna.
|
|
From the roof projected a low, steel hoisting frame with a timber-framed cover above the sheaves, which redirected the hoisting cable from the reversible water wheel into the sloping shaft. In the face of the gable wall were openings for feeding the flatrods of the water wheel which ran down the slope. The mine railway emerged from the gateway at the side of the building. On the slope behind the headframe was the portal to an adit, which was later used by the pub as a drinks cellar under the name Bierstollen ("beer gallery").
|
|
The organisation of reapers in a bandwin from The Farmer's Guide to Scientific and Practical Agriculture (1851) The term was first recorded in 1642 in the Sheriffs records for Aberdeenshire.A. Fenton, The Shape of the Past 1: Essays in Scottish Ethnology, Volume 1 (John Donald, 1985, rpt 2008), , p. 115. It may be derived from the bands of stalks used to tie the sheaves of grain,A. Fenton and M. A. Mackay, eds, An Introduction to Scottish Ethnology: A Compendium of Scottish Ethnology Volume 1 (Edinburgh: Birlinn, 2013), .
|
|
A hydraulic riser tensioner consists of a hydraulic cylinder with sheaves at both sides. The cylinder is connected to a number of high-pressure gas bottles via a medium separator. A wire rope is rigged in the cylinder; one end is connected to the fixed part of the tensioner, the other end is connected to the riser. Fundamentals of Marine Riser Mechanics: Basic Principles and Simplified Analysis, Charles P. Sparks, On board a drill rig tensioners are usually required for drill string compensator, riser tensioner, and guideline tensioner.
|
|
Another advantage of detaching chairs is the ability to remove chairs during severe weather in order to reduce stress on the rope and towers. Furthermore, operating the unladen rope during extreme weather is effective at preventing—or greatly reducing—ice and snow accumulation on the sheaves and rope. This saves considerable time, expense and hazard when opening the chair for operation, which would otherwise require workers to climb each tower and chip away ice and shovel snow. Chairlifts are made in a variety of sizes, carrying from 1 to 8 passengers.
|
|
The Salyr (Salor), a tribe that declined as a result of military defeat before the modern period, are not represented, nor are several smaller tribes or subtribes. The green and red colors appear in this shield because they have been venerated historically by the Turkmen. The central elements are surrounded by sheaves of wheat that allude to the custom to welcome to guests with salt and bread. Atop the wheat and the red circle appear a waxing crescent moon of white, typical of Turkic symbology, and five five-pointed stars also of white.
|
|
Five fixed sheaves were mounted higher up the leg, producing an arrangement similar to a block and tackle but acting in reverse, multiplying the stroke of the piston rather than the force generated. The hydraulic pressure in the driving cylinder was produced by a large open reservoir on the second level. After being exhausted from the cylinder, the water was pumped back up to the reservoir by two pumps in the machinery room at the base of the south leg. This reservoir also provided power to the lifts to the first level.
|
|
The original lifts for the journey between the second and third levels were supplied by Léon Edoux. A pair of hydraulic rams were mounted on the second level, reaching nearly halfway up to the third level. One lift car was mounted on top of these rams: cables ran from the top of this car up to sheaves on the third level and back down to a second car. Each car only travelled half the distance between the second and third levels and passengers were required to change lifts halfway by means of a short gangway.
|
|
In some fields, mechanization includes the use of hand tools. In modern usage, such as in engineering or economics, mechanization implies machinery more complex than hand tools and would not include simple devices such as an un-geared horse or donkey mill. Devices that cause speed changes or changes to or from reciprocating to rotary motion, using means such as gears, pulleys or sheaves and belts, shafts, cams and cranks, usually are considered machines. After electrification, when most small machinery was no longer hand powered, mechanization was synonymous with motorized machines.
|
|
The Clyde trials showed that it was necessary to maintain an internal pressure of about in the pipeline at all times, even during manufacture. Existing cable ships were not large enough, nor were their loading and laying gear sufficiently powerful and robust. Consequently, a number of merchant ships were converted to pipe laying by stripping the interiors, and building in large cylindrical steel tanks, fitting special hauling gear and suitable sheaves and guides. The Petroleum Warfare Department turned to Johnson and Phillips company for special gear to handle and lay the pipe.
|
|
Engine-room of a funicular In a funicular both cars (or trains) are permanently connected to the opposite ends of the same cable, known as a haul rope. At the engine room at upper end of the track the haul rope runs through a system of pulleys. Sheaves- unpowered pulleys allowing the cable to change direction- guide the cable along the track and to and from the drive pulley. The rope pulls one car upwards while the other car descends the slope at the other end of the rope.
|
|
The medieval epic The Tale of Igor's Campaign refers to the "bloody river banks of Nyamiha." Lines from the famous epic detail the gruesome battle: On the Nemiga the spread sheaves are heads, the flails that threshare of steel, lives are laid out on the threshing floor, souls are winnowed from bodies. Nemiga’s gory banks are not sowed goodly-sown with the bones of Russia’s sons. For a long time it was the second largest river flowing through Minsk, until it was adapted for its urban location by containment within a network of pipes.
|
|
Sheaves can be furthermore generalized to stacks in the sense of Grothendieck, usually with some additional representability conditions leading to Artin stacks and, even finer, Deligne–Mumford stacks, both often called algebraic stacks. Sometimes other algebraic sites replace the category of affine schemes. For example, Nikolai Durov has introduced commutative algebraic monads as a generalization of local objects in a generalized algebraic geometry. Versions of a tropical geometry, of an absolute geometry over a field of one element and an algebraic analogue of Arakelov's geometry were realized in this setup.
|
|
In 2016, the governing body of the university, the Harvard Corporation, voted to retire the law school's 80 year old arms. The arms, depicting three garbs (the heraldic term for wheat sheaves), was based in part upon the coat of arms of Isaac Royall Jr., a university benefactor who had endowed the first professorship in the law school. The shield had become a source of contention among a group of law school students, who objected to the Royall family's history as slave-owners.Harvard Law School to ditch controversial shield Steve Annear.
|
|
Eighteen designs were proposed for the reverse of the 2010 cent. On April 16, 2009 the Commission of Fine Arts (CFA) met and selected a design that showed 13 wheat sheaves bound together with a ring symbolizing American unity as one nation. Later this design was withdrawn because it was similar to coinage issued in Germany in the 1920s. The Citizens Coinage Advisory Committee later met and chose a design showing a Union shield with superimposed in a scroll; E Pluribus Unum was also depicted in the upper portion of the shield.
|
|
Over a Riemannian manifold, a metric (field of inner products) is available, and both metric and non-metric contractions are crucial to the theory. For example, the Ricci tensor is a non-metric contraction of the Riemann curvature tensor, and the scalar curvature is the unique metric contraction of the Ricci tensor. One can also view contraction of a tensor field in the context of modules over an appropriate ring of functions on the manifold or the context of sheaves of modules over the structure sheaf; see the discussion at the end of this article.
|
|
Triptolemus receiving wheat sheaves from Demeter and blessings from Persephone, 5th-century BC relief, National Archaeological Museum of Athens The Mysteries are related to a myth concerning Demeter, the goddess of agriculture and fertility as recounted in one of the Homeric Hymns (c. 650 BC). According to the hymn, Demeter's daughter Persephone (also referred to as Kore, "maiden") was assigned the task of painting all the flowers of the earth. Before completion, she was seized by Hades, the god of the underworld, who took her to his underworld kingdom.
|
|
In algebraic geometry, the Horrocks–Mumford bundle is an indecomposable rank 2 vector bundle on 4-dimensional projective space P4 introduced by . It is the only such bundle known, although a generalized construction involving Paley graphs produces other rank 2 sheaves (Sasukara et al. 1993). The zero sets of sections of the Horrocks–Mumford bundle are abelian surfaces of degree 10, called Horrocks–Mumford surfaces. By computing Chern classes one sees that the second exterior power \wedge^2 F of the Horrocks–Mumford bundle F is the line bundle O(5) on P4.
|
|
A rope tow consists of a cable or rope running through a bullwheel (large horizontal pulley) at the bottom and one at the top, powered by an engine at one end. In the simplest case, a rope tow is where passengers grab hold of a rope and are pulled along while standing on their skis or snowboards and are pulled up a hill. The grade of this style of tow is limited by passenger grip strength and the fact that sheaves (pulleys that support the rope above the ground) cannot be used.
|
|
Van Gogh used nature for inspiration, preferring that to abstract studies from imagination. He wrote that rather than making abstract studies: "I am getting well acquainted with nature. I exaggerate, sometime I make change in motif; but for all that, I do not invent the whole picture; on the contrary, I find it already in nature, only it must be disentangled." The close association of peasants and the cycles of nature particularly interested Van Gogh, such as the sowing of seeds, harvest and sheaves of wheat in the fields.
|
|
In mathematics, vector bundles on algebraic curves may be studied as holomorphic vector bundles on compact Riemann surfaces. which is the classical approach, or as locally free sheaves on algebraic curves C in a more general, algebraic setting (which can for example admit singular points). Some foundational results on classification were known in the 1950s. The result of , that holomorphic vector bundles on the Riemann sphere are sums of line bundles, is now often called the Birkhoff–Grothendieck theorem, since it is implicit in much earlier work of on the Riemann–Hilbert problem.
|
|
The Grothendieck–Riemann–Roch theorem sets both theorems in a relative situation of a morphism between two manifolds (or more general schemes) and changes the theorem from a statement about a single bundle, to one applying to chain complexes of sheaves. The theorem has been very influential, not least for the development of the Atiyah–Singer index theorem. Conversely, complex analytic analogues of the Grothendieck–Riemann–Roch theorem can be proved using the index theorem for families. Alexander Grothendieck gave a first proof in a 1957 manuscript, later published.
|
|
Ship's power was by means of four corrugated furnaces with a grate area of that heated two single-ended boilers, in diameter and in length, with a combined heating surface of . They supplied steam at 185 lbf/in2 to her three- cylinder triple expansion engine, which developed 800 horsepower [166 NHP] and gave her a speed of . The two masts could carry sail to steady the ship under normal operating conditions. The ship had a diameter, high cable storage tank and two bow sheaves with a modified cargo winch for cable operations.
|
|
The global sections of sections of a vector bundle over a compact space form a projective module over the ring of smooth functions. All statements for coherent sheaves are true locally. For infinite-dimensional vector spaces, inequivalent topologies lead to inequivalent notions of tensor, and these various isomorphisms may or may not hold depending on what exactly is meant by a tensor (see topological tensor product). In some applications, it is the tensor product of Hilbert spaces that is intended, whose properties are the most similar to the finite-dimensional case.
|
|
However, although roller and ball bearings work well for radial and thrust loading, they are often prone to brinelling when very high impact loading, lateral loading, or vibration are experienced. Babbitt bearings or bronze bushings are often used instead of roller bearings in applications where such loads exist, such as in automotive crankshafts or pulley sheaves, to decrease the possibility of brinelling by distributing the force over a very large surface area. A common cause of brinelling is the use of improper installation procedures. Brinelling often occurs when pressing bearings into holes or onto shafts.
|
|
With Alexander Beilinson, Joseph Bernstein, and Ofer Gabber, Deligne made definitive contributions to the theory of perverse sheaves. This theory plays an important role in the recent proof of the fundamental lemma by Ngô Bảo Châu. It was also used by Deligne himself to greatly clarify the nature of the Riemann-Hilbert correspondence, which extends Hilbert's twenty-first problem to higher dimensions. Prior to Deligne's paper, Zoghman Mebkhout's 1980 thesis and the work of Masaki Kashiwara through D-modules theory (but published in the 80s) on the problem have appeared.
