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1 trivial structure
Большой англо-русский и русско-английский словарь > trivial structure
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2 trivial structure
Математика: тривиальная структура -
3 trivial structure
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4 structure
1) конструкция; строение; структура || структурировать2) сооружение, здание; строительная конструкция3) состав4) текстура5) геол. формация•- finitely generated structure - fish protection structure - locally convex structure - recursively presentable structure - redundant logical structure - strictly finer structure - strongly undecidable structure - weakly saturated structure -
5 тривиальная структура
Большой англо-русский и русско-английский словарь > тривиальная структура
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6 space
1) интервал, промежуток2) пробел || оставлять пробелы3) область; площадь4) пространство || пространственный5) космос, космическое пространство6) полость7) расстояние•- absolutely compact space - absolutely embedded space - absolutely thick space - algebraically parallel space - almost complex space - almost expandable space - almost isomorphic space - almost metric space - almost nonsingular space - almost paracompact space - almost pretopological space - analytically ramified covering space - arcwise connected space - centrally harmonic space - compactly ordered space - completely continuous space - completely degenerate space - completely disconnected space - completely harmonic space - completely metric space - completely normal space - completely reducible space - completely regular space - completely reticulated space - completely separable space - completely separated space - completely symmetric space - completely uniformizable space - constant curvature space - continuous sample space - continuously ordered space - contractible in itself space - countably compactifiable space - countably dimensional space - countably generated space - countably infinite space - countably metacompact space - countably multinormed space - countably normed space - countably paracompact space - countably refinable space - countably subcompact space - finitely productive space - finitely sheeted space - finitely triangulated space - fully normal space - general metrizable space - general topological space - global analytic space - globally symmetric space - hereditarily normal space - hereditarily paracompact space - hereditarily separable space - hereditarily symmetric space - holomorphic tangent space - holomorphically complete space - holomorphically convex space - homotopy associative space - iterated loop space - linearly connected space - linearly ordered space - linearly topologized space - load space - locally bounded space - locally closed space - locally compact space - locally complete space - locally connected space - locally contractible space - locally convex space - locally directed space - locally fine space - locally holomorphic space - locally homogeneous space - locally hyperbolic space - locally linear space - locally metrizable space - locally ringed space - locally separable space - locally simply connected space - locally solid space - locally spherical space - locally star-shaped space - locally symmetric space - locally timelike space - locally triangulable space - monotonically normal space - naturally isomorphic space - naturally ordered space - naturally reductive space - nearly paracompact space - negative metric space - normally separated space - not simply connected space - nowhere connected space - null space of linear transformation - n-way projective space - perfectly normal space - perfectly regular space - perfectly screenable space - perfectly separable space - peripherically bicompact space - peripherically compact space - pointwise paracompact space - projectively metric space - quaternion hyperbolic space - quaternion projective space - quaternion vector space - regularly ordered space - relatively discrete space - relatively strong space - sequentially closed space - sequentially compact space - sequentially complete space - sequentially quasicomplete space - sequentially separable space - simply ordered space - simply partitionable space - space of affine connectedness - space of complex homomorphisms - space of continuous functions - space of finite measure - space of linear interpolation - space of right cosets - space of scalar curvature - strongly bounded space - strongly closed space - strongly compact space - strongly complete space - strongly irreducible space - strongly normal space - strongly normed space - strongly paracompact space - strongly pseudocompact space - strongly pseudometrizable space - strongly rigid space - strongly screenable space - structural space - structure space - topologically complete space - totally disconnected space - totally geodesic space - totally imperfect space - totally normal space - totally orderable space - totally ordered space - water jacket space - weakly closed space - weakly compact space - weakly complete space - weakly covering space - weakly dense space - weakly favorable space - weakly n-dimensional space - weakly paracompact space - weakly regular space - weakly separable space - weakly symmetric spaceto space out — полигр. набирать вразрядку
