Investigators also identified Farook's cellphone number and triangulated his location.
|
|
President Bill Clinton triangulated between the parties and revamped welfare.
|
|
My phone triangulated back to Florida – the police called AT&T.
|
|
Police triangulated a cell phone signal to find the vehicle, Williams said.
|
|
That can't be triangulated without losing ideological credibility — which is what quickly happened.
|
|
He took the little the company itself would say, interviewed analysts, partners and competitors, and triangulated.
|
|
It's a stark contrast to WWE's current buttoned-up, corporate, perfectly triangulated view of pro wrestling.
|
|
His previous narrative short film Absence Of Love tells the triangulated stories of brothers, father, and lover.
|
|
Ola says it informs the driver about the contact details with the GPS triangulated location of the user.
|
|
The table sits atop and around the triangulated Heritage Floor, which inscribes the names of 999 additional women.
|
|
Francie's daughters find themselves stumbling toward sexuality and, in the process, negotiate a triangulated relationship with a neighbor boy.
|
|
Well, there's a lot more sources than that, for starters, because everything is triangulated and checked against other people Right.
|
|
Police earlier claimed that four suspects coordinated the attack with rifles and positioned themselves in triangulated locations on the demonstration route.
|
|
As president, Bill Clinton eventually triangulated to the center as a result of the prevailing political winds of the mid-1990s.
|
|
They triangulated using DNA markers he shared with unacquainted third cousins who had uploaded their DNA sequences to a public database.
|
|
Republicans had shut the government down and lost the argument, he triangulated on the issues and Clinton focused on economic issues.
|
|
Years of reporting, leaks, books, and even a feature film have triangulated the actions and intentions of the people who built it.
|
|
After you take a selfie, the image data is converted into triangulated coordinates for the triangle-shaped robot to plot out on paper.
|
|
Everything US Men's National Team and Borussia Dortmund wünderkid Christian Pulisic says and does is dissected, flipped, refracted, and triangulated by American soccer fans.
|
|
The artist transforms busts and statues into morphing, dancing forms—giving them a triangulated makeover so they flicker, flit, and distort before your eyes.
|
|
Alternatively, she could decide to shut down any Sanders challenge as part of a pivot to a more triangulated position in the general election.
|
|
I was floored the first time one of its personal navigation devices triangulated my car's position onto a city grid sometime in the early 2000s.
|
|
Also, there are countless times that we have seen large, long-term enterprise deals go to a competitor that has successfully triangulated the buying process or leveraged backchannels.
|
|
The obvious analogy is with Jhabvala's own triangulated life—Europe, India, America—and it prompts the perennial question posed of diasporic, post-colonial, mixed-up, or migrant writers.
|
|
Because of the exaggerated coats with battering-ram shoulder pads that triangulated the body in the extreme, and looped with great swaths of scarves tossed around the neck.
|
|
The diversity concern needs to be triangulated to include Latinos, Asian/Pacific Islanders and Native Americans, who are marginalized in the film and television business despite shifting demographic numbers.
|
|
After the Democrats lost three times in a row from 1980 to 1988, they shifted toward the center with Bill Clinton, who triangulated between his party and the GOP.
|
|
This new Senate bill may risk some opposition from the far right for not shedding enough rules, but so far the GOP looks to have effectively triangulated the issue.
|
|
I stop to admire the subtly chamfered cuts on the blue-stained wood blocks, which create a triangulated pattern of light and shadow that recalls traditional western-African textiles.
|
|
Because the same bits of real estate crop up in multiple frames, a given view can be triangulated with other shots so that we are enclosed within an artist's world.
|
|
If more than one camera sees the same fireball—which is usually the case—that meteor's course can be triangulated, with a precision of about ten metres, by comparing the images.
|
|
While MCCs and MNCs aren't specific enough data for device triangulation, there's concern that Cell IDs, which basically record the tower for which your messages are sent through, could be triangulated.
|
|
Inside the addition, all floors are open-plan offices with rows of desks arranged on the bias; the triangulated walls offer circumferential views of the city and the vast Scheldt estuary.
|
|
" During an earlier press conference just after midnight on Friday, Brown said police believe there were multiple shooters who were "triangulated at different positions and different points in the downtown area.
|
|
The police believe four suspects coordinated the attack with rifles, Police Chief David O. Brown said, and positioned themselves in triangulated locations near the end of the route the protesters planned to take.
|
|
For instance, Panamerican Airway radio direction finders on Wake Island, Midway Atoll and Honolulu each picked up distress signals from Earhart and took bearings, which triangulated in the cluster of islands that includes Nikumaroro.
|
|
" Cellphone records, which may have triangulated Little's location at the time of the murder or shown communication between the two men, were not pulled, Rasheed said, because Little and his mother "would not confirm numbers.
|
|
This narrow and tall structure is topped by a triangulated roof plane designed to be read at the street as a low, one-story shed, even as the back portion of the structure climbs much higher.
|
|
The Bermuda Triangle is a region of the Atlantic Ocean triangulated by But the event, which is scheduled for October 1 to 3, isn't quite what it sounds like, its organizer Anthony Dominick Carnovale, told INSIDER.
|
|
Winning over new voters and re-engaging lapsed voters demands an authenticity about our values, that for too long, have been triangulated or modulated in craven attempts to recapture some elusive white suburban or rural voter.
|
|
They triangulated the signal back to its source in North Korea's northeastern highlands at almost the exact moment that the rogue nation distributed a triumphal press release declaring that it had successfully tested its first hydrogen bomb.
|
|
We're eavesdropping on a conversation that was never meant to be heard, and, as a result, we enter a triangulated relationship that veers on the erotic, between Wojnarowicz, his amorous and analytical mind, and the silent listener.
|
|
It fit perfectly in the bizarre nexus that triangulated punk, comedy, and outsider culture and could be found everywhere in the sunset years of 1970s L.A., from The Groundlings to the Weirdos to Matt Groening's Life in Hell.
|
|
The best theories of how an outsider like Trump would lead a successful presidency tended to revolve around him revealing himself a skilled manager and non-ideological dealmaker, and running an administration that effectively triangulated between Democrats and Republicans.
|
|
It was an era of maximalism, where every fashion trend seemed to be big: teased hair, loud makeup, and giant shoulder pads that triangulated into super-cinched waists — which, removed from the context of the period, now look like costumes.
|
|
Since the Pokémon Go app gets GPS signals in addition to Wi-Fi and cell tower-triangulated geolocation, a user would need to shield or block out the "real" GPS signals coming from overhead satellites while spoofing the desired latitude and longitude coordinates.
|
|
There, as part of a project called An Artist Embedded, Mr. Gordon immersed himself in Fryer's notes, letters, diaries and other documents, eventually extracting three characters from them: three lives lived at tangents to Fryer's that together triangulated him and his times.
|
|
So I went to one of the locations Cage chose through chance operations (one of 27, actually, triangulated to form 215 so-called waltzes) — on 72nd Street, across Broadway from Verdi Square — and made a brief video on my cellphone: Waltz 17, No. 2, on Cage's map.
|
|
Depending on the density of cell sites around you at any one point, the location data triangulated from them can not only highlight your home and office, but also point to the bars you frequented, the houses at which you spent the night and the offices of therapists you visited.
|
|
Everything, from the movement of the camera, to the flock of salmon diving in and out of the water, to the triangulated ebbing waves, to the clouds, rain, stars, and sky react to or reflect the music and instruments used, letting you float about in an audio-reactive world awash in turquoise and magenta tones.
|
|
Button-down shirts, denim jackets and pea coats were cut on the slant and curved into the shape of a chrysalis, and suits in houndstooth and tweed had the hips triangulated out and up, like a false front, in an echo of the classic couture silhouette (shoulders slouched forward, stomach sucked in, bones sharp as steel).
|
|
Here, if they can establish a correlation between geotagged phenotypic measurements and the plants' genotypic data (data which the seed giants they're targeting would already hold), the AI-enabled data-capture method could also steer farmers toward the best crop variety to use in a particular location and climate condition — purely based on insights triangulated and unlocked from the data they're capturing.
|
|
Pros: Packed weight of just 2 pounds and 5 ounces, triangulated guyouts offer more interior space, easy set up and takedown, divvy stuff sack makes it easy to fit in a backpack, and its extremely durable aluminum poles are some of the lightest on the marketCons: Minor user complaints of leaking, but the cause could be from a rain fly that isn't properly cinched tightly to allow proper overlap of inner tent body
|
|
Nearly all triangulated categories that arise in practice come from stable ∞-categories. A similar (but more special) enrichment of triangulated categories is the notion of a dg-category. In some ways, stable ∞-categories or dg-categories work better than triangulated categories. One example is the notion of an exact functor between triangulated categories, discussed below.
|
|
The group K_0(C) has a simple description in terms of the triangulated category associated to C. But an example shows that the higher K-groups of a dg-category are not always determined by the associated triangulated category.Dugger & Shipley (2009), Remark 4.9. Thus a triangulated category has a well-defined K_0 group, but in general not higher K-groups. On the other hand, the theory of triangulated categories is simpler than the theory of stable ∞-categories or dg-categories, and in many applications the triangulated structure is sufficient.
|
|
A version of the representability theorem in the case of triangulated categories is due to Amnon Neeman. Together with the preceding remark, it gives a criterion for a (covariant) functor F: C → D between triangulated categories satisfying certain technical conditions to have a right adjoint functor. Namely, if C and D are triangulated categories with C compactly generated and F a triangulated functor commuting with arbitrary direct sums, then F is a left adjoint. Neeman has applied this to proving the Grothendieck duality theorem in algebraic geometry.
|
|
A DG category C is called pre-triangulated if it has a suspension functor \Sigma and a class of distinguished triangles compatible with the suspension, such that its homotopy category Ho(C) is a triangulated category. A triangulated category T is said to have a dg enhancement C if C is a pretriangulated dg category whose homotopy category is equivalent to T.See for a survey of existence and unicity results of dg enhancements dg enhancements. dg enhancements of an exact functor between triangulated categories are defined similarly. In general, there need not exist dg enhancements of triangulated categories or functors between them, for example stable homotopy category can be shown not to arise from a dg category in this way.
|
|
First, if planar regions separated by the graph are not triangulated, i.e. do not have exactly three edges in their boundaries, we can add edges without introducing new vertices in order to make every region triangular, including the unbounded outer region. If this triangulated graph is colorable using four colors or fewer, so is the original graph since the same coloring is valid if edges are removed. So it suffices to prove the four color theorem for triangulated graphs to prove it for all planar graphs, and without loss of generality we assume the graph is triangulated.
|
|
Let D be a triangulated category with arbitrary direct sums. A localizing subcategory of D is a strictly full triangulated subcategory that is closed under arbitrary direct sums.Neeman (2001), Introduction, after Remark 1.4. To explain the name: if a localizing subcategory S of a compactly generated triangulated category D is generated by a set of objects, then there is a Bousfield localization functor L\colon D\to D with kernel S.Krause (2010), Theorem, Introduction.
|
|
For every abelian category A, the derived category D(A) is a triangulated category, containing A as a full subcategory (the complexes concentrated in degree zero). Different abelian categories can have equivalent derived categories, so that it is not always possible to reconstruct A from D(A) as a triangulated category. Alexander Beilinson, Joseph Bernstein and Pierre Deligne described this situation by the notion of a t-structure on a triangulated category D.Beilinson et al. (1982), Definition 1.3.1.
|
|
The homotopy category of spectra and the derived category of a ring are both examples of triangulated categories.
|
|
Figure 1: Closed triangulated polyhedra. (a) Tetrahedron (Td), (b) Trigonal bipyramid (D3h). (c) Octahedron (Oh). (d) Pentagonal bipyramid (D5d).
|
|
A triangulated torus Another triangulation of the torus A triangulated dolphin shape In mathematics, topology generalizes the notion of triangulation in a natural way as follows: :A triangulation of a topological space X is a simplicial complex K, homeomorphic to X, together with a homeomorphism h: K → X. Triangulation is useful in determining the properties of a topological space. For example, one can compute homology and cohomology groups of a triangulated space using simplicial homology and cohomology theories instead of more complicated homology and cohomology theories.
|
|
The benefit of the triangulated and double-triangulated arrangement is that they do not need a panhard bar. The benefits of this are increased articulation and potential ease of installation. Multi-link for solid axle offers a benefit over the independent multi-link in that it is significantly cheaper and much less complex to build.
|
|
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.
|
|
Triangulated City encouraged participants and spectators to view the city as an artistic canvas, with each specific location a place of dialogue and encounter.
|
|
The smash product is compatible with the triangulated category structure. In particular the smash product of a distinguished triangle with a spectrum is a distinguished triangle.
|
|
In: Majer O'Sickley, Ingeborg/von Zadow, Ingeborg [ed.]: Triangulated Visions. Women in Recent German Cinema. Albany: State University of New York Press. 1998. pp. 81-93.
|
|
The reasons to introduce desuspension: #Desuspension makes the category of spaces a triangulated category. #If arbitrary coproducts were allowed, desuspension would result in all cohomology functors being representable.
|
|
Until 1988, whether a simple polygon can be triangulated faster than time was an open problem in computational geometry. Then, discovered an -time algorithm for triangulation,. later simplified by .. Several improved methods with complexity (in practice, indistinguishable from linear time) followed... Bernard Chazelle showed in 1991 that any simple polygon can be triangulated in linear time, though the proposed algorithm is very complex. A simpler randomized algorithm with linear expected time is also known.
