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Every convex centrally symmetric polyhedron P in R < sup > 3 </ sup > admits a pair of opposite ( antipodal ) points and a path of length L joining them and lying on the boundary ∂ P of P, satisfying
Some Related Sentences
Every and convex
Every subset A of the vector space is contained within a smallest convex set ( called the convex hull of A ), namely the intersection of all convex sets containing A.
Every antiparallelogram has an isosceles trapezoid as its convex hull, and may be formed from the diagonals and non-parallel sides of an isosceles trapezoid.
: Every correspondence that maps a compact convex subset of a locally convex space into itself with a closed graph and convex nonempty images has a fixed point.
* Every locally convex topological vector space has a neighbourhood basis consisting of barrelled sets.
* Every metrisable locally convex space with continuous dual carries the Mackey topology, that is, or to put it more succinctly every Mackey space carries the Mackey topology
Every ( bounded ) convex polytope is the image of a simplex, as every point is a convex combination of the ( finitely many ) vertices.
Every and centrally
* Every local authority has been allocated a unique prefix for their stop numbering, this ensures that stop numbers cannot be duplicated, in addition there are national number prefixes-900 for coach stops, 910 for railway stations, 920 for airports, 930 for ferry terminals and 940 for metro and tram stops, the national stop numbers are created centrally and not by local authorities.
Every and symmetric
Every Boolean algebra ( A, ∧, ∨) gives rise to a ring ( A, +, ·) by defining a + b := ( a ∧ ¬ b ) ∨ ( b ∧ ¬ a ) = ( a ∨ b ) ∧ ¬( a ∧ b ) ( this operation is called symmetric difference in the case of sets and XOR in the case of logic ) and a · b := a ∧ b. The zero element of this ring coincides with the 0 of the Boolean algebra ; the multiplicative identity element of the ring is the 1 of the Boolean algebra.
Every symmetric graph without isolated vertices is vertex-transitive, and every vertex-transitive graph is regular.
Every symmetric group has a one-dimensional representation called the trivial representation, where every element acts as the one by one identity matrix.
Every connected symmetric graph must thus be both vertex-transitive and edge-transitive, and the converse is true for graphs of odd degree.
Every and polyhedron
Every and P
* Every quadratic Bézier curve is also a cubic Bézier curve, and more generally, every degree n Bézier curve is also a degree m curve for any m > n. In detail, a degree n curve with control points P < sub > 0 </ sub >, …, P < sub > n </ sub > is equivalent ( including the parametrization ) to the degree n + 1 curve with control points P '< sub > 0 </ sub >, …, P '< sub > n + 1 </ sub >, where.
Every prime ideal P in a Boolean ring R is maximal: the quotient ring R / P is an integral domain and also a Boolean ring, so it is isomorphic to the field F < sub > 2 </ sub >, which shows the maximality of P. Since maximal ideals are always prime, prime ideals and maximal ideals coincide in Boolean rings.
The definition of permanent agriculture as that which can be sustained indefinitely was supported by Australian P. A. Yeomans in his 1973 book Water for Every Farm.
Jeffrey P. Dennis, author of the journal article " The Same Thing We Do Every Night: Signifying Same-Sex Desire in Television Cartoons ," argued that SpongeBob and Sandy are not romantically in love, while adding that he believed that SpongeBob and Patrick " are paired with arguably erotic intensity.
Every object would also have a read timestamp, and if a transaction T < sub > i </ sub > wanted to write to object P, and the timestamp of that transaction is earlier than the object's read timestamp ( TS ( T < sub > i </ sub >) < RTS ( P )), the transaction T < sub > i </ sub > is aborted and restarted.
Every such line meets the sphere of radius one centered in the origin exactly twice, say in P = ( x, y, z ) and its antipodal point (− x, − y, − z ).
* Every irreducible closed subset of P < sup > n </ sup >( k ) of codimension one is a hypersurface ; i. e., the zero set of some homogeneous polynomial.
In mathematics, an integer-valued polynomial ( also known as a numerical polynomial ) P ( t ) is a polynomial whose value P ( n ) is an integer for every integer n. Every polynomial with integer coefficients is integer-valued, but the converse is not true.
" Jeffrey P. Dennis, author of " The Same Thing We Do Every Night: Signifying Same-Sex Desire in Television Cartoons ," argued that the romantic connection between Velma and Daphne Blake is " mostly wishful thinking " because Velma and Daphne " barely acknowledge each other's existence.
# Every submodule of M is a direct summand: for every submodule N of M, there is a complement P such that M = N ⊕ P.
Every and R
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 vector v in determines a linear map from R to taking 1 to v, which can be thought of as a Lie algebra homomorphism.
Every binary relation R on a set S can be extended to a preorder on S by taking the transitive closure and reflexive closure, R < sup >+=</ sup >.
* In any ring R, a maximal ideal is an ideal M that is maximal in the set of all proper ideals of R, i. e. M is contained in exactly 2 ideals of R, namely M itself and the entire ring R. Every maximal ideal is in fact prime.
* Every separable metric space is isometric to a subset of C (), the separable Banach space of continuous functions → R, with the supremum norm.
Every simple R-module is isomorphic to a quotient R / m where m is a maximal right ideal of R. By the above paragraph, any quotient R / m is a simple module.
Every random vector gives rise to a probability measure on R < sup > n </ sup > with the Borel algebra as the underlying sigma-algebra.
* Every left ideal I in R is finitely generated, i. e. there exist elements a < sub > 1 </ sub >, ..., a < sub > n </ sub > in I such that I = Ra < sub > 1 </ sub > + ... + Ra < sub > n </ sub >.
* Every non-empty set of left ideals of R, partially ordered by inclusion, has a maximal element with respect to set inclusion.
Every year since 1982, the W. C. Handy Music Festival is held in the Florence / Sheffield / Muscle Shoals area, featuring blues, jazz, country, gospel, rock music and R & B.
Every adult citizen of this small settlement signed the small petition ; E. K Dyer and his wife, William Johnson, Joseph Otis and his wife, Hiram Walker and his wife, Joseph Pease and R. H. Valentine.
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 >.