TERMIUM Plus^®

Record 1,  Textual support,  English

Record number: 1, Textual support number: 1 DEF

A space which is linear, metric and complete.  2, record 1, English, - Hilbert%20space

Record number: 1, Textual support number: 1 CONT

In mathematics, a Hilbert space is an inner product space that is complete with respect to the norm defined by the inner product. Hilbert spaces serve to clarify and generalize the concept of Fourier expansion and certain linear transformations such as the Fourier transform.  3, record 1, English, - Hilbert%20space

Record 1,  Textual support,  French

Record number: 1, Textual support number: 1 DEF

En théorie quantique, espace linéaire, métrique et complet des états d'un système physique.  2, record 1, French, - espace%20de%20Hilbert

Record number: 1, Textual support number: 1 OBS

Selon D. Hilbert [...] l'état d'un tel système peut être stationnaire (son attracteur est un point fixe), périodique (son attracteur est un cycle limite), quasi périodique (son attracteur est un tore) ou chaotique (son attracteur est étrange). Chaque état peut être représenté par un vecteur normé. Le produit scalaire hilbertien de deux vecteurs fournit l'amplitude de probabilité de la transition entre les deux états physiques qu'ils représentent. Tout espace préhilbertien séparé de dimension finie est un espace hilbertien.  2, record 1, French, - espace%20de%20Hilbert

Record number: 1, Textual support number: 1 PHR

espace hilbertien complexe, espace hilbertien muni de la norme euclidienne, espace hilbertien réel  2, record 1, French, - espace%20de%20Hilbert

Record 1,  Textual support,  Spanish

Record 2,  Textual support,  English

Record number: 2, Textual support number: 1 DEF

A finite set of maps acting on a metric space, with no particular conditions imposed upon the maps.  2, record 2, English, - iterated%20function%20system

Record number: 2, Textual support number: 1 CONT

Iterated function systems provide a convenient framework for the description, classification, and communication of fractals.  2, record 2, English, - iterated%20function%20system

Record number: 2, Textual support number: 1 OBS

hyperbolic IFS: the word hyperbolic ... is sometimes dropped in practice.  2, record 2, English, - iterated%20function%20system

Record number: 2, Textual support number: 2 OBS

See also hyperbolic IFS with condensation, lifted IFS, IFS with probabilities, invariant measure of IFS.  3, record 2, English, - iterated%20function%20system

Record 2,  Textual support,  French

Record number: 2, Textual support number: 1 CONT

Ces deux auteurs présentent les systèmes de fonctions itératives comme une manière unifiée de classifier et d'engendrer les ensembles fractals.  1, record 2, French, - syst%C3%A8me%20de%20fonctions%20it%C3%A9ratives

Record 2,  Textual support,  Spanish

Record 3,  Textual support,  English

Record number: 3, Textual support number: 1 DEF

A metric space in which every Cauchy sequence is convergent to an element in that space.  2, record 3, English, - complete%20space

Record 3,  Textual support,  French

Record 3,  Textual support,  Spanish

Record 4,  Textual support,  English

Record number: 4, Textual support number: 1 CONT

A principal sensor on board the satellite is the Space-Based Visible(SBV) sensor, a visible-band electro-optical camera designed... to perform the first technical and functional demonstration of space-based space surveillance. The principal task of the SBV sensor is to gather metric and photometric information on a variety of resident space objects(RSO).... Currently, the resident space object(RSO) catalog contains more than 8000 entries, consisting of active and inactive satellites, rocket bodies, and debris, with an active subset of over 800 objects.  2, record 4, English, - resident%20space%20object

Record number: 4, Textual support number: 2 CONT

We have created a catalog containing observations of over 1000 resident space objects (RSOs) by the infrared (IR) telescope on the Midcourse Space Experiment. These objects, a mix of satellites, rocket bodies, boosters, and debris, were serendipitously detected while the telescope was performing its primary mission.  3, record 4, English, - resident%20space%20object

Record number: 4, Textual support number: 1 OBS

resident space object; RSO: term and abbreviation officially approved by the Department of National Defence and the Canadian Forces.  4, record 4, English, - resident%20space%20object

Record 4,  Textual support,  French

Record number: 4, Textual support number: 1 OBS

objet spatial en orbite; OSO : terme et abréviation uniformisés par le ministère de la Défense nationale et les Forces canadiennes.  2, record 4, French, - objet%20spatial%20en%20orbite

