78 Sentences With "be bounded by" | Random Sentence Generator

Those agencies' activities will be bounded by the courts, but she'll appoint judges too.

Such a machine, the speculation goes, would not be bounded by bothersome human limitations, such as slowness of thought, emotions, irrational biases and need for sleep.

Her openness to new experiences and natural inquisitiveness would now be bounded by her femininity, by the reality that her gender mattered and in ways that made her unequal in the world.

Both cases imply that the world may need to get used to a less disciplined US president who is not bounded, or doesn't want to be bounded, by traditional diplomatic rules and norms that would have constrained another US president.

The neighborhood is considered to be bounded by UNMIL headquarters to the west and the Spriggs Payne airport to the east.

Using a variation of queue number called the strong queue number, the queue number of a graph product can be bounded by a function of the queue numbers and strong queue numbers of the factors in the product..

In mathematics, the Borel–Carathéodory theorem in complex analysis shows that an analytic function may be bounded by its real part. It is an application of the maximum modulus principle. It is named for Émile Borel and Constantin Carathéodory.

Queens Wharf construction site in William Street, October 2019 The Queen's Wharf development of an entertainment precinct will be bounded by Queen Street, George Street, Alice Street and the Brisbane River. All of William Street will become part of the precinct.

In mathematics, a uniformly bounded family of functions is a family of bounded functions that can all be bounded by the same constant. This constant is larger than the absolute value of any value of any of the functions in the family.

The region appears to be bounded by cubic curves, suggesting that the crossing number, , and may be related to each other by not-yet-proven inequalities. This shape is named after Simon Willerton, who first observed this phenomenon and described the shape of the scatterplots as "fish-like"..

In contrast, the maximum complexity of the ≤k-level is known to be Θ(nk).. A k-level is a special case of a monotone path in an arrangement; that is, a sequence of edges that intersects any vertical line in a single point. However, monotone paths may be much more complicated than k-levels: there exist arrangements and monotone paths in these arrangements where the number of points at which the path changes direction is Ω(n2 − o(1)).; see also . Although a single cell in an arrangement may be bounded by all n lines, it is not possible in general for m different cells to all be bounded by n lines.

Demolition of government buildings in George Street as part of the Queen's Wharf development, August 2017 The Queen's Wharf development of an entertainment precinct will be bounded by Queen Street, George Street, Alice Street and the Brisbane River (including all of William Street). All of the non-heritage buildings on the site will be demolished.

This states that in the absence of sources the internal nodal values of the property ф should be bounded by its boundary values. Hence in a steady state conduction problem without sources and with boundary temperatures of 500 °C and 200 °C all interior values of T should be less than 500 °C and greater than 200 °C.

Supraglacial lakes can occur in all glaciated areas. The retreating glaciers of the Himalaya produce vast and long lived lakes, many kilometres in diameter and scores of metres deep. These may be bounded by moraines; some are deep enough to be density stratified. Most have been growing since the 1950s; the glaciers have been retreating constantly since then.

For example, the Ishim impact structure is conjectured to be bounded by the late Ordivician-early Silurian (c. 445 ± 5 Ma), the two Warburton basins have been linked to the Late Devonian extinction (c. 360 Ma), both Bedout and the Wilkes Land crater have been associated with the severe Permian–Triassic extinction event (c. 252 Ma), Manicouagan (c.

This lacustrine plain is bounded on the north by the Niagara Escarpment. Although quite wide at the eastern end of Lake Erie, the plain narrows considerably along the lake's southern shore. Here, the plain continues to be bounded by the Portage Escarpment, which turns southwest in a series of indefinite hills at Hamburg, Orchard Park, and East Aurora.

Any archaeological deposit, as originally laid down, will be bounded by the edge of the basin of deposition, or will thin down to a feather edge. Therefore, if any edge of the deposit is exposed in a vertical plane view, a part of its original extent must have been removed by excavation or erosion: its continuity must be sought, or its absence explained.

Adriaan Heereboord had argued in Cartesian style, against scholasticism for limitations to be put on disputation, which should be bounded by good faith in the participants. Werenfels went further, regarding "logomachy" as a malaise of the Republic of Letters.Wolfgang Rother, Paratus sum sententiam mutare: The Influence of Cartesian Philosophy at Basle pp. 79–80, in History of Universities, Volume XXII/1 (2007), pp.