|
|
Dirani was an associate member of the Triangulated City. The Triangulated City is a live art event that investigates notions of exchange within the urban environment through the secrets, rumours, messages, myths and memories circulating in a city. Zoukak Theatre Company and Cultural Association hosted Lotos Collective (London/New York) and in collaboration with invited participants, devised the project through a series of participatory workshops. Over three days, in three locations, three performances unfolded simultaneously each evening.
|
|
Unique glass domes springing straight from ground level were used for hothouses and winter gardens. Elaborate covered shopping arcades included large glazed domes at their cross intersections. The large domes of the 19th century included exhibition buildings and functional structures such as gasometers and locomotive sheds. The "first fully triangulated framed dome" was built in Berlin in 1863 by Johann Wilhelm Schwedler and, by the start of the 20th century, similarly triangulated frame domes had become fairly common.
|
|
Once the images are triangulated, image pairs may be viewed in stereo and 3D measurements can be made. The system can automatically generate digital terrain models, which can be reviewed and edited in stereo. Once an accurate 3D surface has been derived, triangulated images may be orthorectified. In addition to this workflow, IMAGINE Photogrammetry supports 3D feature extraction, radiometric adjustment, and a number of additional digital image processing capabilities available from ERDAS IMAGINE, which is included with IMAGINE Photogrammetry.
|
|
An example is the proof of the Bloch–Kato conjecture, where many computations were done at the level of triangulated categories, and the additional structure of ∞-categories or dg-categories was not required.
|
|
The other solution was to add passive receivers that triangulated on the carcinotron broadcasts, allowing the ground stations to produce accurate tracking information on the location of the jammer and allowing them to be attacked.
|
|
From 1928, radio signals from Croydon, Pulham in Norfolk and Lymm in Kent triangulated the position of aircraft; a similar system was set up by Germany in 1940, known as the Battle of the Beams.
|
|
In mathematics, a triangulated category is a category with the additional structure of a "translation functor" and a class of "exact triangles". Prominent examples are the derived category of an abelian category, as well as the stable homotopy category. The exact triangles generalize the short exact sequences in an abelian category, as well as fiber sequences and cofiber sequences in topology. Much of homological algebra is clarified and extended by the language of triangulated categories, an important example being the theory of sheaf cohomology.
|
|
The Euler characteristic of a sphere, triangulated like an icosahedron, is . Since every compact oriented 2-manifold can be triangulated by small geodesic triangles, it follows that : \int_M K dA = 2\pi\,\chi(M) where denotes the Euler characteristic of the surface. In fact if there are faces, edges and vertices, then and the left hand side equals . This is the celebrated Gauss–Bonnet theorem: it shows that the integral of the Gaussian curvature is a topological invariant of the manifold, namely the Euler characteristic.
|
|
3D models are most-often represented as triangulated polyhedra forming a triangle mesh. Non triangular surfaces can be converted to an array of triangles through tessellation. Attributes from the vertices are typically interpolated across mesh surfaces.
|
|
This is done by two techniques namely smoothing and flipping. In mesh smoothing the location of mesh vertices are adjusted. While in Flipping the diagonals of triangulated quadrilateral are exchanged. Flipping improves the quality measure of triangles.
|
|
Writing superheroes: Contemporary childhood, popular culture, and classroom literacy. New York: Teachers College Press. . she pulls together the pieces of her studies into meaningful wholes through the interpretation of triangulated data (e.g., field notes, tape recordings, interviews, artifacts, etc.).
|
|
Generalizing even further it is also possible to define the Grothendieck group for triangulated categories. The construction is essentially similar but uses the relations [X] - [Y] + [Z] = 0 whenever there is a distinguished triangle X → Y → Z → X[1].
|
|
The piece "Poetry on the Move" is an interactive bulletin board. It consists of a computer-operated LED matrix display in the form of a triangulated strip. The project invites participants to upload text messages and post poetry for public display.
|
|
It was shown by that the Schönhardt polyhedron can be generalized to other polyhedra, combinatorially equivalent to antiprisms, that cannot be triangulated. These polyhedra are formed by connecting regular k-gons in two parallel planes, twisted with respect to each other, in such a way that k of the 2k edges that connect the two k-gons have concave dihedrals. Another polyhedron that cannot be triangulated is Jessen's icosahedron, combinatorially equivalent to a regular icosahedron. In a different direction, constructed a polyhedron that shares with the Schönhardt polyhedron the property that it has no internal diagonals.
|
|
Thomas Andrew Bridgeland One or more of the preceding sentences incorporates text from the royalsociety.org website where: (born 1973) is a Professor of Mathematics at the University of Sheffield. He is most well-known for defining Bridgeland stability conditions on triangulated categories.
|
|
The alternative names "triangular graph". or "triangulated graph". have also been used, but are ambiguous, as they more commonly refer to the line graph of a complete graph and to the chordal graphs respectively. Every maximal planar graph is a least 3-connected.
|
|
The notion of almost normal surfaces is due to Hyam Rubinstein. The notion of spun normal surface is due to Bill Thurston. Regina is software which enumerates normal and almost-normal surfaces in triangulated 3-manifolds, implementing Rubinstein's 3-sphere recognition algorithm, among other things.
|
|
Triangulated irregular network TIN overlaid with contour lines A triangulated irregular network (TIN)Also known as a "Triangular Irregular Network". is a representation of a continuous surface consisting entirely of triangular facets, used mainly as Discrete Global Grid in primary elevation modeling. The vertices of these triangles are created from field recorded spot elevations through a variety of means including surveying through conventional, Global Positioning System Real-Time Kinematic (GPS RTK), photogrammetry, or some other means. Associated with three-dimensional data (x, y, and z) and topography, TINs are useful for the description and analysis of general horizontal (x and y) distributions and relationships.
|
|
Geologic modelling is a relatively recent subdiscipline of geology which integrates structural geology, sedimentology, stratigraphy, paleoclimatology, and diagenesis; In 2-dimensions (2D), a geologic formation or unit is represented by a polygon, which can be bounded by faults, unconformities or by its lateral extent, or crop. In geological models a geological unit is bounded by 3-dimensional (3D) triangulated or gridded surfaces. The equivalent to the mapped polygon is the fully enclosed geological unit, using a triangulated mesh. For the purpose of property or fluid modelling these volumes can be separated further into an array of cells, often referred to as voxels (volumetric elements).
|
|
58Muñoz Castiblanco, 2013, p.59Muñoz Castiblanco, 2013, p.63 Research in the 1960s by Eliécer Silva Celis on the rock art of Sáchica showed phytomorphic designs, masked human figures, singular and concentric rings, triangulated heads, and faces where the eyes and noses were drawn, but the mouths absent.
|
|
The engine was mounted on two main support frames that were supported by two tubular struts. The frame structure was triangulated and emanated from the fuselage. The main frames were bolted onto the engine's top quarter. In turn, the frames were attached to the firewall by universal joints.
|
|
He has applied triangulated Calabi-Yau categories to the (additive) categorification of cluster algebras. In 2013, he received and honorary degreeList of honorary degrees of the University of Anwerp in 2013, retrieved 2020-09-01. from the University of Antwerp. In 2014 he received the Sophie Germain Prize.
|
|
The bomb was held in place in the aircraft by a pair of calipers, or triangulated carrying arms, which swung away from either end of the bomb to release it.Flower (2002), p. 31. Diagrams from document produced by Dr Wallis to explain how the bouncing bomb Upkeep worked.
|
|
For example, the wing spar in a small aircraft may in fact be a simple I-beam with a solid cross-section, but in a larger design the upright part of the beam or "web" will be constructed as an open lattice of trusses in a triangulated structure.
|
|
1958 Nota Minx Streamliner 1960 Nota Formula Junior 1962 Nota Sportsman Nota Sports and Racing Cars is an automobile manufacturer in Australia. The company was founded by Guy Buckingham in 1952. He was an aircraft engineer and used his expertise to build triangulated spaceframed sportscars. Possibly Australia's first space-framed cars.
|
|
The bridge is constructed predominantly of greenheart timber. It has two spans, one of and the other of . Each span consists of paired semi-elliptical timber arches of mechanically laminated timber, strengthened with triangulated timber struts, which also support the platform. The paired arches are braced by cast- iron struts.
|
|
People who did not have mobile phones could not play at all. As the industry expanded to the state of New Jersey, a new method of geolocation was deployed. This method triangulated wifi networks near the player to determine his or her physical location. This method was much more precise.
|
|
The tesseract itself can be decomposed into smaller polytopes. For instance, it can be triangulated into 4-dimensional simplices that share their vertices with the tesseract. It is known that there are 92487256 such triangulations and that the least number of 4-dimensional simplices in any of them is 16.
|
|
These directional references, together with a statement provided by Theodosius that "the city of Livias is across the Jordan, twelve [Roman] miles [17.75 km/ 11 m] from Jericho" (Wilkinson)Theodosius Topografia 19 to the east, provide east/west and north/south co-ordinates that when triangulated place Livias at Tall el-Hammam.
|
|
They consisting of a triangulated frame of light steel bars and mesh covered by a thin layer of concrete. These are generally taken to be the first modern architectural thin shells. These are also considered the first geodesic domes. Geodesic domes have been used for radar enclosures, greenhouses, housing, and weather stations.
|
|
In flight steering is accomplished via handles that actuate the canopy brakes, creating roll and yaw. On the ground the aircraft has lever-controlled nosewheel steering. The main landing gear incorporates triangulated spring rod suspension. The aircraft has an empty weight of and a gross weight of , giving a useful load of .
|
|
STL model of the Utah teapot viewed in the MediaWiki 3D extension STL file format is simple and easy to output. Consequently, many computer-aided design systems can output the STL file format. Although the output is simple to produce, some connectivity information is discarded. Many computer-aided manufacturing systems require triangulated models.
|
|
A renderer may support only 3-sided faces, so polygons must be constructed of many of these, as shown above. However, many renderers either support quads and higher-sided polygons, or are able to convert polygons to triangles on the fly, making it unnecessary to store a mesh in a triangulated form.
|
|
The "first fully triangulated framed dome" was built in Berlin in 1863 by Johann Wilhelm Schwedler in a gasometer for the Imperial Continental Gas Association and, by the start of the 20th century, similarly triangulated frame domes had become fairly common. Schwedler built three wrought-iron domes over gasholders in Berlin between 1876 and 1882 with spans of 54.9 meters, one of which survives. Six similar Schwedler-type domes were used over gasholders in Leipzig beginning in 1885 and in Vienna using steel, in the 1890s. Rather than using traditional iron ribs, the domes consist of a thinner arrangement of short straight iron bars connected with pin joints in a lattice shell, with cross-bracing provided by light iron rods.
|
|
A Vierendeel bridge, which lacks diagonal elements in the primary structure The Vierendeel truss is a structure where the members are not triangulated but form rectangular openings, and is a frame with fixed joints that are capable of transferring and resisting bending moments. As such, it does not fit the strict definition of a truss (since it contains non-two-force members): regular trusses comprise members that are commonly assumed to have pinned joints, with the implication that no moments exist at the jointed ends. This style of structure was named after the Belgian engineer Arthur Vierendeel,Vierendeel bruggen who developed the design in 1896. Its use for bridges is rare due to higher costs compared to a triangulated truss.
|
|
In mathematics, the Gabriel–Popescu theorem is an embedding theorem for certain abelian categories, introduced by . It characterizes certain abelian categories (the Grothendieck categories) as quotients of module categories. There are several generalizations and variations of the Gabriel–Popescu theorem, given by (for an AB5 category with a set of generators), , (for triangulated categories).
|
|
Based on the iconic Lola T70 from the 1960s. The chassis differs from the mk3 and mk4, it being a fully triangulated tubular spaceframe with alloy and GRP composite panels. The transmission is borrowed from Porsche and factory engine options are from the GM LS series of V8's, from 450bhp up to 700bhp.
|
|
From 1802 until 1871, the Great Trigonometrical Survey was a project to survey the Indian subcontinent with high precision. Starting from the coastal baseline, mathematicians and geographers triangulated vast distances across the country. One of the key achievements was measuring the height of Himalayan mountains, and determining that Mount Everest is the highest point on Earth.
|
|
Paul Balmer (born 1970) is a Swiss mathematician, working in algebra. He is a professor of mathematics at the University of California, Los Angeles. Balmer received his Ph.D. from the University of Lausanne in 1998, under the supervision of Manuel Ojanguren, with a thesis entitled Groupes de Witt dérivés des Schémas (in French). His research centers around triangulated categories.
|
|
We start with the triangulated subdivision, and choose an independent set of vertices to be removed. After removing the vertices, we retriangulate the subdivision. Because the subdivision is formed by triangles, a greedy algorithm can find an independent set that contains a constant fraction of the vertices. Therefore, the number of removal steps is O(log n).
|
|
Normally the main undercarriage was made up of a pair of vees, sprung with oleo/spring struts and provided with brakes as standard equipment, and a free-castoring tailwheel sprung with triangulated shock cords.Simpson, 2001, p. 574 was fitted to most aircraft, although a small number for Brazil were fitted with a tail skid.Brandley, 1981, p.
|
|
A twisted prism can be made (clockwise or counterclockwise) with the same vertex arrangement. It can be seen as the convex form with 4 tetrahedrons excavated around the sides. However, after this it can no longer be triangulated into tetrahedra without adding new vertices. It has half of the symmetry of the uniform solution: D4 order 4.
|
|
In computer graphics, objects are often represented as triangulated polyhedra in which the object vertices are associated not only with three spatial coordinates but also with other graphical information necessary to render the object correctly, such as colors, reflectance properties, textures, and surface normal; these properties are used in rendering by a vertex shader, part of the vertex pipeline.