|
|
The Twirl King yo-yo champions are based on groups that companies like Duncan sent to schools to perform tricks. King Crimson guitarist Adrian Belew's name appears on a paper Edna Krabappel is grading during detention. Todd Flanders watches a television show that features Gomer Pyle from Gomer Pyle, U.S.M.C.. Bart sees the fictional movie Ernest Needs A Kidney, based on the character Ernest P. Worrell. Rod and Todd Flanders sing the song "Bringing in the Sheaves", because the writers liked having them sing "obscure religious songs". Mrs.
|
|
The CHL unveiled a 100th anniversary logo for the Memorial Cup on October 12, 2017. It included wheat sheaves symbolic of the Canadian Prairies where Regina is located, and the poppy to honour the fallen soldiers to whom the Memorial Cup is dedicated. The CHL and Canada Post produced a 100th anniversary postage stamp, released on May 18, 2018, which featured two Regina players from the inaugural 1919 Memorial Cup. The CHL also distributed a commemorative coin for the event, in cooperation with the Canadian Imperial Bank of Commerce.
|
|
Jimmy, while working at a strip club in Kings Cross, is approached by local mob boss Pando who says he has work for him. Pando gives Jimmy $10,000 to deliver to a woman in Bondi, and when she appears not to be home, he goes for a swim on the beach. Unfortunately the $10,000 is stolen by two street kids while he is swimming, leaving him heavily indebted to the furious Pando and his gang. The street kids, Pete (Evan Sheaves) and Helen (Mariel McClorey), go on a spending spree with their newfound wealth.
|
|
In mathematics, a sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space. The data can be restricted to smaller open sets, and the data assigned to an open set is equivalent to all collections of compatible data assigned to collections of smaller open sets covering the original one. For example, such data can consist of the rings of continuous or smooth real-valued functions defined on each open set. Sheaves are by design quite general and abstract objects, and their correct definition is rather technical.
|
|
In many mathematical branches, several structures defined on a topological space X (e.g., a differentiable manifold) can be naturally localised or restricted to open subsets U \subset X: typical examples include continuous real-valued or complex-valued functions, n times differentiable (real-valued or complex- valued) functions, bounded real-valued functions, vector fields, and sections of any vector bundle on the space. The ability to restrict data to smaller open subsets gives rise to the concept of presheaves. Roughly speaking, sheaves are then those presheaves, where local data can be glued to global data.
|
|
The gatehouse is immediately in front of the house at some little distance in advance; the gate has a red brick lodge on each side of it with ornamental gables and pinnacles. The gate between them is ornamented with the heraldic bearings of the family, the mullet or star of five points, and below them the garbs or wheat-sheaves. These bearings are also sculptured on the parapets, the wheatsheaves forming the pilasters and the mullets the balusters. The timber-work over the gate, with its high pointed roof and small pinnacle, is very picturesque.
|
|
Its screen is made of carved oak, formed in 1883 from one part of the Fleetwood family box pew that was originally situated in the chancel where the choir stalls now sit. In 1883, this pew had been described as "looking like a cross between a railway carriage and the centre piece of a gondola". The wood is carved with emblems of the family including a double- headed eagle, wheat sheaves and a griffin. The screen door comes from the box pew of another prominent local family—the Rigbys of Layton.
|
|
The beam is used to support the ship's anchor when raising it (weighing anchor) or lowering it (letting go), and for carrying the anchor on its stock-end when suspended outside the ship's side. The cathead is furnished with sheaves at the outer end, and the inner end (which is called the cat's-tail) fits down on the cat-beam. The shank painter is a short rope or chain by which the shank of an anchor is held fast to a ship's side when not in use. The process of securing the anchor is called catting and fishing it.
|
|
The arms of nutritionist John Boyd-Orr use two 'garbs' (wheat sheaves) as supporters; the arms of , missiles; the arms of the state of Rio Grande do Norte in Brazil, trees. Letters of the alphabet are used as supporters in the arms of Valencia, Spain. Human supporters can also be allegorical figures, or, more rarely, specifically named individuals. There is usually one supporter on each side of the shield, though there are some examples of single supporters placed behind the shield, such as the imperial eagle of the coat of arms of the Holy Roman Empire.
|
|
For example, Zaritsky, one of the leading ideologues of the universalist school, produced series of paintings focusing on Israeli kibbutzim – his series "Yehiam", and a similar series on Naan (a kibbutz in central Israel), 1950–1952. Both these series include abstractions of the Israeli landscape. Zvi Mairovich one of the founders of New Horizons produced a series of large oil paintings called Mizpe Ramon focousing on the Israeli deseret. Sculptor Dov Feigin produced "Wheat Sheaves" in 1956, and Dadaist Janco painted "Soldiers", "Air raid Alarms" and "Maabarot" (jerry-built communities housing new Jewish immigrants in the 1950s).
|
|
On the gold chief is a lion passant or leopard, a royal symbol of England. (English lions are usually gold with red tongues and claws; however, the default colours for a heraldic lion on a gold field are red with blue tongue and claws.) The three gold sheaves of wheat, or garbs, represent the province's agriculture; the heraldic sheaf of wheat has become a generalized symbol of the province. The helmet above the shield is gold and faces left, a symbol of Saskatchewan's co-sovereign status in Confederation. The mantling is in the national colours of Canada.
|
|
In mathematics, a constructible sheaf is a sheaf of abelian groups over some topological space X, such that X is the union of a finite number of locally closed subsets on each of which the sheaf is a locally constant sheaf. It is a generalization of constructible topology in classical algebraic geometry. In étale cohomology constructible sheaves are defined in a similar way . A sheaf of abelian groups on a Noetherian scheme is called constructible if the scheme has a finite cover by subschemes on which the sheaf is locally constant constructible (meaning represented by an étale cover).
|
|
In an early engineering text a machine is defined as follows: In some fields, mechanization includes the use of hand tools. In modern usage, such as in engineering or economics, mechanization implies machinery more complex than hand tools and would not include simple devices such as an ungeared horse or donkey mill. Devices that cause speed changes or changes to or from reciprocating to rotary motion, using means such as gears, pulleys or sheaves and belts, shafts, cams and cranks, usually are considered machines. After electrification, when most small machinery was no longer hand powered, mechanization was synonymous with motorized machines.
|
|
In the entire Ilhas de Goa, the Taleigão village was officially accorded the privilege by the then Portuguese Governor Afonso de Albuquerque to cut the first sheaves of corn and present it to the benevolent Creator on 21 August. Traditionally, the harvest feast is celebrated with enthralling music of brass bands, colourful ceremonial umbrella, cannon fire, procession and high mass at São Miguel Arcanjo church. This thanks giving ceremony commemorates the Festa da Espiga or Novidade– a time for rejoicing and worship for the cultivators, as a gratitude to the Almighty for the bountiful crop he has gracefully bestowed.
|
|
It is a lift bridge with a clear span of , which lifts vertically to provide a clearance for shipping using the canal. The bridge span is a tied arch and the towers are constructed in tubular steelwork to provide an open aspect to view the lifting counterweight and sheaves. In November 2015, the Lowry opened a new bar and restaurant, called Pier 8, after a 12-week closure on the original bar and restaurant. The new space cost £3m to develop and is part of an ongoing £5m investment programme to improve facilities and reduce the environmental footprint of the complex.
|
|
After 1797, McIntire worked in the style of Boston architect Charles Bulfinch, who had made fashionable here the neoclassical manner of Scottish architect Robert Adam. Unlike Bulfinch, however, whose designs were featured across the East Coast, McIntire built almost exclusively in New England. His wooden or brick houses were typically 3 stories tall, each with 4 rooms around a central hall. In 1799, he went into business with his brothers, Joseph and Angier McIntire, who erected the structures, while at the workshop he oversaw various ornamentations, including the swags, rosettes, garlands and sheaves of wheat which dominate the interior wooden surfaces.
|
|
In mathematics, and especially algebraic geometry, a Bridgeland stability condition, defined by Tom Bridgeland, is an algebro-geometric stability condition defined on elements of a triangulated category. The case of original interest and particular importance is when this derived category is the derived category of coherent sheaves on a Calabi–Yau manifold, and this situation has fundamental links to string theory and the study of D-branes. Such stability conditions were introduced in a rudimentary form by Michael Douglas called \Pi-stability and used to study BPS B-branes in string theory.Douglas, M.R., Fiol, B. and Römelsberger, C., 2005.
|
|
The Binder Twine Festival, or usually Binder Twine, was an annual festival held the first Saturday after Labour Day in Kleinburg, Ontario, Canada. It was one of the most popular festivals in southern Ontario, and marked the beginning of the harvest fair season in the Greater Toronto Area. In April 2020, the committee that organized the festival announced that as a result of increased costs and decreasing number of volunteers, it would discontinue the festival. In the late 19th century, farmers would come to the community to acquire binder twine with which they could bind sheaves of wheat.
|
|
From the 1890s onward, some machinery became available to partially mechanize the processes, such as one- and two-row mechanical pickers (picking the ear, leaving the stover) and corn binders, which are reaper-binders designed specifically for maize (for example, ). The latter produce sheaves that can be shocked. By hand or mechanical picker, the entire ear is harvested, which then requires a separate operation of a maize sheller to remove the kernels from the ear. Whole ears of maize were often stored in corn cribs, and these whole ears are a sufficient form for some livestock feeding use.
|
|
In algebraic geometry, a relative cycle is a type of algebraic cycle on a scheme. In particular, let X be a scheme of finite type over a Noetherian scheme S, so that X \rightarrow S. Then a relative cycle is a cycle on X which lies over the generic points of S, such that the cycle has a well- defined specialization to any fiber of the projection X \rightarrow S. The notion was introduced by Andrei Suslin and Vladimir Voevodsky in 2000; the authors were motivated to overcome some of the deficiencies of sheaves with transfers.
|
|
Cable ships with bow sheaves only required towing astern for some long runs of cable resulting in the unusual feature of two sets of running lights suitable for the stern becoming the effective bow. By the late 1970s the two Artemis class transports converted to cable ships were in need of modernization or replacement. Some shortcomings in design worked against modernization even though two other ships of the same age were slated for major modernization. The class had been designed with a relatively shallow draft of , least draft of the attack transports that had drafts from to .
|
|
Example: coronet of Prince Carl Seven similar coronets, but of a simpler design and with rays in the central position in the front and back and with eight smaller sheaves of gold between the eight rays were made in the eighteenth and nineteenth centuries for the other princes (i. e., Prince Karl (XIII), 1771; Prince Fredrik Adolf, 1771; Prince Oskar (II), 1844; Prince Wilhelm, 1902) and princesses (i. e., Princess Sofia Albertina, 1771; Princess Hedvig Elisabet Charlotta, 1778; Princess Eugenie, 1860), those of the princesses being of similar design, but much smaller. These coronets are set primarily with diamonds, emeralds and pearls.
|
|
The first part of the superstructure erected was the east tower, which began on 4 December 1958. The superstructure was assembled in prefabricated segments at Pacific Murphy's Richmond yard and barged upstream to the construction site, where they were raised into place by a capacity barge crane. The sheaves at the top of each tower were lifted in place during high tides in order to reach the necessary height. The 1960 superstructure replacing the 1919 bascule bridge includes the four truss spans west of the main lift span and one truss span east of the main lift.
|
|
Weyburn is located astride the Williston geological Basin which contains oil deposits, and several wells operate in the vicinity. There are roadside attractions featured here such as a large Lighthouse water tower, wheat sheaves and Prairie Lily. Weyburn is situated near the upper delta of the Souris River. The Souris River continues southeast through North Dakota eventually meeting the Assiniboine River in Manitoba. The Red Coat Trail is primarily asphalt concrete between SK Hwy 6 and SK Hwy 47 where traffic volume reaches about 1,450 vpd east of Weyburn, and over 3,500 vpd within the city on this class 2 highway.
