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, a particular map between particular objects may be called an unnatural isomorphism ( or " this isomorphism is not natural ") if the map cannot be extended to a natural transformation on the entire category.

Conversely, a normal subgroup of index p determines a non-trivial map to up to a choice of " which coset maps to which shows that this map is a bijection.

Suppose S is an immersed submanifold of M. If the inclusion map i: S → M is closed then S is actually an embedded submanifold of M. Conversely, if S is an embedded submanifold which is also a closed subset then the inclusion map is closed.

Conversely, any linear map defined on gives rise to an antilinear map on.

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.

where e is the identity in G. Conversely, given a section s one defines a trivialization Φ by

Conversely, given any element u ∈ F ( A ) we may define a natural transformation Φ: Hom ( A ,–) → F via

Conversely, some elements do not maintain distinct allotropes in different phases – for example phosphorus has numerous solid allotropes, which all revert to the same P < sub > 4 </ sub > form when melted to the liquid state.

Conversely, given a groupoid G in the algebraic sense, let G < sub > 0 </ sub > be the set of all elements of the form x * x < sup >− 1 </ sup > with x varying through G and define G ( x * x < sup >-1 </ sup >, y * y < sup >-1 </ sup >) as the set of all elements f such that y * y < sup >-1 </ sup > * f * x * x < sup >-1 </ sup > exists.

Conversely, a high pH, low CO < sub > 2 </ sub >, or low 2, 3 BPG favors the relaxed form which can better bind oxygen.

Conversely, rows of purl stitches tend to form an embossed ridge relative to a row of knit stitches.

Conversely, donating a hydrogen bond to the amide oxygen or accepting a hydrogen bond from the amide nitrogen should favor the double-bonded form, because the hydrogen bond should be stronger to the charged form than to the uncharged, single-bonded form.

Conversely, it is likely that the Chinese form significantly less than 75 % of the total population of 4. 5 million.

Conversely, given any ring, we can form a category by taking objects A < sub > n </ sub > indexed by the set of natural numbers ( including zero ) and letting the hom-set of morphisms from to be the set of-by-matrices over, and where composition is given by matrix multiplication.

Conversely, any lines that meet to form right angles are perpendicular.

Conversely, the names of deceased enemies of the state, such as Akhenaten, were hacked out of monuments in a form of damnatio memoriae.

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, some words appear to be a prefixed form of an opposite, but the opposite term does not exist, such as inept, which appears to be in-+ * ept ; such a word is known as an unpaired word.

Conversely, any equation can take the canonical form f ( x ) = 0, so equation solving is the same thing as computing ( or finding ) a root of a function.

Conversely, the vacuum brake had the advantage of gradual release long before the Westinghouse automatic air brake, which was originally only available in the direct-release form still common in freight service.

Conversely, a company with a low credit rating might be able to borrow on better terms if it were to form an SPE and transfer significant assets to that subsidiary and issue secured debt securities.

Conversely, given a quadratic form in n variables, its coefficients can be arranged into an n × n symmetric matrix.

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, the Ricci form determines the Ricci tensor by

Conversely, a form of ex post facto law commonly called an amnesty law may decriminalize certain acts or alleviate possible punishments ( for example by replacing the death sentence with lifelong imprisonment ) retroactively.

Conversely, some Christian names such as Lope and Fortun entered the local Arabic lexicon ( Lubb and Fortun ), and others were adopted in translated form ( such as Sa ' ad for Felix ).

The principal connection α on Q can be recovered from the form η by taking Q to be the associated bundle P ×< sub > H </ sub > G. Conversely, the form η can be recovered from α by pulling back along the inclusion P ⊂ Q.