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Page "Hamiltonian mechanics" ¶ 80
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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 smooth surface S has a unique affine plane tangent to it at each point.
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 sufficiently smooth DAE is almost everywhere reducible to this semi-explicit index-1 form.
* 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 set has a choice 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 surjective function has a right inverse.
* Pseudocompact: Every real-valued continuous function on the space is bounded.
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 is a computable function.
Every effectively calculable function ( effectively decidable predicate ) is general recursive italics
Every effectively calculable function ( effectively decidable predicate ) is general recursive.
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 holomorphic function is analytic.
Every completely multiplicative function is a homomorphism of monoids and is completely determined by its restriction to the prime numbers.
Every polynomial P in x corresponds to a function, ƒ ( x )
Every primitive recursive function is a general recursive function.
Every time another object or customer enters the line to wait, they join the end of the line and represent the “ enqueue ” function.
Every function is a method and methods are always called on an object.
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 uniformly continuous function between metric spaces is continuous.
Every continuous function on a compact set is uniformly continuous.
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 group G acts on G, i. e. in two natural but essentially different ways:, or.
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 〉 extends an equivalence of certain subcategories.
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 ).
Water for Every Farm: A practical irrigation plan for every Australian property, K. 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 reduced word is an alternating product of elements of G and elements of H, e. g.
* 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.

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