If-π-E-→-B-is-a-fibre-bundle-then-a-section-is

[permalink] [id link]

+ −

Page "Section (fiber bundle)" ¶ 12

from Wikipedia

Promote Demote Fragment Fix

« More previous Okay Cancel More next »

Some Related Sentences

If and π

If the phase difference is 180 degrees ( π radians ), then the two oscillators are said to be in antiphase.

If the inclination is zero or 180 degrees ( π radians ), the azimuth is arbitrary.

If, instead of 1 matching entry, there are k matching entries, the same algorithm works but the number of iterations must be π ( N / k ) 1 / 2 / 4 instead of πN 1 / 2 / 4.

If a line is perpendicular to another as shown, all of the angles created by their intersection are called right angles ( right angles measure π / 2 radians, or 90 °).

If you measure the circumferences of circles of steadily larger diameters and divide the former by the latter, all three geometries give the value π for small enough diameters but the ratio departs from π for larger diameters unless Ω = 1:

:: Example: If the CSPRNG under consideration produces output by computing bits of π in sequence, starting from some unknown point in the binary expansion, it may well satisfy the next-bit test and thus be statistically random, as π appears to be a random sequence.

# If the injectivity radius of a compact n-dimensional Riemannian manifold is ≥ π then the average scalar curvature is at most n ( n-1 ).

* If π 1 ( M ) is finite then the geometric structure on M is spherical, and M is compact.

* If π 1 ( M ) is virtually cyclic but not finite then the geometric structure on M is S 2 × R, and M is compact.

* If π 1 ( M ) is virtually abelian but not virtually cyclic then the geometric structure on M is Euclidean, and M is compact.

* If π 1 ( M ) is virtually nilpotent but not virtually abelian then the geometric structure on M is nil geometry, and M is compact.

* If π 1 ( M ) is virtually solvable but not virtually nilpotent then the geometric structure on M is sol geometry, and M is compact.

* If π 1 ( M ) has an infinite normal cyclic subgroup but is not virtually solvable then the geometric structure on M is either H 2 × R or the universal cover of SL ( 2, R ).

If it is compact, then the 2 geometries can be distinguished by whether or not π 1 ( M ) has a finite index subgroup that splits as a semidirect product of the normal cyclic subgroup and something else.

* If π 1 ( M ) has no infinite normal cyclic subgroup and is not virtually solvable then the geometric structure on M is hyperbolic, and M may be either compact or non-compact.

If tan ( φ ) tan ( δ ) > 1, then the sun does not set and the sun is already risen at h = π, so h o = π.

If c 1 ∈ C is another pre-image of x in C then the subgroups p # ( π 1 ( C, c )) and p # ( π 1 ( C, c 1 )) are conjugate in π 1 ( X, x ) by p-image of a curve in C connecting c to c 1 .

the set of homotopy classes of those closed curves γ based at x whose lifts γ C in C, starting at c, are closed curves at c. If X and C are path-connected, the degree of the cover p ( that is, the cardinality of any fiber of p ) is equal to the index ( π 1 ( C, c )) of the subgroup p # ( π 1 ( C, c )) in π 1 ( X, x ).

If and E

If there are g ( E ) dE states with energy E to E + dE, then the Boltzmann distribution predicts a probability distribution for the energy:

If, by contrast they are in a trans configuration, then the stereoisomer is assigned an E or Entgegen configuration.

If the 3 generations are then put in a 3x3 hermitian matrix with certain additions for the diagonal elements then these matrices form an exceptional ( grassman -) Jordan algebra, which has the symmetry group of one of the exceptional Lie groups ( F 4 , E 6 , E 7 or E 8 ) depending on the details.

If E / F is a Galois extension, then Aut ( E / F ) is called the Galois group of ( the extension ) E over F, and is usually denoted by Gal ( E / F ).

If E / F is a Galois extension, then Gal ( E / F ) can be given a topology, called the Krull topology, that makes it into a profinite group.