|
|
Methodologically, most of these studies employ a diverse set of tools. Most often, descriptive statistics, qualitative methods including interviews of different kinds, focus group discussions, and participant observation, as well as textual and discourse analyses are employed and triangulated. Most of them also deploy a historical perspective that traces different strands of social and political change across time.
|
|
The Esri TIN format is a popular yet proprietary geospatial vector data format for geographic information system (GIS) software for storing elevation data as a triangulated irregular network. It is developed and regulated by Esri. The Esri TIN format can spatially describe elevation information including breaking edge features. Each points and triangle can carry a tag information.
|
|
The salesman there understood that the craftsmanship displayed in the rod suggested an aptitude for making split-cane fishing rods. Upon examining some four-sided rods (rods that are made from four triangulated strips of bamboo that are laminated lengthwise), Leonard was asked if he could reproduce them. "Yes, and better than those.", was his reply.
|
|
A Vierendeel bridge The Vierendeel truss, unlike common pin-jointed trusses, imposes significant bending forces upon its members — but this in turn allows the elimination of many diagonal elements. It is a structure where the members are not triangulated but form rectangular openings, and is a frame with fixed joints that are capable of transferring and resisting bending moments. While rare as a bridge type due to higher costs compared to a triangulated truss, it is commonly employed in modern building construction as it allows the resolution of gross shear forces against the frame elements while retaining rectangular openings between columns. This is advantageous both in allowing flexibility in the use of the building space and freedom in selection of the building's outer curtain wall, which affects both interior and exterior styling aspects.
|
|
It preys on several other spiders believed to be harmful to humans, including the hobo spider and the brown recluse. The egg sac of the triangulated cobweb spider is made from loosely woven silk, and is about the same size as the spider itself. Each egg sac contains approximately 30 eggs. Cobweb spiders typically live on windows or in dirt areas.
|
|
Mount Shasta is connected to its satellite cone of Shastina, and together they dominate the landscape. Shasta rises abruptly to tower nearly above its surroundings. On a clear winter day, the mountain can be seen from the floor of the Central Valley to the south.In 1878 the Coast and Geodetic Survey triangulated between heliotropes atop Mount Shasta and Mount St. Helena, south.
|
|
The house with two rooms is a contractible 2-complex that is not collapsible. Another such example, popularized by E.C. Zeeman, is the dunce hat. The house with two rooms can also be thickened and then triangulated to be unshellable, despite the thickened house topologically being a 3-ball. The house with two rooms shows up in various ways in topology.
|
|
Bracing works by creating a triangulated truss structure which resists bending or twisting. By comparison, an unbraced cantilever structure bends easily unless it carries a lot of heavy reinforcement. Making the structure deeper allows it to be much lighter and stiffer. To reduce weight and air resistance, the structure may be made hollow, with bracing connecting the main parts of the airframe.
|
|
Instead of a carburettor, a revolving petrol distributor was developed, with the quantity of fuel being regulated by a drip-feed. One advantage of this device was that a wide variety of fuels could be used. The engine was mounted at the rear, on a triangulated tubular chassis, with chain-drive to the wheels. By 1899 they were registered at 17 rue Phil.
|
|
The Dax Rush is a lightweight two-seater sports car. It is offered as a kit, and is a popular choice among Kit Car builders. It has a multi-tube triangulated steel space frame chassis, front engine and rear wheel or four wheel drive. The body is constructed in Glass-Reinforced Polymer (GRP) with optional aluminium side panels and bonnet.
|
|
Triangulated categories were introduced independently by Dieter Puppe (1962) and Jean-Louis Verdier (1963), although Puppe's axioms were less complete (lacking the octahedral axiom (TR 4)).Puppe (1962, 1967); Verdier (1963, 1967). Puppe was motivated by the stable homotopy category. Verdier's key example was the derived category of an abelian category, which he also defined, developing ideas of Alexander Grothendieck.
|
|
The Zeppelin-Lindau D.I had stressed skin fuselage and wings. In mechanical engineering, stressed skin is a type of rigid construction, intermediate between monocoque and a rigid frame with a non-loaded covering. A stressed skin structure has its compression-taking elements localized and its tension- taking elements distributed. Typically, the main frame has rectangular structure and is triangulated by the covering.
|
|
Breaking a polygon into monotone polygons A simple polygon is monotone with respect to a line , if any line orthogonal to intersects the polygon at most twice. A monotone polygon can be split into two monotone chains. A polygon that is monotone with respect to the y-axis is called y-monotone. A monotone polygon with vertices can be triangulated in time.
|
|
Fan triangulation of a convex polygon Fan triangulation of a concave polygon with a unique concave vertex. A fan triangulation is a simple way to triangulate a polygon by choosing a vertex and drawing diagonals to all of the other vertices of the polygon. Not every polygon can be triangulated this way, so this method is usually only used for convex polygons.
|
|
This proof uses the triangulation definition of Catalan numbers to establish a relation between Cn and Cn+1. Given a polygon P with n + 2 sides, first mark one of its sides as the base. If P is then triangulated, we can further choose and orient one of its 2n + 1 edges. There are (4n + 2)Cn such decorated triangulations.
|
|
The rigidly triangulated trellis frame wears 50 mm Marzocchi R.A.C. inverted forks, and has a Sachs/ Öhlins remote reservoir shock attached to a strong, single-sided swing arm. The Marchesini racing wheels wear dual radially mounted Brembo four-piston, two-pad brake calipers matched with 305 mm discs up front, and a 245 mm disc with two-piston caliper at the rear.
|
|
They are also lighter, and from mid 1953 braking performance was improved by disc brakes on all four wheels. The lightweight, multi-tubular, triangulated frame was designed by Heynes. Heynes, Knight and Sayer together developed the aerodynamic body. Made of aluminium in the barchetta style, it is devoid of road-going items such as carpets, weather equipment and exterior door handles.
|
|
The first part introduces the subject visually, encouraging the reader to think about packings not just as static objects but as dynamic systems of circles that change in predictable ways when the conditions under which they are formed (their patterns of adjacency) change. The second part concerns the proof of the circle packing theorem itself, and of the associated rigidity theorem: every maximal planar graph can be associated with a circle packing that is unique up to Möbius transformations of the plane. More generally the same result holds for any triangulated manifold, with a circle packing on a topologically equivalent Riemann surface that is unique up to conformal equivalence. The third part of the book concerns the degrees of freedom that arise when the pattern of adjacencies is not fully triangulated (it is a planar graph, but not a maximal planar graph).
|
|
So another solution was required. Thousands of years ago, many cultures used the plumb bob to find proper alignment and it was decided to use this technique to obtain perfect alignment. Two readings were taken separated by two hours to obtain a very accurate triangulated result. Exact positions of the sun for the Observatory location were taken from a smartphone using an astronomy application.
|
|
Joseph Stephen "Stevie" Woods, Jr. (July 2, 1951 – January 28, 2014) was an American R&B; musician and singer. Fanfare - Volume 6, Issues 1-2 - Page 473 Joel Flegler - 1982 - You hardly notice the music as you do some sorting, filing, old correspondence, making pate, grouting the bath tub Stevie Woods is a pretty young man with a voice triangulated between Johnny Mathis' and Grady Tate's.
|
|
A 3-coloring of the vertices of a triangulated polygon. The blue vertices form a set of three guards, as few as is guaranteed by the art gallery theorem. However, this set is not optimal: the same polygon can be guarded by only two guards. Steve Fisk's proof is so short and elegant that it was chosen for inclusion in Proofs from THE BOOK.
|
|
The Crazy Flyer 2 two-seater was designed to comply with the Fédération Aéronautique Internationale microlight category, including the category's maximum gross weight of . The Crazy Flyer 2 features two-seats-in-tandem accommodation, tricycle landing gear and a single Hirth 2704 engine in pusher configuration. The aircraft carriage is built from triangulated bolted aluminium tubing. The main landing gear incorporates spring rod suspension.
|
|
The remaining squares are triangulated according to some simple rules. For each regular square (no points within and no corner points in its sides), introduce the diagonal. Note that due to the way in which we separated points with the well-balancing property, no square with a corner intersecting a side is one that was warped. As such, we can triangulate squares with intersecting corners as follows.
|
|
The stylus received the signal by capacitive coupling, which could then be decoded back as coordinate information. The acoustic tablet, or spark tablet, used a stylus that generated clicks with a spark plug. The clicks were then triangulated by a series of microphones to locate the pen in space. The system was fairly complex and expensive, and the sensors were susceptible to interference by external noise.
|
|
Topography is the study of terrain, although the word is often used as a synonym for relief itself. When relief is described underwater, the term bathymetry is used. In cartography, many different techniques are used to describe relief, including contour lines and TIN (Triangulated irregular network). Elementary landforms (segments, facets, relief units) are the smallest homogeneous divisions of the land surface, at the given scale/resolution.
|
|
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.
|
|
Nye (2003), p. 53-55. However, for 1953's Mark VIII the Coopers decided to start afresh with a completely new chassis design. A true space frame design uses only straight tubes, properly triangulated to pass loads either in tension or compression.Charubhun & Rodkwan (2004) Following proper engineering practice, when he started to develop plans for the new chassis design Maddock sketched out various straight-tubed space frame designs.
|
|
A rectangle tiled by squares, rectangles, or triangles is said to be a "squared", "rectangled", or "triangulated" (or "triangled") rectangle respectively. The tiled rectangle is perfect if the tiles are similar and finite in number and no two tiles are the same size. If two such tiles are the same size, the tiling is imperfect. In a perfect (or imperfect) triangled rectangle the triangles must be right triangles.
|
|
The outer dome rests upon drum walls five metes thick. The fusion of Persian and Indian architecture can be seen in the dome's shape: the bulbous shape derives from Persian Timurid domes, and the finial with lotus leaf base is derived from Hindu temples. The inner dome has a decorative triangulated pattern modeled after plaster mold work, but here carved in marble. The entire complex is highly symmetrical.
|
|
This tract would eventually become Bay Terraces. The notion of a new subdivision built directly triangulated in what were already considered high-crime areas repelled the great majority of home-buyers. The homes were also priced out of the range of typical residents of the area and most went unsold or, in some cases, unbuilt. Federal subsidies and economic programs were then employed to assist in completing and populating the subdivision.
|
|
Data is collected by a computer and recorded as data points within three- dimensional space, with processing this can be converted into a triangulated mesh and then a computer-aided design model, often as non-uniform rational B-spline surfaces. Hand-held laser scanners can combine this data with passive, visible-light sensors — which capture surface textures and colors — to build (or "reverse engineer") a full 3D model.
|
|
Based on the AC Mk.3 289, the Mk.3 comes with two chassis options. The first utilises refurbished Jaguar suspension whereas the second "Euro" option uses bespoke racing suspension, with double wishbone coilover suspension and cast alloy uprights. The chassis is a steel triangulated backbone type with a GRP semi-monocoque body mounted on top. It's available as a factory built car or in component form for self-assembly.
|
|
Cottancin did not use heavy bars within thin layers of concrete, but dissipated force by using wire meshes and nets distributed throughout the material. His 1889 patent was for wire mesh embedded in concrete slabs, supported by "spinal stiffeners", or triangulated ribs. With his iron or steel trellises he could make plane or curved shapes. The structures that employed his designs typically have plate-like arches and struts.
|
|
The engine was mounted longitudinally behind the passengers and drove the rear wheels through a Citroën C35 5-speed manual transaxle also used in the SM and Maserati Merak. Rear brakes were mounted inboard, following contemporary racing practice. The Series 1 embodied Lotus' performance through light weight mantra, weighing less than . Front suspension consisted of upper A-arms and lower lateral links triangulated by the anti-roll bar.
|
|
This includes a point (0-simplex), a line segment (1-simplex), a triangle (2-simplex) and a tetrahedron (3-simplex). By definition, such a space is homeomorphic to a simplicial complex (more precisely, the geometric realization of an abstract simplicial complex). Such a homeomorphism is referred to as a triangulation of the given space. Many topological spaces of interest can be triangulated, including every smooth manifold (Cairns and Whitehead).
|
|
Some experts suspectpg 190 (see, for example, ) that triangulated categories are not really the "correct" concept. The essential reason is that the cone of a morphism is unique only up to a non-unique isomorphism. In particular, the cone of a morphism does not in general depend functorially on the morphism (note the non-uniqueness in axiom (TR 3), for example). This non- uniqueness is a potential source of errors.
|
|
The Schönhardt polyhedron. 3D model of the Schönhardt polyhedron In geometry, the Schönhardt polyhedron is the simplest non-convex polyhedron that cannot be triangulated into tetrahedra without adding new vertices. It is named after German mathematician Erich Schönhardt, who described it in 1928. The same polyhedra have also been studied in connection with Cauchy's rigidity theorem as an example where polyhedra with two different shapes have faces of the same shapes.
|
|
He also identifies a reply sent from Earth, which is triangulated as coming from a warehouse seven miles away. Led by Brigadier Lethbridge-Stewart, UNIT troops attack the warehouse and engage in a gun battle with troops commanded by General Charles Carrington. Meanwhile, Recovery Seven has returned to Earth. But whilst UNIT is transporting it to the Space Centre more of Carrington's troops stage an ambush and hijack it.
|
|
Mizrahi hired the London-based Foster and Partners as the design architect, and Core Architects as the local architect. He travelled to London to design the building using an exoskeleton structure. The design of the building was revised based on recommendations from RWDI and the organization's wind tunnel testing. The final design no longer features a structural exoskeleton; however, it retains diagonal hangers which maintain a triangulated appearance.
|
|
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.
