Conversely in rings with unity, any simple left R module arises this way.

Conversely, if a highest weight module is integrable, then its highest weight vector v satisfies, where are complex numbers such that

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 ).

A sublinear modulus of continuity can easily found for any uniformly function which is a bounded perturbations of a Lipschitz function: if is a uniformly continuous function with modulus of continuity, and is a Lipschitz function with uniform distance from, then admits the sublinear module of continuity Conversely, at least for real-valued functions, any bounded, uniformly continuous perturbation of a Lipschitz function is a special uniformly continuous function ; indeed more is true as shown below.

Conversely, different types of hulks exist including one that simply " swallows " the probe without yielding a module, requiring the player to purchase a new probe ( and possibly sell useful modules to raise the required funds ).

Conversely, a PXI module installed in a CompactPCI chassis would not utilize the additional clocking and triggering features of the PXI module.

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, 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 existence of Bletchley Park, and of the decrypting achievements there, was never officially shared with the Soviet Union, whose war effort would have greatly benefited from regular decrypting of German messages relating to the Eastern Front.

Conversely, the islands do not receive the upwellings ( cold streams ) that affect the West African coast, so the air temperature is cooler than in Senegal, but the sea is actually warmer, because the orographic relief of some islands, as Sao Miguel with steep mountains, cover it with rich woods and luxuriant vegetation where the dense moisture condense and soak the plants, rocks, soil, logs, moss etc.

Conversely, an absence of secure cycle-parking is a recurring complaint by cyclists from cities with low modal share of cycling.

Conversely, states such as Virginia and Massachusetts in the United States of America did not have sovereign status, but had significant political and economic independence coupled with weak federal control, reducing the incentive to secede.

Conversely, in the English language as a whole, singular verb forms can often be used with nouns ending in "- s " that were once considered plural ( for example: " Physics is my favorite academic subject ").

Conversely the car is stopped by releasing pressure on the cable ( with or without completely detaching ) and applying the brakes.

Conversely, if the same is done with the left hand, a left-handed system results.

Conversely, a column with a low reflux ratio must have a large number of stages, thus requiring a taller column.

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, many natural forces, such as the sun, were associated with multiple deities.

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, wages tend to go up with a decrease in population.

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, Groups incur penalties when attempting to control Groups with opposite alignments or when attempting to destroy groups with the same alignment.

Conversely, John Calvin, Albert Barnes Adam Clarke, John Gill, and John Wesley amongst many other have affirmed this as divine truth and found no problem with its historicity.

Conversely, JPL, through the Caltech lawyers representing the laboratory, allege that Coppedge's termination was simply due to budget cuts and his demotion from team lead was because of harassment complaints and from on-going conflicts with his co-workers.

Conversely, Henig acknowledges that if the US had been a member, its reluctance to engage in war with European states and to enact economic sanctions may have hampered the ability of the League to deal with international incidents.

Conversely, simply having negative relationships with some women does not necessarily mean someone holds misogynistic views.

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, ( f ) can be reached, albeit in a non-trivial manner, by starting with the differential equilibrium equations and the stress boundary conditions on, and proceeding in the manner similar to ( a ) and ( b ).

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, Psychology defines bottom-up processing as an approach wherein there is a progression from the individual elements to the whole.

Conversely, given a commutative diagram, it defines a poset category:

Conversely, a system of n quantities v < sup > i </ sup > that transform like the coordinates x < sup > i </ sup > on V defines a contravariant vector.

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 building can be recovered from the BN pair, so that every BN pair canonically defines a building.

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

Conversely, any operator satisfying the above properties defines a connection on E and a connection in this sense is also known as a covariant derivative on E.

Conversely, an Ehresmann connection H ⊂ TP ( or v: TP → V ) on P defines a principal G-connection ω if and only if it is G-equivariant in the sense that.

Conversely, any such one form defines ( via pullback ) a G-equivariant horizontal 1-form on P, and the space of principal G-connections is an affine space for this space of 1-forms.

Conversely, singly even dimensional manifolds have a skew-symmetric nondegenerate bilinear form on their middle dimension ; if one defines a quadratic refinement of this to a quadratic form ( as on a framed manifold ), one obtains the Arf invariant as a mod 2 invariant.

Conversely, given central idempotents a < sub > 1 </ sub >,..., a < sub > n </ sub > in R that are pairwise orthogonal and have sum 1, then R is the direct sum of the rings Ra < sub > 1 </ sub >,…, Ra < sub > n </ sub >.

Conversely, some regions such as Nuristan, in the northeast, and Hazarajat, in the central mountains of Afghanistan, were virtually untouched by the fighting, and lived in almost complete independence.

Conversely, often in film noir and crime dramas, the alternative narrative is a fiction created by a central character, intentionally — as in The Usual Suspects — or unintentionally — as in Angel Heart.

Conversely, they are a central prey item or forage fish for higher trophic levels.

Conversely, if the central star's energy output significantly increases, the oceans may evaporate, resulting in a greenhouse effect ; this may preclude the oceans from reforming.

Conversely, she is not as central in most forms of established Christianity as she is in Gnosticism, but to some Christian mystics the Sophia is a very important concept.