|
|
Champion reaper, trade card from 1875 Horse-drawn reaper in Canada in 1941 After the first reapers were developed and patented, other slightly different reapers were distributed by several manufacturers throughout the world. The Champion (Combined) Reapers and Mowers, produced by the Champion Interest group (Champion Machine Company, later Warder, Bushnell & Glessner, absorbed in IHC 1902) in Springfield, Ohio in the second half of the 19th century, were highly successful in the 1880s in the United States. Springfield is still known as "The Champion City". Generally, reapers developed into the 1872 invented reaper-binder, which reaped the crop and bound it into sheaves.
|
|
Early 20th century postcards became a vehicle for tall tale telling in the US. Creators of these cards, such as the prolific Alfred Stanley Johnson, Jr., and William H. "Dad" Martin, usually employed trick photography, including forced perspective, while others painted their unlikely tableaus, or used a combination of painting and photography in early examples of photo retouching. The common theme was gigantism: fishing for leviathans, hunting for or riding oversized animals, and bringing in the impossibly huge sheaves. An homage to the genre can be found on the cover of the Eat a Peach (1972) album by The Allman Brothers Band.
|
|
St Catherine's chapel. A chapel dedicated to St Catherine of Alexandria is known to have existed on the site since 1157, when the Prior of Durham agreed to allow Romanus de Hilton to appoint his own chaplain for the chapel, subject to the prior's approval.Huggill, p.58 In return, de Hilton was to provide an annual contribution of 24 sheaves of oats for every draught ox he owned, to the nearby monastery at Monkwearmouth, and was required to attend the mother church of St Peters for the feasts of the Nativity, Easter, Whitsuntide and Saints Peter and Paul.
|
|
These sheaves are usually then 'shocked' into A-shaped conical stooks, resembling small tipis, to allow the grain to dry for several days before being picked up and threshed. Withington's original binder used wire to tie the bundles. There were problems with using wireSterling D. Evans, Bound in Twine: The history and ecology of the Henequen-Wheat Complex for Mexico and the American and Canadian Plains, 1880-1950 (College Station, Texas: Texas A&M; University Press, 2007), p. 4. and it was not long before William Deering invented a binder that successfully used twine and a knotter (invented in 1858 by John Appleby).
|
|
The work was painted during the Swadeshi movement. The movement began as a response to the Partition of Bengal (1905), when Lord Curzon split the largely Muslim eastern areas of Bengal from the largely Hindu western areas. In response, Indian nationalists participating in the swadeshi movement resisted the British by boycotting British goods and institutions, holding meetings and processions, forming committees, and applying diplomatic pressure. The painting's central figure holds multiple items associated with Indian culture and the economy of India in the early twentieth century, such as a book, sheaves of paddy, a piece of white cloth and a garland.
|
|
However, this advantage is totally negated by the relatively large energy consumption required to simply move the cable over and under the numerous guide rollers and around the many sheaves. Approximately 95% of the tractive effort in the San Francisco system is expended in simply moving the four cables at 9.5 miles per hour.Source: San Francisco Municipal Railway Electric cars with regenerative braking do offer the advantages, without the problem of moving a cable. In the case of steep grades, however, cable traction has the major advantage of not depending on adhesion between wheels and rails.
|
|
An invertible sheaf is a coherent sheaf S on a ringed space X, for which there is an inverse T with respect to tensor product of OX-modules, that is, we have :S \otimes T\ isomorphic to OX, which acts as identity element for the tensor product. The most significant cases are those coming from algebraic geometry and complex manifold theory. The invertible sheaves in those theories are in effect the line bundles appropriately formulated. In fact, the abstract definition in scheme theory of invertible sheaf can be replaced by the condition of being locally free of rank 1.
|
|
Then the groups Hi(X,E) for integers i are defined as the right derived functors of the functor E ↦ E(X). This makes it automatic that Hi(X,E) is zero for i < 0, and that H0(X,E) is the group E(X) of global sections. The long exact sequence above is also straightforward from this definition. The definition of derived functors uses that the category of sheaves of abelian groups on any topological space X has enough injectives; that is, for every sheaf E there is an injective sheaf I with an injection E → I.Iversen (1986), Theorem II.3.1.
|
|
The homological mirror symmetry conjecture of Maxim Kontsevich predicts an equality between the Lagrangian Floer homology of Lagrangians in a Calabi–Yau manifold X and the Ext groups of coherent sheaves on the mirror Calabi–Yau manifold. In this situation, one should not focus on the Floer homology groups but on the Floer chain groups. Similar to the pair- of-pants product, one can construct multi-compositions using pseudo- holomorphic n-gons. These compositions satisfy the A_\infty-relations making the category of all (unobstructed) Lagrangian submanifolds in a symplectic manifold into an A_\infty-category, called the Fukaya category.
|
|
Two linear maps S and T in induce the same map between P(V) and P(W) if and only if they differ by a scalar multiple, that is if for some . Thus if one identifies the scalar multiples of the identity map with the underlying field K, the set of K-linear morphisms from P(V) to P(W) is simply . The automorphisms can be described more concretely. (We deal only with automorphisms preserving the base field K). Using the notion of sheaves generated by global sections, it can be shown that any algebraic (not necessarily linear) automorphism must be linear, i.e.
|
|
The Zariski topology in the set-theoretic sense is then replaced by a Zariski topology in the sense of Grothendieck topology. Grothendieck introduced Grothendieck topologies having in mind more exotic but geometrically finer and more sensitive examples than the crude Zariski topology, namely the étale topology, and the two flat Grothendieck topologies: fppf and fpqc. Nowadays some other examples have become prominent, including the Nisnevich topology. Sheaves can be furthermore generalized to stacks in the sense of Grothendieck, usually with some additional representability conditions, leading to Artin stacks and, even finer, Deligne–Mumford stacks, both often called algebraic stacks.
|
|
The category of OX- modules over a fixed locally ringed space (X, OX) is an abelian category. An important subcategory of the category of OX-modules is the category of quasi- coherent sheaves on X. A sheaf of OX-modules is called quasi-coherent if it is, locally, isomorphic to the cokernel of a map between free OX-modules. A coherent sheaf F is a quasi-coherent sheaf which is, locally, of finite type and for every open subset U of X the kernel of any morphism from a free OU- modules of finite rank to FU is also of finite type.
|
|
Ruth is represented in the relief holding a pile of sheaves, she symbolizes the foreign woman that assimilated into the people of Israel and became the founder from which the dynasty from which the kings of Judah began. In her other hand Ruth is holding a candlestick with three candles, that symbolize the power of women in Judaism. The number of candles symbolizes the number of generations that pass between her till the birth of King David, the head of the royal family. That is the reason for the large crown on top of the candlestick.
|
|
The cable cars are pulled by a cable running below the street, held by a grip that extends from the car through a slit in the street surface, between the rails. Each cable is in diameter, running at a constant speed of , and driven by a electric motor located in the central power house (see below), via a set of self-adjusting sheaves. Each cable has six steel strands, with each strand containing 19 wires, wrapped around a sisal rope core (to allow easier gripping). The cables are coated with a tar-like material which serves as a sacrificial lubricant - much like a pencil eraser erodes away rather than the paper.
|
|
In mathematics, Witt vector cohomology was an early p-adic cohomology theory for algebraic varieties introduced by . Serre constructed it by defining a sheaf of truncated Witt rings Wn over a variety V and then taking the inverse limit of the sheaf cohomology groups Hi(V, Wn) of these sheaves. Serre observed that though it gives cohomology groups over a field of characteristic 0, it cannot be a Weil cohomology theory because the cohomology groups vanish when i > dim(V). For Abelian varieties showed that one could obtain a reasonable first cohomology group by taking the direct sum of the Witt vector cohomology and the Tate module of the Picard variety.
|
|
As a liturgical festival, Thanksgiving corresponds to the British and continental European harvest festival, with churches decorated with cornucopias, pumpkins, corn, wheat sheaves, and other harvest bounty. British and European harvest hymns are sung on the Sunday of Thanksgiving weekend. While the actual Thanksgiving holiday is on a Monday, Canadians may gather for their Thanksgiving feast on any day during the long weekend; however, Sunday is considered the most common. Foods traditionally served at Thanksgiving include roasted turkey, stuffing, mashed potatoes with gravy, sweet potatoes, cranberry sauce, sweet corn, various autumn vegetables (mainly various kinds of squashes but also Brussels sprouts), and pumpkin pie.
|
|
After prayers by the Parish priest, fov are presented to him at the parochial house. This act shows the Act of sharing of joy with the Parish Priest. 24 August: The male representatives of the nine Gauncar families and three members of the Comunidade managing committee carry the blessed sheaves, fov, and flower bouquet to Sé Cathedral, Old Goa, which was the capital of Goa until the 18th century and the Sé Cathedral was the main church. The group is received at the church entrance by the Parish Priest of Sé Cathedral with the pealing of the golden bell and playing of the traditional band in the background.
|
|
DESCRIPTION AND SYMBOLISM Obverse In the center of a bronze medallion, two mountains with a pass between them rest in front of a fertile valley and atop a wreath composed of two stylized sheaves of wheat. Behind the mountains a rising sun, and superimposed over the sun's rays are the words, in two lines, KOSOVO CAMPAIGN. The stylized wreath of grain reflects the agricultural character of the area and its economy and symbolizes basic human rights while high-lighting the desire of all for peace, safety and prosperity. The rocky terrain, fertile valley, and mountain pass refer to the Dinartic Alps and the campaign's theater of operations.
|
|
D-modules on different algebraic varieties are connected by pullback and pushforward functors comparable to the ones for coherent sheaves. For a map f: X → Y of smooth varieties, the definitions are this: :DX->Y := OX ⊗f−1(OY) f−1(DY) This is equipped with a left DX action in a way that emulates the chain rule, and with the natural right action of f−1(DY). The pullback is defined as :f∗(M) := DX->Y ⊗f−1(DY) f−1(M). Here M is a left DY-module, while its pullback is a left module over X. This functor is right exact, its left derived functor is denoted Lf∗.
|
|
The opposing band was composed of daring soldiers who were brave and fearless, and who took part in the combat with the others. After the conclusion of this game, those who wore the human skins went around throughout the whole town, entering houses and demanding that those in the houses give them some alms or gifts for the love of Xipe Totec. While in the houses, they sat down on sheaves of tzapote leaves and put on necklaces which were made of ears of corn and flowers. They had them put on garlands and give them pulque to drink, which was their wine.Marshall Saville, 1929, p. 167-168.
|
|
He was a professor at the Paris 13 University in the 1980s and is a professor at the Pierre and Marie Curie University since the 1990s. His field is algebraic analysis, especially Sato's microlocal analysis, together with concepts of the French analyst school (sheaves after Jean Leray and derived category of Alexander Grothendieck). He works closely with Kashiwara, whom he met in Japan already in 1971, who was then in Paris in 1976/77 and with whom he published several books. In 1990, he was an invited speaker at the International Congress of Mathematicians in Kyoto, speaking on sheaf theory for partial differential equations.
|
|
"Bridge Open Tomorrow; Repairs of Hawthorne Span Now About Completed". The Oregonian, May 19, 1931, p. 6. The deck was changed from wood to steel grating in 1945. The bridge was yellow-ochre in color from 1964 to 1998. This 1993 photo also shows the original, narrower sidewalks. In 1985 the lift span sheaves, the grooved wheels that guide the counterweight cables, were replaced. The bridge went through a $21 million renovation from 1998–99, which included replacing the steel grated deck and repainting. The original lead-based paint was completely removed and replaced with 3 layers of new paint that is estimated to last 30 years.
|
|
Palaeontologia sinica, series C, 7(5), 1-120.. This suggests that they spread towards Asia when the ice sheets started to melt. Other evidence suggests that Micromys minutus could have been introduced accidentally through agricultural activities during Neolithic times. Before the harvest mouse had been formally described, Gilbert White reported their nests in Selborne, Hampshire: > They never enter into houses; are carried into ricks and barns with the > sheaves; abound in harvest; and build their nests amidst the straws of the > corn above the ground, and sometimes in thistles. They breed as many as > eight at a litter, in a little round nest composed of the blades or grass or > wheat.
