Conversely, a function u: E < sub > 1 </ sub > → E < sub > 2 </ sub > defined on a basis of E < sub > 1 </ sub > can be uniquely extended to a linear function.

# Conversely if u is a solution of Laplace's equation, then there exist functions v which solve the Cauchy – Riemann equations together with u.

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

Conversely Victor Harbour railway station is spelt with the u.

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.

With Q in place, the loading imposed upon C1 is simply the load current reduced by a factor of β. Conversely, C1 appears " multiplied " by a factor of β to the load.

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, 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.

A hypergraph H may be represented by a bipartite graph BG as follows: the sets X and E are the partitions of BG, and ( x < sub > 1 </ sub >, e < sub > 1 </ sub >) are connected with an edge if and only if vertex x < sub > 1 </ sub > is contained in edge e < sub > 1 </ sub > in H. Conversely, any bipartite graph with fixed parts and no unconnected nodes in the second part represents some hypergraph in the manner described above.

which are linearly independent at each point q in U. Conversely, given such a coframe, there is a unique moving frame X < sub > 1 </ sub >, X < sub > 2 </ sub >, ..., X < sub > n </ sub > which is dual to it, i. e., satisfies the duality relation α < sup > i </ sup >( X < sub > j </ sub >) = δ < sup > i </ sup >< sub > j </ sub >, where δ < sup > i </ sup >< sub > j </ sub > is the Kronecker delta function on U.

Conversely, ( M < sub > pq </ sub >) uniquely determines f ( x, y ).

Conversely, externalism holds that it is things about the world which motivate us, justify our beliefs, determine meaning, etc.

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

Conversely, the following characterization of derived functors holds: given a family of functors R < sup > i </ sup >: A → B, satisfying the above, i. e. mapping short exact sequences to long exact sequences, such that for every injective object I of A, R < sup > i </ sup >( I )= 0 for every positive i, then these functors are the right derived functors of R < sup > 0 </ sup >.

If f is flat, then .< ref > EGA IV < sub > 2 </ sub >, Corollaire 6. 1. 2 .</ ref > Conversely, if this equality holds for all x, X is Cohen-Macaulay, and Y is regular, then f is flat .< ref > EGA IV < sub > 2 </ sub >, Proposition 6. 1. 5.

Conversely, if this identity holds in a ring R for all pairs of elements a and b of the ring, then R is commutative.

Conversely, a business can have negative net assets showing on its balance sheet but still be cash-flow solvent if ongoing revenue is able to meet debt obligations, and thus avoid default: for instance, if it holds long term debt.

Conversely, suppose the estimate holds.

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, let G be any polynomial such that 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, 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, 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, most realists ( specifically, indirect realists ) hold that perceptions or sense data are caused by mind-independent objects.

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.

Next assume for the inductive step that the result has been shown for all χ where | atoms ( χ )-atoms ( ψ )|

In those writings Bahá ' u ' lláh writes that the Universal House of Justice would assume authority over the religion, and would consider matters that had not been covered by himself ; he stated that the members of the institution would be assured of divine inspiration, and have the regard for all peoples and safe-guard their honour.

First, to show that ( 3 ) implies both ( 1 ) and ( 2 ), we assume ( 3 ) and take as t the natural projection of the direct sum onto A, and take as u the natural injection of C into the direct sum.

We assume that u is constant during each timestep.

We assume that u < sub > 0 </ sub >, ..., u < sub > p-1 </ sub > are given to us along with.

The left-hand side of this equation still makes sense if we only assume u to be locally integrable.

Although Bahá ' u ' lláh rued the necessity of spending many years learning multiple languages, when only one could be selected, various authoritative writings do assume foreign languages to be included among the " useful subjects " which Bahá ' ís will probably study.