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CONTRACTION
Contraction may refer to: Linguistics * Contraction (grammar), a shortened word * Poetic contraction, omission of letters for poetic reasons * Elision, omission of sounds ** Syncope (phonology), omission of sounds in a word * Synalepha, merged syllables ** Synaeresis, combined vowels ** Crasis, merged vowels or diphthongs Mathematics and logic * Contraction (operator theory), in operator theory, state of a bounded operator between normed vector spaces after suitable scaling * Contraction hierarchies, in applied mathematics, a technique to speed up shortest-path routing * Contraction mapping, a type of function on a metric space * Edge contraction or vertex contraction, graph operations used in graph theory * Tensor contraction, an operation on one or more tensors that arises from the natural pairing of a finite-dimensional vector space and its dual * Geometric algebra#Extensions of the inner and exterior products, Left contraction and right contraction of multivectors in a geo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contraction Hierarchies
In computer science, the method of contraction hierarchies is a speed-up technique for finding the shortest-path in a graph. The most intuitive applications are car-navigation systems: a user wants to drive from A to B using the quickest possible route. The metric optimized here is the travel time. Intersections are represented by vertices, the road sections connecting them by edges. The edge weights represent the time it takes to drive along this segment of the road. A path from A to B is a sequence of edges (road sections); the shortest path is the one with the minimal sum of edge weights among all possible paths. The shortest path in a graph can be computed using Dijkstra's algorithm but, given that road networks consist of tens of millions of vertices, this is impractical. Contraction hierarchies is a speed-up method optimized to exploit properties of graphs representing road networks. The speed-up is achieved by creating shortcuts in a preprocessing phase which are then used ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Muscle Contraction
Muscle contraction is the activation of tension-generating sites within muscle cells. In physiology, muscle contraction does not necessarily mean muscle shortening because muscle tension can be produced without changes in muscle length, such as when holding something heavy in the same position. The termination of muscle contraction is followed by muscle relaxation, which is a return of the muscle fibers to their low tension-generating state. For the contractions to happen, the muscle cells must rely on the interaction of two types of filaments which are the thin and thick filaments. Thin filaments are two strands of actin coiled around each, and thick filaments consist of mostly elongated proteins called myosin. Together, these two filaments form myofibrils which are important organelles in the skeletal muscle system. Muscle contraction can also be described based on two variables: length and tension. A muscle contraction is described as isometric if the muscle tension changes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contraction (grammar)
A contraction is a shortened version of the spoken and written forms of a word, syllable, or word group, created by omission of internal letters and sounds. In linguistic analysis, contractions should not be confused with crasis, abbreviations and initialisms (including acronyms), with which they share some semantic and phonetic functions, though all three are connoted by the term "abbreviation" in layman’s terms. Contraction is also distinguished from morphological clipping, where beginnings and endings are omitted. The definition overlaps with the term portmanteau (a linguistic ''blend''), but a distinction can be made between a portmanteau and a contraction by noting that contractions are formed from words that would otherwise appear together in sequence, such as ''do'' and ''not'', whereas a portmanteau word is formed by combining two or more existing words that all relate to a singular concept that the portmanteau describes. English English has a number of con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wound Contraction
Wound healing refers to a living organism's replacement of destroyed or damaged tissue by newly produced tissue. In undamaged skin, the epidermis (surface, epithelial layer) and dermis (deeper, connective layer) form a protective barrier against the external environment. When the barrier is broken, a regulated sequence of biochemical events is set into motion to repair the damage. This process is divided into predictable phases: blood clotting (hemostasis), inflammation, tissue growth ( cell proliferation), and tissue remodeling (maturation and cell differentiation). Blood clotting may be considered to be part of the inflammation stage instead of a separate stage. The wound healing process is not only complex but fragile, and it is susceptible to interruption or failure leading to the formation of non-healing chronic wounds. Factors that contribute to non-healing chronic wounds are diabetes, venous or arterial disease, infection, and metabolic deficiencies of old age.Enoch, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elision
In linguistics, an elision or deletion is the omission of one or more sounds (such as a vowel, a consonant, or a whole syllable) in a word or phrase. However, these terms are also used to refer more narrowly to cases where two words are run together by the omission of a final sound. An example is the elision of word-final /t/ in English if it is preceded and followed by a consonant: "first light" is often pronounced /fɜ:s laɪt/. Many other terms are used to refer to particular cases where sounds are omitted. Citation forms and contextual forms A word may be spoken individually in what is called the Lemma (morphology), citation form. This corresponds to the pronunciation given in a dictionary. However, when words are spoken in context, it often happens that some sounds that belong to the citation form are omitted. Elision is not an all-or-nothing process: elision is more likely to occur in some styles of speaking and less likely in others. Many writers have described the styles ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Synaeresis
