Conversely, let G be any polynomial such that Af.

Conversely, any algebra whose associator is alternating is clearly alternative.

Conversely, any algebra for which this is true is clearly alternative.

Conversely, a subset R defines a binary function if and only if, for any x in X and y in Y, there exists a unique z in Z such that ( x, y, z ) belongs to R.

Conversely the equilibrium position is said to be " far to the left " if hardly any product is formed from the reactants.

* The spectrum of any bounded linear operator on a Banach space is a nonempty compact subset of the complex numbers C. Conversely, any compact subset of C arises in this manner, as the spectrum of some bounded linear operator.

Conversely, there are other stars that never rise above the horizon, as seen from any given point on the Earth's surface ( except exactly on the equator ).

* Conversely, corresponding to any partition of X, there exists an equivalence relation ~ on X.

Conversely, any surjection between sets determines a partition on its domain, the set of preimages of singletons in the codomain.

Conversely, Derek Bickerton and others argue that the advent of abstract words provided a mental basis for analyzing higher-order relations, and that any communication system that remotely resembles human language utterly relies on cognitive architecture that co-evolved alongside language.

Conversely any planar graph can be formed from a map in this way.

Conversely, a person may feel like he belongs to one state without having any legal relationship to it.

Conversely, the interior of the box has a constant, zero potential energy .< ref > Actually, any constant, finite potential can be specified within the box.

Conversely, extremely thin jewelry can cause the same tearing in what is commonly referred to as the " cheese cutter effect ", either during sudden torsion or over a long period of wearing, especially if the thin jewelry bears any weight.

Conversely, any Hermitian positive semidefinite matrix M can be written as M = A < sup >*</ sup > A ; this is the Cholesky decomposition.

Conversely, if a double sharp were added to any other note not containing a sharp or flat as indicated by the key signature then the note will be raised two semitones or a whole step with respect to the chromatic scale.

Conversely in rings with unity, any simple left R module arises this way.

Conversely, supplementation with L-phenylalanine, L-tyrosine, L-DOPA, or any of the cofactors will increase their respective concentrations.

Conversely, any choice of μ, full rank matrix U, and positive diagonal entries Λ < sub > i </ sub > yields a non-singular multivariate normal distribution.

Conversely, in the absence of spatial continuity can take any value.

Conversely, the influence of the data at any given point on the initial line propagates with the finite velocity c: there is no effect outside a triangle through that point whose sides are characteristic curves.

Conversely, given any harmonic function in two dimensions, it is the real part of an analytic function, at least locally.

Conversely, if the Turing Machine is expected polynomial-time ( for any given x ), then a considerable fraction of the runs must be polynomial-time bounded, and the coin sequence used in such a run will be a witness.

It is a fact that the ring is a principal ideal ring ; that is, for any ideal I in, there exists an integer n in I such that every element of I is a multiple of n. Conversely, the set of all multiples of an arbitrary integer n is necessarily an ideal, and is usually denoted by ( n ).

Conversely, if is a separable algebraic extension, and if L is any intermediate field, then and are separable extensions.

Given then a normal extension L of K, with automorphism group Aut ( L / K ) = G, and containing α, any element g ( α ) for g in G will be a conjugate of α, since the automorphism g sends roots of p to roots of p. Conversely any conjugate β of α is of this form: in other words, G acts transitively on the conjugates.

that is, by adjoining n < sup > th </ sup > roots of elements of Δ to K. Conversely, if L is a Kummer extension of K, then Δ is recovered by the rule

Conversely, a crossed module with surjective boundary defines a central extension.

If f is unramified at a point x, then f is quasi-finite at x. Conversely, if f is quasi-finite at x, and if also, the local ring of x in the fiber f < sup >− 1 </ sup >( f ( x )), is a field and a finite separable extension of κ ( f ( x )), then f is unramified at x .< ref > EGA IV < sub > 4 </ sub >, Théorème 17. 4. 1 .</ ref >

Conversely, if the data are sparse — that is, if only K out of N Fourier coefficients are nonzero — then the complexity can be reduced to O ( K log N log ( N / K )), and this has been demonstrated to lead to practical speedups compared to an ordinary FFT for N / K > 32 in a large-N example ( N = 2 < sup > 22 </ sup >) using a probabilistic approximate algorithm ( which estimates the largest K coefficients to several decimal places ).

Conversely, Electronic Arts Square, K. K., formed at the same time and based in Japan, was responsible for publishing and marketing games produced by Electronic Arts in Asia.

** Conversely, if ƒ: I → R is absolutely continuous and thus differentiable almost everywhere, and satisfies | ƒ ′( x )| ≤ K for almost all x in I, then ƒ is Lipschitz continuous with Lipschitz constant at most K.

Given a vector space V over a field K, the span of a set S ( not necessarily finite ) is defined to be the intersection W of all subspaces of V which contain S. W is referred to as the subspace spanned by S, or by the vectors in S. Conversely, S is called a spanning set of W.

Conversely, except in dimension 2, if the curvature of a Riemannian manifold has this form for some function K, then the Bianchi identities imply that K is constant and thus that the manifold is ( locally ) a space form.

Conversely, it is possible to 2-colour a K < sub > 5 </ sub > without creating any monochromatic K < sub > 3 </ sub >, showing that R ( 3, 3 ) > 5.

Thus, b < sub > q </ sub > is a symmetric bilinear form over K with matrix A. Conversely, any symmetric bilinear form b defines a quadratic form

Conversely, increasing the external K < sup >+</ sup > concentration raises ( more positive ) the K < sup >+</ sup > equilibrium potential and produces a positive shift in reversal potential.

Conversely, in a conventional gas piston design such as the H & K 416, gas used to operate the firearm is isolated from the breech and contained within the gas cylinder then vented away from other working parts.

Conversely, if the holonomy group of the Riemannian manifold M is contained in Sp ( k ), choose complex structures I < sub > x </ sub >, J < sub > x </ sub > and K < sub > x </ sub > on T < sub > x </ sub > M which make T < sub > x </ sub > M into a quaternionic vector space.

Conversely, larger and cooler bodied animals tend to be K selected.

Conversely if f is a homomorphism from G to K < sub > k </ sub >, then one can color G by using the same color for two vertices in G whenever they are both mapped to the same vertex in K < sub > k </ sub >.