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Every smooth function G over the symplectic manifold generates a one-parameter family of symplectomorphisms and if

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## Some Related Sentences

Every and smooth

__Every__

__smooth__( or differentiable ) map φ: M → N between

__smooth__( or differentiable ) manifolds induces natural linear maps between

**the**corresponding tangent spaces:

__Every__

__smooth__submanifold

**of**R < sup > n </ sup > has an induced Riemannian metric g:

**the**inner product on each tangent space is

**the**restriction

**of**

**the**inner product on R < sup > n </ sup >.

__Every__

__smooth__

**manifold**defined in this way has

**a**natural diffeology, for which

**the**plots correspond to

**the**

__smooth__maps from open subsets

**of**R < sup > n </ sup > to

**the**

**manifold**.

*

__Every__bundle**of**Lie algebras**over****a**__smooth__**manifold**defines**a**Lie algebroid where**the**Lie bracket is defined pointwise**and****the**anchor map is equal to zero.__Every__Sámi settlement had its seita, which had no regular shape,

**and**might consist

**of**

__smooth__or odd-looking stones picked out

**of**

**a**stream,

**of**

**a**small pile

**of**stones,

**of**

**a**tree-stump, or

**of**

**a**simple post.

__Every__compact

__smooth__

**manifold**

**of**dimension 2n, which has only handles

**of**index ≤ n, has

**a**Stein structure provided n > 2,

**and**when n = 2

**the**same holds provided

**the**2-handles are attached with certain framings ( framing less than

**the**Thurston-Bennequin framing ).

__Every__closed

__smooth__4-manifold is

**a**union

**of**two Stein 4-manifolds glued along their common boundary.

*

__Every____smooth__Hilbert**manifold**can be smoothly embedded onto an open subset**of****the**model Hilbert space.
*

__Every__continuous plurisubharmonic**function**can be obtained as**a**limit**of**monotonically decreasing sequence**of**__smooth__plurisubharmonic functions.__Every__camp has one or two directors ;

**the**job

**of**

**the**director is to make

**the**camp run

__smooth__

**and**mostly safe without losing

**the**free-spirited

**and**cosy experience

**of**

**the**camp.

Every and function

__Every__such subset has

**a**smallest element, so to specify our choice

__function__we can simply say that it maps each set to

**the**least element

**of**that set.

__Every__contraction mapping is Lipschitz continuous

**and**hence uniformly continuous ( for

**a**Lipschitz continuous

__function__,

**the**constant k is no longer necessarily less than 1 ).

__Every__effectively calculable

__function__( effectively decidable predicate ) is general recursive italics

__Every__bijective

__function__g has an inverse g < sup >− 1 </ sup >, such that gg < sup >− 1 </ sup > = I ;

__Every__entire

__function__can be represented as

**a**power series that converges uniformly on compact sets.

__Every__holomorphic

__function__can be separated into its real

**and**imaginary parts,

**and**each

**of**these is

**a**solution

**of**Laplace's equation on R < sup > 2 </ sup >.

__Every__completely multiplicative

__function__is

**a**homomorphism

**of**monoids

**and**is completely determined by its restriction to

**the**prime numbers.

__Every__time another object or customer enters

**the**line to wait, they join

**the**end

**of**

**the**line

**and**represent

**the**“ enqueue ”

__function__.

__Every__type that is

**a**member

**of**

**the**type class defines

**a**

__function__that will extract

**the**data from

**the**string representation

**of**

**the**dumped data.

__Every__output

**of**an encoder can be described by its own transfer

__function__, which is closely related to

**the**generator polynomial.

__Every__continuous

__function__in

**the**

__function__space can be represented as

**a**linear combination

**of**basis functions, just as every vector in

**a**vector space can be represented as

**a**linear combination

**of**basis vectors.

Every and G

Group actions / representations:

__Every__group__G__can be considered as**a**category with**a**single object whose morphisms are**the**elements**of**__G__. A functor from__G__to Set is then nothing but**a**group action**of**__G__on**a**particular set, i. e.**a**G-set.__Every__homomorphism f:

__G__→ H

**of**Lie groups induces

**a**homomorphism between

**the**corresponding Lie algebras

**and**.

__Every__open subgroup H is also closed, since

**the**complement

**of**H is

**the**open set given by

**the**union

**of**open sets gH for g in

__G__

*

__Every__connected graph__G__admits**a**spanning tree, which is**a**tree that contains every vertex**of**__G__**and**whose edges are edges**of**__G__.__Every__adjunction 〈 F,

__G__, ε, η 〉 gives rise to an associated monad 〈 T, η, μ 〉 in

**the**category D. The functor

__Every__inner automorphism is indeed an automorphism

**of**

**the**group

__G__, i. e. it is

**a**bijective map from

__G__to

__G__

**and**it is

**a**homomorphism ; meaning ( xy )< sup >

**a**</ sup >

__Every__non-inner automorphism yields

**a**non-trivial element

**of**Out (

__G__), but different non-inner automorphisms may yield

**the**same element

**of**Out (

__G__).

__Every__one

**of**

**the**infinitely many vertices

**of**

__G__can be reached from v < sub > 1 </ sub > with

**a**simple path,

**and**each such path must start with one

**of**

**the**finitely many vertices adjacent to v < sub > 1 </ sub >.

__Every__year at

**the**International Astronautical Congress, three prestigious awards are given out:

**the**Allan D. Emil Memorial Award,

**the**Franck J. Malina Astronautics Medal

**and**

**the**Luigi

__G__. Napolitano Award.

__Every__such regular cover is

**a**principal G-bundle, where

__G__= Aut ( p ) is considered as

**a**discrete topological group.

*

__Every__Polish space is homeomorphic to**a**__G__< sub > δ </ sub > subspace**of****the**Hilbert cube,**and**every__G__< sub > δ </ sub > subspace**of****the**Hilbert cube is Polish.0.435 seconds.