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

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, let a set S be a neighborhood of x if x is not in the closure of the complement of S. The set of all such neighborhoods can be shown to be a neighborhood system for a pretopology.

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, 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, 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.

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

* The spectrum of any bounded linear operator on a Banach space is a nonempty compact subset of the complex numbers C. Conversely, any compact subset of C arises in this manner, as the spectrum of some bounded linear operator.

Conversely, given any partially defined operator U which is isometric on its domain ( which is not

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, the state can directly fund unprofitable business, such as railway services to remote areas, regardless of whether the operator is a private corporation.

Conversely the index theorem for an elliptic complex can easily be reduced to the case of an elliptic operator: the two vector bundles are given by the sums of the even or odd terms of the complex, and the elliptic operator is the sum of the operators of the elliptic complex and their adjoints, restricted to the sum of the even bundles.

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

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, a high PRR / PRF can enhance target discrimination of nearer objects such as a periscope or fast moving missile leading to practices of employing low PRRs for search radar, and very high PRFs for fire control radars, with many dual-purpose and navigation radars, especially naval designs having variable PRRs which might allow a skilled operator to also use a PRR adjustment to enhance and clarify a unclear radar picture, for example in bad sea states where wave action generates false returns, and in general for less clutter, or perhaps a better return signal off a prominent landscape feature ( e. g. a cliff ).

Conversely, any uniformly continuous semigroup is necessarily of this form for some bounded linear operator A.

for all compactly supported functions ƒ and h. Conversely, () characterizes Δ completely, in the sense that it is the only operator with this property.

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, 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, Fleet Captain Honoré Ganteaume later reported the cause as an explosion on the quarterdeck, preceded by a series of minor fires on the main deck among the ship's boats.

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

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, corresponding to any partition of X, there exists an equivalence relation ~ on X.

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

Conversely, Derek Bickerton and others argue that the advent of abstract words provided a mental basis for analyzing higher-order relations, and that any communication system that remotely resembles human language utterly relies on cognitive architecture that co-evolved alongside language.

" Conversely, Pat Graham of Chicago Reader disliked the mix of horror and comedy, writing in his review that " The pop-up humor and smirkiness suggest Raimi's aspiring to the fashionable company of the brothers Coen, though on the basis of this strained effort I'd say he's overshot the mark.

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 blood vessels in the lower legs are under great pressure ( because of the weight of fluid pressing down on them ).

Conversely on occasions he attracted criticism for dogmatically pursuing schemes favoured by the right of his party, notably the privatisation of British Rail, and for closing down most of the coal industry in advance of privatisation.

Conversely, they are interested in the role of vegetation on climate and weather.

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, the cultural divergence at the border became sharper: in theory, a uniform French identity extends from the Atlantic coast to the Rhine, and on the other bank of the Rhine, a uniform German identity begins.

Conversely, the gravity of the satellite on the bulges applies torque on the primary and speeds up its rotation.

Conversely, if the odds of drawing a winning card are numerically lower than the pot odds, the call has a negative expectation, and you can expect to win less money on average than it costs to call the bet.

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 ).