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Manifold

Manifold Man"i*fold, a. [AS. manigfeald. See Many, and Fold.] 1. Various in kind or quality; many in number; numerous; multiplied; complicated. O Lord, how manifold are thy works! --Ps. civ. 24. I know your manifold transgressions. --Amos v. 12. 2. Exhibited at divers times or in various ways; -- used to qualify nouns in the singular number. ``The manifold wisdom of God.' --Eph. iii. 10. ``The manifold grace of God.' --1 Pet. iv. 10. Manifold writing, a process or method by which several copies, as of a letter, are simultaneously made, sheets of coloring paper being infolded with thin sheets of plain paper upon which the marks made by a stylus or a type-writer are transferred.

Manifold Man"i*fold, a. [AS. manigfeald. See Many, and Fold.] 1. Various in kind or quality; many in number; numerous; multiplied; complicated. O Lord, how manifold are thy works! --Ps. civ. 24. I know your manifold transgressions. --Amos v. 12. 2. Exhibited at divers times or in various ways; -- used to qualify nouns in the singular number. ``The manifold wisdom of God.' --Eph. iii. 10. ``The manifold grace of God.' --1 Pet. iv. 10. Manifold writing, a process or method by which several copies, as of a letter, are simultaneously made, sheets of coloring paper being infolded with thin sheets of plain paper upon which the marks made by a stylus or a type-writer are transferred.

Manifold

Manifold Man"i*fold, n. 1. A copy of a writing made by the manifold process. 2. (Mech.) A cylindrical pipe fitting, having a number of lateral outlets, for connecting one pipe with several others. 3. pl. The third stomach of a ruminant animal. [Local, U.S.]

Manifold Man"i*fold, n. 1. A copy of a writing made by the manifold process. 2. (Mech.) A cylindrical pipe fitting, having a number of lateral outlets, for connecting one pipe with several others. 3. pl. The third stomach of a ruminant animal. [Local, U.S.]

Manifold

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.

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.

- (e.g. CT scans). Manifolds can be equipped with additional structure. One important class of manifolds are differentiable manifolds; their differentiable...

- Riemannian manifolds, Darboux's theorem states that all symplectic manifolds are locally isomorphic. The only invariants of a symplectic manifold are global...

- and vector fields. Differentiable manifolds are very important in physics. Special kinds of differentiable manifolds form the basis for physical theories...

- Shing-Tung Yau (1978) who proved the Calabi conjecture. Calabi–Yau manifolds are complex manifolds that are generalizations of K3 surfaces in any number of complex...

- found in: Cardiovascular system - blood vessel manifolds etc. Lymphatic system Respiratory system Manifolds are used in: Pipe organ Scott, John S. (1992)...

- different flavors: compact complex manifolds are much closer to algebraic varieties than to differentiable manifolds. For example, the Whitney embedding...

- is made in whether we are dealing with say, topological 3-manifolds, or smooth 3-manifolds. Phenomena in three dimensions can be strikingly different...

- mathematics. All manifolds are topological manifolds by definition. Other types of manifolds are formed by adding structure to a topological manifold (e.g. differentiable...

- pseudo-Riemannian manifolds, among which Riemannian manifolds and Lorentzian manifolds, with applications to General Relativity. In particular, SageManifolds implements...

- infinite-dimensional manifolds; that is, manifolds that are modeled after a topological vector space; for example, Fréchet, Banach and Hilbert manifolds. Riemannian...

- Riemannian manifolds, Darboux's theorem states that all symplectic manifolds are locally isomorphic. The only invariants of a symplectic manifold are global...

- and vector fields. Differentiable manifolds are very important in physics. Special kinds of differentiable manifolds form the basis for physical theories...

- Shing-Tung Yau (1978) who proved the Calabi conjecture. Calabi–Yau manifolds are complex manifolds that are generalizations of K3 surfaces in any number of complex...

- found in: Cardiovascular system - blood vessel manifolds etc. Lymphatic system Respiratory system Manifolds are used in: Pipe organ Scott, John S. (1992)...

- different flavors: compact complex manifolds are much closer to algebraic varieties than to differentiable manifolds. For example, the Whitney embedding...

- is made in whether we are dealing with say, topological 3-manifolds, or smooth 3-manifolds. Phenomena in three dimensions can be strikingly different...

- mathematics. All manifolds are topological manifolds by definition. Other types of manifolds are formed by adding structure to a topological manifold (e.g. differentiable...

- pseudo-Riemannian manifolds, among which Riemannian manifolds and Lorentzian manifolds, with applications to General Relativity. In particular, SageManifolds implements...

- infinite-dimensional manifolds; that is, manifolds that are modeled after a topological vector space; for example, Fréchet, Banach and Hilbert manifolds. Riemannian...

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