In linguistics, synaeresis (; also spelled syneresis) is a phonological process of sound change in which two adjacent vowels within a word are ''combined'' into a single syllable. The opposite process, in which two adjacent vowels are pronounced separately, is known as " diaeresis". For any given word, speakers generally hold a traditional view about the ''standard'' pronunciation of that word. When realized in a careful reading style, each particular word is associated with this single, ''standard'' phonetic form. However, each word also possesses multiple non-standard or reduced phonetic forms which are produced in a greater range of contexts. These multiple variations in the pronunciation of a single word are referred to as allophonic variants. To classify one of these other forms as an allophonic variant of a word means that pronouncing the word in this way will not change the intended meaning of the word. Synaeresis is one of various phonological processes in which seg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uterine Contraction
Uterine contractions are muscle contractions of the uterine smooth muscle that occur during the menstrual cycle and labour. Uterine contractions occur throughout the menstrual cycle in the non-pregnant state and throughout gestation. Throughout menstrual cycle Uterine contractions that occur throughout the menstrual cycle, also termed ''endometrial waves'' or ''contractile waves'', appear to involve only the sub-endometrial layer of the myometrium. Follicular and luteal phase In the early follicular phase, uterine contractions in the non-pregnant woman occur 1—2 times per minute and last 10–15 seconds with a low intensity of usually 30 mmHg or less. This sub-endometrial layer is rich in estrogen and progesterone receptors. The frequency of contractions increases to 3–4 per minute towards ovulation. During the luteal phase, the frequency and intensity decrease, possibly to facilitate any implantation. Menstruation If implantation does not occur, the frequency of contraction ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contraction Mapping
In mathematics, a contraction mapping, or contraction or contractor, on a metric space (''M'', ''d'') is a function ''f'' from ''M'' to itself, with the property that there is some real number 0 \leq k < 1 such that for all ''x'' and ''y'' in ''M'', : The smallest such value of ''k'' is called the Lipschitz constant of ''f''. Contractive maps are sometimes called Lipschitzian maps. If the above condition is instead satisfied for ''k'' ≤ 1, then the mapping is said to be a . More generally, the idea of a contractive mapping can be defined for maps between metric spaces. Thus, if (''M'', ''d'') and (''N'', ''d) are two metric spaces, then is a contractive mapping if there is a constant such that : [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contraction (operator Theory)
In operator theory, a bounded operator ''T'': ''X'' → ''Y'' between normed vector spaces ''X'' and ''Y'' is said to be a contraction if its operator norm , , ''T'' , , ≤ 1. This notion is a special case of the concept of a contraction mapping, but every bounded operator becomes a contraction after suitable scaling. The analysis of contractions provides insight into the structure of operators, or a family of operators. The theory of contractions on Hilbert space is largely due to Béla Szőkefalvi-Nagy and Ciprian Foias. Contractions on a Hilbert space If ''T'' is a contraction acting on a Hilbert space \mathcal, the following basic objects associated with ''T'' can be defined. The defect operators of ''T'' are the operators ''DT'' = (1 − ''T*T'')½ and ''DT*'' = (1 − ''TT*'')½. The square root is the square root of a matrix, positive semidefinite one given by the spectral theorem. The defect spaces \mathcal_T a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edge Contraction
In graph theory, an edge contraction is an operation that removes an edge from a graph while simultaneously merging the two vertices that it previously joined. Edge contraction is a fundamental operation in the theory of graph minors. Vertex identification is a less restrictive form of this operation. Definition The edge contraction operation occurs relative to a particular edge, e. The edge e is removed and its two incident vertices, u and v, are merged into a new vertex w, where the edges incident to w each correspond to an edge incident to either u or v. More generally, the operation may be performed on a set of edges by contracting each edge (in any order). The resulting induced graph is sometimes written as G/e. (Contrast this with G \setminus e, which means removing the edge e.) As defined below, an edge contraction operation may result in a graph with multiple edges even if the original graph was a simple graph. However, some authors disallow the creation of multip ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tensor Contraction
In multilinear algebra, a tensor contraction is an operation on a tensor that arises from the natural pairing of a finite-dimensional vector space and its dual. In components, it is expressed as a sum of products of scalar components of the tensor(s) caused by applying the summation convention to a pair of dummy indices that are bound to each other in an expression. The contraction of a single mixed tensor occurs when a pair of literal indices (one a subscript, the other a superscript) of the tensor are set equal to each other and summed over. In Einstein notation this summation is built into the notation. The result is another tensor with order reduced by 2. Tensor contraction can be seen as a generalization of the trace. Abstract formulation Let ''V'' be a vector space over a field ''k''. The core of the contraction operation, and the simplest case, is the natural pairing of ''V'' with its dual vector space ''V''∗. The pairing is the linear transformation from the tensor p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Syncope (phonology)
In phonology, syncope (; from grc, , , cutting up) is the loss of one or more sounds from the interior of a word, especially the loss of an unstressed vowel. It is found in both synchronic and diachronic analyses of languages. Its opposite, whereby sounds are added, is epenthesis. Synchronic analysis Synchronic analysis studies linguistic phenomena at one moment of a language's history, usually the present, in contrast to diachronic analysis, which studies a language's states and the patterns of change across a historical timeframe. In modern languages, syncope occurs in inflection, poetry, and informal speech. Inflections In languages such as Irish and Hebrew, the process of inflection can cause syncope: * In some verbs : (to play) should become * (I play). However, the addition of the causes syncope and the second-last syllable vowel is lost so becomes . : (katav), (he) wrote, becomes (katvu), (they) wrote, when the third-person plural ending (-u) is added. * I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
