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, a spherical wave generated by a point source placed in the focus is transformed into a plane wave propagating as a collimated beam along the axis.

Conversely, an incoming plane wave parallel to the axis will be focused to a point at the focal point.

Conversely, they could also be very simple, as some collectors just get a piece of paper, draw a runway on it, place it over a table, add their plane models and call it their model airport.

Conversely, the surface of a sphere cannot be unfolded onto a flat plane without distorting the distances.

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.

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, given a configuration of a conic and six lines which tangent to it in the plane, we may define the double cover of the plane ramified over the union of these 6 lines.

Conversely, a plane can be turned into a helicoid by choosing a line, or axis, on the plane then twisting the plane around that axis.

Conversely, when carbon's hybridization changes from sp < sup > 2 </ sup > to sp < sup > 3 </ sup >, the out of plane bending force constants at the transition state increase and an inverse SKIE is observed with typical values of 0. 8 to 0. 9.

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

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

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.

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, extra lives are earned by collecting heart points, which are earned by defeating enemies or collecting Hearts, with an extra life earned for every 100 points earned.

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, points are deducted from a panellist who gives " answers which are not only wrong, but pathetically obvious ", typically answers that are generally believed to be true but in fact are not.

Conversely, if the length-scale decreases and the physical parameters approach fixed values, then we have ultraviolet fixed points.

Conversely, Mark Chapman's England's Amateurs site states that the 1908 and 1912 teams were Great Britain, and points to the fact that photographic evidence shows the team playing with the Union flag on their shirts.

Conversely, a pixel in a zoomed region of a Buddhabrot image can be affected by initial points from regions far outside the one being rendered.

Conversely, iteration may give the appearance of points diverging away from a single point ; this would be the case for an unstable fixed point.

Conversely, the perennial strategy may sometimes be the more effective survival strategy, because the plant has a head start every spring with growing points, roots, and stored energy that have survived through the winter.

Conversely, any pair of lattice points with this property constitute a fundamental pair, and furthermore, they generate the same lattice.

Conversely, Clover points out that the villain of slasher films is often a male whose masculinity, and sexuality more generally, are in crisis.

Conversely, only employed are paid any yellow points, the more the higher their class.

This rational curve sends the zeros of G to each of the coordinate points of ; that is, all but one of the vanish for a zero of G. Conversely, any rational normal curve passing through the n + 1 coordinate points may be written parametrically in this way.

Conversely, the histogram for a very bright image with few dark areas and / or shadows will have most of its data points on the right side and center of the graph.