|
|
Also in 1996, Varshney published "Optimizing Triangle Strips for Fast Rendering". The study introduced new algorithms for rendering triangle strips in conjuncture with partially triangulated models. Describing their more efficient triangle strip algorithm, Varshney et al. write: > By using triangle strips ... , we can describe the triangulation using the > strip ... and assuming the convention that the ith triangle is described by > the ith, (i + 1)st, and (i + 2)nd vertices of the sequential strip.
|
|
Dragons Teeth on the left, and Drumohar Peak and Rogach Peak dominating the island. Astrolabe Island, located at , is an island long, lying in the Bransfield Strait northwest of Cape Ducorps, Trinity Peninsula in Antarctica. It was discovered by the French expedition, 1837-40, under Captain Jules Dumont d'Urville, and named by him for his chief expedition ship, the Astrolabe. The island was photographed from the air and triangulated by FIDASE, 1956–57.
|
|
Terrain is commonly modelled either using vector (triangulated irregular network or TIN) or gridded (Raster image) mathematical models. In the most applications in environmental sciences, land surface is represented and modelled using gridded models. In civil engineering and entertainment businesses, the most representations of land surface employ some variant of TIN models. In geostatistics, land surface is commonly modelled as a combination of the two signals – the smooth (spatially correlated) and the rough (noise) signal.
|
|
The bridge carries four lanes of traffic, two lanes in each direction. The portions over the river are four consecutive spans, each long. The spans are built from triangulated steel girders, using a through-truss design where the roadway passes in an open tunnel between the left and right trusses and between the lower and upper truss work. The roadway has relatively limited vertical clearance for tall vehicles due to the upper truss members.
|
|
Therefore, we can decompose each polygon of our subdivision in triangles, and restrict our data structure to the case of subdivisions formed exclusively by triangles. Kirkpatrick gives a data structure for point location in triangulated subdivisions with O(n) storage space and O(log n) query time. The general idea is to build a hierarchy of triangles. To perform a query, we start by finding the top-level triangle that contains the query point.
|
|
It is the oldest surviving truss bridge in the world, consisting of strutted and triangulated trusses of moderate span, supported on piled trestles; as such, it is probably an evolution of the strutted bridge. The Kapellbrücke almost burned down on 18 August 1993, destroying two thirds of its interior paintings. Shortly thereafter, the Kapellbrücke was reconstructed and again opened to the public on 14 April 1994 for a total of CHF 3.4 million.
|
|
Lamarque succumbs to the plague but returns to his senses when an extra helmet is forced onto his head. Afterwards, the army surrounds the redoubt of the National Patriots from which the radiation causing the plague has been emanating; the academics’ colleague Dr. Plotnik had triangulated the source. The troops make short work of the fascists and capture Slidell and his "master mind," a Dr. Falk. The whole story of Slidell's diabolic scheme comes out.
|
|
The different observation angles are triangulated using a modified least squares minimisation approach, which now includes weightings based on image quality to produce the full observed trajectory . A shutter system within the lens of each observatory encodes a unique non-repeating De Bruijn sequence into each fireball. This provides accurate, absolute timing information for the duration of the trajectory to 0.4 ms. Purpose written software uses entry parameters to determine orbits for each meteoroid.
|
|
Steel joists and Joist Girders being erected. In structural engineering, the open web steel joist (OWSJ) is a lightweight steel truss consisting, in the standard form, of parallel chords and a triangulated web system, proportioned to span between bearing points. The main function of an OWSJ is to provide direct support for roof or floor deck and to transfer the load imposed on the deck to the structural frame i.e. beam and column.
|
|
Kherson TV Tower ( "Kherson TV Tower") is a tall space framed Ukrainian truss communications tower that is made of steel. The building is uniquely built, having been built by using the cross bracing system. The tower is a truss TV tower, specifically, a Vierendeel truss tower, wherein a structure's members are not triangulated but form rectangular openings instead (see Vierendeel Truss). The tower has an antenna that measures and a roof that measures .
|
|
Donnington Bridge has a single arch span of 170 feet between supports and an overall width of 56 feet 8 inches. It is constructed of reinforced concrete deck slab cast integrally with 10 pre- stressed concrete legs triangulated to meet the hinges enclosed within the abutments. The abutments are clad externally with precast concrete units faced with Criggion Green and Blue Shap stone and the fascias of the bridge are calcined flint.
|
|
The Replicar, inspired by the 1959 Le Mans 24hr winning Aston Martin DBR1 has a GRP body, triangulated space-frame and uses a Mazda MX5 (Mk1/2/2.5) as the donor. All-up weight is ¾ ton, slightly lighter than the DBR1, so a build with a standard 1.8 MX5 Mk2.5 would produce in excess of 200 bhp/ton. Currently in production with MEV Ltd. in the U.K. and Exomotive in the USA.
|
|
STL format is not the most memory- and computationally efficient method for transferring this data, but STL is often used to import the triangulated geometry into the CAM system. The format is commonly available, so the CAM system will use it. In order to use the data, the CAM system may have to reconstruct the connectivity. As STL files do not save the physical dimension of a unit, a CAM system will ask for it.
|
|
More specifically, he is a proponent of tensor-triangular geometry, an umbrella topic which covers geometric aspects of algebraic geometry, modular representation theory, stable homotopy theory, and other areas, by means of relevant tensor-triangulated categories. Balmer was an Invited Speaker at the International Congress of Mathematicians in Hyderabad in 2010, with a talk on Tensor Triangular Geometry. In 2012, he became a fellow of the American Mathematical Society. He was awarded the Humboldt Prize in 2015.
|
|
In this case, the figure 8 is said to be homologous to the sum of its lobes. Two open manifolds with similar boundaries (up to some bending and stretching) may be glued together to form a new manifold which is their connected sum. This geometric analysis of manifolds is not rigorous. In a search for increased rigour, Poincaré went on to develop the simplicial homology of a triangulated manifold and to create what is now called a chain complex.
|
|
The stable homotopy category is additive: maps can be added by using a variant of the track addition used to define homotopy groups. Thus homotopy classes from one spectrum to another form an abelian group. Furthermore the stable homotopy category is triangulated (Vogt (1970)), the shift being given by suspension and the distinguished triangles by the mapping cone sequences of spectra :X\rightarrow Y\rightarrow Y\cup CX \rightarrow (Y\cup CX)\cup CY \cong \Sigma X.
|
|
A careless merchant seaman of convoy SC 118 fired a pyrotechnic snowflake projector aboard the Norwegian freighter SS Vannik in the pre-dawn darkness of 4 February. observed the snowflake display, reported sighting the convoy, and was promptly sunk by Beverly and Vimy after Bibb and Toward triangulated the submarine's location from the sighting report, using High-Frequency radio Direction-Finder (HF/DF or Huff-Duff). The destroyers rescued 44 of the submarine's crew.Waters December 1966 p.
|
|
Bridgeland's 2002 Annals paper introduced spaces of stability conditions on triangulated categories, replacing the traditional rational slope of moduli problems by a complex phase. This far-reaching innovation gives a rigorous mathematical language for describing D-branes and creates a new area of deep interaction between theoretical physics and algebraic geometry. It has been a central component of subsequent work on homological mirror symmetry. Bridgeland's research has been funded by the Engineering and Physical Sciences Research Council (EPSRC).
|
|
A tick mark at the end of each line gives the Z coordinate perpendicular to the galactic plane. If the plaque is found, only some of the pulsars may be visible from the location of its discovery. Showing the location with as many as 14 pulsars provides redundancy so that the location of the origin can be triangulated even if only some of the pulsars are recognized. The data for one of the pulsars is misleading.
|
|
The Euclidean minimum spanning tree of a set of points is a subset of the Delaunay triangulation of the same points, and this can be exploited to compute it efficiently. For modelling terrain or other objects given a set of sample points, the Delaunay triangulation gives a nice set of triangles to use as polygons in the model. In particular, the Delaunay triangulation avoids narrow triangles (as they have large circumcircles compared to their area). See triangulated irregular network.
|
|
Schramm credits the full result to William Thurston, but the relevant portion of Thurston's lecture notes again only states the result explicitly for triangulated polyhedra. In contrast, there exist polyhedra that do not have an equivalent form with an inscribed sphere or circumscribed sphere.; . Any two polyhedra with the same face lattice and the same midsphere can be transformed into each other by a projective transformation of three-dimensional space that leaves the midsphere in the same position.
|
|
The interplane struts were N-form while the cabane structure included two fully triangulated forward struts connecting to the forward spar, and a pair of single struts connecting to the rear spar. Ailerons were only fitted on the upper planes. Its welded steel tube fuselage was flat sided, with the single seat open cockpit behind the trailing edge of the upper wing. The straight edged fin and rudder appeared small though the latter extended down to the keel.
|
|
The CBR1000RR's wheelbase also increased, measuring ; a increase over the 954. Accommodating the longer swingarm was another reason the CBR1000RR power plant shared nothing with the 954. Shortening the engine compared to the 954 meant rejecting the conventional in-line layout. Instead, engineers positioned the CBR1000RR's crankshaft, main shaft and countershaft in a triangulated configuration, with the countershaft located below the main shaft, dramatically shortening the engine front to back, and moving the swingarm pivot closer to the crankshaft.
|
|
Point cloud cleaning and decimation ::Regardless of the methodology of the data acquisition, the resulting point cloud is usually filtered and cleaned from unwanted objects, e.g. vegetation. Decrease of the overall point cloud density might be required depending on the outcrop surface complexity and size of the dataset. : 4. 3D triangulation and triangle mesh optimization :: In order to enable the possibility of model texturing, the edited point cloud is transformed into a triangulated irregular network (triangle mesh).
|
|
345 as each claimed that the other man had fired first. Soon after, they measured and triangulated the shooting, but could not determine from which angle Hamilton had fired. Burr's shot hit Hamilton in the lower abdomen above his right hip. The bullet ricocheted off Hamilton's second or third false rib, fracturing it and causing considerable damage to his internal organs, particularly his liver and diaphragm, before becoming lodged in his first or second lumbar vertebra.
|
|
Ivan Bohuš, "Mení sa výška štítov?" Tatry, 2007. Greiner was convinced that his own observation about Gerlachovský Peak's relative height was right, but because he considered the altimeter and quadrant insufficiently precise instruments, he triangulated the elevations of several of the Tatra peaks from the vicinity of the town of Poprád (today Poprad, Slovakia), not far from Káposztafalva (Hrabušice), in the fall of 1838Zofia Paryska-Radwańska and Witold Henryk Paryski, Encyklopedia tatrzańska. 1973. after he obtained a very accurate theodolite from a friend.
|
|
Muir Beach Overlook contains several historic base-end stations. From these stations, soldiers viewed ships and triangulated the distance, speed, and direction of these ships in coordination with different stations.National Park Service These stations were mostly important for artillery units stationed on the coast to attack any invasion.National Park Service: Muir Beach Overlook They gained particular importance during World War II immediately after the bombing of Pearl Harbor when many in California feared San Francisco or Los Angeles would be the next target.
|
|
Being the first all-Italian Bimota it came with a 750 cc Ducati 90° V-twin engine with Desmodromic valve-train in different levels of tune and styling. The frame is made of Chrome-Molybdenum steel tubing and uses a Triangulated Upper Space Frame or "Birdcage" design. The engine is a stressed member and the swingarm pivots in engine's crankcase. The DB1s triple-trees, clip-ons, rear-sets and several other bits are made of lightweight, hot stamped and billet Avional 14 aluminum.
|
|
Constrained Delaunay triangulations are also useful for minimizing the size of a TIN, since they have fewer nodes and triangles where breaklines are not densified. The TIN model was developed in the early 1970s as a simple way to build a surface from a set of irregularly spaced points. The first triangulated irregular network program for GIS was written by W. Randolph Franklin, under the direction of David Douglas and Thomas Peucker (Poiker), at Simon Fraser University in 1973.Franklin, W. R. (1973).
|
|
By 1913, F.W. Cotton had engaged in hill climbs and trials, and recognised the limitations of the "diamond frame" design, little different from a bicycle. He designed his own, and had examples made by Levis. In 1914 he patented the "triangulated frame" to protect his design that was a Cotton feature until the Second World War. The First World War intervened and it was not until 1918 that the Cotton Motor Company was founded; the first Cotton motorcycle appeared in 1920.
|
|
Because very small changes in its edge lengths can cause much bigger changes in its angles, physical models of the polyhedron appear to be flexible. As with the simpler Schönhardt polyhedron, the interior of Jessen's icosahedron cannot be triangulated into tetrahedra without adding new vertices. However, because it has Dehn invariant equal to zero, it is scissors-congruent to a cube, meaning that it can be sliced into smaller polyhedral pieces that can be rearranged to form a solid cube.
|
|
Another alternative built is the theory of stable ∞-categories. The homotopy category of a stable ∞-category is canonically triangulated, and moreover mapping cones become essentially unique (in a precise homotopical sense). Moreover, a stable ∞-category naturally encodes a whole hierarchy of compatibilities for its homotopy category, at the bottom of which sits the octahedral axiom. Thus, it is strictly stronger to give the data of a stable ∞-category than to give the data of a triangulation of its homotopy category.
|
|
The video from the six cameras is then triangulated and combined to create a three-dimensional representation of the ball's trajectory. Hawk-Eye is not infallible, but is accurate to within 3.6 millimetres and generally trusted as an impartial second opinion in sports. It has been accepted by governing bodies in tennis, cricket and association football as a means of adjudication. Hawk-Eye is used for the Challenge System since 2006 in tennis and Umpire Decision Review System in cricket since 2009.