|
|
Thanks to the story Inamura no Hi: The Burning Rice Fields by Tsunezo Nakai (translated and published in English by Sara Cone Bryant) and Lafcadio Hearn's Gleanings in Buddha-Fields (1897), Hirogawa (then Hiro-Mura) is often referred to the home of "A Living God": Goryo Hamaguchi (1820-1885). In 1854, Goryo Hamaguchi saved many lives from the tsunami struck the Kii Peninsula following the big earthquake. He set fires to rice sheaves (inamura) to help guide those in great danger to safety on the hilltop. He also devoted himself to help fellow villagers find jobs (hiring them) and build confidence by constructing a huge seawall.
|
|
The spire height will follow Gaudí's intention, which according to the report will work with the existing foundation. The Evangelists' spires will be surmounted by sculptures of their traditional symbols: a winged bull (Saint Luke), a winged man (Saint Matthew), an eagle (Saint John), and a winged lion (Saint Mark). The central spire of Jesus Christ is to be surmounted by a giant cross; its total height () will be less than that of Montjuïc hill in Barcelona, as Gaudí believed that his creation should not surpass God's. The lower spires are surmounted by communion hosts with sheaves of wheat and chalices with bunches of grapes, representing the Eucharist.
|
|
A reaper cutting rye in Germany in 1949 Hand reaping is done by various means, including plucking the ears of grains directly by hand, cutting the grain stalks with a sickle, cutting them with a scythe, or a scythe fitted with a grain cradle. Reaping is usually distinguished from mowing, which uses similar implements, but is the traditional term for cutting grass for hay, rather than reaping cereals. The stiffer, dryer straw of the cereal plants and the greener grasses for hay usually demand different blades on the machines. The reaped grain stalks are gathered into sheaves (bunches), tied with string or with a twist of straw.
|
|
The corn-rick is later broken down and the sheaves threshed to separate the grain from the straw. Collecting spilt grain from the field after reaping is called gleaning, and is traditionally done either by hand, or by penning animals such as chickens or pigs onto the field. Hand reaping is now rarely done in industrialized countries, but is still the normal method where machines are unavailable or where access for them is limited (such as on narrow terraces). The more or less skeletal figure of a reaper with a scythe – known as the "Grim Reaper" – is a common personification of death in many Western traditions and cultures.
|
|
In North America, the C3's top speed is limited by the factory via a washer on the end of the boss shaft of the V-belt transmission. This washer limits how close the belt sheaves can come together, thus limiting the potential front diameter of the belt at full throttle. Removal of the washer is possible with simple tools and will increase the top speed to an RPM limited of 40 mph, although damage caused by modification is excluded from the Yamaha warranty. In Europe the Giggle Primary sheave variator (Part No 15PE76200000 ) is different from its US C3 version (Part No 3XYE7620010).
|
|
Translated from the French. Charles IX bestowed the Royal Order of Jehova or Jehova Order at his coronation in 1606—perhaps as Calvinist alternative or reaction to the Catholic devotion to the Name of Jesus implied in his brother's coronation order. Charles X Gustav's Order of the Name of Jesus took the form of a similar circular medallion bearing the letters IHS in diamonds surrounded by a border of diamonds in the center of a cross formed of four enameled Vasa sheaves and hanging from a pink ribbon worn around the neck, of which one example survives in the collections of the Royal Armory.Conforti, Michael and Guy Walton (eds.).
|
|
Any quality leaf shutter of the 1960s could achieve at least 1/500 s flash sync. Greater FP shutter X-sync speed would require further strengthening the curtains, by using exotic materials, allowing them to move even faster and widen the slits. Copal collaborated with Nippon Kogaku to improve the Compact Square shutter for the Nikon FM2 (Japan) of 1982 by using honeycomb pattern etched titanium foil, stronger and lighter than plain stainless steel, for its blade sheaves. This permitted cutting shutter-curtain travel time by nearly half to 3.6 ms (at 6.7 m/s) and allowed 1/200 s flash X-sync speed.
|
|
Jacques Goulet died November 26, 1688 and was interred in the church cemetery at L'Ange-Gardien two days later. In 1694, Goulet's estate was inventoried. It consisted of one plow, more than 700 sheaves of wheat, two horses, 10 head of cattle, three pigs, 10 chickens, a stone house, a barn, a stable, 33 arpents of cleared land and various other items. A plaque affixed to La Poterie's St. Pierre church reads: :Jacques Goulet né le 17 Avril 1615 a Normandel et Louise Goulet née a La Poterie le 26 Juillet 1628 epouse de René Le Tartre partis de La Poterie pour Le Canada.
|
|
It is equivalent to require that around each x, there exists an open affine subset such that , where f is a non-zero divisor in A. The sum of two effective Cartier divisors corresponds to multiplication of ideal sheaves. There is a good theory of families of effective Cartier divisors. Let be a morphism. A relative effective Cartier divisor for X over S is an effective Cartier divisor D on X which is flat over S. Because of the flatness assumption, for every S'\to S, there is a pullback of D to X \times_S S', and this pullback is an effective Cartier divisor.
|
|
Principle of rope-shovel operation. A power shovel (also stripping shovel or front shovel or electric mining shovel or electric rope shovel) is a bucket- equipped machine, usually electrically powered, used for digging and loading earth or fragmented rock and for mineral extraction.US Department of the Treasury, IRS: Appendix I - Glossary of Mining Terms Power shovels are a type of rope/cable excavator, where the digging arm is controlled and powered by winches and steel ropes, rather than hydraulics like in the more common hydraulic excavators. Basics parts of a power shovel include the track system, cabin, cables, rack, stick, boom foot-pin, saddle block, boom, boom point sheaves and bucket.
|
|
Caroline Nichols Churchill (December 23, 1833 – 1926) was a Canadian-born writer and newspaper editor in the United States, best known as the editor of the Queen Bee, a feminist publication prominent during the Colorado Suffrage movement. As a travel writer and editor, Churchill aimed to promote female independence in the post Civil War West, culminating ultimately in the right to vote in the state of Colorado. Her publications Over the Purple Hills, Over the Evergreen Hills, and Little Sheaves detailed the growth of California as well as her experiences in Texas, Missouri, Kansas, Indian Territory and later Colorado. In 1988, she was inducted into the Colorado Women's Hall of Fame.
|
|
Autumn pictures: harvesting, tillage and sowing. Winter images: the peasants sweep the snow off the roofs, whip up the loaded donkeys to the village, in the foreground there is a worker with a spade offering his services while the background depicts the masterpiece of the Azerbaijani architecture of the 15th century – the “Blue Mosque” in Tabriz. The spring landscape is woven in vivid colors: trees in bloom, a shepherd with a flock of sheep, a girl listening to the sounds of his reed-pipe, and an old man with a tobacco pipe, talking to a peasant. The summertime picture: harvesting, women and children bind sheaves and take them off the field.
|
|
This discussion of tensors so far assumes finite dimensionality of the spaces involved, where the spaces of tensors obtained by each of these constructions are naturally isomorphic.The double duality isomorphism, for instance, is used to identify V with the double dual space V∗∗, which consists of multilinear forms of degree one on V∗. It is typical in linear algebra to identify spaces that are naturally isomorphic, treating them as the same space. Constructions of spaces of tensors based on the tensor product and multilinear mappings can be generalized, essentially without modification, to vector bundles or coherent sheaves. where the case of finitely generated projective modules is treated.
|
|
In the gardens of the Petergof palace near Saint Petersburg there is a memorial bench with a small sculpture bust of the Grand Duchess. Her rooms there have been preserved just as they were at the time of her death. Six sheaves of wheat made of diamonds, which came to Hesse on one of the dresses in Alexandra's trousseau, were transformed into a tiara by Anna around 1900. This tiara is now the traditional wedding tiara of the Hessian princely family, and was last worn by Floria of Faber-Castell when in 2003, she married Donatus, Hereditary Prince of Hesse, Adini's husband's great-great grandson by his second marriage.
|
|
Typically, residential and industrial evaporative coolers use direct evaporation, and can be described as an enclosed metal or plastic box with vented sides. Air is moved by a centrifugal fan or blower (usually driven by an electric motor with pulleys known as "sheaves" in HVAC terminology, or a direct-driven axial fan), and a water pump is used to wet the evaporative cooling pads. The cooling units can be mounted on the roof (down draft, or downflow) or exterior walls or windows (side draft, or horizontal flow) of buildings. To cool, the fan draws ambient air through vents on the unit's sides and through the damp pads.
|
|
The national emblem of North Macedonia depicts two curved garlands of sheaves of wheat, tobacco leaves and opium poppy fruits, tied by a ribbon decorated with embroidery of traditional Macedonian folk motifs. In the center of the ovoid frame are depicted a mountain, a lake and a sunrise. The features of the national coat of arms contain a rising sun which symbolizes freedom, the Šar Mountains with its peak named Ljuboten or Mount Korab and the river Vardar,World Around Us — the Encyclopaedia for Children and Youth, XI edition, Školska knjiga, Zagreb, 1987, vol. II (A-M), page 242Со замената на сликата се менува и објаснувањето, Пирин преоѓа во Кораб with Lake Ohrid.
|
|
Braverman was born in Moscow.. He earned in 1993 a BA degree in mathematics from the University of Tel Aviv, where in 1998 he received a Ph.D. (Kazhdan-Laumon Representations of Finite Chevalley Groups, Character Sheaves and Some Generalization of the Lefschetz-Verdier Trace Formula) under supervision of Joseph Bernstein. From 1997 to 1999 he was a C.L.E. Moore instructor at Massachusetts Institute of Technology and in 2004 Benjamin Peirce Lecturer at Harvard University. He was an associate professor at Brown University from 2004 to 2009 and then a full professor from 2009 to 2015. He is a full professor at University of Toronto since 2015 and an associate faculty member at Perimeter Institute for Theoretical Physics.
|
|
A marine riser tensioner is a device used on an offshore drilling vessel which provides a near constant upward force on the drilling riser independent of the movement of the floating drill vessel. Aker Kvaerner MH Marine Riser Tensioner (MRT) The marine riser is connected to the wellhead on the sea bed and therefore the tensioner must manage the differential movements between the riser and the rig. If there were no tensioner and the rig moves downward, the riser would buckle; if the rig rises then high forces would be transmitted to the riser and it would stretch and be damaged. Tensioners have historically been composed of hydraulic actuated cylinders with wire sheaves.
|
|
Lawvere, Quantifiers and Sheaves ;Internal languages: This can be seen as a formalization and generalization of proof by diagram chasing. One defines a suitable internal language naming relevant constituents of a category, and then applies categorical semantics to turn assertions in a logic over the internal language into corresponding categorical statements. This has been most successful in the theory of toposes, where the internal language of a topos together with the semantics of intuitionistic higher-order logic in a topos enables one to reason about the objects and morphisms of a topos "as if they were sets and functions". This has been successful in dealing with toposes that have "sets" with properties incompatible with classical logic.
|
|
In the 1980s, Atiyah and Bott investigated gauge theory, using the Yang–Mills equations on a Riemann surface to obtain topological information about the moduli spaces of stable bundles on Riemann surfaces. In 1983 he spoke to the Canadian Mathematical Society in a talk he called "A topologist marvels at Physics". He is also well known in connection with the Borel–Bott–Weil theorem on representation theory of Lie groups via holomorphic sheaves and their cohomology groups; and for work on foliations. With Chern he worked on Nevanlinna theory, studied holomorphic vector bundles over complex analytic manifolds and introduced the Bott-Chern classes, useful in the theory of Arakelov geometry and also to algebraic number theory.