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7 topology
мат.- boundedly weak topology - jointly continious topology - locally convex topology - rational sequence topology - topology of bounded convergenc - topology of convergence in measure - topology of extended real - topology of local ring - topology of locally uniform convergence - topology of metric space - topology of pointwise convergence - topology of precompact convergence - topology simple convergencetopology with consistent structure of vector space — топология с совместной структурой векторного пространства
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8 cohomology
1) верхний
2) верхняя гомология
3) когомология
4) когомологический ∙ absolute cohomology group ≈ абсолютная когомологическая группа adjusted cohomology sequence ≈ усовершенствованная когомологическая последовательность cohomology [contrahomology] suspension ≈ когомологическая надстройка cohomology of uniform spaces ≈ когомология равномерных пространств curvature cohomology class ≈ когомологический класс direct cohomology group ≈ прямая группа когомологий extraordinary cohomology theor ≈ экстраординарная теория когомологий flat cohomology ring ≈ кольцо бемольных когомологий infinite dimensional cohomology ≈ бесконечномерная когомология integral cohomology class ≈ целочисленный класс когомологий motive cohomology functor ≈ функтор мотивных когомологий partially exact cohomology ≈ частично точная когомология rational cohomology class ≈ рациональный класс когомологий relative cohomology group ≈ группа относительных когомологий transgressive cohomology class ≈ трансгрессив-ный когомологический класс unitary cohomology class ≈ унитарный класс когомологий weak cohomology group ≈ группа слабых когомологий - algebraic cohomology - cellular cohomology - cohomology algebra - cohomology class - cohomology diagram - cohomology dimension - cohomology functor - cohomology group - cohomology invariant - cohomology manifold - cohomology object - cohomology obstruction - cohomology of algebras - cohomology operation - cohomology operator - cohomology representation - cohomology ring - cohomology sequence - cohomology set - cohomology space - cohomology sphere - cohomology structure - cohomology theor - cohomology transgression - commutative cohomology - continuous cohomology - cubic cohomology - differential cohomology - equivariant cohomology - etale cohomology - extraordinary cohomology - filtrated cohomology - flat cohomology - group cohomology - local cohomology - noncommutative cohomology - p-adic cohomology - primitive cohomology - rational cohomology - relative cohomology - singular cohomology - smooth cohomology - spectral cohomology - square-integrable cohomology - standard cohomology - trivial cohomology - two-stage cohomology - vector cohomology - weak cohomology (математика) когомологияБольшой англо-русский и русско-английский словарь > cohomology
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9 group
1) группа, ансамбль || групповой- roughing mill group2) совокупность; комплект3) группировка || группировать(ся)5) класс; категория || классифицировать; категоризировать6) хим. остаток7) сгусток; скопление8) узел9) матем. группа- absolute free group - absolute homotopy group - absolutely irreducible group - absolutely simple group - additively written group - adele group - adelic group - algebraically compact group - algebraically simple group - almost connected group - almost cyclic group - almost ordered group - almost periodic group - almost simple group - alternating form group - cancellative group - cellular homology group - characteristically simple group - complementing group - completely anisotropic group - completely discontinuous group - completely divisible group - completely indecomposable group - completely integrally closed group - deficient group - direct homology group - direct indecomposable group - doubly transitive group - finitely defined group - finitely generated group - finitely presented group - finitely related group - first homology group - first homotopy group - freely generated group - full linear group - full orthogonal group - full rotation group - full symmetric group - full unimodular group - group of classes of algebras - group of covering transformations - group of finite rank - group of infinite order - group of infinite rank - group of inner automorphisms - group of linear equivalence - group of linear forms - group of linear manifold - group of principal ideles - group of real