In certain cases, we can abstract particular aspects of the holomovement (e.g. light, electrons, sound, etc.), but more generally, all forms of the holomovement merge and are inseparable. Thus in its totality, the holomovement is not limited in any specifiable way at all. It is not required to conform to any particular order, or to be bounded by any particular measure.

The government refused the demand, stating that the political reform has to be bounded by the NPCSC decision. In an opinion poll carried out by Chinese University of Hong Kong, only 36.1% of 802 people surveyed between 8–15 October accept NPCSC's decision but 55.6% are willing to accept if the HKSAR Government would democratise the nominating committee during the second phase of public consultation period.

In the above form, the functional to be extended must already be bounded by a sublinear function. In some applications, this might close to begging the question. However, in locally convex spaces, any continuous functional is already bounded by the norm, which is sublinear. One thus hasIn category-theoretic terms, the field is an injective object in the category of locally convex vector spaces.

Shore Acres is a neighborhood of Staten Island, one of the five boroughs of New York City. It is situated along the Upper New York Bay, just north of Fort Wadsworth and south of Rosebank. Shore Acres is generally considered to be bounded by Bay Street on the west, the Upper New York Bay on the east, Nautilus Street on the north, and Arthur Von Briesen Park on the south.

In bioinformatics problems involving the folding structure of RNA, single-page book embeddings represent classical forms of nucleic acid secondary structure, and two-page book embeddings represent pseudoknots. Other applications of book embeddings include abstract algebra and knot theory. There are several open problems concerning book thickness. It is unknown whether the book thickness of an arbitrary graph can be bounded by a function of the book thickness of its subdivisions.

The false coverage rate (FCR) is, in a sense, the FDR analog to the confidence interval. FCR indicates the average rate of false coverage, namely, not covering the true parameters, among the selected intervals. The FCR gives a simultaneous coverage at a 1-\alpha level for all of the parameters considered in the problem. Intervals with simultaneous coverage probability 1−q can control the FCR to be bounded by q.

The boundedness problem for Datalog asks, given a Datalog program, whether it is bounded, i.e., the maximal recursion depth reached when evaluating the program on an input database can be bounded by some constant. In other words, this question asks whether the Datalog program could be rewritten as a nonrecursive Datalog program. Solving the boundedness problem on arbitrary Datalog programs is undecidable, but it can be made decidable by restricting to some fragments of Datalog.

The Sugar Grove is generally agreed to be bounded by the intersection of Bow Hill Road, Sugar Grove Road, and Elliots Creek Road. Craigs Mountain Road (VA 674) is the only way into Sugar Grove. From Pilot Road (VA 615) to the end of state maintenance on Bow Hill Road, it is approximately six miles, three and one half of those miles being a gravel road. Roads in the area have often been overlooked.

It stated, : "On the petition of sundry inhabitants for a new township to be organized and erected comprising No. 6 in the 13th Range. Ordered that said Township No. 6 in the 13th Range be set off and erected into a new Township by the name of Parma, to be bounded by the original lines of said Township." Phillip Henninger House. Built in 1842, it is listed on the National Register of Historic Places.

Then there appears no rational basis for preferring one function over another. A universal prior insures that although two agents may have different initial probability distributions for the data input, the difference will be bounded by a constant. So universal priors do not eliminate an initial bias, but they reduce and limit it. Whenever we describe an event in a language, either using a natural language or other, the language has encoded in it our prior expectations.

There are a few things to keep in mind when choosing a value for : # The sender must not transmit too fast. should be bounded by the receiver’s ability to process packets. # must be smaller than the number of sequence numbers (if they are numbered from zero to ) to verify transmission in cases of any packet (any data or ACK packet) being dropped. # Given the bounds presented in (1) and (2), choose to be the largest number possible.

Because an excellent ring R is a G-ring, it is Noetherian by definition. Because it is universally catenary, every maximal chain of prime ideals has the same length. This is useful for studying the dimension theory of such rings because their dimension can be bounded by a fixed maximal chain. In practice, this means infinite dimensional Noetherian rings which have an inductive definition of maximal chains of prime ideals, giving an infinite dimensional ring, cannot be constructed.

The Parish would be bounded by Clontarf Parish (confusingly also dedicated to St. John the Baptist) to the east, St. Mobhi's Church, Glasnevin, to the West, and St. Pappan's Church, Santry to the North. Since 2016 Drumcondra (and North Strand) also serve the Parish of St. George and St. Thomas, which is to the South of Drumcondra Church. The church contains a memorial to parishioners who fought in the Great War.Drumcondra Church Great War Memorial Irish War Memorials.

