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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

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## 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**>.

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