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Page "Quadratic form" ¶ 18
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Conversely and given
Conversely, a current of one ampere is one coulomb of charge going past a given point per second:
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, 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, 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, given central idempotents a < sub > 1 </ sub >,..., a < sub > n </ sub > in R that are pairwise orthogonal and have sum 1, then R is the direct sum of the rings Ra < sub > 1 </ sub >,…, Ra < sub > n </ sub >.
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, only the wiki users interested in a given project need look at its associated wiki pages, in contrast to high-traffic mailing lists which may burden subscribers with many messages, regardless of their relevance.
Conversely, given a harmonic function, it is the real part of an analytic function, ( at least locally ).
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.
Conversely, surveys conducted among living donors postoperatively and in a period of five years following the procedure have shown extreme regret in a majority of the donors, who said that given the chance to repeat the procedure, they would not.
Conversely, given an ordered tree, and conventionally draw the root at the top, then the child nodes in an ordered tree can be drawn left-to-right, yielding an essentially unique planar embedding ( up to embedded homotopy, i. e., moving the edges and nodes without crossing ).
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 ( 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.
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.
Conversely, suppose we are given ( U, V, W ) satisfying
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, it is hard to believe, given the length and intensity of the struggle between Máel Sechnaill and Brian, that the High King would surrender his title without a fight.
Conversely, an algorithm to test for solvability in arbitrary integers could be used to test a given equation for solvability in natural numbers by applying that supposed algorithm to the equation obtained from the given equation by replacing each unknown by the sum of the squares of four new unknowns.
Conversely, a disease that is easily transmitted but has a short duration might spread widely during 2002 but is likely to have a low prevalence at any given point in 2003 ( due to its short duration ) but a high incidence during 2002 ( as many people develop the disease ).
Conversely, given a commutative diagram, it defines a poset category:

Conversely and quadratic
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, every such quadratic Hamiltonian induces a sub-Riemannian manifold.
Conversely, for every set of invariants satisfying these relations, there is a quadratic form over K with these invariants.
Conversely, singly even dimensional manifolds have a skew-symmetric nondegenerate bilinear form on their middle dimension ; if one defines a quadratic refinement of this to a quadratic form ( as on a framed manifold ), one obtains the Arf invariant as a mod 2 invariant.

Conversely and form
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, 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, 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, the Ricci form determines the Ricci tensor by
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.

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