If the cause of the crash is uncertain, this number is rendered as 48454C50, which stands for " HELP " in hexadecimal ASCII characters ( 48 = H, 45 = E, 4C = L, 50 = P ).

If M is an R module and is its ring of endomorphisms, then if and only if there is a unique idempotent e in E such that and.

If a particle of charge q moves with velocity v in the presence of an electric field E and a magnetic field B, then it will experience a force

A measure μ is monotonic: If E 1 and E 2 are measurable sets with E 1 ⊆ E 2 then

A measure μ is countably subadditive: If E 1 , E 2 , E 3 , … is a countable sequence of sets in Σ, not necessarily disjoint, then

A measure μ is continuous from below: If E 1 , E 2 , E 3 , … are measurable sets and E n is a subset of E n + 1 for all n, then the union of the sets E n is measurable, and

If and →

If X and Y are Banach spaces over the same ground field K, the set of all continuous K-linear maps T: X → Y is denoted by B ( X, Y ).

The tensor product X ⊗ Y from X and Y is a K-vector space Z with a bilinear function T: X × Y → Z which has the following universal property: If T ′: X × Y → Z ′ is any bilinear function into a K-vector space Z ′, then only one linear function f: Z → Z ′ with exists.

If this limit exists, then it may be computed by taking the limit as h → 0 along the real axis or imaginary axis ; in either case it should give the same result.

* Scanning: If a is the next symbol in the input stream, for every state in S ( k ) of the form ( X → α • a β, j ), add ( X → α a • β, j ) to S ( k + 1 ).

If f: X → Y morphism of pointed spaces, then every loop in X with base point x 0 can be composed with f to yield a loop in Y with base point y 0 .

Likewise, a functor from G to the category of vector spaces, Vect K , is a linear representation of G. In general, a functor G → C can be considered as an " action " of G on an object in the category C. If C is a group, then this action is a group homomorphism.

Tensor products: If C denotes the category of vector spaces over a fixed field, with linear maps as morphisms, then the tensor product defines a functor C × C → C which is covariant in both arguments.

If f: A 1 → A 2 and g: B 1 → B 2 are morphisms in Ab, then the group homomorphism Hom ( f, g ): Hom ( A 2 , B 1 ) → Hom ( A 1 , B 2 ) is given by φ g o φ o f. See Hom functor.

If f: X 1 → X 2 and g: Y 1 → Y 2 are morphisms in C, then the group homomorphism Hom ( f, g ): Hom ( X 2 , Y 1 ) → Hom ( X 1 , Y 2 ) is given by φ g o φ o f.

If f: X → Y is a continuous map, x 0 ∈ X and y 0 ∈ Y with f ( x 0 ) = y 0 , then every loop in X with base point x 0 can be composed with f to yield a loop in Y with base point y 0 .

If K is a subset of ker ( f ) then there exists a unique homomorphism h: G / K → H such that f = h φ.

If and are groups, a homomorphism from to is a function ƒ: → such that

If f: M → N is any function, then we have f id M

If it does, however, it is unique in a strong sense: given any other inverse limit X ′ there exists a unique isomorphism X ′ → X commuting with the projection maps.

If G and H are Lie groups, then a Lie-group homomorphism f: G → H is a smooth group homomorphism.

If the lifetime of this transition, τ 21 is much longer than the lifetime of the radiationless 3 → 2 transition τ 32 ( if τ 21 ≫ τ 32 , known as a favourable lifetime ratio ), the population of the E 3 will be essentially zero ( N 3 ≈ 0 ) and a population of excited state atoms will accumulate in level 2 ( N 2 > 0 ).

If R = Π i in I R i is a product of rings, then for every i in I we have a surjective ring homomorphism p i : R → R i which projects the product on the i-th coordinate.

If φ: M → N is a local diffeomorphism at x in M then dφ x : T x M → T φ ( x ) N is a linear isomorphism.

0.453 seconds.