|
|
Roman building ingenuity extended over bridges, aqueducts, and covered amphitheatres. Their sewerage and water-supply works were remarkable and some systems are still in operation today. The only aspect of Roman construction for which very little evidence survives is the form of timber roof structures, none of which seem to have survived intact. Possibly, triangulated roof trusses were built, this being the only conceivable way of constructing the immense spans achieved, the longest exceeding 30 metres (see List of ancient Greek and Roman roofs).
|
|
This was the first Bentley to dispense with a leaf-sprung front beam axle. It followed Rolls-Royce's lead from 1936 and instead used a new design of independent front suspension in its completely new chassis. Low rate open coil springs sat within pairs of triangulated wishbones holding the front wheels at their outer point. The upper wishbones acted on a piston-type hydraulic damper, the arms at the bottom were set wide apart so that the rearward one could act as a torque member under braking.
|
|
For example, in a dysfunctional family in which there is alcoholism present, the non-drinking parent will go to a child and express dissatisfaction with the drinking parent. This includes the child in the discussion of how to solve the problem of the alcoholic parent. Sometimes the child can engage in the relationship with the parent, filling the role of the third party, and thereby being "triangulated" into the relationship. Alternatively, the child may then go to the alcoholic parent, relaying what they were told.
|
|
After graduating from Yale University where he studied civil engineering, he went to work for the United States Coast Survey Service, and was in the expedition that first triangulated the entire coast. After retiring from the Service and subsequent to his 1832 marriage, he went into business on Wall Street, becoming a member of the firm, Christmas, Prime, Livingston, & Costa. The business failed 10 years later, and he retired to his country place near New Brunswick, New Jersey. In 1860, he returned to New York.
|
|
He took them to his secret lair and triangulated the last location of the stealth ship he had leased. The Green Arrow and the Black Canary then persuaded him to accompany them on the search, which brought them to a castle in Leichestershire, England. They evaded several traps and finally discovered a cryogenics tube containing the compressed form of former Justice Leaguer Plastic Man. Dodger continued to work alongside "Team Arrow" and fought a team of metahumans who claimed to represent the League of Assassins.
|
|
Three 12.50-metre-long, presumably triangulated trusses, "which were inserted into a ledge at the back of stone architecture, carried the slightly vaulted roof." All the fourteen columns are connected by a screening wall, with entrances in the eastern and western facades. This building represents an example of the unusual combination of wood and stone in the same architectural structure for an Egyptian temple. The attribution to Emperor Trajan is based on a carving inside the kiosk structure, depicting the emperor burning incense before Osiris and Isis.
|
|
An irregular volume in space can be approximated by an irregular triangulated surface, and irregular tetrahedral volume elements. In numerical analysis, complicated three-dimensional shapes are commonly broken down into, or approximated by, a polygonal mesh of irregular tetrahedra in the process of setting up the equations for finite element analysis especially in the numerical solution of partial differential equations. These methods have wide applications in practical applications in computational fluid dynamics, aerodynamics, electromagnetic fields, civil engineering, chemical engineering, naval architecture and engineering, and related fields.
|
|
Now given a polygon Q with n + 3 sides, again mark one of its sides as the base. If Q is triangulated, we can further mark one of the sides other than the base side. There are (n + 2)Cn + 1 such decorated triangulations. Then there is a simple bijection between these two kinds of decorated triangulations: We can either collapse the triangle in Q whose side is marked, or in reverse expand the oriented edge in P to a triangle and mark its new side.
|
|
Creating a papercraft raised relief map via a Digital Elevation Model (DEM) is a low cost alternative to many other methods. The method involves converting the DEM to a triangulated irregular network (TIN), unfolding the TIN, printing the unfolded TIN on paper, and assembling the printout into a physical 3D model. This method allows raised relief maps to be constructed without the need for specialized equipment or extensive training. The degree of realism and accuracy of the resulting maps is similar to that of layer stacking models.
|
|
The bike had a prototype sprung frame built under the Bentley and Draper patents. The frame as far back as the gearbox bracket was normal K. Behind this however is a triangulated tubular swinging fork assembly worked in a trunnion bearing. From the rear fork-ends two seta-stays were pivoted and connected to the sprung part of the frame below the saddle by a system of links and spindles incorporating two coil springs. Friction dampers were fitted to these links and there were also two more at the bottom pivots at the fork-ends.
|
|
Based on the need for three shapeshifters, Walter surmises that Newton is trying to use the same technology that he and William Bell had pioneered for crossing the universes, by placing three vibrational sources triangulated around the target. Walter begins to collect equipment to create interference with the vibrations to prevent the crossing. Another corpse is found, that of a bank manager that appears to have been killed by a shapeshifter. Realizing both men would have access to secured areas in their workplaces, they use these locations as two points on Netwon's triangle.
|
|
Experiments were made mixing lime with other materials to provide a hydraulic mortar, but there was still no equivalent of the Roman concrete. In England, France and the Dutch Republic, cut and gauged brickwork was used to provide detailed and ornate facades. The triangulated roof truss was introduced to England and used by Inigo Jones and Christopher Wren. Many tools have been made obsolete by modern technology, but the line gauge, plumb-line, the carpenter's square, the spirit level, and the drafting compass are still in regular use.
|
|
Spruance had no idea where the Japanese were until a radio transmission from Ozawa was triangulated at a point west of his task force on the night of the 18th. A radar-equipped Martin PBM Mariner patrol bomber discovered the 1st Mobile Fleet at 01:15 on 19 June, but its message was not received for another eight hours due to radio troubles. The early morning searches by the Americans were not successful, but the Japanese had been tracking them continuously since 01:00.Brown 2009, pp. 257–258; Polmar & Genda, I, pp.
|
|
In addition to hi-fi, Vereker worked on cars, boats, computers and lighting systems. He was an enthusiast for bicycle design, and assisted Brompton Bicycle, a start-up company making folding bicycles, with a £40,000 guarantee for its overdraft. Also passionate about sailing, he designed boats: working with boat manufacturer British Hunter, he developed a boat which he called the Windex 49. The prototype of his last venture, with a triangulated mast and a computer-controlled system of active water ballast, was launched on the day he died.
|
|
The Georgia Dome, built in 1992 on an oval plan, uses instead a triangulated pattern in a system patented as the "Tenstar Dome". The Millennium Dome was completed as the largest cable dome in the world with a diameter of 320 meters and uses a different system of membrane support, with cables extending down from the 12 masts that penetrate the membrane. The first cable dome to use rigid steel frame panels as roofing instead of a translucent membrane was begun for an athletic center in North Carolina in 1994.
|
|
The KAM theorem established that periodic orbits can follow complex trajectories; in particular, they may form braids that can be investigated using Floer homology. In one class of finite element methods, boundary-value problems for differential equations involving the Hodge-Laplace operator may need to be solved on topologically nontrivial domains, for example, in electromagnetic simulations. In these simulations, solution is aided by fixing the cohomology class of the solution based on the chosen boundary conditions and the homology of the domain. FEM domains can be triangulated, from which the simplicial homology can be calculated.
|
|
He dismantles his radio station and attaches it to his mother's old Jeep, creating a mobile transmitter so his position can't be triangulated. Pursued by the police and the FCC, Nora drives the Jeep around while Mark broadcasts. The harmonizer he uses to disguise his voice breaks, and with no time left to fix it, Mark decides to broadcast his final message as himself. They finally drive up to the crowd of protesting students, and Mark tells them that the world belongs to them and that they should make their own future.
|
|
The parallel location of the Bicol Volcanic Belt, or Philippine Fault Zone, to the Deep Philippine Trench practically contributed to the triangulated distribution of events with faults or volcanic abnormalities within the earthquake belts in the Bicol Region. It has been observed that the Bicol Volcanic Belt or Chain had a span of 240 km. from Camarines Norte in the North down to Sorsogon in the South with a total of 16 volcanoes separately spread over by about 24 km. apart and rested parallel along the 200 km.
|
|
One of these remotes is at the TIS, and is referred to as the "remote at Master". Each remote interrogates an AIS pod (see below) loaded on each aircraft flying on range, and receives the response and relays it to the TIS. ; Airborne Instrumentation : Antiquated ACMI systems triangulated each pod's position and relayed that TSPI back to the CCS. Modern ACMI systems no longer triangulate; instead, a GPS unit is installed in each Airborne Instrumentation Subsystem (AIS) pod to calculate its own position, thereby relieving the CCS of the triangulation algorithm.
|
|
Singular homology is a related theory which is better adapted to theory rather than computation. Singular homology is defined for all topological spaces and obviously depends only on the topology, not any triangulation; and it agrees with simplicial homology for spaces which can be triangulated. Nonetheless, because it is possible to compute the simplicial homology of a simplicial complex automatically and efficiently, simplicial homology has become important for application to real-life situations, such as image analysis, medical imaging, and data analysis in general. Another related theory is Cellular homology.
|
|
Suppose that, instead of an n-1-dimensional simplex, we have a d-dimensional polytope with n vertices. Then there are at least n-d fully labeled simplices, where "fully labeled" indicates that every label on the simplex has a different color. For example, if a (two-dimensional) polygon with n vertices is triangulated and colored according to the Sperner criterion, then there are at least n-2 fully labeled triangles. The general statement was conjectured by Atanassov in 1996, who proved it for the case d=2.
|
|
Ravenel's conjectures exerted influence on the field through the founding of the approach of chromatic homotopy theory. The first of the seven conjectures, then the nilpotence conjecture, is now the nilpotence theorem. The telescope conjecture, which was #4 on the original list, remains of substantial interest because of its connection with the convergence of an Adams–Novikov spectral sequence. While opinion is against the truth of the original statement, investigations of associated phenomena (for a triangulated category in general) have become a research area in its own right.
|
|
An operator then relayed this information to the bomber crew over voice channels, and indicated when to drop the bombs. The British introduced similar systems, notably the Oboe system. This used two stations in England that operated on different frequencies and allowed the aircraft to be triangulated in space. To ease pilot workload only one of these was used for navigation – prior to the mission a circle was drawn over the target from one of the stations, and the aircraft was directed to fly along this circle on instructions from the ground operator.
|
|
By 17:50 several land-based radio stations had triangulated Flight 19's position as being within a radius of ; Flight 19 was north of the Bahamas and well off the coast of central Florida, but nobody transmitted this information on an open, repetitive basis. At 18:04, Taylor radioed to his flight "Holding 270, we didn't fly far enough east, we may as well just turn around and fly east again". By that time, the weather had deteriorated even more and the sun had since set. Around 18:20, Taylor's last message was received.
|
|
The fixed landing gear has twin wheels on each of the three vertical shock absorber-equipped struts. The main leading gear units are mounted on triangulated tubular structures, while the nose gear is bracketed to the cockpit bulkhead via a watertight seal in the planing bottom. The main wheels have hydraulic brakes operated from the pedals, complete with a parking hand brake, while the nose unit is fully castoring. The nose, which is covered by large glazed panels, has a bow chine and planing bottom built as a unit with the flight deck, which is higher than the main cabin floor.
|
|
A linear time algorithm is known to report all directions in which a given simple polygon is monotone.. It was generalized to report all ways to decompose a simple polygon into two monotone chains (possibly monotone in different directions.). Point in polygon queries with respect to a monotone polygon may be answered in logarithmic time after linear time preprocessing (to find the leftmost and rightmost vertices). A monotone polygon may be easily triangulated in linear time. For a given set of points in the plane, a bitonic tour is a monotone polygon that connects the points.
|
|
The car was a classic Chapman design, being extremely light and simple; the body was made up of lightweight panels bolted to heavily- triangulated tube frameSetright, L.J.K., "Lotus: The Golden Mean", in Northey, Tom, ed. World of Automobiles (London: Orbis, 1974), Volume 11, p.1228. (almost spaceframe) chassis. Thus the car was rigid, strong and light, maintaining the 16's forward weight distribution despite the engine moving behind the driver. It was powered initially by a 2,467 cc Coventry Climax FPF (3.70" x 3.50") four cylinder DOHC engine inherited from the Grand Prix version of Lotus 16.
|
|
This triangulated fork causes the front end of a motorcycle to rise slightly when braking hard, as the mechanical braking forces rotate 'downward' relative to the fork's pivot point. This action can be disconcerting to riders used to telescopic forks, which have the opposite reaction to braking forces ('brake dive'). Several motorcycle manufacturers licensed the Earles patent forks for racing motorcycles in 1953, such as MV Agusta and BMW Motorcycle, while other companies (such as Douglas motorcycle) used the Earles design on their roadsters or off-road machines. BMW used Earles forks on all their motorcycles between 1955 and 1968.
|
|
The company is responsible for the design of the coupe version's roof structure and gullwing doors (available as from 2014). The vehicle will feature an aluminium-hybrid body mounted onto a fully triangulated, jig welded roundtube spaceframe chassis to maximize strength and minimizing weight while still keeping production costs reasonable. Power will come from a specially tuned, 6.162 litre/376 cui LS3 Corvette engine delivering in "GT" trim and in "GTA" trim, which is said to meet emissions standards across Europe and in North America, which will be the MK VI's primary markets. Also featured are powerful, 6-piston (front) resp.
|
|
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.
|
|
It was one of the first hotels to have its ballroom and conference rooms located on lower floors, and a heliport was located on the roof to shuttle guests from nearby airports. The outdoor patio located above street level along St. Paul Street contained a large rotating sculpture by José de Rivera. "A Wishing Star," 12 feet high and 15 feet across, was made of triangulated arms whose undersides were stainless steel and top goldplated.The Dallas Morning News, "Mr deRivera to Supervise Installations", January 12, 1956 The Statler played an important role establishing Dallas as a business center for the Southwest.