A tectonic block is a part of the Earth's crust that can be treated as a solid rigid crustal block or lithospheric section. A tectonic block may be bounded by faults. It may move from one place to another because of a tectonic shift, and they may also be rotated. A tectonic block may have a proper name for example, the Muness Phyllite Block (which is located in Unst and Uyea in Scotland), or the South China Block.

Downtown Visalia is the central business district of Visalia, California, United States, which is located close to the geographic center of the metropolitan area. The area features an array of public art and unique shopping opportunities. The Downtown area is the hub for the city's public transport transit center. Downtown is generally thought to be bounded by Giddings Street on the west, Murray Avenue on the north, Ben Maddox Way on the east, and the Sequoia (198) Freeway on the south.

Faulted southeastern side of Svyatoy Nos peninsula, Lake Baikal – active faulting shown by faceted spurs. Artificial rendering of the Albertine Rift showing four of its rift lakes A rift lake is a lake formed as a result of subsidence related to movement on faults within a rift zone, an area of extensional tectonics in the continental crust. They are often found within rift valleys and may be very deep. Rift lakes may be bounded by large steep cliffs along the fault margins.

A small resort developed there in the late nineteenth and early twentieth centuries. Very little remains besides an exceptionally fine spring house sheltering the original spring. Today the term "Cascade," much like the term "Midtown," can refer to a much larger area than what might be shown on official maps. Generally today Cascade might be bounded by I-20 on the north, I-285 on the west, the ridges on the south side of Utoy Creek, and the pre-1954 city limits around Greenwood Cemetery.

McCord planned to develop Willowick Place on the former Willowick Court site.Sarnoff, Nancy. "With sales creeping along, second tower to go rental." Houston Chronicle. November 10, 2008. Retrieved on November 26, 2008. The community was supposed to consist of 62 houses in a area. The community was to be bounded by Las Palmas Street, West Alabama Street, Weslayan Street and West Main Street. The house prices will range from $2.5 million to $5 million U.S. dollars. The lots were priced from $900,000 to $2 million.

Lincoln Yards is a mixed-use development project located on the North Side of Chicago between the Lincoln Park and Bucktown communities. It will consist of several high-rises that will include apartments, condos, office, retail, and entertainment. Lincoln Yards will occupy more than 50 acres of land located on both sides of the North Branch of the Chicago River. It will be bounded by Webster Avenue to the north, Clybourn Avenue to the east, North Avenue to the south, and the Kennedy Expressway to the west.

A portion of the Hotel District The Hotel District is a neighborhood in Downtown Atlanta, Georgia, United States. The district's name is derived from it being the home to many hotels, one of them being the famous Westin Peachtree Plaza Hotel. The Hotel District is generally considered to be bounded by the Downtown Connector to the east, Five Points to the south, Centennial Olympic Park to the west, and Midtown to the north. The district's primary thoroughfare is Peachtree Street, which contains most of the restaurants, hotels, and office buildings.

The polygon-circle graphs are a generalization of the circle graphs, which are intersection graphs of the chords of a circle, and the trapezoid graphs, intersection graphs of trapezoids that all have their vertices on the same two parallel lines. They also include the circular arc graphs.Spider graphs, Information System on Graph Classes and their Inclusions, retrieved 2016-07-11. Polygon-circle graphs are not, in general, perfect graphs, but they are near-perfect, in the sense that their chromatic numbers can be bounded by an (exponential) function of their clique numbers..

It stated, : "On the petition of sundry inhabitants for a new township to be organized and erected comprising No. 6 in the 13th Range. Ordered that said Township No. 6 in the 13th Range be set off and erected into a new Township by the name of Parma, to be bounded by the original lines of said Township." On the same day, a public notice was issued to qualified electors by the County Commissioners. They met at the house of Samuel Freeman on April 3, 1826 to elect township officers according to the law.

R corresponds roughly to repeated attempts to create and discern a pattern. Dembski then asserts that R can be bounded by 10120. This number is supposedly justified by a result of Seth Lloyd in which he determines that the number of elementary logic operations that can have been performed in the universe over its entire history cannot exceed 10120 operations on 1090 bits. Dembski's main claim is that the following test can be used to infer design for a configuration: There is a target pattern T that applies to the configuration and whose specified complexity exceeds 1.