line - group of recursive permutations - group of right quotients - idele class group - linearly ordered group - linearly transitive group - locally bicompact group - locally closed group - locally compact group - locally connected group - locally cyclic group - locally defined group - locally embeddable group - locally finite group - locally free group - locally infinite group - locally nilpotent group - locally normal group - locally solvable group - multiply primitive group - multiply transitive group - nonsolvable group - n-th homotopy group - ordered pair group - principal congruence group - properly orthogonal group - properly unimodular group - pure projective group - pure rotation group - pure simple group - quasipure projective group - quotient divisible group - residually nilpotent group - restricted holonomy group - sharply transitive group - simply ordered group - simply reducible group - simply transitive group - singular cogomology group - singular homology group - solvable group - stable group - strictly transitive group - strongly polycyclic group - subsolvable group - supersolvable group - totally ordered group - totally projective group - totally reducible group - triply transitive group - unitary symmetry group - unitary transformation group - value group - weak homology group - weakly mixing groupgroup with multiple operators — группа с многоместными операторами, мультиоператорная группа
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10 manifold
1) коллектор; магистраль2) гребёнка4) геом. многообразие5) патрубок6) анат. летошка7) рампа; батарея газовых баллонов8) многократный; многократно9) камера; распределитель10) многообразный; разнообразный; разнородный•manifold with boundary — многообразие с границей, многообразие с краем
- almost homogeneous manifold - almost orientable manifold - almost parallelizable manifold - almost smooth manifold - completely parallelizable manifold - finitely compact manifold - finitely triangulated manifold - globally harmonic manifold - holomorphically convex manifold - locally homogeneous complex manifold - locally plane manifold - locally symmetric manifold - locally trivial manifold - locally unknotted manifold - maximal integral manifold - orbitally asymptotically stable manifold - strongly harmonic manifold - unlimited covering manifold - weighted homogeneous manifoldmanifold without boundaries — многообразие без границ, многообразие с краем
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11 sheaf
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12 capital
1. n столица; главный город2. n прописная, заглавная или большая букваcapital letter — прописная буква; заглавная буква
3. a столичный, главный4. a прописной, заглавный, большой5. a главный, основной, самый важный; капитальныйcapital error — основная ошибка; роковое заблуждение
6. a юр. караемый смертью; тяжкийcapital crime — преступление, за которое предусматривается смертная казнь
7. a разг. превосходный, отличный8. a уст. относящийся к голове9. n эк. основной капитал10. n эк. акционерный капиталstructure of capital — структура капитала; строение капитала
impaired capital — капитал, который меньше объявленной суммы
composition of capital — состав капитала; структура капитала
11. n фин. основная сумма12. n капитал, капиталисты, класс капиталистовlocked-up capital — капитал, вложенный в неликвидные активы
13. n выгода, преимущество14. a эк. относящийся к капиталу15. a эк. относящийся к основному капиталу16. n архит. капительСинонимический ряд:1. chief (adj.) cardinal; chief; dominant; first; foremost; important; key; leading; main; number one; outstanding; paramount; predominant; preeminent; pre-eminent; premier; primary; principal; star; stellar; vital2. egregious (adj.) egregious; flagrant; glaring; gross; rank3. excellent (adj.) A1; bang-up; banner; best; blue-ribbon; bully; champion; choice; classic; classical; crack; excellent; famous; fine; first-class; first-rate; first-string; five-star; front-rank; good; Grade A; great; incomparable; par excellence; prime; quality; royal; skookum; sovereign; splendid; stunning; superb; superior; tiptop; top; topflight; top-notch; whiz-bang4. serious (adj.) deadly; fatal; heinous; major; serious5. center (noun) center; governmental seat; headquarters6. metropolis (noun) center of government; metropolis; municipality; principal city; seat of government7. moneys (noun) finances; funds; moneys8. resources (noun) assets; cash; fortune; interests; investment; means; money; principal; property; resources; wealth; wherewithal9. upper case (noun) large; large-size letter; majuscule; uncial; uncial letter; upper case; upper case letterАнтонимический ряд:bad; debts; inferior; mean; minor; poor; secondary; subordinate; trivial; unimportant -
13 minute
1. n астр. мат. минута2. n короткий промежуток времени, мгновение; моментfor a minute — на минуту, на мгновение
wait a minute! — обожди минуту!, погоди!, сейчас!