Record 4,  Textual support,  Spanish

Record 5,  Textual support,  English

Record number: 5, Textual support number: 1 CONT

The Raffaello Multi-Purpose Logistics Module(MPLM), built by the Italian Space Agency(ASI), is the second of three such pressurized modules that will serve as the International Space Station's "moving vans", carrying laboratory racks filled with equipment, experiments and supplies to and from the International Space Station aboard the space shuttle. Construction of ASI's Raffaello module was the responsibility of Alenia Aerospazio in Turin, Italy. Raffaello was delivered to Kennedy Space Center from Italy in July 1999 by a special Beluga cargo aircraft. The cylindrical module is about 6. 4 meters(21 feet) long and 4. 6 meters(15 feet) in diameter. It weighs about 9, 000 pounds(almost 4. 1 metric tons). It can carry up to 20, 000 pounds(9. 1 metric tons) of cargo packed into 16 standard space station equipment racks. Although built in Italy, Raffaello and two additional MPLMs are owned by the U. S. They were provided in exchange for Italian access to U. S. research time on the station.  9, record 5, English, - Rafaello%20multipurpose%20logistics%20module

Record number: 5, Textual support number: 1 OBS

Rafaello multipurpose logistics module; Rafaello logistic module; Raffaello cargo module: terms officially approved by the International Space Station official approval Group (ISSOAG).  10, record 5, English, - Rafaello%20multipurpose%20logistics%20module

Record number: 5, Textual support number: 1 PHR

Raffaello logistics carrier hatch.  10, record 5, English, - Rafaello%20multipurpose%20logistics%20module

Record 5,  Textual support,  French

Record number: 5, Textual support number: 1 OBS

L'«Italian Multi-Purpose Laboratory Modules» (MPLMs) est un élément construit sur le modèle du COF (Colombus) européen et abritera l6 emplacements normalisés aptes à recevoir des charges italiennes, européennes ou américaines. [...] L'ASI [Agence spatiale italienne] construit également les «Node-2» et «Node-3» pour le compte de la NASA.  9, record 5, French, - module%20logistique%20polyvalent%20Rafaello

Record number: 5, Textual support number: 2 OBS

module logistique polyvalent Rafaello; module logistique Rafaello; module Rafaello : termes uniformisés par le Groupe de travail de la terminologie de la Station spatiale internationale (GTTSSI).  10, record 5, French, - module%20logistique%20polyvalent%20Rafaello

Record 5,  Textual support,  Spanish

Record 6,  Textual support,  English

Record number: 6, Textual support number: 1 DEF

A set G with a binary operation (usually called multiplication) whose domain is the set of all ordered pairs of members of G, whose range is contained in G, and which satisfies the conditions: (1) there is a member of G ... such that its product with any member, in either order, is that same member; (2) for each member of G there is a member such that the product of the two, in either order, is the identity; (3) the associative law holds.  2, record 6, English, - group

Record number: 6, Textual support number: 1 OBS

Let F denote a set of transformations on a metric space X.... F is called a group if it is a semigroup of invertible transformations....  3, record 6, English, - group

Record 6,  Textual support,  French

Record number: 6, Textual support number: 1 DEF

Ensemble dont tous les éléments sont symétrisables, dont un élément est neutre, et qui est muni d'une loi de composition interne associative telle la différence symétrique, l'addition, la multiplication, etc. L'intersection d'une famille de sous-groupes d'un groupe G est encore un sous-groupe de G.  2, record 6, French, - groupe

Record number: 6, Textual support number: 1 OBS

Ce concept fondamental des mathématiques, de la mécanique, de la physique et de la dynamique complexe remonte à la fin du XVIIIe siècle dans les travaux de Lagrange et de Gauss sur les formes quadratiques à coefficients entiers et sur les équations algébriques. En 1829, N.H. Abel découvre les groupes commutatifs, et en 1830 E. Galois définit les groupes finis de permutation. En 1854, le théorème de A. Cayley montre que tout groupe est isomorphe à un groupe de transformations. En 1870 C. Jordan introduit le concept de groupe quotient et en 1872 F. Klein fixe le cadre géométrique de l'étude en montrant que les groupes opèrent sur des ensembles. S. Lie (1848-1899) a introduit les groupes continus de transformation et O. Schreier a fondé en 1926 la théorie des groupes topologiques.  2, record 6, French, - groupe

Record number: 6, Textual support number: 1 PHR

Le groupe opère sur un ensemble.  2, record 6, French, - groupe

Record number: 6, Textual support number: 2 PHR

déterminer, engendrer un groupe par un ensemble, former, munir un groupe d'une opération interne.  2, record 6, French, - groupe

