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, Applesoft lacked the ( remainder ) operator that had been present in Integer BASIC.

Conversely, given any partially defined operator U which is isometric on its domain ( which is not

Conversely, once a basis for A has been chosen, the products of basis elements can be set arbitrarily, and then extended in a unique way to a bilinear operator on A, i. e., so the resulting multiplication satisfies the algebra laws.

Conversely, the state can directly fund unprofitable business, such as railway services to remote areas, regardless of whether the operator is a private corporation.

Conversely the index theorem for an elliptic complex can easily be reduced to the case of an elliptic operator: the two vector bundles are given by the sums of the even or odd terms of the complex, and the elliptic operator is the sum of the operators of the elliptic complex and their adjoints, restricted to the sum of the even bundles.

Conversely, any topology can be induced in this way by the correct choice of closure operator.

Conversely, let A be a self-adjoint operator on a Hilbert space H. Then

Conversely, a high PRR / PRF can enhance target discrimination of nearer objects such as a periscope or fast moving missile leading to practices of employing low PRRs for search radar, and very high PRFs for fire control radars, with many dual-purpose and navigation radars, especially naval designs having variable PRRs which might allow a skilled operator to also use a PRR adjustment to enhance and clarify a unclear radar picture, for example in bad sea states where wave action generates false returns, and in general for less clutter, or perhaps a better return signal off a prominent landscape feature ( e. g. a cliff ).

Conversely, any uniformly continuous semigroup is necessarily of this form for some bounded linear operator A.

for all compactly supported functions ƒ and h. Conversely, () characterizes Δ completely, in the sense that it is the only operator with this property.

Conversely, suppose we are given ( U, V, W ) satisfying

for some real-valued functions a and b depending, respectively, on x and y. Conversely, given any such pair of real-valued functions, there exists a vector field X satisfying 1. and 2.

Conversely, the following characterization of derived functors holds: given a family of functors R < sup > i </ sup >: A → B, satisfying the above, i. e. mapping short exact sequences to long exact sequences, such that for every injective object I of A, R < sup > i </ sup >( I )= 0 for every positive i, then these functors are the right derived functors of R < sup > 0 </ sup >.

Conversely if f ( z ) is a holomorphic function on the unit disc satisfying

Conversely, if ƒ is a holomorphic function in the upper half-plane satisfying

Conversely, a cooperative game can also be defined with a characteristic cost function satisfying.

Conversely any blowup of the plane in points satisfying these conditions is a del Pezzo surface.

Conversely, given two one-parameter unitary groups U ( t ) and V ( s ) satisfying the braiding relation

Conversely, if G contains a proper non-trivial normal subgroup N, then the composition of the natural surjective group homomorphism G → G / N with the regular representation of G / N produces a representation π of G which has kernel N. Taking χ to be the character of some non-trivial subrepresentation of π, we have a character satisfying the hypothesis in the direct statement above.

Conversely, for every set of invariants satisfying these relations, there is a quadratic form over K with these invariants.

Conversely, for a given set of natural numbers satisfying the above inequality, there exists a uniquely decodable code over an alphabet of size with those codeword lengths.

Conversely, given any Lie algebra with a direct sum decomposition satisfying these three conditions, the linear map σ, equal to the identity on and minus the identity on, is an involutive automorphism.