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"nonadjacent" Definitions
  1. not adjacent: such as
  2. not having a common endpoint or border
  3. not having the vertex and one side in common

38 Sentences With "nonadjacent"

How to use nonadjacent in a sentence? Find typical usage patterns (collocations)/phrases/context for "nonadjacent" and check conjugation/comparative form for "nonadjacent". Mastering all the usages of "nonadjacent" from sentence examples published by news publications.

In geometry, the triaugmented dodecahedron is one of the Johnson solids (J61). It can be seen as a dodecahedron with three pentagonal pyramids (J2) attached to nonadjacent faces.
Fe(III), Co(III), Ni(III), and Ni(IV) derivatives are known. In some cases, the oxidation induces rearrangement of the C2B9 cage to give complexes where the carbon centers are nonadjacent.
Each channel consists of two redundantly paired tracks, and the paired tracks are nonadjacent to minimize the effect of contamination on the tape surface. This redundant track scheme was previously used on the MIT Whirlwind tape system.
Adjacent dialects typically have relatively high degrees of mutual intelligibility, but the degree of mutual intelligibility between nonadjacent dialects varies considerably. In some cases speakers of nonadjacent dialects may not understand each other's speech.Hockett, Charles F., 1958, pp. 323–326 develops a model of language complexes; he uses the term "L-complex" A survey conducted during the 1980s and 1990s found that the differences between Ottawa, the Severn Ojibwe dialect spoken in northwestern Ontario and northern Manitoba, and the Algonquin dialect spoken in western Quebec result in low levels of mutual intelligibility.
Let S be an (a,b)-separator, that is, a vertex subset that separates two nonadjacent vertices a and b. Then S is a minimal (a,b)-separator if no proper subset of S separates a and b. More generally, S is called a minimal separator if it is a minimal separator for some pair (a,b) of nonadjacent vertices. Notice that this is different from minimal separating set which says that no proper subset of S is a minimal (u,v)-separator for any pair of vertices (u,v).
In geometry, the triaugmented hexagonal prism is one of the Johnson solids (J57). As the name suggests, it can be constructed by triply augmenting a hexagonal prism by attaching square pyramids (J1) to three of its nonadjacent equatorial faces.
The NH groups are nonadjacent. A common route to imidazol-2-ones involves condensation of ureas and acyloins. Some are of interest in the pharmaceuticals. 4-Imidazolones arise from the condensation of amidines with 1,2-dicarbonyls such as glyoxal.
In graph theory, a vertex subset S \subset V is a vertex separator (or vertex cut, separating set) for nonadjacent vertices a and b if the removal of S from the graph separates a and b into distinct connected components.
Forming a prime word by switching the position of nonadjacent letters in the base word is a distant transposition. There is significantly less priming effect in a distant transposition than a close transposition, no matter how distant the two letters are from each other.
Moreover, except for complete graphs, equals the minimum of over all nonadjacent pairs of vertices . -connectivity is also called biconnectivity and -connectivity is also called triconnectivity. A graph which is connected but not -connected is sometimes called separable. Analogous concepts can be defined for edges.
Switching {X,Y} in a graph A two-graph is equivalent to a switching class of graphs and also to a (signed) switching class of signed complete graphs. Switching a set of vertices in a (simple) graph means reversing the adjacencies of each pair of vertices, one in the set and the other not in the set: thus the edge set is changed so that an adjacent pair becomes nonadjacent and a nonadjacent pair becomes adjacent. The edges whose endpoints are both in the set, or both not in the set, are not changed. Graphs are switching equivalent if one can be obtained from the other by switching.
The structure of a foldamer is stabilized by noncovalent interactions between nonadjacent monomers. Foldamers are studied with the main goal of designing large molecules with predictable structures. The study of foldamers is related to the themes of molecular self-assembly, molecular recognition, and host–guest chemistry.
Some optional enhanced channel rejection requirements (for both adjacent and nonadjacent channels) are specified in this amendment in order to improve the immunity of the communication system to out-of-channel interference. They only apply to OFDM transmissions in the 5 GHz band used by the IEEE 802.11a physical layer.
In geometry, the metabidiminished icosahedron is one of the Johnson solids (J62). The name refers to one way of constructing it, by removing two pentagonal pyramids from a regular icosahedron, replacing two sets of five triangular faces of the icosahedron with two adjacent pentagonal faces. If two pentagonal pyramids are removed to form nonadjacent pentagonal faces, the result is instead the pentagonal antiprism.