|
|
A standard scenario in many computer applications is a collection of points (measurements, dark pixels in a bit map, etc.) in which one wishes to find a topological feature. Homology can serve as a qualitative tool to search for such a feature, since it is readily computable from combinatorial data such as a simplicial complex. However, the data points have to first be triangulated, meaning one replaces the data with a simplicial complex approximation. Computation of persistent homology involves analysis of homology at different resolutions, registering homology classes (holes) that persist as the resolution is changed.
|
|
If there is one intersected side, the square becomes three triangles by adding the long diagonals connecting the intersection with opposite corners. If there are four intersected sides, we split the square in half by adding an edge between two of the four intersections, and then connect these two endpoints to the remaining two intersection points. For the other squares, we introduce a point in the middle and connect it to all four corners of the square as well as each intersection point. At the end of it all, we have a nice triangulated mesh of our point set built from a quadtree.
|
|
The main function of the lower girder is to act as a tie; this counteracts the side-forces of the arch, avoiding the arch's usual side-forces on its foundations. As this is a railway bridge, where suspended deck bridges are a problem owing to swaying of their deck, this girder also has a stiffening function. Brunel used a form of his balloon flange girder for both girders. The upper arch girder uses the triangulated form of the early experiment, with a flat top plate and without any vertical web below the flange box at all.
|
|
In 1986, commercial rapid prototyping was started by Hull when he founded 3D Systems in Valencia, California. Hull realized that his concept was not limited to liquids and therefore gave it the generic name “stereolithography” (3D printing),History of 3D and filed broad patent claims covering any “material capable of solidification” or “material capable of altering its physical state.” Hull built up a patent portfolio covering many fundamental aspects of today's additive manufacturing technologies such as data preparation via triangulated models (STL file format) and slicing, and exposure strategies such as alternating hatch directions. Microsoft Word – LANE-2004-EOS-DMLS.
|
|
The problem of minimum weight triangulation of a point set was posed by , who suggested its application to the construction of triangulated irregular network models of land countours, and used a greedy heuristic to approximate it. conjectured that the minimum weight triangulation always coincided with the Delaunay triangulation, but this was quickly disproved by , and indeed showed that the weights of the two triangulations can differ by a linear factor.See also . The minimum-weight triangulation problem became notorious when included it in a list of open problems in their book on NP-completeness, and many subsequent authors published partial results on it.
|
|
Aerial view of Esplanade – Theatres on the Bay Aluminium sunshades ornament the roof of the Esplanade. The building was designed by two architectural firms working in conjunction: by DP Architects (DPA) of Singapore and the London-based Michael Wilford & Partners (MWP), although the latter left the project in May 1995. The design consists of two rounded space frames fitted with triangulated glass elements and sunshades, which balance outward views with solar shading. The original design, presented to the public in 1994, consisted of unadorned glass cases over the theatres, and initially elicited criticisms from the public, including calling it "two copulating aardvarks".
|
|
Exact thresholds are only known for certain two-dimensional lattices that can be broken up into a self-dual array, such that under a triangle-triangle transformation, the system remains the same. Studies using numerical methods have led to numerous improvements in algorithms and several theoretical discoveries. Simply duality in two dimensions implies that all fully triangulated lattices (e.g., the triangular, union jack, cross dual, martini dual and asanoha or 3-12 dual, and the Delaunay triangulation) all have site thresholds of 1/2, and self-dual lattices (square, martini-B) have bond thresholds of 1/2.
|
|
Scott started making boat engines in 1900. He patented his first engine in 1904 (Patent GB 3367 of 1904) and started motorcycle production in 1908 with a vertical two-stroke 450 cc twin, with patented triangulated frame, chain drive, neutral-finder, kick starter (Patent GB 27667 of 1908), and two-speed gearbox. His patented two-stroke engine designs are still the basis of modern two-stroke engines and features such as the first kick start, monoshock suspension, efficient radiators, rotary inlet valves, drip-feed lubricators and centrestands continue to this day. He formed The Scott Motorcycle Company in 1908.
|
|
Pairs of doors under large suspended, tiered awnings provide entry to the church either side of the eastern wall. The eastern wall is of a folded triangular form with bricks laid on the diagonal, housed within a triangulated band of perimeter windows and decorated with a diamond shaped leadlight window with a burning tree motif. The western wall houses sash windows to the kitchen and sanctuary and is clad in timber cabin mould chamfer boards. The steeply pitched roof of the building is clad in ribbed aluminium sheeting with three dormer windows on the north and south sides between the trusses.
|
|
Snelson's unique sculpture style is well articulated in Needle Tower. The structure style displayed is known as "tensegrity," a description given by Snelson's former professor Buckminster Fuller to the melding of tension and structural integrity. According to Snelson: > Tensegrity describes a closed structural system composed of a set of three > or more elongate compression struts within a network of tension tendons, the > combined parts mutually supportive in such a way that the struts do not > touch one another, but press outwardly against nodal points in the tension > network to form a firm, triangulated, prestressed, tension and compression > unit.
|
|
The basic theory of Verdier was written down in his dissertation, published finally in 1996 in Astérisque (a summary had earlier appeared in SGA 4½). The axiomatics required an innovation, the concept of triangulated category, and the construction is based on localization of a category, a generalization of localization of a ring. The original impulse to develop the "derived" formalism came from the need to find a suitable formulation of Grothendieck's coherent duality theory. Derived categories have since become indispensable also outside of algebraic geometry, for example in the formulation of the theory of D-modules and microlocal analysis.
|
|
In 1554 he studied medicine in Bologna and went to Milan the same year to listen to lectures by Girolamo Cardano, but he soon returned to Prague, where he became a professor of mathematics at the Charles University of Prague in 1555. He published the Aphorismi Metoposcopici in 1561, dealing with divination and diagnosis by interpreting lines on the forehead. He triangulated the area around Prague and co-authored a map of it in 1563; the map is unfortunately lost now. In 1564 he received the Emperor's privilege stating that no astrological prognostication could be printed in Prague before he had seen and approved it.
|
|
In the Rocket Launch Spotter (RLS) application, each array consists of four microphones and processing equipment. Analyzing the time delays between an acoustic wavefront’s interaction with each microphone in the array UTAMS provides an azimuth of origin. The azimuth from each tower is reported to the UTAMS processor at the control station, and a POO is triangulated and displayed. The UTAMS subsystem can also detect and locate the point of impact (POI), but, due to the difference between the speeds of sound and light, it may take UTAMS as long as 30 seconds to determine the POO for a rocket launch 13 km away.
|
|
Analyzing the time delays between an acoustic wavefront's interaction with each microphone in the array UTAMS provides an azimuth of origin. The azimuth from each tower is reported to the UTAMS processor at the control station, and a POO is triangulated and displayed. The UTAMS subsystem can also detect and locate the point of impact (POI), but, due to the difference between the speeds of sound and light, it may take UTAMS as long as 30 seconds to determine the POO for a rocket launch 13 km away. This means UTAMS may detect a rocket POI prior to the POO, providing very little if any warning time.
|
|
Lambton also ordered an altitude and azimuth circle with a theodolite. The equipment arrived in 1801. Although a baseline was measured in Bangalore between October and December 1800, this appears to have been rejected (it was not connected to the triangulations) and another baseline was made in 1804 (using better equipment and on better terrain) to compare with the Madras baseline whose measurement began on 10 April 1802 from St. Thomas Mount and was completed with seven and a half miles measured by 22 May 1802. They then triangulated their way to Bangalore where the 1804 baseline was measured by John Warren to check the survey accuracy.
|
|
Location of radio-tagged animals by triangulation is a widely applied research technique for studying the movement of animals. The technique was first used in the early 1960s, when the technology used in radio transmitters and batteries made them small enough to attach to wild animals, and is now widely deployed for a variety of wildlife studies. Most tracking of wild animals that have been affixed with radio transmitter equipment is done by a field researcher using a handheld radio direction finding device. When the researcher wants to locate a particular animal, the location of the animal can be triangulated by determining the direction to the transmitter from several locations.
|
|
Eric Lengyel is a computer scientist specializing in game engine development, computer graphics, and geometric algebra. He holds a Ph.D. in Computer Science from the University of California, Davis and a master's degree in Mathematics from Virginia Tech. Lengyel is an expert in font rendering technology for 3D applications and is the inventor of the Slug font rendering algorithm, which allows glyphs to be rendered directly from outline data on the GPU with full resolution independence. Lengyel is also the inventor of the Transvoxel algorithm, which is used to seamlessly join multiresolution voxel data at boundaries between different levels of detail that have been triangulated with the Marching cubes algorithm.
|
|
The Jiri plain is an area of gravel plain extending across areas of Southern Ras Al Khaimah, Eastern Sharjah and Western Fujairah, United Arab Emirates (UAE). The area, some 15 miles in length and 8 miles in breadth, is triangulated with the villages of Khatt and Habhab to the North; Adhen to the East and Dhaid to the South. To the West the plain is enclosed by sand dunes. The soil of the Jiri plain is darkened by debris brought down by seasonal waters from the mountains, which helps to define its rich, loamy character and high carbonate content (from the outwash of Cretaceous limestone).
|
|
Putting these together, the octahedral axiom asserts the "third isomorphism theorem": :(Z/X)/(Y/X)\cong Z/Y. If the triangulated category is the derived category D(A) of an abelian category A, and X, Y, Z are objects of A viewed as complexes concentrated in degree 0, and the maps X\to Y and Y\to Z are monomorphisms in A, then the cones of these morphisms in D(A) are actually isomorphic to the quotients above in A. Finally, formulates the octahedral axiom using a two-dimensional commutative diagram with 4 rows and 4 columns. also give generalizations of the octahedral axiom.
|
|
Command-Aire 3C3 msn 513 NC6688, showing salient characteristics, including the triangulated cabane that was simplified on later models The Command-Aire did not at first appear to offer much of an advancement over the vast multitude of three seat biplanes built around the ubiquitous Curtiss OX-5 engine to similar designs, with similar dimensions and construction methods, many of which were already in production. Indeed, the OX-5 era was coming to an end. The vast quantities of war-surplus engines, which had swamped the market in the immediate post-war period, were running low. Only by the smaller details can it be distinguished from its brethren.
|
|
From that time he began to specialise in surveying, and served on the North Borneo Boundary Commission in 1901, helping in the construction of several maps and the definition of boundaries. His most important position was in command of a destroyer, which he permitted to collide with a liberty boat, resulting in his being posted to dockside watch- keeping jobs.Military History, December 2001, "Naval Struggle in Darkest Africa" He then went to China and made the first triangulated survey of the Yangtze River from 1905–1908. After China, he was posted to Africa, and from 1911-1914 was in command of a survey ship on the Gambia river.
|
|
A grizzled prospector arrives in a pristine mountain valley and decides to dig for gold in a grassy meadow beside a river. Over the course of several days, he pans through shovelfuls of dirt to count the gold specks, and then begins digging a deeper hole once he has triangulated the likely source. After his first night camping at the site, he spots a great horned owl tending its treetop nest at the edge of the valley. When he climbs up and reaches the nest, the mother owl's watchful gaze from a nearby tree causes him to replace three of the four eggs he had taken for his breakfast.
|
|
Alfred Scott's first motorcycle was developed from his own twin- cylinder engine design which he hand built and fitted to the steering head of a bicycle. These engines were used to power equipment such as lathes and light machinery and Scott had been involved in the manufacture of 'Premier' pedal cycles. He developed this prototype into a motorcycle and six were produced under contract by friends with a car company called Jowett in Bradford. Scott patented an early form of caliper brakes in 1897 (Patent GB 1626 of 1897), designed a fully triangulated frame, rotary induction valves, and used unit construction for his motorcycle engine.
|
|
The correspondence problem, finding matches between two images so the position of the matched elements can then be triangulated in 3D space is the key issue here. Once you have the multiple depth maps you have to combine them to create a final mesh by calculating depth and projecting out of the camera – registration. Camera calibration will be used to identify where the many meshes created by depth maps can be combined together to develop a larger one, providing more than one view for observation. By the stage of Material Application you have a complete 3D mesh, which may be the final goal, but usually you will want to apply the color from the original photographs to the mesh.
|
|
Then there is the nature of transitions between points: are they abrupt or gradual. Finally, there is whether a method is global (it uses the entire data set to form the model), or local where an algorithm is repeated for a small section of terrain. Interpolation is a justified measurement because of a spatial autocorrelation principle that recognizes that data collected at any position will have a great similarity to, or influence of those locations within its immediate vicinity. Digital elevation models, triangulated irregular networks, edge-finding algorithms, Thiessen polygons, Fourier analysis, (weighted) moving averages, inverse distance weighting, kriging, spline, and trend surface analysis are all mathematical methods to produce interpolative data.
|
|
Generally three conductors are required per AC 3-phase circuit, although single-phase and DC circuits are also carried on towers. Conductors may be arranged in one plane, or by use of several cross-arms may be arranged in a roughly symmetrical, triangulated pattern to balance the impedances of all three phases. If more than one circuit is required to be carried and the width of the line right-of-way does not permit multiple towers to be used, two or three circuits can be carried on the same tower using several levels of cross-arms. Often multiple circuits are the same voltage, but mixed voltages can be found on some structures.
|
|
Concrete truss bridges are rarely constructed, and few exist. The vertical web of the beam was a series of triangulated concrete diagonal struts along the centerline, and the diagonal angles of the struts varied across the bridge so they would align with pipes from the center pylon, in the eventual faux cable-stayed appearance. The concrete walkway deck was to act as the horizontal bottom flange of a wide I-beam, and the concrete roof canopy was to function as the horizontal top flange of the I-beam. The walkway was thus nearer to ground level than in a standard design where the walkway is placed on top of the structural support system.
