Conversely, let G be any polynomial such that Af.

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, if F is left adjoint to G, and G is naturally isomorphic to G ′ then F is also left adjoint to G ′.

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.

Conversely, every Polish space is homeomorphic to a G < sub > δ </ sub >- subset of the Hilbert cube.

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

Conversely, one can show that given a manifold M and a principal H-bundle P over M, and a 1-form η with these properties, then P is locally isomorphic as an H-bundle to the principal homogeneous bundle G → G / H.

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.

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.

A section Γ of dπ: TP / G → TM such that Γ: TM → TP / G is a linear morphism of vector bundles over M, can be identified with a principal connection in P. Conversely, a principal connection as defined above gives rise to such a section Γ of TP / G.

Conversely, given a left kG module M, then M is a k vector space, and multiplication with an element g of G yields a k-linear automorphism of M ( since g is invertible in kG ), which describes a group homomorphism G → GL ( M ).

Conversely, experimenters would consider as impressive such statements as the following, which, if they turned out to be hits, are so unusual as to be really significant:

Conversely, the vowel marks of the Tigrinya abugida and the Amharic abugida ( ironically, the original source of the term " abugida ") have been so completely assimilated into their consonants that the modifications are no longer systematic and have to be learned as a syllabary rather than as a segmental script.

Conversely, most heat-treatable alloys are precipitation hardening alloys, which produce the opposite effects that steel does.

Conversely, most realists ( specifically, indirect realists ) hold that perceptions or sense data are caused by mind-independent objects.

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, many fighter aircraft, such as the F-16, are often used as ' bomb trucks ,' despite being designed for aerial combat.

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, because space is expanding, and more distant objects are receding ever more quickly, light emitted by us today may never " catch up " to very distant objects.

Conversely, certain general principles ( for example, neighbourliness, or charity ) are seen to be universal and consistent.

Conversely, modern biological sciences ( including even concepts such as molecular ecology ) are intimately entwined and dependent on the methods developed through biotechnology and what is commonly thought of as the life sciences industry.

Conversely beetles are prey of various invertebrates and vertebrates including insects, fish, reptiles, birds and mammals.

Conversely, factors that favor plate columns are: presence of solids in feed, high liquid rates, large column diameters, complex columns, columns with wide feed composition variation, columns with a chemical reaction, absorption columns, columns limited by foundation weight tolerance, low liquid rate, large turn-down ratio and those processes subject to process surges.

Conversely, computer implementations are significant in applying ideas from discrete mathematics to real-world problems, such as in operations research.

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, Harris maintains that the fact-value distinction is a confusion, proposing that values are really a certain kind of fact.

If neither A nor B includes the idea of existence, then " some A are B " simply adjoins A to B. Conversely, if A or B do include the idea of existence in the way that " triangle " contains the idea " three angles equal to two right angles ", then " A exists " is automatically true, and we have an ontological proof of A's existence.

Conversely, the tiny meson mass mass differences responsible for meson oscillations are often expressed in the more convenient inverse picoseconds.

Conversely, BBC critic Mark Kermode believes that " the movie industries of Britain and America are inextricably intertwined ", citing numerous examples of how Hollywood provides work to British production staff and studios, whilst Britain enables Hollywood to base their prestigious productions at UK studios.

Conversely, in functional code, the output value of a function depends only on the arguments that are input to the function, so calling a function f twice with the same value for an argument x will produce the same result f ( x ) both times.

Conversely, the bodies of people who had certain medical conditions are useful for research into those conditions.

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, rifle bullets can pierce light armor and are easier to shoot accurately, but even a carbine such as the Colt M4 is larger and / or longer than a submachine gun, making it harder to maneuver in close quarters.

Conversely, if either of these last two expressions is defined, then so is the other ( and again they are equal ).

Conversely, a number that is greater than zero is called positive ; zero is usually thought of as neither positive nor negative.

Conversely, unlike a human being, an animal does not objectify itself, as “ the subject ”, nor its products as ideas, “ the object ”, because an animal engages in directly self-sustaining actions that have neither a future intention, nor a conscious intention.

Conversely, neither senator supported the bill and it was not considered in the Senate.

Conversely, if statistics were uncovered which contradicted a cherished theory, the sources were denounced as faulty.

Conversely, suppose that **ya is in the null space of Af.

Conversely, if he gives a heavy rating to his own reading, and finds more accurate facts in it than in the others, a point is chalked up for the intrinsic, objective meaningfulness of this type of mediumistic material.

Conversely, the Radical Republicans criticized him for moving too slowly in abolishing slavery.

Conversely, an adiabatic process that is irreversible and extracts no work is in an isenthalpic process, such as viscous drag, progressing towards a nonnegative change in entropy.

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, Carnegie a titan of industry seems to embody all of the qualities of Spencerian survival of the fittest.

Conversely, British English favours fitted as the past tense of fit generally, whereas the preference of American English is more complex: AmEng prefers fitted for the metaphorical sense of having made an object " fit " ( i. e., suited ) for a purpose ; in spatial transitive contexts, AmEng uses fitted for the sense of having made an object conform to an unchanged object that it surrounds ( e. g., " fitted X around Y ") but fit for the sense of having made an object conform to an unchanged object that surrounds it ( e. g., " fit X into Y "); and for the spatial senses ( both intransitive and transitive ) of having been matching with respect to contour, with no alteration of either object implied, AmEng prefers fit (" The clothes fit.

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, Howard Marshall writes that the speeches were not entirely the inventions of the author and, while they may not be verbatim, nevertheless records the general idea.

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

Conversely, towed artillery was and remains cheaper to build and maintain.

Conversely, paintings which came out of his workshop that were not necessarily physically worked on by Cuyp but merely overseen by him technically, were marked with A. C. to show that it was his instruction which saw the paintings ’ completion.

Conversely, the withdrawal syndrome may also be a trigger for relapse.

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

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