|
|
It is, however, in algebraic geometry and related fields where Grothendieck did his most important and influential work. From about 1955 he started to work on sheaf theory and homological algebra, producing the influential "Tôhoku paper" (Sur quelques points d'algèbre homologique, published in the Tohoku Mathematical Journal in 1957) where he introduced abelian categories and applied their theory to show that sheaf cohomology can be defined as certain derived functors in this context. Homological methods and sheaf theory had already been introduced in algebraic geometry by Jean-Pierre Serre and others, after sheaves had been defined by Jean Leray. Grothendieck took them to a higher level of abstraction and turned them into a key organising principle of his theory.
|
|
His abelian category concept had at least partially been anticipated by others. David Buchsbaum in his doctoral thesis written under Eilenberg had introduced a notion of "exact category" close to the abelian category concept (needing only direct sums to be identical); and had formulated the idea of "enough injectives". The Tôhoku paper contains an argument to prove that a Grothendieck category (a particular type of abelian category, the name coming later) has enough injectives; the author indicated that the proof was of a standard type. In showing by this means that categories of sheaves of abelian groups admitted injective resolutions, Grothendieck went beyond the theory available in Cartan–Eilenberg, to prove the existence of a cohomology theory in generality.
|
|
Local residents say Charley came from Cape Breton, but other sources say he moved from Port aux Basques. Both accounts may be correct, as many people living on the Port au Port Peninsula arrived via the south-west coast of the island. The tiny community promised good fishing and a ready supply of lumber, so Peter and Charley and their families stayed. Peter, had what would be considered a small family in an area where having 15 children was not unusual-probably not more than five or six- including at least two sons, one of whom was Isaac Jesso's father, Peter Thomas Jr. At least, he was called Peter in Sheaves Cove.
|
|
Unbinding the Sheaves, written in 1964 was described as a prairie memoir by the author, Ethel Kirk Grayson. The novel is viewed as a reflection of the authors memories in Saskatchewan during the pioneer days in the steam engine era. The story focuses on the excitement that the steam engine train and new settlers brought to the townsfolk of the city of Moose Jaw, and the way people lived during this changing time. The novel is described to have no constant story line as it jumps from one year to another and then back, it also changes the setting as the story takes the readers on trips to other provinces, such as Alberta and Manitoba.
|
|
The first needs of sheaf theory were for sheaves of abelian groups; so taking the category C as the category of abelian groups was only natural. In applications to geometry, for example complex manifolds and algebraic geometry, the idea of a sheaf of local rings is central. This, however, is not quite the same thing; one speaks instead of a locally ringed space, because it is not true, except in trite cases, that such a sheaf is a functor into a category of local rings. It is the stalks of the sheaf that are local rings, not the collections of sections (which are rings, but in general are not close to being local).
|
|
" "On the Nemíga the sheaves are laid out with heads; men thresh with flails in hedgerows; on the barn-floor they spread out life; they winnow the soul from the body." "On the blood-stained Nemíga the banks were sown with bane,—sown with the bones of the sons of Russia." "Prince Vséslav was a judge to his subjects, he appointed cities for the princes: but he himself at night raced like a wolf from Kiev to the Idol [or, (accepting the reading of the text unaltered)—to the Lord] of Tmutarakáń, raced, like a wolf across the path of the great Khors." "To him at Polotsk they rang the bells early for matins at Saint Sophia; and he at Kíev heard the sound.
|
|
Let be a smooth map between (smooth) manifolds M and N, and suppose is a smooth function on N. Then the pullback of f by φ is the smooth function φ∗f on M defined by . Similarly, if f is a smooth function on an open set U in N, then the same formula defines a smooth function on the open set φ−1(U) in M. (In the language of sheaves, pullback defines a morphism from the sheaf of smooth functions on N to the direct image by φ of the sheaf of smooth functions on M.) More generally, if is a smooth map from N to any other manifold A, then is a smooth map from M to A.
|
|
New Haven, CT: Yale University Press. p. 682. . The public performance had been postponed for so long because Ives had been alienated from the American classical establishment. Ever since his training with Horatio Parker at Yale, Ives had suffered their disapproval of the mischievous unorthodoxy with which he pushed the boundaries of European classical structures to create soundscapes that recalled the vernacular music- making of his New England upbringing. Like Ives's other compositions that honor the European and American inheritances, the Second Symphony makes no complete quotation of popular American tunes, but tunes such as "Camptown Races", "Bringing In the Sheaves", "Long, Long Ago", "Turkey in the Straw" and "America the Beautiful", are alluded to and reshaped into original themes.
|
|
The Sri Lanka Mitra Vibhushana (, Decoration of Sri Lankan Friendship) is a Sri Lankan honour, for Heads of State and Heads of Government with which Sri Lanka has friendly relations “in appreciation of their friendship towards and solidarity with the people of Sri Lanka”. The recipient of the honour is awarded a citation and a silver medal, which is to be worn around the neck, studded and adorned with nine kinds of Sri Lankan gems (Nawaratna) with the symbols of a lotus, the globe, sun, moon and sheaves of rice. The ribbon on medal 6.5 Centimeters wide. The honour takes precedence over the National Honours awarded to non Sri Lankans, and will be awarded by the President as and when he/she deems fit.
|
|
The coat of arms of Pennsylvania is an official emblem of the state, alongside the seal and state flag, and was adopted in 1778. The flag of the Commonwealth of Pennsylvania consists of a blue field on which the state coat of arms is embroidered. The Pennsylvania coat of arms features a shield crested by an American bald eagle, flanked by horses, and adorned with symbols of Pennsylvania's strengths—a ship carrying state commerce to all parts of the world; a clay-red plough, a symbol of Pennsylvania's rich natural resources; and three golden sheaves of wheat, representing fertile fields and Pennsylvania's wealth of human thought and action. An olive branch and cornstalk cross limbs beneath—symbols of peace and prosperity.
|
|
In Fall 2015 a group of law students calling itself Royall Must Fall and inspired by Rhodes Must Fall called for the retirement of the Harvard Law School shield, publishing an open letter to law school dean Martha Minow in the Harvard Law Record and posting signs and posters throughout the campus. Depicting three wheat sheaves, the shield incorporated the coat of arms of Isaac Royall Jr., a Harvard benefactor who had endowed the law school's first professorship. The shield had become a source of contention among Royall Must Fall activists because of the Royall family's history as slave-owners. The movement's inception was accompanied by several controversial incidents, most notably when black tape was mysteriously placed over the portraits of prominent African-American faculty members.
|
|
Arranged around it are the Loo, where threshing and other activities took place, living rooms (Döns) and sleeping compartments (alcoves or Alkoven) for the farm hands (Hofgesinde) together with the stalls for the horses (Peerboos), cattle (Boos) and small livestock. The bedchambers of well-to-do farmer and his family were wall bed in alcoves in the so-called Pesel, which could even be heated, whereas the farm labourers were only kept warm by the cattle and the stored straw and hay. The hay, which gave this type of house its name, was kept above the Boos, whilst grain was stored over the living area of the house. Before being threshed, sheaves from the harvest were stacked above the Loo on a sort of slatted floor (Spaltenboden).
|
|
Divisions of labour between men, women, and animals that are still in place in Indonesian rice cultivation, were carved into relief friezes on the ninth century Prambanan temples in Central Java: a water buffalo attached to a plough; women planting seedlings and pounding grain; and a man carrying sheaves of rice on each end of a pole across his shoulders (pikulan). In the sixteenth century, Europeans visiting the Indonesian islands saw rice as a new prestige food served to the aristocracy during ceremonies and feasts. Rice production in Indonesian history is linked to the development of iron tools and the domestication of Wild Asian Water Buffalo as water buffalo for cultivation of fields and manure for fertiliser. Rice production requires exposure to the sun.
|
|
For any scheme X, let Ét(X) be the category of all étale morphisms from a scheme to X. This is the analog of the category of open subsets of X (that is, the category whose objects are varieties and whose morphisms are open immersions). Its objects can be informally thought of as étale open subsets of X. The intersection of two objects corresponds to their fiber product over X. Ét(X) is a large category, meaning that its objects do not form a set. An étale presheaf on X is a contravariant functor from Ét(X) to the category of sets. A presheaf F is called an étale sheaf if it satisfies the analog of the usual gluing condition for sheaves on topological spaces.
|
|
The arms are derived from matters with which Ware is associated — the barge rudders reference the bargemen of Ware, with the red and white striping on the rudders being the livery colours of the City of London, associating the Ware bargemen's free entry rights to that City (q.v.); the crossed coach horns reference the town's long history as a coaching town; and the sheaves of barley reference the malting history of Ware. The motto of the town, "cave" (Latin for "beware") was suggested by the College of Heralds, with the intent of its being a pun on the town's name. With the River Lea flowing through the centre of Ware, transport by water was for many years a significant industry.
|
|
The philosophy of topos theory promoted by Alexander Grothendieck says that the category of sheaves on a space can serve as the space itself. Consequently, in non- commutative algebraic geometry one often defines Proj in the following fashion: Let R be a graded C-algebra, and let Mod-R denote the category of graded right R-modules. Let F denote the subcategory of Mod-R consisting of all modules of finite length. Proj R is defined to be the quotient of the abelian category Mod-R by F. Equivalently, it is a localization of Mod-R in which two modules become isomorphic if, after taking their direct sums with appropriately chosen objects of F, they are isomorphic in Mod-R.
|
|
Especially in wet climates, such as those of Britain, the degree of shedding of rainwater by the stack's outer surface is an important factor, and the stacking of loose hay was developed into a skilled-labor task that in its more advanced forms even involved thatching the top. In many stacking methods (with or without thatched tops), stems were oriented in sheaves, which were laid in oriented sequence. With the advent of large bales since the 1960s, today hay is often stored outdoors because the outer surface of the large bale performs the weather-shedding function. The large bales can also be stacked, which allows a given degree of exposed surface area to count for a larger volume of protected interior hay.
|
|
A horse pulling a threshing-board on a threshing floor Sheaves of grain would be opened up and the stalks spread across the threshing floor. Pairs of donkeys or oxen (or sometimes cattle, or horses) would then be walked round and round, often dragging a heavy threshing board behind them, to tear the ears of grain from the stalks, and loosen the grain itself from the husks. After this threshing process, the broken stalks and grain were collected and then thrown up into the air with a wooden winnowing fork or a winnowing fan. The chaff would be blown away by the wind; the short torn straw would fall some distance away; while the heavier grain would fall at the winnower's feet.
|
|
If an abelian category has enough injectives, we can form injective resolutions, i.e. for a given object X we can form a long exact sequence :0\to X \to Q^0 \to Q^1 \to Q^2 \to \cdots and one can then define the derived functors of a given functor F by applying F to this sequence and computing the homology of the resulting (not necessarily exact) sequence. This approach is used to define Ext, and Tor functors and also the various cohomology theories in group theory, algebraic topology and algebraic geometry. The categories being used are typically functor categories or categories of sheaves of OX modules over some ringed space (X, OX) or, more generally, any Grothendieck category.
|
|
In mathematics, the constant sheaf on a topological space X associated to a set A is a sheaf of sets on X whose stalks are all equal to A. It is denoted by or AX. The constant presheaf with value A is the presheaf that assigns to each non-empty open subset of X the value A, and all of whose restriction maps are the identity map . The constant sheaf associated to A is the sheafification of the constant presheaf associated to A. In certain cases, the set A may be replaced with an object A in some category C (e.g. when C is the category of abelian groups, or commutative rings). Constant sheaves of abelian groups appear in particular as coefficients in sheaf cohomology.
|
|
In 1931 the bank was granted a coat of arms from the College of Arms, symbolising the 1927 acquisition of the Western Australian Bank. The arms featured an emu and a black swan (which is symbolic of Western Australia) rampant supporting a shield surmounted by a kangaroo and the emblem of the rising sun. On the shield are shown a ship, two sheaves of wheat, a sheep, a cow, and a crossed pick and spade, representing the principal industries of Australia at the time: pastoral, agricultural, mining and shipping. The motto included was "Sic fortis Etruria crevit", translated as "Thus strong Etruria prospered", a line taken from Virgil's Second Georgic and an early motto of the Colony of New South Wales.