|
|
The work of the Cassinis left its mark on the world; toponyms known as "Cassini signs" still exist, revealing where triangulated measurements at that time were made. Hand- drawn map of one side of the Valley of Vesdre by French geographers (led by the Cassini family) from 1745 to 1748 The "map of Cassini" or "map of the Academy" is the first general map of the kingdom of France. It was drawn up by the Cassini family—primarily César-François Cassini de Thury (Cassini III) and his son Jean-Dominique Cassini (Cassini IV)—during the 18th century. The adopted scale is one ligne to 100 toises, or 1:86,400 (the measuring apparatus contained 864 lines).
|
|
The Schönhardt polyhedron is combinatorially equivalent to the regular octahedron: its vertices, edges, and faces can be placed in one-to-one correspondence with the features of a regular octahedron. However, unlike the regular octahedron, three of its edges have concave dihedral angles, and these three edges form a perfect matching of the graph of the octahedron; this fact is sufficient to show that it cannot be triangulated. The six vertices of the Schönhardt polyhedron can be used to form fifteen unordered pairs of vertices. Twelve of these fifteen pairs form edges of the polyhedron: there are six edges in the two equilateral triangle faces, and six edges connecting the two triangles.
|
|
GSI3D utilises a digital elevation model, surface geological linework and downhole borehole and geophysical data to enable the geologist to construct cross sections by correlating boreholes and the outcrops to produce a geological fence diagram. Mathematical interpolation between the nodes along the drawn sections and the limits of the units produces a solid model comprising a stack of triangulated objects each corresponding to one of the geological units present. Scientists draw their sections based on facts such as borehole logs correlated by intuition – the shape 'looks right' to a geologist. This 'looks right' element pulls on the geologists' wealth of understanding of earth processes, examination of exposures and theoretical knowledge gathered over a career in geology.
|
|
During 1949–1951 he held an appointment at the Institute for Advanced Study during which he proved Moise's theorem that every 3-manifold can be triangulated in an essentially unique way. Moise joined the School Mathematics Study Group when it started in 1958, as a member of the geometry writing team. The team produced several course outlines and sample pages for a 10th grade geometry course, and then Moise and Floyd L. Downs wrote a geometry textbook, based on the team's approach, that was published in 1964. The textbook used metric postulates instead of Euclid's postulates, a controversial approach supported by some mathematicians such as Saunders Mac Lane but opposed by others such as Alexander Wittenberg and Morris Kline.
|
|
On a 1923 trip Shoemaker triangulated the locations of several peaks, which led to the first map of the high country. The first major protective action for the Mission Range came on October 21, 1931 when 67,000 acres of land along the east side of the Mission Divide were classified as the Mission Mountains Primitive Area. The Great Pacific Railway Company owned 30 percent of this land at the time of the classification, which was exchanged over the course of years for other land in the Flathead National Forest. Further stories about the Mission Mountains and the surrounding area can be found in the local books, In the Shadows of the Missions and Indian Trails and Grizzly Tales.
|
|
A generalization of Sperner's lemma to polytopes guarantees that, if this polytope is triangulated and labeled in an appropriate manner, there are at least n − d sub-simplices with a full labeling; each of these simplices corresponds to an (approximate) envy-free allocation in which each partner receives a different combination of pieces. However, the combinations might overlap: one partner might get the "morning" and "evening" shifts while another partner might get "evening" and "evening". Although these are different selections, they are incompatible. section 4 of proves that an envy-free division to two partners with disjoint pieces might be impossible if m = k = 2, but is always possible if m = 2 and k = 3 (i.e.
|
|
This Soviet deployment in the Pacific was analysed by U.S. intelligence as likely a reaction to a submarine loss. U.S. SOSUS Naval Facilities (NAVFACs) in the North Pacific were alerted and requested to review acoustic records on 8 March 1968 to identify any possible anomalous signal. Acoustic data from four AFTAC sites and the Adak, Alaska SOSUS array triangulated a potential event location to within 5 nautical miles, a site hundreds of miles away from where the Soviet Navy had been searching. Several SOSUS arrays recorded a possibly related event on 8 March 1968, and upon examination produced sufficient triangulation by lines-of-bearing to provide the U.S. Navy with a locus for the probable wreck site.
|
|
Start with a UV parametric point in a freeform surface, calculate the xyz point and the normal, and offset from the point along the normal in a way consistent with the tool definition so that the cutter is now tangent to the surface at that point. Problems: may collide or gouge with the model elsewhere, and there is no way to tell this is happening except with a full implementation of the triangulated approach. Most published academics believe this is the way to find cutter locations, and that the problem of collisions away from the point of contact is soluble. However, nothing printed so far comes close to handling real world cases.
|
|
Other examples of ribbed domes made entirely of reinforced concrete include the Methodist Hall in Westminster, London, the Augsburg Synagogue, and the Orpheum Theater in Bochum. The 1928 Leipzig Market Hall by Deschinger and Ritter featured two 82 meter wide domes. The thin domical shell was further developed with the construction of two domes in Jena, Germany in the early 1920s. To build a rigid planetarium dome, Walther Bauersfeld constructed a triangulated frame of light steel bars and mesh with a domed formwork suspended below it. By spraying a thin layer of concrete onto both the formwork and the frame, he created a 16 meter wide dome that was just 30 millimeters thick. The second dome was still thinner at 40 meters wide and 60 millimeters thick.
|
|
These surveys were started in the 1870s by John Spence Browning, the Chief Surveyor for Nelson. From this 360-degree viewpoint, survey marks in neighbouring regions (including Wellington in the North Island) could be triangulated and the local surveys connected. In 1962, Dr Ian Reilly from the now defunct Department of Scientific and Industrial Research calculated the geographic centre of New Zealand (including Stewart Island and some smaller islands in addition to the North and South Island, but excluding the Chathams) to be in a forest in Spooners Range southwest of Nelson at . Owing to the coarse nature of the underlying data (use of rectangular areas of 7.5 minutes of arc on each side), the centre calculated by Dr Reilly has quite large error margins.
|
|
The proof goes as follows: First, the polygon is triangulated (without adding extra vertices). The vertices of the resulting triangulation graph may be 3-colored.To prove 3-colorability of polygon triangulations, we observe that the weak dual graph to the triangulation (the undirected graph having one vertex per triangle and one edge per pair of adjacent triangles) is a tree, since any cycle in the dual graph would form the boundary of a hole in the polygon, contrary to the assumption that it has no holes. Whenever there is more than one triangle, the dual graph (like any tree) must have a vertex with only one neighbor, corresponding to a triangle that is adjacent to other triangles along only one of its sides.
|
|
In homological algebra in mathematics, the homotopy category K(A) of chain complexes in an additive category A is a framework for working with chain homotopies and homotopy equivalences. It lies intermediate between the category of chain complexes Kom(A) of A and the derived category D(A) of A when A is abelian; unlike the former it is a triangulated category, and unlike the latter its formation does not require that A is abelian. Philosophically, while D(A) makes isomorphisms of any maps of complexes that are quasi- isomorphisms in Kom(A), K(A) does so only for those that are quasi- isomorphisms for a "good reason", namely actually having an inverse up to homotopy equivalence. Thus, K(A) is more understandable than D(A).
|
|
Tribosphenid mammals were originally grouped on the basis of triangular or V-shaped (tribosphenic) molars. Since then, other unrelated mammal groups have been found to have tribosphenic molars, such as the australosphenidans (a group that includes the still extant monotremes), suggesting that as a synapomorphy this is fundamentally useless as it evolved multiple times among mammals. However, a clade between the aforementioned groups, the "true Tribosphenida" or Boreosphenida, is still identifiable, united by characteristics such as the lack of a mesial cingulid and of a triangulated trigonid on the last premolar. They are also united by postcranial features such as the presence of a modern ear (though this too has evolved independently in many other groups, like monotremes), modern shoulder blades, and several features of the hindlimb.
|
|
Boreosphenida (from boreas, "northern wind" and sphen, "wedge") were early mammals that originated in the Northern Hemisphere and had tribosphenic molars (three-cusped cheek teeth). In boreosphenidans, the mandibular angle is placed posteriorly and the primitive postdentary trough (hole in the mandible) is absent (in contrast to Kuehneotheriidae, Eupantotheria, and Australosphenida.) They share the tribosphenic molars with the Australosphenida but differ from them by having cingulid cuspules but lacking a continuous mesial cingulid. Boreosphenidans also lack the triangulated trigonid on the last premolar found in Early Cretaceous mammals. They differ from Shuotherium (a monotreme- relative) in having the talonid placed posterior to the trigonid (like in modern tribosphenic mammals) in the lower molars, but upper molars similar to those of Shuotherium.
|
|
The sound's source was roughly triangulated to , a remote point in the south Pacific Ocean west of the southern tip of South America. The sound was detected by the Equatorial Pacific Ocean autonomous hydrophone array, a system of hydrophones primarily used to monitor undersea seismicity, ice noise, and marine mammal population and migration. This is a stand-alone system designed and built by NOAA's Pacific Marine Environmental Laboratory (PMEL) to augment NOAA's use of the U.S. Navy Sound Surveillance System (SOSUS), which was equipment originally designed to detect Soviet submarines. According to the NOAA description, the sound "rose" in frequency over about one minute and was of sufficient amplitude to be heard on multiple sensors, at a range of over .
|
|
In terms of armament, the early CR.42s were outfitted with a single 7.7 mm and one 12.7 mm Breda-SAFAT machine gun, which was installed in the decking of the upper fuselage and fired directly through the propeller. As per Italian tradition, a counter for the rounds fired was present amongst the cockpit's instrumentation. The fuselage of the CR.42 was composed of a welded steel-tube triangulated framework built of light-alloy formers; while the forward fuselage was covered by metal panelling, fabric covered the exterior rear of the cockpit. The rigidly-braced wings used a structure that was constructed mainly of light duralumin alloys and steel; the leading edge was metal-skinned while the rest of the wing's exterior was covered with fabric.
|
|
Road Town Fort formed part of a formidable defensive network of forts around Road Town erected at this time. Road Town itself was triangulated with Fort Burt in the western entrance to the harbour, Fort George at the eastern entrance, Road Town Fort in the middle above the main jetty, and Fort Charlotte set high above on Harrigan's Hill. Some of the original walls remain visible from Main Street below. It is possible that the Road Town Fort was built on the remains of an earlier Dutch stockade; it is known that two forts erected by the British in Road Town were built on what were thought (by them) to be earlier Dutch sites, but they are believed to be Fort Burt and Fort George.
|
|
Aston Martin Virage engine bay Interior When compared to the preceding V8, the design was fresh and more modern. The Virage was more similar in design language to the Lagonda than the V8 it replaced. Indeed, the chassis was an evolution of the Lagonda's, with a de Dion tube rear suspension, located by triangulated radius rods and a Watts linkage, and a double wishbone unit at the front. To cut costs, many of the less-important pieces came from other companies, as had been the case for Aston Martin automobiles of the past. The sleek headlights and taillights were sourced from the Audi 200 and the Volkswagen Scirocco respectively, while General Motors, Jaguar, and Ford provided the steering column, climate control panel, wing mirrors and dash switches.
|
|
In order to calculate its location relative to a triangulated surface, the position of a horizontal torus on the Z-axis must be found where it is tangent to a fixed line, and this requires the solution of a general quartic equation to be calculated. Over 10% of the computational time in a CAM system can be consumed simply calculating the solution to millions of quartic equations. A program demonstrating various analytic solutions to the quartic was provided in Graphics Gems Book V. However, none of the three algorithms implemented are unconditionally stable. In an updated version of the paper, which compares the 3 algorithms from the original paper and 2 others, it is demonstrated that computationally stable solutions exist only for 4 of the possible 16 sign combinations of the quartic coefficients.
|
|
Domes built in the 19th, 20th, and 21st centuries benefited from more efficient techniques for producing iron and steel as well as advances in structural analysis. Metal-framed domes of the 19th century often imitated earlier masonry dome designs in a variety of styles, especially in church architecture, but were also used to create glass domes over shopping arcades and hothouses, domes over locomotive sheds and exhibition halls, and domes larger than any others in the world. The variety of domed buildings, such as parliaments and capitol buildings, gasometers, observatories, libraries, and churches, were enabled by the use of reinforced concrete ribs, lightweight papier-mâché, and triangulated framing. In the 20th century, planetarium domes spurred the invention by Walther Bauersfeld of both thin shells of reinforced concrete and geodesic domes.
|
|
The four-man party was composed of Lawrence A. Warner, leader and geologist, Charles F. Passel, geologist and radio operator, Harold P. Gilmour "Gil", recorder and collector of biological specimens and Loran Wells "Joe", photographer and observer. The extensive Warpasgiljo Glacier was discovered and named for these four members (WARner + PASsel + GILmour + JOe) of the Geological Party Expedition. The Geological Party's Expedition mapped and geologically surveyed most of the southern portion of the Edsel Ford Range, and also investigated the different natural resources of the area. They also triangulated and measured accurately to help create improved maps of the region. The four-man Geological Party Expedition left the West Base on 17 October 1940 and returned 82 days later on 7 January 1941 traveling a total of 691 nautical miles on board their dog sleds.
|
|
On the C3-225, an additional removable fuel tank was added in the fuselage, and the wing tank acted as a header tank. The prototype had a conventional undercarriage similar to those used on most World War One aircraft, with a pair of vees braced from the lower longerons, connected with a spreader bar and suspension provided by bungee cords. This was replaced with a split axle undercarriage on the C3-1 and C3-2, which had the legs braced to the opposite lower longerons. From the C3-3 onwards, each undercarriage leg was triangulated with two struts braced to a central keel in the bottom of the fuselage, and one oleo strut on each side to the upper longeron, providing a greater range of movement and reducing camber changes.