Resonances appear as small denominators in the expansion. The existence of resonances and small denominators led to the important question of stability in the planetary problem: do planets, in nearly circular orbits around a star, remain in stable or bounded orbits over time?Chierchia 2010 In 1963, Vladimir Arnold proved using KAM theory a kind of stability of the planetary problem: there exists a set of positive measure of quasiperiodic orbits in the case of the planetary problem restricted to the plane. In the KAM theory, chaotic planetary orbits would be bounded by quasiperiodic KAM tori.

On one occasion, the prisoners threatened to strike because "pyjamas they'd ordered from the Eaton's catalogue failed to arrive on time" (they thought the guards might have stolen the order). However, relations between the prisoners and their guards were often amicable and it was rumoured that the camp staff were being supplied with alcohol distilled by the prisoners. Whitewater was the only POW camp in North America not to be bounded by a fence or barbed wire, as its isolation made escape unfeasible. Members of the Veterans' Guard of Canada served as guards at the camp.

There exist other unique properties of the least absolute deviations line. In the case of a set of (x,y) data, the least absolute deviations line will always pass through at least two of the data points, unless there are multiple solutions. If multiple solutions exist, then the region of valid least absolute deviations solutions will be bounded by at least two lines, each of which passes through at least two data points. More generally, if there are k regressors (including the constant), then at least one optimal regression surface will pass through k of the data points.

The neighborhood is generally agreed to be bounded by Rock Creek Park on the east, Western Avenue (which divides D.C. and Maryland) and Tennyson Street on the north, and Reno Road to the west. Opinions differ on the southern boundary, where Chevy Chase meets Forest Hills, but many residents consider it to be Broad Branch Road between 32nd and 27th streets. The main roads leading in and out of Chevy Chase, D.C. are Connecticut Avenue, Nebraska Avenue, Reno Road, Military Road and Western Avenue. The area is served by the M4, L1, L2, L8, E2, E4 and E6 Metrobus lines.

A rectified cube is a cuboctahedron – edges reduced to vertices, and vertices expanded into new faces A birectified cube is an octahedron – faces are reduced to points and new faces are centered on the original vertices. A rectified cubic honeycomb – edges reduced to vertices, and vertices expanded into new cells. In Euclidean geometry, rectification, also known as critical truncation or complete-truncation is the process of truncating a polytope by marking the midpoints of all its edges, and cutting off its vertices at those points. The resulting polytope will be bounded by vertex figure facets and the rectified facets of the original polytope.

Given two integers a and b, the algorithm performs O(\log\ a + \log\ b) arithmetic operations on numbers with at most O(\log\ a + \log\ b) bits. At the same time, the number of arithmetic operations cannot be bounded by the number of integers in the input (which is constant in this case, there are always only two integers in the input). Due to the latter observation, the algorithm does not run in strongly polynomial time. Its real running time depends on the magnitudes of a and b and not only on the number of integers in the input.

For a top-hat beam, the upper integration limits may be bounded by rmax, such that r ≤ rmax − R. Thus, the limited grid coverage in the r direction does not affect the convolution. To convolve reliably for physical quantities at r in response to a top-hat beam, we must ensure that rmax in photon transport methods is large enough that r ≤ rmax − R holds. For a Gaussian beam, no simple upper integration limits exist because it theoretically extends to infinity. At r >> R, a Gaussian beam and a top-hat beam of the same R and S0 have comparable convolution results.

The accompanying plot shows these two solutions as surfaces in a space with horizontal axes of (sample excess kurtosis) and (sample squared skewness) and the shape parameters as the vertical axis. The surfaces are constrained by the condition that the sample excess kurtosis must be bounded by the sample squared skewness as stipulated in the above equation. The two surfaces meet at the right edge defined by zero skewness. Along this right edge, both parameters are equal and the distribution is symmetric U-shaped for α = β < 1, uniform for α = β = 1, upside-down-U-shaped for 1 < α = β < 2 and bell-shaped for α = β > 2.

The Lanes are a collection of narrow lanes in Brighton, in the city of Brighton and Hove famous for their small shops (including several antique shops) and narrow alleyways. The Lanes are commonly taken to be bounded by North Street to the north, Ship Street to the west and Prince Albert Street and the north side of Bartholomew Square to the south. The eastern boundary is less well-defined and can be considered either East Street or Market Street. Meeting House Lane is one of the wider lanes which meets with the busy shopping road of North Street and eventually winds around to Market Street.

