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, the Oxford Dictionary of National Biography describes it as " updating and abridging " that book.

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 every partition of comes from an equivalence relation in this way, according to which if and only if and belong to the same set of the partition.

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 any planar graph can be formed from a map in this way.

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, specifying the symmetry can define the structure, or at least clarify what we mean by an invariant, geometric language in which to discuss it ; this is one way of looking at the Erlangen programme.

Conversely, the object-side numerical aperture is related to the f-number by way of the magnification ( tending to zero for a distant object ):

Conversely, many theorems that hold in universal algebra do not generalise all the way to category theory.

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

Conversely, cartridge names often reflect nothing related to the cartridge in any obvious way ; for example, the. 218 Bee uses a bullet of 224 / 1000-inch diameter, fired through a. 22-in bore, etc.

Conversely, once a basis for A has been chosen, the products of basis elements can be set arbitrarily, and then extended in a unique way to a bilinear operator on A, i. e., so the resulting multiplication satisfies the algebra laws.

Conversely if this sequence starts this way, then g must be zero.

Conversely, records which originate from a common source ( or fonds ) should be kept together – preferably physically, but, where that is not practicable, certainly intellectually in the way in which they are catalogued and arranged in finding aids – in accordance with what is sometimes termed the principle of archival integrity.

Conversely, any topology can be induced in this way by the correct choice of closure operator.

Conversely, how do the latter achieve superior societal health while having little in the way of the religious values or institutions?

Conversely, the emergence of energy shots has gone the opposite way with much smaller packaging.

Conversely, less than one Yellow Warbler nest in three on average suffers from predation in one way or another, while two out of three Mangrove and Golden Warbler nests are affected.

Conversely, every method for evaluating conditionals can be seen as a way for performing revision.

Conversely, any median graph can be represented as the set of solutions to a 2-satisfiability instance in this way.

Conversely, since it is a type of formal third-party certification, museums using this name space obtain a way to assure visitors of the site's validity.

Conversely, a swing seat is one that could easily swing either way.

Conversely, the topological charge only makes sense in the ordered phase and not at all in the disordered phase, because in some hand-waving way there is a " topological condensate " in the disordered phase which randomizes the field from point to point.

Conversely, Eric only seems to find Jackie attractive when not hearing her voice in any way, stating at one point: " Good God, she is hot!

Conversely, every cograph can be represented in this way by a cotree.

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

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

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

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, in more recent times, Russian existentialist philosopher Lev Shestov viewed Job as the embodiment of the battle between reason ( which offers general and seemingly comforting explanations for complex events ) and faith in a personal god, and one man's desperate cry for him.

Conversely, if ƒ: C → C is a function which is differentiable when regarded as a function on R < sup > 2 </ sup >, then ƒ is complex differentiable if and only if the Cauchy – Riemann equations hold.

Conversely, every point on the line can be interpreted as a number in an ordered continuum which includes the real numbers.

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, there are Grothendieck topologies which do not come from topological spaces.

Conversely, a high pH, low CO < sub > 2 </ sub >, or low 2, 3 BPG favors the relaxed form which can better bind oxygen.

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

Conversely, Trotsky held that socialism in one country would economically constrain the industrial development of the USSR, and thus required assistance from the new socialist countries that had arisen in the developed world, which was essential for maintaining Soviet democracy, in 1924 much undermined by civil war and counter-revolution.

Conversely, the Šar Mountains, which are located in the northwestern part, block cold northern winds.

Conversely, the Roman poet Ovid provides a second etymology, in which he says that the month of May is named for the maiores, Latin for " elders ," and that the following month ( June ) is named for the iuniores, or " young people " ( Fasti VI. 88 ).

Conversely, some areas which were merely roadside suburbs in the 1950s are now valuable urban land on which original structures are being removed through gentrification and the land used for other purposes.

Conversely, Scheme contains multiple coherent subsets that suffice to construct the rest of the language as library macros, and so the language designers do not even bother to say which portions of the language must be implemented as language constructs, and which must be implemented as parts of a library.

Conversely, a metrizable space is separable if and only if it is second countable, which is the case if and only if it is Lindelöf.