|
|
Then men swarm together and, with spears and shields, form a wall to hide him, and place him back on a man's shoulders and take him back to their camp, where he is again buried in leaves. A group of elders among the men, then return to the women's camp, and successively hand over, first clumps of grass, which the younger boys receive and hold at their chests, and then bundles of sticks, which they grasp after throwing the sheaves of grass away. The men then leave, gathered grass and place it back at their camp on the initiand, while the women pack up and shift camp several miles away. While doing so, they must sing certain songs and eat a restricted diet.
|
|
Traditionally all such cutting could be called reaping, although a distinction between reaping of grain grasses and mowing of hay grasses has long existed; it was only after a decade of attempts at combined grain reaper/hay mower machines (1830s to 1840s) that designers of mechanical implements began resigning them to separate classes.. Mechanical reapers substantially changed agriculture from their appearance in the 1830s until the 1860s through 1880s, when they evolved into related machines, often called by different names (self-raking reaper, harvester, reaper-binder, grain binder, binder), that collected and bound the sheaves of grain with wire or twine.. Today reapers and grain binders have been largely replaced by combines in commercial farming, but some smaller farms still use them.
|
|
One such was given in 2009 by Voevodsky, another in 2010 by van den Berg and Garner. A general solution, building on Voevodsky's construction, was eventually given by Lumsdaine and Warren in 2014. At the PSSL86 in 200786th edition of the Peripatetic Seminar on Sheaves and Logic, Henri Poincaré University, September 8-9 2007 Awodey gave a talk titled "Homotopy type theory" (this was the first public usage of that term, which was coined by AwodeyPreliminary list of PSSL86 participants). Awodey and Warren summarized their results in the paper "Homotopy theoretic models of identity types", which was posted on the ArXiv preprint server in 2007 and published in 2009; a more detailed version appeared in Warren's thesis "Homotopy theoretic aspects of constructive type theory" in 2008.
|
|
He shifted attention from the study of individual varieties to the relative point of view (pairs of varieties related by a morphism), allowing a broad generalization of many classical theorems. The first major application was the relative version of Serre's theorem showing that the cohomology of a coherent sheaf on a complete variety is finite-dimensional; Grothendieck's theorem shows that the higher direct images of coherent sheaves under a proper map are coherent; this reduces to Serre's theorem over a one-point space. In 1956, he applied the same thinking to the Riemann–Roch theorem, which had already recently been generalized to any dimension by Hirzebruch. The Grothendieck–Riemann–Roch theorem was announced by Grothendieck at the initial Mathematische Arbeitstagung in Bonn, in 1957.
|
|
The first Stiefel–Whitney class classifies smooth real line bundles; in particular, the collection of (equivalence classes of) real line bundles are in correspondence with elements of the first cohomology with Z/2Z coefficients; this correspondence is in fact an isomorphism of abelian groups (the group operations being tensor product of line bundles and the usual addition on cohomology). Analogously, the first Chern class classifies smooth complex line bundles on a space, and the group of line bundles is isomorphic to the second cohomology class with integer coefficients. However, bundles can have equivalent smooth structures (and thus the same first Chern class) but different holomorphic structures. The Chern class statements are easily proven using the exponential sequence of sheaves on the manifold.
|
|
A colonnade of heavy load bearing oak timber pillars and a visible upper oak-construction inside Karlsladen defines the architecture of the single inner room. As part of the restoration the elongated lofty building was cleared of the remnants of prior use, including the use of part of the barn as a pig stable for some years, and the division of part of it into a number of floors for storage of grain and sheaves. The result is that the original heavy timber construction all the way up to the thatched roof is visible today. During the restoration it was necessary to replace the first meter of the lower part of many of the load bearing oak pillars due to rot and wear.
|
|
Divisions of labour between men, women, and animals that are still in place in Indonesian rice cultivation, were carved into relief friezes on the ninth century Prambanan temples in Central Java: a water buffalo attached to a plough; women planting seedlings and pounding grain; and a man carrying sheaves of rice on each end of a pole across his shoulders (pikulan). In the sixteenth century, Europeans visiting the Indonesian islands saw rice as a new prestige food served to the aristocracy during ceremonies and feasts. Rice production in Indonesian history is linked to the development of iron tools and the domestication of wild Asian water buffalo as water buffalo for cultivation of fields and manure for fertiliser. Rice production requires exposure to the sun.
|
|
He received in 1966 from Harvard University his bachelor's degree and in 1971 from Columbia University his PhD under the supervision of Lipman Bers with thesis Sheaves of Holomorphic Functions with Boundary Conditions and Sheaf Cohomology in Banach Algebras. At the University of Wisconsin, Madison, Nagel was from 1970 to 1972 an instructor, from 1972 to 1974 an assistant professor, from 1974 to 1977 an associate professor, and from 1977 to 2012 a full professor, retiring in December 2012 as professor emeritus. He was chair of the mathematics department in 1991–1993 and in 2011–2012, and Associate Dean for Natural Sciences in the College of Letters and Science in 1993–1998. He was a Guggenheim Fellow for the academic year 1987–1988.
|
|
The celebration was officially addressed to the youth, who represented the "New Era" created by the King. Following the creation of the paramilitary youth organization Straja Țării, the Restoration Day parades changed their organization, being held on ANEF stadium and included sports exercises and choreography, but the purpose was kept: glorifying the King and his deeds. At the end, the youth used their bodies to write "Carol 2" and then they formed the monogram of the king. Carol II received from the members of Straja Țării from across the country gifts of sheaves of wheat, garlands of flowers and soil, while cyclists brought a pitcher of water from Vadul Crișului, where he landed in 1930 when coming back to Romania.
|
|
Princess Elizabeth was attended by eight bridesmaids: The Princess Margaret (her younger sister), Princess Alexandra of Kent (her first cousin), Lady Caroline Montagu-Douglas-Scott (daughter of the Duke of Buccleuch), Lady Mary Cambridge (her second cousin), Lady Elizabeth Lambart (daughter of the Earl of Cavan), Lady Pamela Mountbatten (Philip's first cousin), Margaret Elphinstone (her first cousin), and Diana Bowes-Lyon (her first cousin). Her cousins Prince William of Gloucester and Prince Michael of Kent served as page boys. The bridesmaids wore wreaths "in their hair of miniature white sheaves, Lilies and London Pride, modelled in white satin and silver lame", while the pages wore Royal Stewart tartan kilts. The best man was the Marquess of Milford Haven, the groom's maternal first cousin.
|
|
In coherent sheaf theory, pushing to the limit of what could be done with Serre duality without the assumption of a non-singular scheme, the need to take a whole complex of sheaves in place of a single dualizing sheaf became apparent. In fact the Cohen–Macaulay ring condition, a weakening of non-singularity, corresponds to the existence of a single dualizing sheaf; and this is far from the general case. From the top-down intellectual position, always assumed by Grothendieck, this signified a need to reformulate. With it came the idea that the 'real' tensor product and Hom functors would be those existing on the derived level; with respect to those, Tor and Ext become more like computational devices.
|
|
We can think of a locally ringed space X as a parametrised family of local rings, depending on x in X. A more careful discussion dispels any mystery here. One can speak freely of a sheaf of abelian groups, or rings, because those are algebraic structures (defined, if one insists, by an explicit signature). Any category C having finite products supports the idea of a group object, which some prefer just to call a group in C. In the case of this kind of purely algebraic structure, we can talk either of a sheaf having values in the category of abelian groups, or an abelian group in the category of sheaves of sets; it really doesn't matter. In the local ring case, it does matter.
|
|
The Presidential $1 Coin Act required that the cent, beginning in 2010, "shall bear an image emblematic of President Lincoln's preservation of the United States of America as a single and united country". On , 2009, the Commission of Fine Arts (CFA) met and recommended a design that showed 13 wheat sheaves bound together with a ring symbolizing American unity as one nation. Subsequently, this design was withdrawn because it was similar to coins issued in Germany in the 1920s. The Citizens Coinage Advisory Committee (CCAC) also met and recommended a design showing a Union shield with superimposed in a scroll; E pluribus unum was also depicted in the upper portion of the shield. In June 2009 the CFA met again and this time selected a design featuring a modern rendition of the American flag.
|
|
The pressure in the bell will be adjusted to suit the depth at which the divers will lock out while the bell is being lowered, so that the pressure change can be slow without unduly delaying operations. The bell is deployed over the side of the vessel or platform using a gantry or A-frame or through a moon pool. Deployment usually starts by lowering the clump weight, which is a large ballast weight suspended from a cable which runs down one side from the gantry, through a set of sheaves on the weight, and up the other side back to the gantry, where it is fastened. The weight hangs freely between the two parts of the cable, and due to its weight, hangs horizontally and keeps the cable under tension.
|
|
At 8:30 am, President of the feast marches under the cover of a colourful ceremonial umbrella to the São Miguel Arcanjo church to the beats of brass band. From the church the parishioners proceed in a procession to the field at Tolliant earmarked by the Comunidade for cutting of the sheaves. In 90's the procession used to be led by dhol caxia (drum)and a trumpet, followed by Adao representing the village tribes dressed in colourful costumes and dancing with bamboo sticks and swords. They are followed by flag of holy trinity (previously it was Portuguese flag)and the parishioners, the Confrades carrying the statue of the patron São Miguel Arcanjo on Charol, the feast President, the Parish priest, and the brass band playing religious tunes.
|
|
Superstring theory predicts that spacetime is 10-dimensional, consisting of a Lorentzian manifold of dimension 4 (usually assumed to be Minkowski space or De sitter or anti-De Sitter space) along with a Calabi-Yau manifold X of dimension 6 (which therefore has complex dimension 3). In this string theory open strings must satisfy Dirichlet boundary conditions on their endpoints. These conditions require that the end points of the string lie on so-called D-branes (D for Dirichlet), and there is much mathematical interest in describing these branes. Open strings with endpoints fixed on D-branes In the B-model of topological string theory, homological mirror symmetry suggests D-branes should be viewed as elements of the derived category of coherent sheaves on the Calabi-Yau 3-fold X.Aspinwall, P.S., 2005.
|
|
The second paper of Kazhdan and Lusztig established a geometric setting for definition of Kazhdan–Lusztig polynomials, namely, the geometry of singularities of Schubert varieties in the flag variety. Much of the later work of Lusztig explored analogues of Kazhdan–Lusztig polynomials in the context of other natural singular algebraic varieties arising in representation theory, in particular, closures of nilpotent orbits and quiver varieties. It turned out that the representation theory of quantum groups, modular Lie algebras and affine Hecke algebras are all tightly controlled by appropriate analogues of Kazhdan–Lusztig polynomials. They admit an elementary description, but the deeper properties of these polynomials necessary for representation theory follow from sophisticated techniques of modern algebraic geometry and homological algebra, such as the use of intersection cohomology, perverse sheaves and Beilinson–Bernstein–Deligne decomposition.
|
|
Roman sarcophagus with Cupids holding seasonal garlands; episodes from the story of Theseus & Ariadne above the swags; on the lid, Cupids race chariots. Ca. 120–150 AD. Metropolitan Museum, New York Representations of the seasons on Roman sarcophagi typically showed the gifts that nature had to offer people during each season, and thus also evoked associations with the cycle of nature and of life. The sarcophagus showing Cupids holding seasonal garlands in New York's Metropolitan Museum furnishes a good example. The Cupids here hold garlands composed of various flowers, fruits, and agricultural products, each associated with a different one of the four seasons: on the very left, flowers, representing spring, then sheaves of grain representing summer, then fruit (especially grapes and grape leaves) representing autumn, and then lastly olives representing winter.