In many parts of riverine eastern Bengal, with long stretches of low lands, the railways had to be built on embankments which hindered the free flow of water. In a brief case study of Eastern Bengal Railway it has been revealed that the water regime of the Rajshahi Division of present Bangladesh was destabilized by the way railway exposed itself to the Chalan Beel. From the beginning of the twentieth century the beel (pond or wetland) began to be bounded by the Calcutta-Siliguri Main Line on the west and by the Santahar-Bogra Line on the north. These lines affected feeding of the beel.

Training involved inter alia bombing runs in which bombs made of concrete were dropped onto heath surfaces east of the railway line. Among those housed on the airfield were forced labourers from Eastern Europe as well as Soviet and Polish POWs. Their labour was used to expand the facilities including road construction in and around the military area. Eventually the military area stretched all the way to the Höpen (a hill) in the southwest, extended beyond the Reichsstrasse 3 in the east and was supposed to be bounded by a new ring road going north from Schneverdingen towards Wintermoor in the west and the Wintermoorer Strasse in the north.

1974 image of Bridgeton Cross It started as a small weaving village in 1705, when the third John Walkinshaw marked out a portion of his Goosefauld estate for rent.Barrowfield House (Mitchell Library, Glasgow Collection, 1844), The Glasgow Story However, not much interest was shown until 1775 when Rutherglen Bridge was built over the River Clyde and the area became known as Bridge Town (or Brig Toun in Scots). A major employer was carpet manufacturer James Templeton & Co. Bridgeton used to be bounded by a village named Mile-End to the north, however this district seems to have vanished over the years, resulting in Bridgeton's boundary moving north to Crownpoint Road.

This unnamed footpath extends in the same general direction as the road, and was followed as far as 150 m. However, it seems to disappear about 400 meters before reaching Destierro River.Ibid.: 43 Both the Iroquois and Pocora causeways offered formalized, controlled, and ceremonial access to the central part of Las Mercedes-1 architectural complex. The roads go in opposite directions from the center of the site along a route perpendicular to the hydrographic system. The geographic context of Las Mercedes-1, located between streams and rivers on all sides, has raised the question of whether the sphere of influence of a chiefly political center might be bounded by hydrographic systems.

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).

There is no precise definition of the Grand Canal Dock area but it is generally understood to be bounded by the Liffey to the north, South Lotts Road to the east (or Barrow Street if separating South Lotts as its own area), Grand Canal Street to the south and Macken Street to the west (although some maps show the area including as far west as the corner of Leeson Street and Fitzwilliam Place). Grand Canal Dock contains Grand Canal Dock railway station (also known as Barrow Street Station), the national Waterways Ireland Visitor Centre, the site of the planned U2 Tower, and a number of other notable buildings.

In 1899, the New York Athletic Club approached Lawrence Van Etten, an architect renowned for designing golf courses, for a request to construct an 18-hole course within the park. The proposed course would be bounded by Pelham Manor to the north; the Harlem River and Port Chester Railroad (now Northeast Corridor) tracks to the west; and Shore Road to the southeast. The city was building Van Cortlandt Park's golf course at the time, but the Bronx district parks commissioner approved Van Etten's plan. Originally, the club wanted to construct a park on Hunter Island, but Van Etten felt that the island was too small for a full 18-hole course.

Downtown Vancouver is bounded by Burrard Inlet to the north. The downtown area is generally considered to be bounded by Burrard Inlet to the north, Stanley Park and the West End to the west, False Creek to the south, and the Downtown Eastside to the east. Most sources include the full downtown peninsula (adding the West End neighbourhood and Stanley Park) as downtown Vancouver, but the City of Vancouver defines them as separate neighbourhoods. Besides the readily identifiable office towers of the financial and central business districts, Downtown Vancouver also includes residential neighbourhoods in the form of high-rise apartment and condominiums, in Yaletown and Coal Harbour.

