Conversely every positive functional φ gives a corresponding inner product < ƒ, g >< sub > φ </ sub > = φ ( g * ƒ ).

Conversely, if a suitable notion of parallel transport is available, then a corresponding connection can be obtained by differentiation.

Conversely, the corresponding expression for computer, powerful computers is preferred over * strong computers.

Conversely, if a set of edges forms a forest, then by repeatedly removing leaves from this forest it can be shown by induction that the corresponding set of columns is independent.

Conversely, given a generalized Cartan matrix, one can recover its corresponding Lie algebra.

Conversely, any effect observed in an accelerated reference frame should also be observed in a gravitational field of corresponding strength.

Conversely, as with any filter base, the local basis allows to get back the corresponding neighbourhood filter as.

Conversely, while Bayes rules with respect to proper priors are virtually always admissible, generalized Bayes rules corresponding to improper priors need not yield admissible procedures.

Conversely, one could define a potential corresponding to pH as a potential difference between a solute and pH neutral water, separated by porous membrane ( that is permeable to hydrogen ions ).

Conversely, an increase in height without a corresponding increase in airspeed will put the aircraft above a survivable un-cushioned impact height, and eventually above a height where rotor inertia can be converted to sufficient lift to enable a survivable landing.

Thus, for example, a quantity X which is known to lie in the range can be represented by the affine form, for some k. Conversely, the form implies that the corresponding quantity X lies in the range.

Conversely, ketones tend to combine with water to form the corresponding geminal diols.

Conversely, each conserved quantity has a corresponding symmetry.

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, 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 every partition of comes from an equivalence relation in this way, according to which if and only if and belong to the same set of the partition.

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 ).

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.

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.

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.

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, if B satisfies both of the conditions 1 and 2, then there is a unique topology on X for which B is a base ; it is called the topology generated by B.

Conversely, if R is a symmetric relation over a set X, one can interpret it as describing an undirected graph with the elements of X as the vertices and the pairs in R as the edges.

A hypergraph H may be represented by a bipartite graph BG as follows: the sets X and E are the partitions of BG, and ( x < sub > 1 </ sub >, e < sub > 1 </ sub >) are connected with an edge if and only if vertex x < sub > 1 </ sub > is contained in edge e < sub > 1 </ sub > in H. Conversely, any bipartite graph with fixed parts and no unconnected nodes in the second part represents some hypergraph in the manner described above.

for some real-valued functions a and b depending, respectively, on x and y. Conversely, given any such pair of real-valued functions, there exists a vector field X satisfying 1. and 2.

Conversely, if X is projective, then the pullback of under the closed immersion of X into a projective space is very ample.

Conversely, a complete variety is close to being a projective variety: Chow's lemma states that if X is a complete variety, there is a projective variety Z and a birational morphism Z → X.

Conversely, if X is a Hausdorff space and ker f is a closed set, then the coimage of f, if given the quotient space topology, must also be a Hausdorff space.