|
|
Let X be a noetherian scheme. Let C be a subset of the objects of the category of coherent OX- modules which contains the zero sheaf and which has the property that, for any short exact sequence 0 \to A' \to A \to A \to 0 of coherent sheaves, if two of A, A′, and A′ are in C, then so is the third. Let X′ be a closed subspace of the underlying topological space of X. Suppose that for every irreducible closed subset Y of X′, there exists a coherent sheaf G in C whose fiber at the generic point y of Y is a one-dimensional vector space over the residue field k(y). Then every coherent OX-module whose support is contained in X′ is contained in C.EGA III, Théorème 3.1.
|
|
In mathematics, coherent duality is any of a number of generalisations of Serre duality, applying to coherent sheaves, in algebraic geometry and complex manifold theory, as well as some aspects of commutative algebra that are part of the 'local' theory. The historical roots of the theory lie in the idea of the adjoint linear system of a linear system of divisors in classical algebraic geometry. This was re-expressed, with the advent of sheaf theory, in a way that made an analogy with Poincaré duality more apparent. Then according to a general principle, Grothendieck's relative point of view, the theory of Jean-Pierre Serre was extended to a proper morphism; Serre duality was recovered as the case of the morphism of a non-singular projective variety (or complete variety) to a point.
|
|
The coronet of the heir apparent The Crown Prince's Coronet was made for Charles X Gustav to wear at the coronation of Christina as her designated heir. It was hurriedly made in two weeks time from parts of an earlier queen's crown. It has the form of a radial crown with eight triangular rays or spikes and has survived intact except for the addition by Gustav III for his coronation in 1772 of two black enameled sheaves of grain, the heraldic emblem of the Vasa dynasty, one between the front two rays and the other between the back two rays, replacing the smaller ornaments still found between the other rays. Originally worn over an ermine lined hat, the heir apparent's coronet is now worn with a cap of light blue satin covered with gold embroidery.
|
|
The Hanbidge name was popular in the Stratford-on-Slaney district as evidenced by the many headstones of this name now in the St. John the Baptist Church graveyard. William Hanbidge has written a memoir which describes in interesting detail, some of the stages of calico and linen production from flax grown in this district in the 1800s. Hanbidge said that flax was sown in Springtime and "in due time was pulled up and tied in sheaves and carted off to the 'blind arch' of Kelsha Bride" (Kelsha and Gibstown were bridges over the Slaney and the 'blind arch' was an arch over a very deep pool separated from the river). The flax was put under water ('bogged' they called it) to help to separate the fibre from the stalk.
|
|
The Durbanville municipal council assumed a coat of arms, designed by Ivan Mitford-Barberton and H. Ellis Tomlinson, in April 1948,Western Cape Archives : Durbanville Municipal Minutes (12 April 1948). and registered them at the Bureau of Heraldry in February 1981.The National Archives and Records Service of South Africa (NARSSA) The arms, derived from those of Sir Benjamin d'Urban, were : Or, on a chevron between in chief two six-pointed stars Sable and in base a bunch of grapes proper, three garbs Or. In layman's term, the shield is gold and depicts, from top to bottom, two black six-pointed stars, a blue chevron bearing three golden sheaves of wheat, and a bunch of grapes. The crest was a red sphinx charged with three golden rings, and the motto Sit nomine digna.
|
|
The university library Facilities available inside the building include a concert hall, a theater, a museum, administrative services, a library, a swimming pool, a police station, a post office, a laundry, a hairdresser's salon, several canteens, bank offices and ATMs, shops, cafeterias, a bomb shelter, etc. Along with the university administration, the Museum of Earth Sciences and four of the main faculties – Faculty of Mechanics and Mathematics, the Faculty of Geology, the Faculty of Geography, and the Faculty of Fine and Performing Arts – now reside in the Main building. The star on the top of the tower is large enough to include a small room and a viewing platform; it weighs 12 tons. The building's facades are ornamented with giant clocks, barometers, thermometers, statues, carved wheat sheaves, and Soviet crests.
|
|
Flat belt on a belt pulley Belt and pulley system Cone pulley driven from above by a line shaft A belt and pulley system is characterized by two or more pulleys in common to a belt. This allows for mechanical power, torque, and speed to be transmitted across axles. If the pulleys are of differing diameters, a mechanical advantage is realized. A belt drive is analogous to that of a chain drive; however, a belt sheave may be smooth (devoid of discrete interlocking members as would be found on a chain sprocket, spur gear, or timing belt) so that the mechanical advantage is approximately given by the ratio of the pitch diameter of the sheaves only, not fixed exactly by the ratio of teeth as with gears and sprockets.
|
|
Triptolemus received wheat sheaves from Demeter and blessings from Persephone, 5th century BC relief, National Archaeological Museum of Athens Orphicism and Pythagoreanism, two common ancient Greek religions, suggested a different way of life, based on a concept of purity and thus purification ( katharsis) — a form of asceticism in the original sense: askēsis initially signifies a ritual, then a specific way of life. Vegetarianism was a central element of Orphicism and of several variants of Pythagoreanism. Empedocles (5th century BC) justified vegetarianism by a belief in the transmigration of souls: who could guarantee that an animal about to be slaughtered did not house the soul of a human being? However, it can be observed that Empedocles also included plants in this transmigration, thus the same logic should have applied to eating them.Dodds, pp.154–5.
|
|
This can be adjusted by tying off the umbilicals inside the bell to limit deployment length, which must often be done in any case, to prevent the divers from approaching known hazards in the water. Depending on circumstances, there may also be a surface stand-by diver, with attendant in case there is an emergency where the surface diver could assist. The team be under the direct control of the diving supervisor and will also include a winch operator, and may include a dedicated surface gas panel operator. Deployment usually starts by lowering the clump weight, which is a large ballast weight suspended from a cable which runs down one side from the gantry, through a set of sheaves on the weight, and up the other side back to the gantry, where it is fastened.
|
|
The cable ship (CS) Great Northern,Built by Denton Gray and Company, West Hartlepool, 1870, purchased by Hooper's in 1871, with four cable tanks, two bow sheaves and cable laying machinery for laying the 1871 Vladivostock - Nagasaki - Shanghai - Hong Kong cable. CS Hooper pictured here as CS Silvertownin 1901 after sale and renaming in 1881. The company had considered a trans Atlantic cable from England the United States via Bermuda and ordered a ship capable of carrying the entire cable proposed for the England-Bermuda segment. The ship was to be named Great Western but the cable plan was abandoned, with cable and ship completed, in favor of a cable on the east coast of South America with a new company, the Western and Brazilian Telegraph Company, and the ship renamed .
|
|
In the one usually titled "Joseph Gathering Corn" we see Joseph standing at the left giving orders and one of the men involved in the task standing inside an opening in the pyramid collecting the sheaves. Most of the images in the Genesis mosaics at San Marco derive from the so-called Cotton Genesis, one of the earliest illustrated Christian manuscripts.British Library, codex Otho B. VI. The 5th century manuscript is so named for its first known owner Robert Cotton, and was severely damaged by fire in 1731; cf. Weitzmann and Kessler 1986, 3-7. As for the relationship between manuscript and mosaic, Weitzmann 1984, 142, is quite emphatic when he says, "Cotton Genesis was the direct model of San Marco"; cf. Weitzmann and Kessler 1986, 18-20.
|
|
Diagram of the operation of a tiller using a ship's wheel and tiller ropes. The steering gear of earlier ships' wheels sometimes consisted of a double wheel where each wheel was connected to the other with a wooden spindle that ran through a barrel or drum. The spindle was held up by two pedestals that rested on a wooden platform, often no more than a grate. A tiller rope or tiller chain (sometimes called a steering rope or steering chain) ran around the barrel in five or six loops and then down through two tiller rope/ chain slots at the top of the platform before connecting to two sheaves just below deck (one on either side of the ship's wheel) and thence out to a pair of pulleys before coming back together at the tiller and connecting to the ship's rudder.
|
|
He took the initiative in appointing managing committees of Gauncars to administer and monitor the distribution of agricultural land (aforamento & shares) and collection of revenue from the agricultural produce, which was used for the welfare of village community and paying dividends (zonos). As a result of these reforms and transparency in the system, the Comunidade of Taleigão prospered economically from the rice cultivation on vast tracts of land and earned the distinction of being the granary of Ilhas de Goa. As a tradition, on 24 August the President of the feast and the representatives of gauncars present the first sheaves of corn to the Governor who is the custodian of Comunidade land. As a part of the Hindu culture, the then Gauncars who were Hindus offered the first fruits of nature to god and sought blessings from the village deity.
|
|
These are differential equations involving connections on vector bundles or principal bundles, or involving sections of vector bundles, and so there are strong links between gauge theory and geometric analysis. These equations are often physically meaningful, corresponding to important concepts in quantum field theory or string theory, but also have important mathematical significance. For example, the Yang–Mills equations are a system of partial differential equations for a connection on a principal bundle, and in physics solutions to these equations correspond to vacuum solutions to the equations of motion for a classical field theory, particles known as instantons. Gauge theory has found uses in constructing new invariants of smooth manifolds, the construction of exotic geometric structures such as hyperkähler manifolds, as well as giving alternative descriptions of important structures in algebraic geometry such as moduli spaces of vector bundles and coherent sheaves.
|
|
On the opposite side of the building, between the first and second > stories, a wide bay window projects outward for some distance, its roof > forming a balcony of considerable dimensions, enclosed by rails of dark > brownstone. The features of this window are two panes of bent glass, eight > by ten feet in size, which are said to be the largest of their kind in the > country. Above the arch of the doorway four pilasters, faced with terra > cotta flower and basket work, and capped with elaborately carved brownstone > copings, extend to the height of the building, terminating at either corner > of the gable. At every suitable space on the front of the club house there > is an abundance of delicated carvings and moulding, while each of the > windows is supported on sheaves of slender columns, crowned with richly > foliated capitals.
|
|
The Yawuru are a coastal people whose basic diet consisted of seafood - fish, turtles, stingrays, dugong, crabs and mangrove shells - but also sand monitors, flying foxes, and bush food foraged in the semi-arid pindan scrub country, divided into edible bush fruits for which they have over 90 terms, covering such things as wattle seed and native tubers, to wallabies, goanna and varieties of birds from native hens and crested pigeons to the bush turkey. Maritime fruits were prepared, after fermentation, by heating them in a baler shell over hot coals. Maritime hunting technology consisted of fishing spears, fishing boomerangs, fish-stunning poisons (bunjuda), nets made of massed grass sheaves (marukutju:n) shoved through waters to corner fish., and by building rock ponds fenced with stakes fashioned from mangrove wood, whose base was woven with spinifex to trap fish in the tidal outflows.
|
|
A replica 16th-century English bronze culverin (near) and an iron portpiece The castle was already obsolete by the time it had been completed, as European military design had moved beyond curved bastions, embracing the angular designs seen in the later star forts. Nonetheless, it remained operational as an artillery fort for the rest of the century, with an initial garrison in 1540 of 24 men under the command of Chute, rising to 28 men and the captain after 1542. Although it had been fitted with gunloops for handguns from the very start, the castle initially relied heavily on archers for its own protection against attack from the land. It had stocks of 140 longbows and 560 sheaves of arrows in 1568, for example, probably for use by the local militia in the event of a war.
|
|
Frank Montgomery School was founded in 1935. The school mainly took in children from the senior classes of existing schools in the nearby farming villages of Sturry and Westbere, and the coal mining village of Hersden.'Book charts the history of local schools', in The Kentish Gazette (UK newspaper), 16 September 2010 It was originally named Sturry Central School. Mr G.E. Draper-Hunt was the first headmaster, remaining in post until his retirement in 1958.Gerry Warren, 'Pupils Leave a Bit of Past Behind at New School' in The Kentish Gazette (UK newspaper), 21 June 2012 Until its replacement by Spires Academy school in 2007, the school's uniform of bottle green, and shield showing the white horse of the county of Kent, a coal mine tower and wheat sheaves, with the motto Strive for the Right, remained the same.