Creating a teragon, the Koch snowflake Horned triangle or teragonic triangle Albeverio, Sergio; Andrey, Sergio; Giordano, Paolo; and Vancheri, Alberto (1997). The Dynamics of Complex Urban Systems, p.222. Springer. . Quadratic Koch island/Minkowski fractal A teragon is a polygon with an infinite number of sides, the most famous example being the Koch snowflake ("triadic Koch teragon"). Typically, a teragon will be bounded by one or more self-similar fractal curves, which are created by replacing each line segment in an initial figure with multiple connected segments, then replacing each of those segments with the same pattern of segments, then repeating the process an infinite number of times for every line segment in the figure.

A lineage zone, also called a consecutive range zone, are biozones which are defined by being a specific segment of an evolutionary lineage. For example, a zone can be bounded by the highest occurrence of the ancestor of a particular of a taxon and the lowest occurrence of its descendant, or between the lowest occurrence of a taxon and the lowest occurrence of its descendant. Lineage zones are different from most other biozonecan s because they need that the segments its bounded by are successive segments of an evolutionary lineage. This makes them similar to chronostratigraphical units - however, lineage zones, being a biozone, are restricted by the actual spatial range of fossils.

Southern right whale dolphins have a circumpolar distribution across the Southern Hemisphere, generally occurring in cool temperate to Sub- Antarctic waters between 30°S and 65°S. The precise boundary of their range has not been estimated or closely studied but the southern limit of the species appears to be bounded by the Antarctic Convergence while the northern limit seems bounded by the Tropical Convergence although rare sightings beyond these limits have been recorded. Most sightings of the southern right whale dolphins occur in offshore and deep waters, with temperatures ranging between 1 and 20 °C. In regions where deep waters approach the coast and in upwelling areas, they have occasionally been observed near shore.

If the points are chosen as elements of a low-discrepancy sequence, this is the quasi-Monte Carlo method. A remarkable result, the Koksma–Hlawka inequality (stated below), shows that the error of such a method can be bounded by the product of two terms, one of which depends only on f, and the other one is the discrepancy of the set {x1, ..., xN}. It is convenient to construct the set {x1, ..., xN} in such a way that if a set with N+1 elements is constructed, the previous N elements need not be recomputed. The rectangle rule uses points set which have low discrepancy, but in general the elements must be recomputed if N is increased.

Located on the northern shore of a narrow isthmus, the CBD extends from the Auckland waterfront on the Waitematā Harbour southwards along Queen Street and a number of other parallel-running streets. The CBD is generally considered to be bounded by the main motorways that surround all non-harbour sides, with State Highway 1 forming the southern and western boundaries, and State Highway 16 / Grafton Gully forming the eastern boundary. The CBD has an area of , similar to the Sydney CBD, and twice as large as the CBDs of Wellington and Christchurch.Auckland's CBD at a glance (CBD website of the Auckland City Council) The CBD is to a substantial part located on reclaimed land of the Waitematā Harbour.

The problem of finding the smallest odd cycle transversal, or equivalently the largest bipartite induced subgraph, is also called odd cycle transversal, and abbreviated as OCT. It is NP-hard, as a special case of the problem of finding the largest induced subgraph with a hereditary property (as the property of being bipartite is hereditary). All such problems for nontrivial properties are NP-hard. The equivalence between the odd cycle transversal and vertex cover problems has been used to develop fixed-parameter tractable algorithms for odd cycle transversal, meaning that there is an algorithm whose running time can be bounded by a polynomial function of the size of the graph multiplied by a larger function of k.

Akhbaris consider themselves to be bounded by the Hadith of the two weighty things, where the Prophet Muhammad instructed his followers to follow the Quran and Ahl al-Bayt. Therefore, even for new events occurring during the Major Occultation, Akhbaris continue to follow traditions of Ahlul Bayt, as per the saying of Imam Muhammad al-Mahdi where he said "As for the new events, which will occur (during my occultation) turn to the narrators of our traditions, because they are my proof to you, while I am the proof of Allah to them"Bahar al-Anwar Vol. 53, p. 181 Akhbari reject fatāwa based on ijtihad, they also reject the permissibility of writing exegesis of the Qur'an without quoting the narrations of the infallible Ahlu l-Bayt.

The latter mountainous region is, however, not generally referred to as Highveld, whose boundary at this point runs just inside the Lesotho-Free State border, about 2000 m. From its eastern boundary, the Highveld slopes gently downwards to be bounded by the Great Karoo to the south, the Kalahari desert to the west, the Bushveld to the north, the Mpumalanga Lowveld to the northeast, KwaZulu-Natal to the east, and the Lesotho Highlands, or Mountains, to the southeast. The Highveld covers an area of almost 400,000 km2, or roughly 30% of South Africa's land area. The Highveld terrain is generally devoid of mountains, consisting of rolling plains, especially in the Free State, sometimes interrupted by rocky ridges such as the Witwatersrand, the Magaliesberg, and Vredefort Dome.

