[permalink] [id link]
Let σ be a signature consisting only of a unary function symbol f. The class K of σ-structures in which f is one-to-one is a basic elementary class.
from
Wikipedia
Some Related Sentences
Let and σ
Let be a random sample of size n — that is, a sequence of independent and identically distributed random variables drawn from distributions of expected values given by µ and finite variances given by σ < sup > 2 </ sup >.
Let X be a random variable with finite expected value μ and finite non-zero variance σ < sup > 2 </ sup >.
Let X < sub > 1 </ sub > and X < sub > 2 </ sub > be two random variables with means and finite variances of μ < sub > 1 </ sub > and μ < sub > 2 </ sub > and σ < sub > 1 </ sub > and σ < sub > 2 </ sub > respectively.
Let ρ be the correlation coefficient between X < sub > 1 </ sub > and X < sub > 2 </ sub > and let σ < sub > i </ sub >< sup > 2 </ sup > be the variance of X < sub > i </ sub >.
Let B be a complex Banach algebra containing a unit e. Then we define the spectrum σ ( x ) ( or more explicitly σ < sub > B </ sub >( x )) of an element x of B to be the set of those complex numbers λ for which λe − x is not invertible in B.
A connection ∇ on a vector bundle E → M defines a notion of parallel transport on E along a curve in M. Let γ: → M be a smooth path in M. A section σ of E along γ is said to be parallel if
Let X be a random variable with unimodal distribution, mean μ and finite, non-zero variance σ < sup > 2 </ sup >.
* Let K < sup > a </ sup > be an algebraic closure of K containing L. Every embedding σ of L in K < sup > a </ sup > which restricts to the identity on K, satisfies σ ( L ) = L. In other words, σ is an automorphism of L over K.
Let M be a structure of signature σ and N a substructure of M. N is an elementary substructure of M if and only if for every first-order formula φ ( x, y < sub > 1 </ sub >, …, y < sub > n </ sub >) over σ and all elements b < sub > 1 </ sub >, …, b < sub > n </ sub > from N, if M x φ ( x, b < sub > 1 </ sub >, …, b < sub > n </ sub >), then there is an element a in N such that M φ ( a, b < sub > 1 </ sub >, …, b < sub > n </ sub >).
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 the state of the stream leaving stage R be denoted by a vector Af and the operating variables of stage R by Af.
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 signature
Let be any be any linear function which is invariant under the involution, then composing it with the sesquilinear duality pairing gives a symmetric bilinear form on whose signature is an invariant of the knot.
Let V be an n-dimensional vector space, equipped with a metric tensor ( of possibly mixed signature ).
Let and consisting
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
The group performed and sang a medley consisting of " What the World Needs Now Is Love " and The Beatles ' " All You Need Is Love " on 23 February 1969 and performed and sang " Aquarius / Let the Sunshine In " on 18 May 1969, the day after the medley fell from the Hot 100 summit.
Let g be a Lie algebra, h a maximal commutative Lie subalgebra consisting of semi-simple elements ( sometimes called Cartan subalgebra ) and let V be a finite dimensional representation of g. If g is semisimple, then g = g and so all weights on g are trivial.
Let e < sub > i </ sub > denote the trivial path at vertex i. Then we can associate to the vertex i, the projective KΓ module KΓe < sub > i </ sub > consisting of linear combinations of paths which have starting vertex i. This corresponds to the representation of Γ obtained by putting a copy of K at each vertex which lies on a path starting at i and 0 on each other vertex.
Let A be a superalgebra over a commutative ring K. The submodule A < sub > 0 </ sub >, consisting of all even elements, is closed under multiplication and contains the identity of A and therefore forms a subalgebra of A, naturally called the even subalgebra.
Let Λ be the lattice in R < sup > d </ sup > consisting of points with integer coordinates ; Λ is the character group, or Pontryagin dual, of R < sup > d </ sup >.
# Let G be a connected graph and let H be the clutter on consisting of all edge sets of spanning trees of G. Then is the collection of all minimal edge cuts in G.
Let B and C be two different bases of a vector space V, and let us mark with the matrix which has columns consisting of the C representation of basis vectors b < sub > 1 </ sub >, b < sub > 2 </ sub >, ..., b < sub > n </ sub >:
Let E < sub > i </ sub > be a basis of sections of TG consisting of left-invariant vector fields, and θ < sup > j </ sup > be the dual basis of sections of T < sup >*</ sup > G such that θ < sup > j </ sup >( E < sub > i </ sub >) = δ < sub > i </ sub >< sup > j </ sup >, the Kronecker delta.
Let G be the complex special linear group SL ( 2, C ), with a Borel subgroup consisting of upper triangular matrices with determinant one.
Let p be a point of M. Consider the space consisting of smooth maps defined in some neighborhood of p. We define an equivalence relation on as follows.
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.
Let M be a complex manifold, and write O < sub > M </ sub > for the sheaf of holomorphic functions on M. Let O < sub > M </ sub >* be the subsheaf consisting of the non-vanishing holomorphic functions.
0.760 seconds.