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.

We define Thm ( C ) to be the set of all formulas that are valid in C. Conversely, if X is a set of formulas, let Mod ( X ) be the class of all frames which validate every formula from X.

Conversely, let Q be any orthogonal matrix which does not have − 1 as an eigenvalue ; then

Conversely, let A be a self-adjoint operator on a Hilbert space H. Then

C. Conversely, if X is a set of formulas, let Mod ( X ) be the

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, any surjection between sets determines a partition on its domain, the set of preimages of singletons in the codomain.

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.

Conversely, the symbol width could be set at 8, even if only values 0 and 1 are used ; these data would only require a 2-color table.

Conversely, one-dimensional orthogonal projectors are extreme points of the set of density operators.

Conversely, from a partial order on a partition of a set S one can construct a preorder on S. There is a 1-to-1 correspondence between preorders and pairs ( partition, partial order ).

Each convex set containing X must ( by the assumption that it is convex ) contain all convex combinations of points in X, so the set of all convex combinations is contained in the intersection of all convex sets containing X. Conversely, the set of all convex combinations is itself a convex set containing X, so it also contains the intersection of all convex sets containing X, and therefore the sets given by these two definitions must be equal.

Conversely, a set which is not bounded is called unbounded.

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 ).

Given a vector space V over a field K, the span of a set S ( not necessarily finite ) is defined to be the intersection W of all subspaces of V which contain S. W is referred to as the subspace spanned by S, or by the vectors in S. Conversely, S is called a spanning set of W.

Conversely, given any ring, we can form a category by taking objects A < sub > n </ sub > indexed by the set of natural numbers ( including zero ) and letting the hom-set of morphisms from to be the set of-by-matrices over, and where composition is given by matrix multiplication.

Conversely, a phonetic character set is written precisely as it is spoken, but with the disadvantage that slight pronunciation differences introduce ambiguities.

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 R is a symmetric relation over a set X, one can interpret it as describing an undirected graph with the elements of X as the vertices and the pairs in R as the edges.

Conversely, it being set apart implies the opposite-that someone took the clothes off in an ordinary manner ; furthermore, the Greek text uses the word, entetuligmenon, " having been folded up ", seeming to imply some intentional action had been taken on the soudarion.

Conversely, if X is a Hausdorff space and ker f is a closed set, then the coimage of f, if given the quotient space topology, must also be a Hausdorff space.

Conversely, techniques have been proposed for generating models of GRNs that best explain a set of time series observations.

Conversely, at least under U. S. Law, nonpersons such as animals cannot commit crimes.

Conversely, U. S. mortar platoons needed clearings in which to work ; these were few and dangerous, being pre-ranged by German troops, so mortar support was often unavailable to rifle platoons.

Conversely, the drop of U. S. productivity growth in the 1970s and 1980s was in response to the decrease of continual public capital investment and not the decline of technological innovation.

Conversely, at least under U. S. Law, nonpersons such as animals cannot commit crimes.

Conversely, S. cerevisiae has well-developed peroxisomes, while S. pombe does not.

Conversely, S. pombe has large, repetitive centromeres ( 40 – 100 kb ) more similar to mammalian centromeres, and degenerate replication origins of at least 1kb.

Conversely, at least under U. S. Law, nonpersons such as animals cannot commit crimes.

A tangent plane can be " rolled " along S, and as it does so the point of contact traces out a curve on S. Conversely, given a curve on S, the tangent plane can be rolled along that curve.

Suppose S is an immersed submanifold of M. If the inclusion map i: S → M is closed then S is actually an embedded submanifold of M. Conversely, if S is an embedded submanifold which is also a closed subset then the inclusion map is closed.

As the tangent plane is rolled on S, the point of contact traces out a curve on S. Conversely, given a curve on S, the tangent plane can be rolled along that curve.

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

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

Conversely the equilibrium position is said to be " far to the left " if hardly any product is formed from the reactants.

Conversely, function application is considered to be left-associative, so that is equivalent to.

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

Conversely, non-spontaneous electrochemical reactions can be driven forward by the application of a current at sufficient voltage.

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

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, when one wants to compute an arbitrary number ( N ) of discrete samples of one cycle of a continuous DTFT, it can be done by computing the relatively simple DFT of s < sub > N </ sub >, as defined above.

Conversely, one might expect that inertial motions, once identified by observing the actual motions of bodies and making allowances for the external forces ( such as electromagnetism or friction ), can be used to define the geometry of space, as well as a time coordinate.

Conversely, since Imhotep was known as the " Son of Ptah ," his mother was sometimes claimed to be Sekhmet, the patron of Upper Egypt whose consort was Ptah.

That is, the motivational internalist believes that there is an internal, necessary connection between one's conviction that X ought to be done and one's motivation to do X. Conversely, the motivational externalist ( or moral externalist ) claims that there is no necessary, internal connection between moral convictions and moral motives.

Conversely, every formally real field can be equipped with a compatible total order, that will turn it into an ordered field.

Conversely, Walter Burkert suggests that the Hellene cult worship of Poseidon as a horse god may be connected to the introduction of the horse and war-chariot from Anatolia to Greece around 1600 BC.

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.