|
|
In fact the whole wheat field has been brought far closer to the house than would really have been the case; it is "invented, or transposed from further away. If read literally, the sheaves of corn would be thrusting through the porch of Auberies itself".Egerton, 84 The painting has been described as unusual, as an outdoor conversation piece showing the subjects against an agricultural background rather than in the gardens of their own houses, but this is also seen in other early Gainsboroughs. A group portrait of his from about 1754 shows the parents and two daughters of The Gravenor Family (illustrated below) with a square version of a similar composition with two oaks on the left behind the standing father and seated mother, and the daughters to their right, close up to the edge of standing corn.
|
|
The approximating functors are required to be "k-excisive" – such functors are called polynomial functors by analogy with Taylor polynomials – which is a simplifying condition, and roughly means that they are determined by their behavior around k points at a time, or more formally are sheaves on the configuration space of k points in the given space. The difference between the kth and (k-1)st functors is a "homogeneous functor of degree k" (by analogy with homogeneous polynomials), which can be classified. For the functors T_kF to be approximations to the original functor F, the resulting approximation maps F \to T_kF must be n-connected for some number n, meaning that the approximating functor approximates the original functor "in dimension up to n"; this may not occur. Further, if one wishes to reconstruct the original functor, the resulting approximations must be n-connected for n increasing to infinity.
|
|
In an address to the 1994 International Congress of Mathematicians in Zürich, speculated that mirror symmetry for a pair of Calabi–Yau manifolds X and Y could be explained as an equivalence of a triangulated category constructed from the algebraic geometry of X (the derived category of coherent sheaves on X) and another triangulated category constructed from the symplectic geometry of Y (the derived Fukaya category). Edward Witten originally described the topological twisting of the N=(2,2) supersymmetric field theory into what he called the A and B model topological string theories. These models concern maps from Riemann surfaces into a fixed target—usually a Calabi–Yau manifold. Most of the mathematical predictions of mirror symmetry are embedded in the physical equivalence of the A-model on Y with the B-model on its mirror X. When the Riemann surfaces have empty boundary, they represent the worldsheets of closed strings.
|
|
The importance of rice in Indonesian culture is demonstrated through the reverence of Dewi Sri, the rice goddess of ancient Java and Bali. Evidence of wild rice on the island of Sulawesi dates from 3000 BC. Historic written evidence for the earliest cultivation, however, comes from eighth century stone inscriptions from the central island of Java, which show kings levied taxes in rice. The images of rice cultivation, rice barn, and mouse pest investing a rice field is evident in Karmawibhangga bas-reliefs of Borobudur. Divisions of labour between men, women, and animals that are still in place in Indonesian rice cultivation, were carved into relief friezes on the ninth century Prambanan temples in Central Java: a water buffalo attached to a plough; women planting seedlings and pounding grain; and a man carrying sheaves of rice on each end of a pole across his shoulders (pikulan).
|
|
If a Néron model exists then it is unique up to unique isomorphism. In terms of sheaves, any scheme A over Spec(K) represents a sheaf on the category of schemes smooth over Spec(K) with the smooth Grothendieck topology, and this has a pushforward by the injection map from Spec(K) to Spec(R), which is a sheaf over Spec(R). If this pushforward is representable by a scheme, then this scheme is the Néron model of A. In general the scheme AK need not have any Néron model. For abelian varieties AK Néron models exist and are unique (up to unique isomorphism) and are commutative quasi-projective group schemes over R. The fiber of a Néron model over a closed point of Spec(R) is a smooth commutative algebraic group, but need not be an abelian variety: for example, it may be disconnected or a torus.
|
|
Zephyranthes candida, with common names that include autumn zephyrlily, white windflower, white rain lily, and Peruvian swamp lily, is a species of rain lily native to South America including Argentina, Uruguay, Paraguay, and Brazil. The species is widely cultivated as an ornamental and reportedly naturalized in many places (South Africa, the Indian subcontinent, Zimbabwe, Seychelles, central and southern China, Korea, Nansei-shoto (Ryukyu Islands), Bhutan, Solomon Islands, Queensland, Nauru, Tonga, Society Islands, Mariana Islands, southeastern United States (from Texas to North Carolina), the Lesser Antilles, and Peru).Kew World Checklist of Selected Plant FamiliesBiota of North American Program Leaves are a deep glossy green and measure 3 mm wide. Flowers, which bud late in August (when propagated in the Northern Hemisphere) at first resemble a new leaf, but emerge from their papery sheaves to a stunning whiteness; they are erect in perianth white and sometimes pinkish abaxially. The leaf-like bract is 1.8 to 4 cm.
|
|
The Yanov Torah is a hand-written copy of the Torah assembled from the individual sheaves of Torah manuscripts, smuggled into the Janowska concentration camp during the Holocaust in World War II. The Janowska, also known as the Yanov death camp, located not far from the Lwów Ghetto, was a place of execution of tens of thousands of Polish Jews between September 1941 and November 1943. A Sefer Torah, the holiest book within Judaism venerated by Jews, was reassembled by prisoners from manuscripts unearthed at the Lwów's Jewish cemetery. Following World War II it was smuggled out of the then Soviet Union, and brought to Los Angeles. It has been donated to the rabbinical programs at Hebrew Union College,Torah's tale is kept alive, Duke Helfand, November 20, 2008[accessed on 5-3-2009] where it is taken on tour to various synagogues and assemblies, so that the story of its history can be told.
|
|
Later in 1998, a Scholar at the St. Peter's Pontifical Seminary, Bangalore studying under Anthony Raymond Ceresko and Gnana Robinson researched specifically on Job and Harishchandra focusing on the problem of suffering. Solomon's research brought out the many facets of suffering where his scholarship is profoundly visible as he sheaves through the views on suffering in the Old Testament as he quotes from the Pentateuch and the other books of the Old Testament with a comprehensive bibliography but the conclusions that he drew are an eye opener for those viewing suffering as a reason of our own follies. In the final analysis, Solomon looks into the possibilities of a more humane understanding of suffering overcoming Dogma and providing for repentance or rather an opportunity to set right the past and move forward. Solomon wrote, The solution of the problem of suffering in Christianity is that God also suffers along with the sufferer and helps him to endure it for His glory.
|
|
Incorporated into the Ottoman Empire in 1517 with all of Palestine, Beit Hanoun appeared in the 1596 tax registers as being in the Nahiya of Gaza, part of Gaza Sanjak. It had a population of 36 Muslim households and paid a fixed tax rate of 33,3% on wheat, barley, summer crops, fruit trees, occasional revenues, goats and/ or beehives; a total of 9,300 akçe.Hütteroth and Abdulfattah, 1977, p. 147 Pierre Jacotin named the village Deir Naroun on his map from 1799.Karmon, 1960, p. 173 In 1838 Edward Robinson passed by, and described how "all were busy with the wheat harvest; the reapers were in the fields; donkeys and camels were moving homewards with their high loads of sheaves; while on the threshing-floors near the village I counted not less than thirty gangs of cattle.."Robinson and Smith, 1841, vol 2, pp. 371 -372 He further noted it as a Muslim village, located in the Gaza district.Robinson and Smith, 1841, vol 3, Appendix 2, p.
|
|
A presheaf F on a topological space is called a sheaf if it satisfies the sheaf condition: whenever an open subset is covered by open subsets Ui, and we are given elements of F(Ui) for all i whose restrictions to Ui ∩ Uj agree for all i, j, then they are images of a unique element of F(U). By analogy, an étale presheaf is called a sheaf if it satisfies the same condition (with intersections of open sets replaced by pullbacks of étale morphisms, and where a set of étale maps to U is said to cover U if the topological space underlying U is the union of their images). More generally, one can define a sheaf for any Grothendieck topology on a category in a similar way. The category of sheaves of abelian groups over a scheme has enough injective objects, so one can define right derived functors of left exact functors.
|
|
It follows that the Chern classes of a vector bundle E depend only on the class of E in the Grothendieck group K_0(X). By definition, for a scheme X, K_0(X) is the quotient of the free abelian group on the set of isomorphism classes of vector bundles on X by the relation that [B] = [A] + [C] for any short exact sequence as above. Although K_0(X) is hard to compute in general, algebraic K-theory provides many tools for studying it, including a sequence of related groups K_i(X) for integers i>0. A variant is the group G_0(X) (or K_0'(X)), the Grothendieck group of coherent sheaves on X. (In topological terms, G-theory has the formal properties of a Borel–Moore homology theory for schemes, while K-theory is the corresponding cohomology theory.) The natural homomorphism K_0(X)\to G_0(X) is an isomorphism if X is a regular separated Noetherian scheme, using that every coherent sheaf has a finite resolution by vector bundles in that case.
|
|
The total mileage distance was 10.7. Electric powered cars with overhead lines began replacing cable cars on the Red Line on August 30, 1898 as a more economical and faster means of mass transit. Cables were removed immediately, but the expense of extracting the underground pulleys, sheaves and other steel/iron fittings was too much, and in most instances they were just covered over as streets were gradually repaired and resurfaced with bricks, cobblestones / Belgian blocks or later concrete / asphalt. With the switchover, The Baltimore City Passenger Railway Company was absorbed into Baltimore's merged trolley monopoly in the late 1890s with the formation of the United Railways and Electric Company (later the Baltimore Transit Company after a bankruptcy and reorganization in 1935, adding transit diesel powered buses to the extensive streetcar system), and power was generated at the newly constructed pile of the massive huge red brick Pratt Street Power Plant, situated on the waterfront at municipal Pier 4, facing the Northwest Branch of the Patapsco River and its "Basin" (later known as the Inner Harbor).
|
|
The East Block as viewed from the observation platform of the Peace TowerDesigned by Thomas Stent and Augustus Laver, the East Block is an asymmetrical structure built in the Victorian High Gothic style, with load bearing masonry walls being nearly 0.9 m (3 ft) thick at the ground level, expanding to 2.1 m (7 ft) thick at the base of the main tower. These are all clad in a rustic Nepean sandstone exterior and dressed stone trim around windows and other edges, as well as displaying a multitude of stone carvings, including gargoyles, grotesques, and friezes, keeping with the style of the rest of the parliamentary complex. The rear of the East BlockThis detail continues on the interior of the East Block, where emblems, such as wheat sheaves, were carved in stone originally to indicate the various government departments housed nearby. The level of quality and luxury of the offices initially indicated the status of the inhabitant: large, wood panelled chambers with marble fireplaces and richly decorated plaster ceilings served for ministers of the Crown; intricate, but somewhat less detailed cornices were sufficient for senior bureaucrats; and basic, machine-made woodwork and concrete fireplace mantles filled rooms set aside for clerks.
|
|
It introduces the first theme, which is picked up by the voices on "In convertendo Dominus", reappearing slightly changed in B on "Converte, Domine" and again in unison of all voices, marked fff, at the beginning of A'. A solo section of the organ leads from a climax reached at the end of B to the tranquil beginning of C. In parts A and C the tenors begin singing, whereas the altos begin part B. The "carrying of the sheaves" is expressed by a divided choir, alternating in singing the same pattern higher and higher, choir 1 a four-part female choir, choir 2 the altos and a four-part men's choir, ending the section in eight parts. A reviewer of a recording summarized in 1967: > Van Nuffel was a completely new name to me — a Belgian contemporary of > Kodály who died in 1953 at the age of 70 — but I certainly want to hear more > of his music: his setting … is in the traditional nineteenth-century idiom > with a touch of modality suggesting certain passages in Puccini and early > Vaughan Williams, but it is a powerful and moving piece, rising out of a > brooding darkness to a big impassioned outburst, and dying away again.
|
|