In this way, the mixing time can be bounded by the time for the two coupled chains to synchronize. Chapter six discusses a technique called "strong stationary times" with which, for some Markov chains, one can prove that choosing a stopping time randomly from a certain distribution will result in a state drawn from the stable distribution. After a chapter on lower bounds on mixing time based on the "bottleneck ratio" and isoperimetric number, the next two chapters of the first part cover two important examples: card shuffling and random walks on graphs. Chapters 10 and 11 consider two more parameters closely related to the mixing time, the hitting time at which the Markov chain first reaches a specified state, and the cover time at which it has first reached all states.

Since all sets S_i are sets of suffixes of a finite set of codewords, there are only finitely many different candidates for S_i. Since visiting one of the sets for the second time will cause the algorithm to stop, the algorithm cannot continue endlessly and thus must always terminate. More precisely, the total number of dangling suffixes that the algorithm considers is at most equal to the total of the lengths of the codewords in the input, so the algorithm runs in polynomial time as a function of this input length. By using a suffix tree to speed the comparison between each dangling suffix and the codewords, the time for the algorithm can be bounded by O(nk), where n is the total length of the codewords and k is the number of codewords.

The definition of a unit distance graph may naturally be generalized to any higher-dimensional Euclidean space. Any graph may be embedded as a set of points in a sufficiently high dimension; show that the dimension necessary to embed a graph in this way may be bounded by twice its maximum degree. The dimension needed to embed a graph so that all edges have unit distance, and the dimension needed to embed a graph so that the edges are exactly the unit distance pairs, may greatly differ from each other: the 2n-vertex crown graph may be embedded in four dimensions so that all its edges have unit length, but requires at least n − 2 dimensions to be embedded so that the edges are the only unit-distance pairs.

As showed, every planar graph has a planar straight-line drawing in which the number of distinct slopes is a function of the degree of the graph. Their proof follows a construction of for bounding the angular resolution of planar graphs as a function of degree, by completing the graph to a maximal planar graph without increasing its degree by more than a constant factor, and applying the circle packing theorem to represent this augmented graph as a collection of tangent circles. If the degree of the initial graph is bounded, the ratio between the radii of adjacent circles in the packing will also be bounded by the ring lemma,. which in turn implies that using a quadtree to place each graph vertex on a point within its circle will produce slopes that are ratios of small integers.

Many maps however consider South Jamaica to be bounded by Linden Boulevard to the north, and Rockaway Boulevard and Baisley Boulevard to the south, with the section north of Linden Boulevard (including the South Jamaica Houses) defined as part of Jamaica. Other maps consider the area between Linden Boulevard and Baisley/Rockaway Boulevards to be a southern subsection of South Jamaica called Baisley Park; Baisley Pond Park, the Baisley Park Houses, the Baisley Park Branch of Queens Public Library, and the Baisley Park Bus Depot are located in this area. The neighborhood south of Rockaway and Baisley Boulevards to the Belt Parkway (including Rochdale Village) historically has been considered part of South Jamaica, but is now often mapped as Springfield Gardens North or Rochdale. The three sections constitute the western half of Queens Community Board 12.

A lemma of Brian White shows that the minimum area double bubble must be a surface of revolution. For, if not, it would be possible to find two orthogonal planes that bisect both volumes, replace surfaces in two of the four quadrants by the reflections of the surfaces in the other quadrants, and then smooth the singularities at the reflection planes, reducing the total area. Based on this lemma, Michael Hutchings was able to restrict the possible shapes of non-standard optimal double bubbles, to consist of layers of toroidal tubes.. Additionally, Hutchings showed that the number of toroids in a non-standard but minimizing double bubble could be bounded by a function of the two volumes. In particular, for two equal volumes, the only possible nonstandard double bubble consists of a single central bubble with a single toroid around its equator.

