[permalink] [id link]

Let R be a fixed superalgebra ( assumed to be unital and associative ).

from
Wikipedia

## Some Related Sentences

Let and R

__Let__the state of the stream leaving stage

__R__

**be**denoted by

**a**vector Af

**and**the operating variables of stage

__R__by Af.

__Let__P

**be**the root of the unbalanced subtree, with

__R__

**and**L denoting the right

**and**left children of P respectively.

The Beatles ' 1968 track " Back in the U. S. S.

__R__" references the instrument in its final verse ("__Let__me hear your balalaikas ringing out / Come**and**keep your comrade warm ").
Suppose that in

**a**mathematical language L, it is possible**to**enumerate all of the defined numbers in L.__Let__this enumeration**be**defined by the function G: W →__R__, where G**(**n ) is the real number described by the nth description in the sequence.
Gloria Gaynor

**(**born September 7, 1949 ) is an American singer, best known for the disco era hits ; " I Will Survive "**(**Hot 100 number 1, 1979 ), " Never Can Say Goodbye "**(**Hot 100 number 9, 1974 ), "__Let__Me Know**(**I Have**a**Right )"**(**Hot 100 number 42, 1980 )**and**" I Am What I Am "**(**__R__& B number 82, 1983**).**__Let__us call the class of all such formulas

__R__. We are faced with proving that every formula in

__R__is either refutable or satisfiable.

__Let__H

**be**

**a**Hilbert space,

**and**let H * denote its dual space, consisting of all continuous linear functionals from H into the field

__R__or C. If x is an element of H, then the function φ < sub > x </ sub >, defined by

If V is

**a**real vector space, then we replace V by its complexification V ⊗< sub >__R__</ sub > C**and**let g denote the induced bilinear form on V ⊗< sub >__R__</ sub > C.__Let__W**be****a**maximal isotropic subspace, i. e.**a**maximal subspace of V such that g |< sub > W </ sub > = 0.__Let__V

**be**

**a**vector space over

**a**field K,

**and**let

**be**

**a**quadratic form on V. In most cases of interest the field K is either

__R__, C or

**a**finite field.

__Let__

**(**M, g )

**be**

**a**Riemannian manifold

**and**ƒ: M < sup > m </ sup > →

__R__< sup > n </ sup >

**a**short C < sup >∞</ sup >- embedding

**(**or immersion ) into Euclidean space

__R__< sup > n </ sup >, where n ≥ m + 1.

Let and be

__Let__every policeman

**and**park guard keep his eye on John

**and**Jane Doe, lest one piece of bread

__be__placed undetected

**and**one bird survive.

__Let__us assume that it would

__be__possible for an enemy

**to**create an aerosol of the causative agent of epidemic typhus

**(**Rickettsia prowazwki ) over City A

**and**that

**a**large number of cases of typhus fever resulted therefrom.

__Let__p

__be__the minimal polynomial for T, Af, where the Af, are distinct irreducible monic polynomials over F

**and**the Af are positive integers.

__Let__V

__be__

**a**finite-dimensional vector space over an algebraically closed field F, e.g., the field of complex numbers.

__Let__N

__be__

**a**positive integer

**and**let V

__be__the space of all N times continuously differentiable functions F on the real line which satisfy the differential equation Af where Af are some

**fixed**constants.

__Let__Q

__be__

**a**nonsingular quadric surface bearing reguli Af

**and**Af,

**and**let **zg

__be__

**a**Af curve of order K on Q.

__Let__us take

**a**set of circumstances in which I happen

**to**

__be__interested on the legislative side

**and**in which I think every one of us might naturally make such

**a**statement.

__Let__it

__be__granted then that the theological differences in this area between Protestants

**and**Roman Catholics appear

**to**

__be__irreconcilable.

__Let__us therefore put first things first,

**and**make sure of preserving the human race at whatever the temporary price may

__be__''.

Let and fixed

__Let__L < sub > n </ sub >

**be**the space of all complex n × n matrices,

**and**let adX

**be**the linear operator defined by adX Y = for some

__fixed__X ∈ L < sub > n </ sub >.

__Let__

**be**the set of non-negative integers

**(**natural numbers ), let n

**be**any

__fixed__constant,

**and**let

**be**the set of-tuples of natural numbers.

__Let__P

**be**the point of application of the force F

**and**let

**R**

**be**the vector locating this point in

**a**

__fixed__frame.

__Let__

**R**

**be**

**a**ring

**and**let Mod < sub >

**R**</ sub >

**be**the category of modules over

**R**.

__Let__B

**be**in Mod < sub >

**R**</ sub >

**and**set T

**(**B ) = Hom < sub >

**R**</ sub >( A, B ), for

__fixed__A in Mod < sub >

**R**</ sub >.

__Let__the likelihood function

**be**considered

__fixed__; the likelihood function is usually well-determined from

**a**statement of the data-generating process.

__Let__f

**be**

**a**

__fixed__integrable function

**and**let T

**be**the operator of convolution with f, i. e., for each function g we have

__Let__δ < sub > x </ sub > denote the Dirac measure centred on some

__fixed__point x in some measurable space

**(**X, Σ

**).**

__Let__

**a**set of basic propositional connectives

**be**

__fixed__

**(**for instance, in the case of superintuitionistic logics, or in the case of monomodal logics

**).**

__Let__N > 1

**be**

**a**

__fixed__integer

**and**consider the polynomials f < sub > 1 </ sub >, ..., f < sub > N </ sub > in variables X < sub > 1 </ sub >, ..., X < sub > N </ sub > with coefficients in an algebraically closed field k

**(**in fact, it suffices

**to**assume k = C

**).**

The minimal separators also form an algebraic structure: For two

__fixed__vertices**a****and**b of**a**given graph G, an**(****a**, b )- separator S can**be**regarded as**a**predecessor of another**(****a**, b )- separator T, if every path from**a****to**b meets S before it meets T. More rigorously, the predecessor relation is defined as follows:__Let__S**and**T**be**two**(****a**, b )- separators in ' G '.__Let__A

**be**

**a**set consisting of N distinct i-element subsets of

**a**

__fixed__set U (" the universe ")

**and**B

**be**the set of all

**(**i − r )- element subsets of the sets in A.

0.363 seconds.