manifold

manifold
—manifoldly, adv. —manifoldness, n.
/man"euh fohld'/, adj.
1. of many kinds; numerous and varied: manifold duties.
2. having numerous different parts, elements, features, forms, etc.: a manifold program for social reform.
3. using, functioning with, or operating several similar or identical devices at the same time.
4. (of paper business forms) made up of a number of sheets interleaved with carbon paper.
5. being such or so designated for many reasons: a manifold enemy.
n.
6. something having many different parts or features.
7. a copy or facsimile, as of something written, such as is made by manifolding.
8. any thin, inexpensive paper for making carbon copies on a typewriter.
9. Mach. a chamber having several outlets through which a liquid or gas is distributed or gathered.
10. Philos. (in Kantian epistemology) the totality of discrete items of experience as presented to the mind; the constituents of a sensory experience.
11. Math. a topological space that is connected and locally Euclidean. Cf. locally Euclidean space.
v.t.
12. to make copies of, as with carbon paper.
[bef. 1000; ME; OE manigf(e)ald (adj.). See MANY, -FOLD]
Syn. 1. various, multitudinous. See many. 2. varied, divers, multifarious.
Ant. 1. simple, single.

* * *

In mathematics, a topological space (see topology) with a family of local coordinate systems related to each other by certain classes of coordinate transformations.

Manifolds occur in algebraic geometry, differential equations, and classical dynamics. They are studied for their global properties by the methods of algebra and algebraic topology and form a natural domain for the global analysis of differential equations. See also tensor analysis.

* * *

      in mathematics, a generalization and abstraction of the notion of a curved surface; a manifold is a topological space that is modeled closely on Euclidean space locally but may vary widely in global properties. Each manifold is equipped with a family of local coordinate systems that are related to each other by coordinate transformations belonging to a specified class. Manifolds occur in algebraic and differential geometry, differential equations, classical dynamics, and relativity. They are studied for their global properties by the methods of analysis and algebraic topology, and they form natural domains for the global analysis of differential equations, particularly equations that arise in the calculus of variations. In mechanics they arise as “phase spaces”; in relativity, as models for the physical universe; and in string theory, as one- or two-dimensional membranes and higher-dimensional “branes.”

* * *


Universalium. 2010.

Игры ⚽ Поможем сделать НИР
Synonyms:
, , , , / , ,


Look at other dictionaries:

  • manifold — [ manifɔld ] n. m. • 1930; mot angl., pour manifold paper ♦ Anglic. 1 ♦ Carnet comportant plusieurs séries de feuilles et de papier carbone. 2 ♦ (1960) Techn. Ensemble de vannes et de conduits orientant un fluide vers un réservoir ou des… …   Encyclopédie Universelle

  • manifold — [man′ə fōld΄] adj. [ME < OE manigfeald: see MANY & FOLD] 1. having many and various forms, features, parts, etc. [manifold wisdom] 2. of many sorts; many and varied; multifarious: used with a plural noun [manifold duties] 3. being such in many …   English World dictionary

  • Manifold — Man i*fold, a. [AS. manigfeald. See {Many}, and {Fold}.] 1. Various in kind or quality; many in number; numerous; multiplied; complicated. [1913 Webster] O Lord, how manifold are thy works! Ps. civ. 24. [1913 Webster] I know your manifold… …   The Collaborative International Dictionary of English

  • manifold — manifóld s. n., pl. manifólde Trimis de siveco, 10.08.2004. Sursa: Dicţionar ortografic  MANIFÓLD s.n. 1. (Anglicism) Carnet de note, de facturi etc. cu cotor. 2. (tehn.) Colector; conductă de aducţie. ♦ Claviatură. [< engl., fr. manifold] …   Dicționar Român

  • Manifold — Man i*fold, n. 1. A copy of a writing made by the manifold process. [1913 Webster] 2. (Mech.) A cylindrical pipe fitting, having a number of lateral outlets, for connecting one pipe with several others; as, the exhaust manifold of an automobile… …   The Collaborative International Dictionary of English

  • Manifold — Man i*fold, v. t. [imp. & p. p. {Manifolded}; p. pr. & vb. n. {Manifolding}.] To take copies of by the process of manifold writing; as, to manifold a letter. [1913 Webster] …   The Collaborative International Dictionary of English

  • manifold — I adjective assorted, considerable, divers, diverse, diversified, innumerable, many, miscellaneous, multifarious, multifold, multiform, multiple, multiplex, multiplicate, multitudinous, myriad, numerous, populous, profuse, several, sundry,… …   Law dictionary

  • Manifold —   [ mænɪfəʊld], John Streeter, australischer Schriftsteller und Musikhistoriker, * Melbourne 21. 4. 1915, ✝ Brisbane 19. 4. 1985; verfasste v. a. satirische, aber auch romantische Verse sowie Lyrik über den Krieg. Bekannt wurde er auch als… …   Universal-Lexikon

  • manifold — [adj] abundant, many assorted, complex, copious, different, diverse, diversified, diversiform, multifarious, multifold, multiform, multiple, multiplied, multitudinous, multivarious, numerous, sundry, varied, various; concepts 564,762,781 Ant. one …   New thesaurus

  • manifold — ► ADJECTIVE formal or literary 1) many and various. 2) having many different forms. ► NOUN 1) a pipe or chamber branching into several openings. 2) (in an internal combustion engine) the part conveying air and fuel from the carburettor to the… …   English terms dictionary

  • Manifold — For other uses, see Manifold (disambiguation). The sphere (surface of a ball) is a two dimensional manifold since it can be represented by a collection of two dimensional maps. In mathematics (specifically in differential geometry and topology),… …   Wikipedia

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”