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, the Tayledras live in Vales they create, centered on a Heartstone, fed by ley-lines and used to maintain a number of spells which maintain the suitable growth of foliage which becomes a beautiful and exotic locale, with magically powered springs of cool, warm, and hot water, as many for bathing as for swimming and trysting, and monumental trees far beyond the range of what could ever possibly be grown naturally.

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, a standard line on which voice service has been unsubscribed ( such as an ADSL dry loop ) may still accept calls to the 958 test exchange but not allow calls to standard numbers.

Conversely, the Belgian Blue's meat tenderness has been argued to be just as tender because there are a large number of smaller muscle fibers.

Conversely, if the firm is able to get bulk discounts of an input, then it could have economies of scale in some range of output levels even if it has decreasing returns in production in that output range.

Conversely, the defensive team will know that the offense has to cover a good deal of ground in a single play, will expect a forward pass, and will know from earlier study something of the propensities of the offense they face.

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, Clausewitz has also been seen as " The preeminent military and political strategist of limited war in modern times.

Conversely, if the odds of drawing a winning card are numerically lower than the pot odds, the call has a negative expectation, and you can expect to win less money on average than it costs to call the bet.

Conversely, every preorder is the reachability relationship of a directed graph ( for instance, the graph that has an edge from x to y for every pair ( x, y ) with x ≤ y ).

Conversely, in the bleak Orwellian world of " The High Ones "— where the Soviets have won the Third World War and gained control of the whole world — the dissidents still have some hope, precisely because space flight has not been abandoned.

Conversely, active directed panspermia has been proposed to secure and expand life in space.

Conversely, Baptists are underrepresented, a reflection of their quite recent expansion in numbers ; there has been only one Roman Catholic president, although they are currently the largest single denomination, and there have been no Lutheran, Pentecostal, or Latter Day Saint presidents.

Conversely, birds of prey-which show distinct reverse sexual dimorphism — tend to be monogamous for long periods or mate for life ; some species like the Snail kite will choose new mates every year, polygyny is noted in many Harriers and polyandry has been observed in the Harris ' Hawk ( notable for being the only bird of prey to regularly live and hunt in family and social groups ) and the aforementioned Galapagos hawk.

Conversely, ska and reggae, popular among traditionalist skinheads, has influenced several punk musicians.

Conversely, once the hardware and software for an anti-lock braking system has been designed to meet its required deadlines, no further performance gains are obligatory.

Conversely, the southern part has tended to sink to compensate, causing flooding of the Low Countries and Denmark.

Conversely, Slam poetry movement founder Marc Smith has been critical of the commercially successful Def Poetry television and Broadway live stage shows produced by Russell Simmons, decrying it as " an exploitive entertainment that diminished the value and aesthetic of performance poetry ".

Conversely, the Court has approved routine warrantless seizures, for example " where there is probable cause to believe that a criminal offense has been or is being committed.

Conversely, Sinhalese has also borrowed from the original Vedda language, words and grammatical structures, differentiating it from its related Indo-Aryan languages.

Conversely, Elijah Delmedigo ( c. 1458 – c. 1493 ), in his Bechinat ha-Dat endeavored to show that the Zohar could not be attributed to Shimon bar Yochai, arguing that if it were his work, the Zohar would have been mentioned by the Talmud, as has been the case with other works of the Talmudic period, that had bar Yochai known by divine revelation the hidden meaning of the precepts, his decisions on Jewish law from the Talmudic period would have been adopted by the Talmud, that it would not contain the names of rabbis who lived at a later period than that of Simeon ; and that if the Kabbalah was a revealed doctrine, there would have been no divergence of opinion among the Kabbalists concerning the mystic interpretation of the precepts.

Conversely, migration of Cockney speakers has led to migration of the dialect.

Conversely, if M is positive definite, it has an eigendecomposition P < sup >− 1 </ sup > DP where P is unitary, D diagonal, and all diagonal elements of D are real and positive.

As stated earlier, an adjunction between categories C and D gives rise to a family of universal morphisms, one for each object in C and one for each object in D. Conversely, if there exists a universal morphism to a functor G: C → D from every object of D, then G has a left adjoint.