Record number: 6, Textual support number: 3 PHR

groupe abélien, additif, affine, alterné, archimédien, automorphe, classique, commutatif, compact, congru, conjugué, continu, cyclique, dérivé, discret, distingué, dual, énantiomorphe, fini, fonctionnel, fondamental, fractal, homomorphe, infini, invariant, isomorphe, libre, linéaire, localement compact, modulaire, monogène, monstrueux, multiplicatif, non linéaire, ordonné, ornemental, orthogonal affine, parfait, partiel, projectif, quotient, résoluble, semi-simple, simple, simplectique, sporadique, symétrique, topologique, unimodulaire, unitaire, universel.  2, record 6, French, - groupe

Record number: 6, Textual support number: 4 PHR

groupe à réseau invariant, groupe d'automorphismes, de Cartan, de Chevalley, de Galois, de Jordan, de Klein, de Lie, de Lorentz, de Mathieu, de période, de permutation, de renormalisation, des classes, des déplacements, des dilatations, des entiers, des homothéties-translations, de similitude, des rotations, de substitution, de Sylow, de symétrie, de transformations, de translations, d'homotopies, d'isotropie, d'opérateurs sur un ensemble.  2, record 6, French, - groupe

Record 6,  Textual support,  Spanish

Record number: 6, Textual support number: 1 DEF

En matemáticas, estructura que consiste en un conjunto de elementos y una operación interna entre ellos que cumple las propiedades asociativas, elemento neutro y elemento simétrico.  1, record 6, Spanish, - grupo

Record number: 6, Textual support number: 1 OBS

grupo: término y definición extraídos del CAPITAL Business Dictionary con la autorizacíon de LID Editorial Empresarial.  2, record 6, Spanish, - grupo

Record 7,  Textual support,  English

Record number: 7, Textual support number: 1 DEF

Any topological space which has a metric defined on it.  2, record 7, English, - metric%20space

Record 7,  Textual support,  French

Record number: 7, Textual support number: 1 DEF

Espace muni d'une fonction à valeur réelle qui mesure la distance entre paires de points placés dans cet espace.  3, record 7, French, - espace%20m%C3%A9trique

Record number: 7, Textual support number: 1 PHR

espace métrique équivalent.  3, record 7, French, - espace%20m%C3%A9trique

Record 7,  Textual support,  Spanish

Record 8,  Textual support,  English

Record number: 8, Textual support number: 1 DEF

The collage theorem tells us that to find an IFS whose attractor is close to or looks like a given set, one must try to find a set of transformations, contraction mappings on a suitable space within which the given set lies, such that the union, or collage, of the images of the given set under the transformations is close to or looks like the given set. The degree to which two images look alike is measured using the Hausdorff metric.  1, record 8, English, - collage%20theorem

Record 8,  Textual support,  French

Record number: 8, Textual support number: 1 DEF

Théorème selon lequel, pour obtenir un système de fonctions itérées dont l'attracteur ressemble à un ensemble de référence, il faut retracer - dans l'espace métrique de ce dernier - toutes les transformations affines génératrices d'images qui, une fois collées ensemble, composent une image similaire à celle de l'ensemble de référence.  1, record 8, French, - th%C3%A9or%C3%A8me%20du%20collage

Record number: 8, Textual support number: 1 OBS

Le degré de similarité est calculé avec la mesure de Hausdorff ou celle de Hutchinson. Concept développé par M.F. Barnsley dans «Fractals Everywhere».  1, record 8, French, - th%C3%A9or%C3%A8me%20du%20collage

Record 8,  Textual support,  Spanish

Record 9,  Textual support,  English

Record number: 9, Textual support number: 1 CONT

Lets F denote a set of transformations on a metric space X... F is called a group if it is a semigroup of invertible transformations....  2, record 9, English, - semigroup

Record 9,  Textual support,  French

Record number: 9, Textual support number: 1 DEF

(...) un couple formé d'un ensemble S et d'une loi de composition interne associative définie sur S.  1, record 9, French, - semigroupe

Record 9,  Textual support,  Spanish

Record 10,  Textual support,  English

Record number: 10, Textual support number: 1 CONT

Since(R, T) is a metric topological space, it is also a Hausdorff space, and function [phi-(i]), being a diffeomorphism, is also a homeomorphism from an open set of R to an open set of [the energy hypersurface].  2, record 10, English, - diffeomorphism

Record 10,  Textual support,  French

Record number: 10, Textual support number: 1 CONT

Difféomorphisme d'un ouvert U d'un R-espace vectoriel normé E dans un ouvert V d'un R-espace vectoriel normé F : Application de U dans V qui est bijective, continûment différentiable et dont la bijection réciproque est aussi continûment différentiable.  1, record 10, French, - diff%C3%A9omorphisme

Record 10,  Textual support,  Spanish