Equivalently, every -critical graph (a graph that requires colors but for which every proper subgraph requires fewer colors) is -constructible.A proof can also be found in . Alternatively, every graph that requires colors may be formed by combining the Hajós construction, the operation of identifying any two nonadjacent vertices, and the operations of adding a vertex or edge to the given graph, starting from the complete graph ., p. 184.
Valentine, J. Randolph, 1994, pp. 42–43. While each of these dialects has undergone innovations that make them distinctive, their status as part of the Ojibwe language complex is not in dispute. The relatively low degrees of mutual intelligibility between some nonadjacent Ojibwe dialects led Rhodes and Todd to suggest that Ojibwe should be analyzed as a linguistic subgroup consisting of several languages.Rhodes, Richard and E. Todd, 1981, p. 52.
Among his literary contemporaries, Richard Kostelanetz has also produced literature in audio, video, holography, prints, book-art, computer-based installations, among other new media. Though he coined the term "polyartist" to characterize people who excel at two or more nonadjacent arts, he considers that, since nearly all his creative work incorporates language or literary forms, it represents Writing reflecting polyartistry. "Wordsand" (1978–81) was a traveling early retrospective of his work in several media.
Interspersed repetitive DNA is found in all eukaryotic genomes. They differ from tandem repeat DNA in that rather than the repeat sequences coming right after one another, they are dispersed throughout the genome and nonadjacent. The sequence that repeats can vary depending on the type of organism, and many other factors. Certain classes of interspersed repeat sequences propagate themselves by RNA mediated transposition; they have been called retrotransposons, and they constitute 25–40% of most mammalian genomes.
A rigid graph is an embedding of a graph in a Euclidean space which is structurally rigid. That is, a graph is rigid if the structure formed by replacing the edges by rigid rods and the vertices by flexible hinges is rigid. A graph that is not rigid is called flexible. More formally, a graph embedding is flexible if the vertices can be moved continuously, preserving the distances between adjacent vertices, with the result that the distances between some nonadjacent vertices are altered.
The Fredrick C. Sorensen House in Ephraim, a Type II pair house with window- door-window cluster at center room. Note pair of internal chimneys piercing roof ridge. While some pair-houses are individually listed on the National Register of Historic Places (NRHP), a collection of such houses in Utah, nonadjacent and disconnected, have been documented as the Scandinavian- American Pair-house Thematic Group. These houses span four Utah counties and represent the "multi-cultural nature of early Mormon society".
If the faces of the pentagonal antiprism are all regular, it is a semiregular polyhedron. It can also be considered as a parabidiminished icosahedron, a shape formed by removing two pentagonal pyramids from a regular icosahedron leaving two nonadjacent pentagonal faces; a related shape, the metabidiminished icosahedron (one of the Johnson solids), is likewise form from the icosahedron by removing two pyramids, but its pentagonal faces are adjacent to each other. The two pentagonal faces of either shape can be augmented with pyramids to form the icosahedron.
A closely related theorem by states that an n-vertex strongly connected digraph with the property that, for every two nonadjacent vertices u and v, the total number of edges incident to u or v is at least 2n − 1 must be Hamiltonian. Ore's theorem may also be strengthened to give a stronger conclusion than Hamiltonicity as a consequence of the degree condition in the theorem. Specifically, every graph satisfying the conditions of Ore's theorem is either a regular complete bipartite graph or is pancyclic .
Free energy diagram of the folding of a foldamer. Foldamers can vary in size, but they are defined by the presence of noncovalent, nonadjacent interactions. This definition excludes molecules like poly(isocyanates) (commonly known as (polyurethane)) and poly(prolines) as they fold into helices reliably due to adjacent covalent interactions., Foldamers have a dynamic folding reaction [unfolded → folded], in which large macroscopic folding is caused by solvophobic effects (hydrophobic collapse), while the final energy state of the folded foldamer is due to the noncovalent interactions.
