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, for real-valued functions f ( t ), the Hartley transform is given from the Fourier transform's real and imaginary parts:

Conversely, the creation by an author of an imaginary country — such as Ruritania or Graustark — does not automatically transform that imaginary country into a fantasy world, even if the location would be impossible in reality owing to a lack of land to contain it ; but such Ruritanian romances may be pushed toward the category of fantasy worlds by the introduction of, say, witches and wise women, where it is not clear if their magic is effectual.

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.

Conversely, one has the Mellin transform

Conversely, the animated series adhered to the character's intended transformation method of splitting into two forms, save for an animation error in " Surprise Party ", which saw an unusually small Sky Lynx transform directly from shuttle mode to lynx mode and in " The Quintesson Journal " when Sky Lynx transforms from lynx mode to shuttle mode.

Conversely, the vast majority of early attempts at proper excavation techniques failed to accurately measure or record stratigraphy, thereby failing to provide a secure context for artefact finds making interpretations extremely limited in scope.

Conversely, he rejected calls from the opposition Liberals to cut taxes as a stimulus measure.

Conversely, by the Riesz representation theorem, each positive linear form on arises as integration with respect to a Radon measure and is thus a continuous positive linear form on.

Conversely, if the engine is placed in front of the cabin, it might act as a battering ram and plow through obstacles in the airplane's path, providing an additional measure of safety.

Conversely, the minimum primary current a CT can accurately measure is " light load ," or 10 % of the nominal current ( there are, however, special CTs designed to measure accurately currents as small as 2 % of the nominal current ).

Conversely, sufferers have said that daily application of emulsifying ointment to often-affected areas acts as a preventive measure.

Conversely, if the probing stylus enters a film thick enough to have several layers of nodules so it cannot be spread laterally, or if it enters on top of a cobblestone in a single layer, then it will measure not only the real hardness of the diamond bonding, but an apparent hardness even greater because the internal compressive stress in those nodules would provide further resistance to penetration of the material by the stylus.

Conversely, if the knitter follows the pattern with a gauge of 6 st / inch, the sweater will measure ~ 33 " around the bustline ( 200 st / 6st / inch ) -- too tight!

Conversely, suppose that **ya is in the null space of 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, a current of one ampere is one coulomb of charge going past a given point per second:

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, 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, any algebra whose associator is alternating is clearly alternative.

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, if a Boolean ring A is given, we can turn it into a Boolean algebra by defining x ∨ y := x + y + ( x · y ) and x ∧ y := x · y.

Conversely, because space is expanding, and more distant objects are receding ever more quickly, light emitted by us today may never " catch up " to very distant objects.

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 it may generate too many points in areas where the curve is close to linear.

Conversely, if the second theory is correct, then the Athenians were merely reacting to the Persians attacking them.

Conversely, every Bayesian procedure is admissible.

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

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 in francophone Canada, one hundredth of a Canadian dollar is informally called a sou ( penny ), though cent is official in both English and French.

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

* 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, 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, movies about the supernatural are not necessarily always horrific.

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

Conversely, not all humour, even on such topics as politics, religion or art is necessarily " satirical ", even when it uses the satirical tools of irony, parody, and burlesque.

Conversely, if ( A, m, e, inv ) is a group object in one of those categories, then m necessarily coincides with the given operation on A, e is the inclusion of the given identity element on A, inv is the inversion operation and A with the given operation is an abelian group.

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, some of the songs that topped Billboard did not necessarily top these other charts.

Conversely, thread-safe code does not necessarily have to be reentrant ( see below for examples ).

Conversely, some parasitoids do somewhat shorten the lives of their hosts or constrain their reproduction, but without necessarily killing them as a part of their interaction.

Conversely, if we say that Paul has the goal of going into graduate school, he may not necessarily believe that he will be able to accomplish this.

Conversely, as Lefschetz shows, whenever a graph G has a set of cycles with this property, they necessarily form the face cycles of an embedding of the graph onto the sphere.

To summarize, M is a symmetric space G / K with a compact isotropy group K. Conversely, symmetric spaces with compact isotropy group are Riemannian symmetric spaces, although not necessarily in a unique way.

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

Conversely, the McMurdo Dry Valleys of Antarctica, although they have been ice-free for thousands of years, are not necessarily polar desert: they are kept " dry " by katabatic wind.

Conversely, stations that use " Move Closer to Your World " do not necessarily use the " Action News " name or format either.

Conversely, raising an objection does not necessarily imply that the objector disagrees with the proposal itself ; he may simply believe it would be better to take a formal vote.