Conversely, any metric unchanged by Ricci flow is Ricci-flat.

Conversely, any metric unchanged by normalized Ricci flow is Einstein.

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, 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.

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

Conversely, rows of purl stitches tend to form an embossed ridge relative to a row of knit stitches.

Conversely, donating a hydrogen bond to the amide oxygen or accepting a hydrogen bond from the amide nitrogen should favor the double-bonded form, because the hydrogen bond should be stronger to the charged form than to the uncharged, single-bonded form.

Conversely, it is likely that the Chinese form significantly less than 75 % of the total population of 4. 5 million.

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, any lines that meet to form right angles are perpendicular.

Conversely, the names of deceased enemies of the state, such as Akhenaten, were hacked out of monuments in a form of damnatio memoriae.

Conversely, except in dimension 2, if the curvature of a Riemannian manifold has this form for some function K, then the Bianchi identities imply that K is constant and thus that the manifold is ( locally ) a space form.

Conversely, some words appear to be a prefixed form of an opposite, but the opposite term does not exist, such as inept, which appears to be in-+ * ept ; such a word is known as an unpaired word.

Conversely, any equation can take the canonical form f ( x ) = 0, so equation solving is the same thing as computing ( or finding ) a root of a function.

Conversely, the vacuum brake had the advantage of gradual release long before the Westinghouse automatic air brake, which was originally only available in the direct-release form still common in freight service.

Conversely, a company with a low credit rating might be able to borrow on better terms if it were to form an SPE and transfer significant assets to that subsidiary and issue secured debt securities.

Conversely, given a quadratic form in n variables, its coefficients can be arranged into an n × n symmetric matrix.

Thus, b < sub > q </ sub > is a symmetric bilinear form over K with matrix A. Conversely, any symmetric bilinear form b defines a quadratic form

Conversely, a form of ex post facto law commonly called an amnesty law may decriminalize certain acts or alleviate possible punishments ( for example by replacing the death sentence with lifelong imprisonment ) retroactively.

Conversely, some Christian names such as Lope and Fortun entered the local Arabic lexicon ( Lubb and Fortun ), and others were adopted in translated form ( such as Sa ' ad for Felix ).

The principal connection α on Q can be recovered from the form η by taking Q to be the associated bundle P ×< sub > H </ sub > G. Conversely, the form η can be recovered from α by pulling back along the inclusion P ⊂ Q.

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

Conversely, mapping the data flow between the components determines the logical topology of the network.

for all vectors w. Conversely, each covector α determines a unique vector v by this equation.

Conversely, a normal subgroup of index p determines a non-trivial map to up to a choice of " which coset maps to which shows that this map is a bijection.

Conversely, minimal compliance with a safety statute does not always absolve a defendant if the trier of fact determines that the reasonable person should have taken actions beyond and in excess of what the statute required.

Conversely, any sequence that satisfies a linear recurrence determines a rational function when used as the coefficients of a Taylor series.

Any point x gives rise to a continuous function p < sub > x </ sub > from the one element topological space 1 ( all subsets of which are open ) to the space X by defining p < sub > x </ sub >( 1 ) = x. Conversely, any function from 1 to X clearly determines one point: the element that it " points " to.

Conversely, a connection on E determines a connection on F ( E ), and these two constructions are mutually inverse.

produces a unique composition of n. Conversely, every composition of n determines an assignment of pluses and commas.

Conversely, a decomposition with these extra properties determines an involution on that is on and on.

Conversely, when local politics determines that it is no longer a crime, they may be decriminalized.

Conversely, ( M < sub > pq </ sub >) uniquely determines f ( x, y ).

Conversely, the density determines the wave function modulo a phase factor, providing the formal foundation of density functional theory.

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, symmetric tensors are defined as invariants: given the natural action of the symmetric group on the tensor algebra, the symmetric tensors are the subspace on which the symmetric group acts trivially.

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.