The Bondy–Chvátal theorem operates on the closure cl(G) of a graph G with n vertices, obtained by repeatedly adding a new edge uv connecting a nonadjacent pair of vertices u and v with until no more pairs with this property can be found. :Bondy–Chvátal Theorem (1976). A graph is Hamiltonian if and only if its closure is Hamiltonian. As complete graphs are Hamiltonian, all graphs whose closure is complete are Hamiltonian, which is the content of the following earlier theorems by Dirac and Ore.
Ore's theorem is a generalization of Dirac's theorem that, when each vertex has degree at least , the graph is Hamiltonian. For, if a graph meets Dirac's condition, then clearly each pair of vertices has degrees adding to at least . In turn Ore's theorem is generalized by the Bondy–Chvátal theorem. One may define a closure operation on a graph in which, whenever two nonadjacent vertices have degrees adding to at least , one adds an edge connecting them; if a graph meets the conditions of Ore's theorem, its closure is a complete graph.
However, the square of the subgraph of edges of weight at most is Hamiltonian. By the triangle inequality for metric spaces, its Hamiltonian cycle has edges of weight at most ... This approximation ratio is best possible. For, any unweighted graph can be transformed into a metric space by setting its edge weights to and setting the distance between all nonadjacent pairs of vertices to . An approximation with ratio better than in this metric space could be used to determine whether the original graph contains a Hamiltonian cycle, an NP-complete problem.
The final partial structure consists of a thiazoline ring with a terminal alkene substituent, as determined by electron ionization mass spectrometry (EI-MS) and 13C NMR. The chemical shifts of ring carbons adjacent to the sulfur and nitrogen heteroatoms were compared to 13C NMR data from model compounds. This allowed for the determination of these heteroatoms' locations in the ring, and subsequently the existence of the thiazoline ring itself. With these partial structures established, their connectivity was evaluated via HMBC spectroscopy, a 2D NMR technique which allows for the determination of heteronuclear J-coupling values for nonadjacent carbons and protons.
A unit distance drawing of the Möbius-Kantor graph in which some nonadjacent pairs are also at unit distance from each other. Some sources define a graph as being a unit distance graph if its vertices can be mapped to distinct locations in the plane such that adjacent pairs are at unit distance apart, disregarding the possibility that some non-adjacent pairs might also be at unit distance apart. For instance, the Möbius-Kantor graph has a drawing of this type. According to this looser definition of a unit distance graph, all generalized Petersen graphs are unit distance graphs.
This DOC is broken into two near but nonadjacent areas that envelop Lucca and are separated by the Serchio River. The western (and larger) portion of the DOC reaches Pescaglia in the north and Massarosa to the west, while the eastern portion of the DOC abuts Pescia to the east, Villa Basilica to the north and Capannori and Porcari to the south. The soil of Colline Lucchesi is often composed of clay mixed with gravel, and many of the parcels in this area favor the production of Merlot. Both sections of the DOC are at the foot of the Apennine Mountains.
The straight skeleton of a polygon is defined by a continuous shrinking process in which the edges of the polygon are moved inwards parallel to themselves at a constant speed. As the edges move in this way, the vertices where pairs of edges meet also move, at speeds that depend on the angle of the vertex. If one of these moving vertices collides with a nonadjacent edge, the polygon is split in two by the collision, and the process continues in each part. The straight skeleton is the set of curves traced out by the moving vertices in this process.
If a graph G is formed from the Rado graph by deleting any finite number of edges or vertices, or adding a finite number of edges, the change does not affect the extension property of the graph. For any pair of sets U and V it is still possible to find a vertex in the modified graph that is adjacent to everything in U and nonadjacent to everything in V, by adding the modified parts of G to V and applying the extension property in the unmodified Rado graph. Therefore, any finite modification of this type results in a graph that is isomorphic to the Rado graph., Section 1.3: Indestructibility.
In this case, Lovász shows that one can find a spanning tree such that two nonadjacent neighbors u and w of the root v are leaves in the tree. A greedy coloring starting from u and w and processing the remaining vertices of the spanning tree in bottom-up order, ending at v, uses at most Δ colors. For, when every vertex other than v is colored, it has an uncolored parent, so its already-colored neighbors cannot use up all the free colors, while at v the two neighbors u and w have equal colors so again a free color remains for v itself.
