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 initial feedback is not strong, the print-run of the book may be reduced, the marketing budget cut or, in some cases, the book is dropped from publication altogether.

Conversely, he rejected calls from the opposition Liberals to cut taxes as a stimulus measure.

Conversely, other existentialist thinkers argue that human beings might be said to actively engage each other and the universe as they communicate and create, and loneliness is merely the feeling of being cut off from this process.

Conversely, HPHT treatment is used to modify and remove color from either rough or cut diamonds — but only certain diamonds are treatable in this manner.

Conversely, noise pollution is mitigated by cut sections since an effective blockage of line of sight sound propagation is created by the depressed roadway design.

Conversely, dwelling in the foam any longer than strictly required to melt the cut path can lead to excessively thick kerf.

Conversely, every admissible statistical procedure is either a Bayesian procedure or a limit of Bayesian procedures.

Conversely, when the economic limit is lowered, the life of the well is lengthened.

Conversely, in the limit we have infinitely rapid, or diabatic passage ; the configuration of the state remains unchanged:

Conversely the use of true brass seems to have declined in Western Europe during this period in favour of gunmetals and other mixed alloys but by the end of the first Millennium AD brass artefacts are found in Scandinavian graves in Scotland, brass was being used in the manufacture of coins in Northumbria and there is archaeological and historical evidence for the production of brass in Germany and The Low Countries areas rich in calamine ore which would remain important centres of brass making throughout the medieval period, especially Dinant – brass objects are still collectively known as dinanterie in French.

Conversely, the end of the Cold War marked by the fall of the Berlin Wall in 1989 resulted in a reduction in the duration of Cold War civil wars of 92 % or, phrased another way, a roughly ten-fold increase in the rate of resolution of Cold War civil wars.

Conversely, an important faction may have an interest in helping fund the campaign of smaller factions with a very different political agenda, so that these smaller parties end up weakening their own agenda.

Conversely, modern social democracy emphasises a program of gradual legislative reform of capitalism in order to make it more equitable and humane, while the theoretical end goal of building a socialist society is either completely forgotten or redefined in a pro-capitalist way.

Conversely, developed countries, most economically developed countries ( MEDCs ), First World nations and " industrialized nations " are the opposite end of the spectrum.

Conversely defeat by an external power could mean the end of a ruler and his people, who were absorbed into the victorious confederacy.

Conversely if the player harms non-hostile NPCs and collects dark Force powers then the game will end with the dark side ending.

Conversely, a non-LRU is a part, component, or assembly used in the repair of an LRU, when the LRU has failed and has been removed from the end item for repair.

Conversely, Gloucester Rugby have garnered an unfortunate reputation for leading the table at the end of the regular season, only to fall short of winning the Premiership title in 2003, 2007 and 2008.

Conversely, on the next line, the end of " I come to bury Caesar, not to praise him " has an extra syllable because omitting the word " him " would make the sentence unclear, but adding a syllable at the end would not disrupt the meter.

Conversely if byte values 13 and 10 have meanings other than end of line, then they must be encoded as and respectively.

Conversely, in February 2012, SB Nation columnist Travis Hughs said that " Key Arena is so poorly designed for hockey that even a single season there would be unacceptable ", referring to the arrangement of seating on only one end of the rink, a consequence of the renovation favoring basketball-type bleacher arrangements-the same problems with sight lines that caused the Thunderbirds to negotiate for a new arena nearby.

Conversely, show hunter and jumper riders may use a flatter end to encourage forward movement, such as the Prince of Wales design.

Conversely, in an internal ( female ) thread ( e. g., in a nut ), the major and minor diameters are minimum dimensions, therefore the thread profile must end flat at D < sub > min </ sub > but may be rounded out beyond D < sub > maj </ sub >.

Conversely, simply generating steam at process pressure instead of high enough pressure to generate power at the top end also has lost opportunity cost.

Conversely, near the end of the video, the wolf shrinks enough to be able to squeeze under the door.

Conversely, the hottest AFC team at the end of the season was the 10-6 Seattle Seahawks.

Conversely, people who generally tend to blame others for negative events, believe that such events will end soon, and do not let such events affect too many aspects of their lives display what is called an optimistic explanatory style.

Conversely, the southern half of its passage through Lincolnshire and its northern end, near Washingborough, are accepted as having had a raised bank on each side ; the one on the upland side would not be a feature well adapted to a catchwater drain.

Conversely, specimens of unusual appearance are less likely to end up as part of a predator's diet than would be " justified " if consumption of food items was related to their abundance within the population in a straightforward way.

Conversely, if the DA survives until the end of human civilization ( in the year 5000, say ) then it will have dramatically beaten the odds against the expectations of the Copernican principle.

Conversely, elves of the Tolkien mould have become standardized staple characters of modern fantasy to such an extent that breaking the norms for how an elf is supposed to be and behave has become an end in itself.