|
|
In 1929, the Monospar Company Ltd was formed to pursue new techniques of designing cantilever wings, based on the work of Swiss engineer Helmuth J. Stieger, who headed the company. Helmuth John Stieger was born in Zurich in 1902 and educated at the Swiss Federal Polytechnic then the Imperial College of Science in London. While working as a designer for William Beardmore and Company, he formed his own ideas about wing design and evolved an improved method of building and stressing wings for which he was later granted a British Patent in December 1927. The principle behind this Patent No. 306,220 was that the wing needed only one spar with torsion loads resisted by an efficient system of strong compression struts with triangulated bracing in the form of thin wires.
|
|
In mathematics, a normal surface is a surface inside a triangulated 3-manifold that intersects each tetrahedron so that each component of intersection is a triangle or a quad (see figure). A triangle cuts off a vertex of the tetrahedron while a quad separates pairs of vertices. A normal surface may have many components of intersection, called normal disks, with one tetrahedron, but no two normal disks can be quads that separate different pairs of vertices since that would lead to the surface self-intersecting. A normal surface intersects a tetrahedron in (possibly many) triangles (see above left) and quads (see above right) Dually, a normal surface can be considered to be a surface that intersects each handle of a given handle structure on the 3-manifold in a prescribed manner similar to the above.
|
|
Jaguar C-Type frame In a (tubular) spaceframe chassis, the suspension, engine, and body panels are attached to a three-dimensional skeletal frame of tubes, and the body panels have little or no structural function. To maximize rigidity and minimize weight, the design makes maximum use of triangles, and all the forces in each strut are either tensile or compressive, never bending, so they can be kept as thin as possible. The first true spaceframe chassis were produced in the 1930s by Buckminster Fuller and William Bushnell Stout (the Dymaxion and the Stout Scarab) who understood the theory of the true spaceframe from either architecture or aircraft design. The 1951 Jaguar C-Type racing sports car that won the Le Mans 24 hours twice, had a lightweight, multi-tubular, triangulated frame, over which an aerodynamic aluminum body was crafted.
|
|
The sound's source was roughly triangulated to a remote point in the south Pacific Ocean west of the southern tip of South America, and the sound was detected several times by the Equatorial Pacific Ocean autonomous hydrophone array. According to the NOAA description, it "rises rapidly in frequency over about one minute and was of sufficient amplitude to be heard on multiple sensors, at a range of over ." The NOAA's Dr. Christopher Fox did not believe its origin was man-made, such as a submarine or bomb, nor familiar geological events such as volcanoes or earthquakes. While the audio profile of Bloop does resemble that of a living creature, the source was a mystery both because it was different from known sounds and because it was several times louder than the loudest recorded animal, the blue whale.
|
|
Kimmel's interest in recent years has been non-rigid shape processing and analysis, medical imaging, computational biometry, deep learning, numerical optimization of problems with a geometric flavor, and applications of metric and differential geometry. Kimmel is an author of two books, an editor of one, and an author of numerous articles. He is the founder of the Geometric Image Processing Lab , and a founder and advisor of several successful image processing and analysis companies. Kimmel's contributions include the development of fast marching methods for triangulated manifolds (together with James Sethian), the geodesic active contours algorithm for image segmentation, a geometric framework for image filtering (named Beltrami flow after the Italian mathematician Eugenio Beltrami), and the Generalized Multidimensional Scaling (together with his students the Bronstein brothers) with which he was able to compute the Gromov- Hausdorff distance between surfaces.
|
|
Arriving at the scene he meets with local investigators and FBI Special Agent Paul Pryzwarra (Val Kilmer), and informs them of his findings. He learns about and is invited to examine a partially burned body pulled from the river, identified as Claire Kuchever (Paula Patton), which was reported to the authorities minutes before the explosion. Pryzwarra is impressed with Doug's detective expertise, and asks him to join a newly formed governmental detective unit whose first case is to investigate the bombing. Led by Dr Alexander Denny (Adam Goldberg), they investigate the events before the explosion by using a program called "Snow White", which enables them to look into the past (4 days, 6 hours, 3 minutes, 45 seconds, 14.5 nanoseconds) in detail by (according to Pryzwarra) using several satellites to form a triangulated image of events.
|
|
In homological algebra, the mapping cone is a construction on a map of chain complexes inspired by the analogous construction in topology. In the theory of triangulated categories it is a kind of combined kernel and cokernel: if the chain complexes take their terms in an abelian category, so that we can talk about cohomology, then the cone of a map f being acyclic means that the map is a quasi-isomorphism; if we pass to the derived category of complexes, this means that f is an isomorphism there, which recalls the familiar property of maps of groups, modules over a ring, or elements of an arbitrary abelian category that if the kernel and cokernel both vanish, then the map is an isomorphism. If we are working in a t-category, then in fact the cone furnishes both the kernel and cokernel of maps between objects of its core.
|
|
The 90 degree V8 engine has part-hemispherical combustion chambers with two overhead valves per cylinder operated by push-rods from a single chain-driven camshaft positioned centrally high up in the vee. Aluminium alloy pistons with steel connecting rods run in a cast chrome-iron block with sand-cast high- tensile light alloy heads and crankcase housing a short stiff dynamically balanced crankshaft carried on five bearings."The power unit has a cast-iron block, light alloy head and crankcase, with a short stiff dynamically balanced crankshaft carried on five bearings."—. However, the source does not mention a chrome-iron block, aluminium alloy pistons, steel connecting rods, or the light alloy components being sand-cast or high-tensile The nose of the crankshaft carries a torsional vibration damper, a four or six-bladed fan, and the pulley for the triangulated thin belt drive for the dynamo and water pump.
|
|
One passes between the first two by "pivoting" about X, to the third by pivoting about Z, and to the fourth by pivoting about X′. All enclosures in this diagram are commutative (both trigons and the square) but the other commutative square, expressing the equality of the two paths from Y′ to Y, is not evident. All the arrows pointing "off the edge" are degree 1: :300px This last diagram also illustrates a useful intuitive interpretation of the octahedral axiom. In triangulated categories, triangles play the role of exact sequences, and so it is suggestive to think of these objects as "quotients", Z' = Y/X and Y' = Z/X. In those terms, the existence of the last triangle expresses on the one hand :X' = Z/Y\ (looking at the triangle Y \to Z \to X' \to ), and :X' = Y'/Z' (looking at the triangle Z' \to Y' \to X' \to ).
|
|
The organization still plays a major role in the sport's development in the US and EU. With racing taking precedence, several teams began to think in new ways as to how the trucks could be built. Towards the end of 1988, Gary Cook and David Morris debuted Equalizer, a truck with a combination of coil springs and shock absorbers as the main source of suspension rather than the standard of leaf springs and shock absorbers. In 1989, Jack Willman Sr., now with his own truck, Taurus, debuted a new truck which used a solid axle suspension system made of parallel four-link suspensions and coilovers that together weighed in at close to . However, the biggest innovation came from Chandler, also in 1989, when the CAD-designed Bigfoot #8 debuted featuring a full tubular chassis and a long-travel suspension system made of triangulated four-link suspensions, bump stops, limit straps, cantilevers, and shock absorbers charged with nitrogen gas.
|
|
4 World Trade Center reflecting water of the Hudson River, viewed from One World Observatory in 2017 The above-ground portion of the building dedicated for retail use (which consists of the ground floor, the three floors immediately above the ground floor as well as the two floors below ground), accommodates offices using two distinct floor shapes. From floors 7 through 46, the typical floor space is 36,350 square feet (3,376 square meters) in the shape of a parallelogram (which is designed to echo the configuration of the site). From floors 48 through 63 the floor space is 28,000 sq ft (2,600 square meters) in the shape of a trapezoid, shaped so that it opens toward the tip of Manhattan Island and also triangulated to face One World Trade Center. The tower includes five levels of mechanical floors. The New York Power Authority selected UTC Power to provide 12 PureCell Model 400 fuel cells that will be used to provide electricity, water and heat.
|
|
The five Platonic solids – the regular tetrahedron, cube, octahedron, dodecahedron, and icosahedron – viewed as two-dimensional surfaces, have the property that any flag (a triple of a vertex, edge, and face that all meet each other) can be taken to any other flag by a symmetry of the surface. More generally, a map embedded in a surface with the same property, that any flag can be transformed to any other flag by a symmetry, is called a regular map. If a regular map is used to generate a clean dessin, and the resulting dessin is used to generate a triangulated Riemann surface, then the edges of the triangles lie along lines of symmetry of the surface, and the reflections across those lines generate a symmetry group called a triangle group, for which the triangles form the fundamental domains. For example, the figure shows the set of triangles generated in this way starting from a regular dodecahedron.
|
|
The inversive distance has been used to define the concept of an inversive-distance circle packing: a collection of circles such that a specified subset of pairs of circles (corresponding to the edges of a planar graph ) have a given inversive distance with respect to each other. This concept generalizes the circle packings described by the circle packing theorem, in which specified pairs of circles are tangent to each other.. Although less is known about the existence of inversive distance circle packings than for tangent circle packings, it is known that, when they exist, they can be uniquely specified (up to Möbius transformations) by a given maximal planar graph and set of Euclidean or hyperbolic inversive distances. This rigidity property can be generalized broadly, to Euclidean or hyperbolic metrics on triangulated manifolds with angular defects at their vertices.. However, for manifolds with spherical geometry, these packings are no longer unique.. In turn, inversive-distance circle packings have been used to construct approximations to conformal mappings.
|
|
In the 1970s up to 60% of the Royal Australian Survey Corps' capability was engaged on PNG surveys and mapping. 8 Fd Svy Sqn, assisted by 1, 2 and 4 Fd Svy Sqns, completed the geodetic and topographic surveys, acquired survey point identification/spot and supplementary air photography and field checked compiled/preliminary maps. All five field survey squadrons (Australia and PNG based) compiled maps on photogrammetric stereo-plotters using mainly Skai Piksa photography; and Army Survey Regiment photogrammetrically triangulated the air photography, compiled maps using photogrammetric stereo-plotters, cartographically completed and printed the maps, and cartographically derived and printed the JOG.Coulthard-Clark, CD, 2000, Australia's Military Mapmakers – The Royal Australian Survey Corps 1915–96, Oxford University Press, On 26 June 1980 the Australian High Commissioner for PNG presented a complete three volume Atlas of the maps in the 1:100,000 series to the Prime Minister of PNG, Sir Julius Chan. The preface to this atlas states, in part: “The Royal Australian Survey Corps during and since World War II has been engaged almost continuously upon a programme of Survey and Mapping in PNG.
|
|
Inserted into a nationally important Nash set-piece terrace of neoclassical form, the RCP projects a raised linear form perpendicular to the terrace to create a series of gardens and spaces around the building, with annexes for lecture hall and an historic timber panelled room preserved from the earlier Colleges. Using modern reinforced concrete technology and highly expressive structural methods, the volumes are made to 'float in space' on the slimmest of supports to dissolve spatial boundaries between inside and out. The work makes implicit references to the work of the 'high modernists' from le Corbusier and Mies to the 'Scandinavian modernism' of Aalto, Asplund and Jacobsen as well as the contemporary Brutalist aesthetics of the era, yet developing a personal idiom of opened cantilevered volumes, long perspectives, triangulated form, and clarity of concept and structure that is entirely Lasdun's own. This building, however, is finished in luxurious white Sicilian marble, Murano glass mosaic tiles, polished brass and black engineering brick, and was one of the first post-War buildings to be awarded Grade I listing for national and international significance and influence on the work of others.
|
|
The German Junkers J.I armoured fuselage ground-attack sesquiplane of 1917 used a Hugo Junkers-designed multi-tube network of several tubular wing spars, placed just under the corrugated duralumin wing covering and with each tubular spar connected to the adjacent one with a space frame of triangulated duralumin strips — usually in the manner of a Warren truss layout — riveted onto the spars, resulting in a substantial increase in structural strength at a time when most other aircraft designs were built almost completely with wood-structure wings. The Junkers all-metal corrugated-covered wing / multiple tubular wing spar design format was emulated after by American aviation designer William Stout for his 1920s-era Ford Trimotor airliner series, and by Russian aerospace designer Andrei Tupolev for such aircraft as his Tupolev ANT-2 of 1922, upwards in size to the then-gigantic Maksim Gorki of 1934. A design aspect of the Supermarine Spitfire wing that contributed greatly to its success was an innovative spar boom design, made up of five square concentric tubes that fitted into each other. Two of these booms were linked together by an alloy web, creating a lightweight and very strong main spar.
|
|
Accompanied by his son Bartholemew, Mercator meticulously triangulated his way around the forests, hills and steep sided valleys of Lorraine, difficult terrain as different from the Low Countries as anything could be. He never committed anything to paper but he may have confided in his friend Ghim who would later write: "The journey through Lorraine gravely imperiled his life and so weakened him that he came very near to a serious breakdown and mental derangement as a result of his terrifying experiences." Mercator returned home to convalesce, leaving Bartholemew to complete the survey. No map was published at the time but Mercator did provide a single drawn copy for the Duke and later he would incorporate this map into his atlas. Chronologia title page The trip to Lorraine in 1564 was a set back for his health but he soon recovered and embarked on his greatest project yet, a project which would extend far beyond his cartographic interests. The first element was the Chronologia, a list of all significant events since the beginning of the world compiled from his literal reading of the Bible and no less than 123 other authors of genealogies and histories of every empire that had ever existed.
|
|