3. v рассчитывать время по минутам; хронометрировать4. a мелкий, мельчайший5. a подробный, детальный6. a незначительный, несущественный; мелкий7. a мелочный8. a тех. точный, прецизионный9. n заметка, набросок, короткая запись10. n протокол11. v набрасывать начерно; делать заметки, записывать12. v вести протокол, протоколироватьСинонимический ряд:1. detailed (adj.) critical; detailed; exact; precise2. full (adj.) blow-by-blow; circumstantial; clocklike; full; itemised; itemized; particular; particularised; particularized; thorough3. little (adj.) casual; inconsiderable; insignificant; light; little; minor; petty; shoestring; small-beer; trivial; unimportant4. small (adj.) diminutive; infinitesimal; microscopic; miniature; miniscule; minuscule; small5. tiny (adj.) dwarf; dwarfish; itsy-bitsy; itty-bitty; lilliputian; midget; minikin; peewee; pint-size; pocket; pocket-size; pygmy; teensy; teensy-weensy; teenty; teeny; teeny-weeny; tiny; wee; weensy; weeny6. instant (noun) breathing; crack; flash; instant; jiffy; moment; second; shake; split second; trice; twinkle; twinkling; winkАнтонимический ряд:big; broad; bulky; capacious; colossal; commodious; comprehensive; considerable; enormous; extensive; general; great; heavy; huge; important -
14 Creativity
Put in this bald way, these aims sound utopian. How utopian they areor rather, how imminent their realization-depends on how broadly or narrowly we interpret the term "creative." If we are willing to regard all human complex problem solving as creative, then-as we will point out-successful programs for problem solving mechanisms that simulate human problem solvers already exist, and a number of their general characteristics are known. If we reserve the term "creative" for activities like discovery of the special theory of relativity or the composition of Beethoven's Seventh Symphony, then no example of a creative mechanism exists at the present time. (Simon, 1979, pp. 144-145)Among the questions that can now be given preliminary answers in computational terms are the following: how can ideas from very different sources be spontaneously thought of together? how can two ideas be merged to produce a new structure, which shows the influence of both ancestor ideas without being a mere "cut-and-paste" combination? how can the mind be "primed," so that one will more easily notice serendipitous ideas? why may someone notice-and remember-something fairly uninteresting, if it occurs in an interesting context? how can a brief phrase conjure up an entire melody from memory? and how can we accept two ideas as similar ("love" and "prove" as rhyming, for instance) in respect of a feature not identical in both? The features of connectionist AI models that suggest answers to these questions are their powers of pattern completion, graceful degradation, sensitization, multiple constraint satisfaction, and "best-fit" equilibration.... Here, the important point is that the unconscious, "insightful," associative aspects of creativity can be explained-in outline, at least-by AI methods. (Boden, 1996, p. 273)There thus appears to be an underlying similarity in the process involved in creative innovation and social independence, with common traits and postures required for expression of both behaviors. The difference is one of product-literary, musical, artistic, theoretical products on the one hand, opinions on the other-rather than one of process. In both instances the individual must believe that his perceptions are meaningful and valid and be willing to rely upon his own interpretations. He must trust himself sufficiently that even when persons express opinions counter to his own he can proceed on the basis of his own perceptions and convictions. (Coopersmith, 1967, p. 58)he average level of ego strength and emotional stability is noticeably higher among creative geniuses than among the general population, though it is possibly lower than among men of comparable intelligence and education who go into administrative and similar positions. High anxiety and excitability appear common (e.g. Priestley, Darwin, Kepler) but full-blown neurosis is quite rare. (Cattell & Butcher, 1970, p. 315)he insight that is supposed to be required for such work as discovery turns out to be synonymous with the familiar process of recognition; and other terms commonly used in the discussion of creative work-such terms as "judgment," "creativity," or even "genius"-appear to be wholly dispensable or to be definable, as insight is, in terms of mundane and well-understood concepts. (Simon, 1989, p. 376)From the sketch material still in existence, from the condition of the fragments, and from the autographs themselves we can draw definite conclusions about Mozart's creative process. To invent musical ideas he did not need any stimulation; they came to his mind "ready-made" and in polished form. In contrast to Beethoven, who made numerous attempts at shaping his musical ideas until he found the definitive formulation of a theme, Mozart's first inspiration has the stamp of finality. Any Mozart theme has completeness and unity; as a phenomenon it is a Gestalt. (Herzmann, 1964, p. 28)Great artists enlarge the limits of one's perception. Looking at the world through the eyes of Rembrandt or Tolstoy makes one able to perceive aspects of truth about the world which one could not have achieved without their aid. Freud believed that science was adaptive because it facilitated mastery of the external world; but was it not the case that many scientific theories, like works of art, also originated in phantasy? Certainly, reading accounts of scientific discovery by men of the calibre of Einstein compelled me to conclude that phantasy was not merely escapist, but a way of reaching new insights concerning the nature of reality. Scientific hypotheses require proof; works of art do not. Both are concerned with creating order, with making sense out of the world and our experience of it. (Storr, 1993, p. xii)The importance of self-esteem for