The City of Seattle also uses the term Delridge more loosely to describe an informal collection of neighborhoods near the Delridge valley. This area is not precisely defined, but often is considered to be bounded by the Duwamish River to the north and east, unincorporated White Center to the south, and West Seattle to the west along 35th Avenue SW. That area includes (north to south, east to west) the Pigeon Point, Youngstown, Puget Ridge, Riverview, High Point, Highland Park, Westwood, and Roxhill neighborhoods, and some industrial areas near the river. Pigeon Point is the northern end of the bluff above the Duwamish, east of the old Youngstown neighborhood that surrounds the steel mill, in what real estate listings often now call North Delridge. South Delridge has also replaced Westwood on some maps, but neither of the new half- Delridge terms have entered common speech among longtime area residents.

A priority queue is a data structure for maintaining a collection of items with numerical priorities, having operations for finding and removing the item with the minimum priority value. Comparison- based priority queues such as the binary heap take logarithmic time per update, but other structures such as the van Emde Boas tree or bucket queue may be faster for inputs whose priorities are small integers. These data structures can be used in the selection sort algorithm, which sorts a collection of elements by repeatedly finding and removing the smallest element from the collection, and returning the elements in the order they were found. A priority queue can be used to maintain the collection of elements in this algorithm, and the time for this algorithm on a collection of elements can be bounded by the time to initialize the priority queue and then to perform find and remove operations.

A graph with an odd cycle transversal of size 2: removing the two blue bottom vertices leaves a bipartite graph. Odd cycle transversal is an NP-complete algorithmic problem that asks, given a graph G = (V,E) and a number k, whether there exists a set of k vertices whose removal from G would cause the resulting graph to be bipartite. The problem is fixed-parameter tractable, meaning that there is an algorithm whose running time can be bounded by a polynomial function of the size of the graph multiplied by a larger function of k.. The name odd cycle transversal comes from the fact that a graph is bipartite if and only if it has no odd cycles. Hence, to delete vertices from a graph in order to obtain a bipartite graph, one needs to "hit all odd cycle", or find a so-called odd cycle transversal set.

West Hills was originally part of Owensmouth (founded 1912) and renamed Canoga Park (1931).Gabe Fuentes, "Museum Recalls Era When It Was Chic to be Named Canoga Park," Los Angeles Times, San Fernando Valley edition, October 11, 1987, page 7 Under the leadership of Joel Schiffman, residents of a three-square-mile area in western Canoga Park began a petition campaign in 1987 to separate from the larger community and establish a neighborhood of their own to be called West Hills, the same name that a 303-home subdivision in a nearby unincorporated area had carried for years. The Los Angeles city district of 4,700 single-family homes and 35 businesses would be bounded by Roscoe Boulevard on the north, Woodlake Avenue, Sherman Way and Platt Avenue on the east, Victory Boulevard on the south and the county line on the west. Proponents said the change would give the area "political clout" and increase property values.

The Kantian thesis claims that in order for the subject to have any experience at all, then it must be bounded by these forms of presentations (Vorstellung). Some scholars have offered this position as an example of psychological nativism, as a rebuke to some aspects of classical empiricism. Kant's thesis concerning the transcendental ideality of space and time limits appearances to the forms of sensibility—indeed, they form the limits within which these appearances can count as sensible; and it necessarily implies that the thing- in-itself is neither limited by them nor can it take the form of an appearance within us apart from the bounds of sensibility (A48-49/B66). Yet the thing-in- itself is held by Kant to be the cause of that which appears, and this is where an apparent paradox of Kantian critique resides: while we are prohibited from absolute knowledge of the thing-in-itself, we can impute to it a cause beyond ourselves as a source of representations within us.

Europe is taken to be bounded by large bodies of water to the north, west and south; Europe's limits to the east and northeast are usually taken to be the Ural Mountains, the Ural River, and the Caspian Sea; to the southeast, the Caucasus Mountains, the Black Sea and the waterways connecting the Black Sea to the Mediterranean Sea. A medieval T and O map printed by Günther Zainer in 1472, showing the three continents as domains of the sons of Noah — Asia to Sem (Shem), Europe to Iafeth (Japheth), and Africa to Cham (Ham) Islands are generally grouped with the nearest continental landmass, hence Iceland is considered to be part of Europe, while the nearby island of Greenland is usually assigned to North America, although politically belonging to Denmark. Nevertheless, there are some exceptions based on sociopolitical and cultural differences. Cyprus is closest to Anatolia (or Asia Minor), but is considered part of Europe politically and it is a member state of the EU. Malta was considered an island of Northwest Africa for centuries, but now it is considered to be part of Europe as well.