Pierre Cardin used his name as a brand, initially a prestigious fashion brand, then in the 1960s extended successfully into perfumes and cosmetics. From about 1988 the brand was licensed extensively, and appeared on "wildly nonadjacent products such as baseball caps and cigarettes". alt=Pierre Cardin-branded pen A 2005 article in the Harvard Business Review commented that the extension into perfumes and cosmetics was successful as the premium nature of the Pierre Cardin brand transferred well into these new, adjacent categories, but that the owners of the brand mistakenly attributed this to the brand's strength rather than to its fit with the new product categories. The extensive licensing eroded the brand's credibility, but brought in much revenue; in 1986 Women's Wear Daily (WWD) estimated Cardin's annual income at over US$10 million.
Ontario Heritage Plaque in Ojibwe at the Battle of the Thames historical site Because the dialects of Ojibwe are at least partly mutually intelligible, Ojibwe is usually considered to be a single language with a number of dialects, i.e. Ojibwe is "... conventionally regarded as a single language consisting of a continuum of dialectal varieties since ... every dialect is at least partly intelligible to the speakers of the neighboring dialects."Rhodes, Richard, and Evelyn Todd, 1981, p. 52. The degree of mutual intelligibility between nonadjacent dialects varies considerably; recent research has shown that there is strong differentiation between the Ottawa dialect spoken in southern Ontario and northern Michigan; the Severn Ojibwa dialect spoken in northern Ontario and Manitoba; and the Algonquin dialect spoken in southwestern Quebec.Valentine, J. Randolph, 1994.
Gray wolf in YellowStone National Park A clear example of humans ecosynthesiszing would be through the introduction of a species to cause a trophic cascade, which is the result of indirect effects between nonadjacent trophic levels in a food chain or food web, such as the top predator in a food chain and a plant.Christina Eisenberg, (2010), The wolf's tooth : keystone predators, trophic cascades, and biodiversity, The most famous example of a trophic cascade is that of the introduction of wolves to Yellowstone National Park, which had extradionary effects to the ecosystem. Yellowstone had a massive population of elk because they had no predators, which caused the local aspen population and other vegetation to significantly decrease in population size. However, the introduction of wolves controlled the elk population and indirectly affected the aspen and other vegetation, bringing the ecosystem back to sustainability.
The vertex-connectivity of an input graph G can be computed in polynomial time in the following wayThe algorithm design manual, p 506, and Computational discrete mathematics: combinatorics and graph theory with Mathematica, p. 290-291 consider all possible pairs (s, t) of nonadjacent nodes to disconnect, using Menger's theorem to justify that the minimal-size separator for (s, t) is the number of pairwise vertex-independent paths between them, encode the input by doubling each vertex as an edge to reduce to a computation of the number of pairwise edge-independent paths, and compute the maximum number of such paths by computing the maximum flow in the graph between s and t with capacity 1 to each edge, noting that a flow of k in this graph corresponds, by the integral flow theorem, to k pairwise edge-independent paths from s to t.
It is straightforward to verify that every -constructible graph requires at least colors in any proper graph coloring. Indeed, this is clear for the complete graph , and the effect of identifying two nonadjacent vertices is to force them to have the same color as each other in any coloring, something that does not reduce the number of colors. In the Hajós construction itself, the new edge forces at least one of the two vertices and to have a different color than the combined vertex for and , so any proper coloring of the combined graph leads to a proper coloring of one of the two smaller graphs from which it was formed, which again causes it to require colors. Hajós proved more strongly that a graph requires at least colors, in any proper coloring, if and only if it contains a -constructible graph as a subgraph.
More specifically, define the Hajós number of a -chromatic graph to be the minimum number of steps needed to construct from , where each step forms a new graph by combining two previously formed graphs, merging two nonadjacent vertices of a previously formed graph, or adding a vertex or edge to a previously formed graph. They showed that, for an -vertex graph with edges, . If every graph has a polynomial Hajós number, this would imply that it is possible to prove non-colorability in nondeterministic polynomial time, and therefore imply that NP = co-NP, a conclusion considered unlikely by complexity theorists.. However, it is not known how to prove non-polynomial lower bounds on the Hajós number without making some complexity-theoretic assumption, and if such a bound could be proven it would also imply the existence of non-polynomial bounds on certain types of Frege system in mathematical logic. The minimum size of an expression tree describing a Hajós construction for a given graph may be significantly larger than the Hajós number of , because a shortest expression for may re-use the same graphs multiple times, an economy not permitted in an expression tree.

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