creative expression appears to be almost beyond disproof. Without a high regard for himself the individual who is working in the frontiers of his field cannot trust himself to discriminate between the trivial and the significant. Without trust in his own powers the person seeking improved solutions or alternative theories has no basis for distinguishing the significant and profound innovation from the one that is merely different.... An essential component of the creative process, whether it be analysis, synthesis, or the development of a new perspective or more comprehensive theory, is the conviction that one's judgment in interpreting the events is to be trusted. (Coopersmith, 1967, p. 59)In the daily stream of thought these four different stages [preparation; incubation; illumination or inspiration; and verification] constantly overlap each other as we explore different problems. An economist reading a Blue Book, a physiologist watching an experiment, or a business man going through his morning's letters, may at the same time be "incubating" on a problem which he proposed to himself a few days ago, be accumulating knowledge in "preparation" for a second problem, and be "verifying" his conclusions to a third problem. Even in exploring the same problem, the mind may be unconsciously incubating on one aspect of it, while it is consciously employed in preparing for or verifying another aspect. (Wallas, 1926, p. 81)he basic, bisociative pattern of the creative synthesis [is] the sudden interlocking of two previously unrelated skills, or matrices of thought. (Koestler, 1964, p. 121)11) The Earliest Stages in the Creative Process Involve a Commerce with DisorderEven to the creator himself, the earliest effort may seem to involve a commerce with disorder. For the creative order, which is an extension of life, is not an elaboration of the established, but a movement beyond the established, or at least a reorganization of it and often of elements not included in it. The first need is therefore to transcend the old order. Before any new order can be defined, the absolute power of the established, the hold upon us of what we know and are, must be broken. New life comes always from outside our world, as we commonly conceive that world. This is the reason why, in order to invent, one must yield to the indeterminate within him, or, more precisely, to certain illdefined impulses which seem to be of the very texture of the ungoverned fullness which John Livingston Lowes calls "the surging chaos of the unexpressed." (Ghiselin, 1985, p. 4)New life comes always from outside our world, as we commonly conceive our world. This is the reason why, in order to invent, one must yield to the indeterminate within him, or, more precisely, to certain illdefined impulses which seem to be of the very texture of the ungoverned fullness which John Livingston Lowes calls "the surging chaos of the unexpressed." Chaos and disorder are perhaps the wrong terms for that indeterminate fullness and activity of the inner life. For it is organic, dynamic, full of tension and tendency. What is absent from it, except in the decisive act of creation, is determination, fixity, and commitment to one resolution or another of the whole complex of its tensions. (Ghiselin, 1952, p. 13)[P]sychoanalysts have principally been concerned with the content of creative products, and with explaining content in terms of the artist's infantile past. They have paid less attention to examining why the artist chooses his particular activity to express, abreact or sublimate his emotions. In short, they have not made much distinction between art and neurosis; and, since the former is one of the blessings of mankind, whereas the latter is one of the curses, it seems a pity that they should not be better differentiated....Psychoanalysis, being fundamentally concerned with drive and motive, might have been expected to throw more light upon what impels the creative person that in fact it has. (Storr, 1993, pp. xvii, 3)A number of theoretical approaches were considered. Associative theory, as developed by Mednick (1962), gained some empirical support from the apparent validity of the Remote Associates Test, which was constructed on the basis of the theory.... Koestler's (1964) bisociative theory allows more complexity to mental organization than Mednick's associative theory, and postulates "associative contexts" or "frames of reference." He proposed that normal, non-creative, thought proceeds within particular contexts or frames and that the creative act involves linking together previously unconnected frames.... Simonton (1988) has developed associative notions further and explored the mathematical consequences of chance permutation of ideas....Like Koestler, Gruber (1980; Gruber and Davis, 1988) has based his analysis on case studies. He has focused especially on Darwin's development of the theory of evolution. Using piagetian notions, such as assimilation and accommodation, Gruber shows how Darwin's system of ideas changed very slowly over a period of many years. "Moments of insight," in Gruber's analysis, were the culminations of slow long-term processes.... Finally, the information-processing approach, as represented by Simon (1966) and Langley et al. (1987), was considered.... [Simon] points out the importance of good problem representations, both to ensure search is in an appropriate problem space and to aid in developing heuristic evaluations of possible research directions.... The work of Langley et al. (1987) demonstrates how such search processes, realized in computer programs, can indeed discover many basic laws of science from tables of raw data.... Boden (1990a, 1994) has stressed the importance of restructuring the problem space in creative work to develop new genres and paradigms in the arts and sciences. (Gilhooly, 1996, pp. 243-244; emphasis in original)Historical dictionary of quotations in cognitive science > Creativity
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