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Conversely and any
Conversely, let G be any polynomial such that Af.
Conversely, any algebra whose associator is alternating is clearly alternative.
Conversely, any algebra for which this is true is clearly alternative.
Conversely, a subset R defines a binary function if and only if, for any x in X and y in Y, there exists a unique z in Z such that ( x, y, z ) belongs to R.
Conversely the equilibrium position is said to be " far to the left " if hardly any product is formed from the reactants.
* 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, 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 any planar graph can be formed from a map in this way.
Conversely, a person may feel like he belongs to one state without having any legal relationship to it.
Conversely, the interior of the box has a constant, zero potential energy .< ref > Actually, any constant, finite potential can be specified within the box.
Conversely, extremely thin jewelry can cause the same tearing in what is commonly referred to as the " cheese cutter effect ", either during sudden torsion or over a long period of wearing, especially if the thin jewelry bears any weight.
Conversely, any Hermitian positive semidefinite matrix M can be written as M = A < sup >*</ sup > A ; this is the Cholesky decomposition.
Conversely, if a double sharp were added to any other note not containing a sharp or flat as indicated by the key signature then the note will be raised two semitones or a whole step with respect to the chromatic scale.
Conversely in rings with unity, any simple left R module arises this way.
Conversely, supplementation with L-phenylalanine, L-tyrosine, L-DOPA, or any of the cofactors will increase their respective concentrations.
Conversely, any choice of μ, full rank matrix U, and positive diagonal entries Λ < sub > i </ sub > yields a non-singular multivariate normal distribution.
Conversely, in the absence of spatial continuity can take any value.
Conversely, the influence of the data at any given point on the initial line propagates with the finite velocity c: there is no effect outside a triangle through that point whose sides are characteristic curves.
Conversely, given any harmonic function in two dimensions, it is the real part of an analytic function, at least locally.
Conversely, if the Turing Machine is expected polynomial-time ( for any given x ), then a considerable fraction of the runs must be polynomial-time bounded, and the coin sequence used in such a run will be a witness.
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 ).

Conversely and metric
Conversely, a complete subset of a metric space is closed.
Equipped with this notion of length, a Riemannian manifold is a metric space, meaning that it has a distance function d ( p, q ) whose value at a pair of points p and q is the distance from p to q. Conversely, the metric tensor itself is the derivative of the distance function ( taken in a suitable manner ).
Conversely, using the last line as a definition one shows that the expression so defined is a connection compatible with the metric, i. e. is a Levi-Civita connection.
Conversely, any metric unchanged by Ricci flow is Ricci-flat.
Conversely a compact metric space is second-countable.

Conversely and unchanged
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, in the limit we have infinitely rapid, or diabatic passage ; the configuration of the state remains unchanged:

Conversely and by
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 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, 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, these arguments were disputed by those who claimed Dominion was widely misunderstood, and conservatively inclined commenters saw the change as part of a much larger attempt by Liberals to " re-brand " or re-define Canadian history.
Conversely, an absence of secure cycle-parking is a recurring complaint by cyclists from cities with low modal share of cycling.
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 the car is stopped by releasing pressure on the cable ( with or without completely detaching ) and applying the brakes.
Conversely, factors that favor plate columns are: presence of solids in feed, high liquid rates, large column diameters, complex columns, columns with wide feed composition variation, columns with a chemical reaction, absorption columns, columns limited by foundation weight tolerance, low liquid rate, large turn-down ratio and those processes subject to process surges.
Conversely, non-spontaneous electrochemical reactions can be driven forward by the application of a current at sufficient voltage.
Conversely, badly managed food aid can create problems by disrupting local markets, depressing crop prices, and discouraging food production.
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, when a piece of land is separated from the mainland by a man-made canal, for example the Peloponnese by the Corinth Canal, it is generally not considered an island.
Conversely, people who revere or venerate religious images are ( by iconoclasts ) called " iconolaters ".
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, take the new statement by Jim, who is tall, " is grossly overweight.
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.
Given a field ordering ≤ as in Def 1, the elements such that x ≥ 0 forms a positive cone of F. Conversely, given a positive cone P of F as in Def 2, one can associate a total ordering ≤< sub > P </ sub > by setting x ≤ y to mean y − x ∈ P. This total ordering ≤< sub > P </ sub > satisfies the properties of Def 1.
Conversely, to convert from degrees to radians, multiply by π / 180.

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