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Page "Volume form" ¶ 7
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## Some Related Sentences

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 n
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 system of n quantities v < sup > i </ sup > that transform like the coordinates x < sup > i </ sup > on V defines a contravariant vector.
Conversely, the DHT is equivalent to computing the DFT of x < sub > n </ sub > multiplied by 1 + i, then taking the real part of the result.
Conversely, if A is invertible, F is algebraically closed, and A < sup > n </ sup > is diagonalizable for some n that is not an integer multiple of the characteristic of F, then A is diagonalizable.
Conversely, given a quadratic form in n variables, its coefficients can be arranged into an n × n symmetric matrix.
Conversely, if the ( restricted ) holonomy of a 2n-dimensional Riemannian manifold is contained in SU ( n ), then the manifold is a Ricci-flat Kähler manifold.
Conversely, if weak or normal ( m, n, k ) is a win, then any larger weak ( m, n, k ) is a win.
Conversely, if n is prime, then there exists a primitive root modulo n, or generator of the group ( Z / nZ )*.
Conversely, if n is composite, the algorithm will always return composite: if the algorithm returns prime, then this will occur in either step 4 or step 6.
which are linearly independent at each point q in U. Conversely, given such a coframe, there is a unique moving frame X < sub > 1 </ sub >, X < sub > 2 </ sub >, ..., X < sub > n </ sub > which is dual to it, i. e., satisfies the duality relation α < sup > i </ sup >( X < sub > j </ sub >) = δ < sup > i </ sup >< sub > j </ sub >, where δ < sup > i </ sup >< sub > j </ sub > is the Kronecker delta function on U.
Conversely, a polynomial time algorithm ( e. g., one that requires n < sup > 20 </ sup > steps for n-digit keys ) may be too slow for any practical use.
produces a unique composition of n. Conversely, every composition of n determines an assignment of pluses and commas.
that is, by adjoining n < sup > th </ sup > roots of elements of Δ to K. Conversely, if L is a Kummer extension of K, then Δ is recovered by the rule

Conversely and )-
Conversely, is ( m + 1 )- times bounded by, or:

Conversely and structure
Conversely, specifying the symmetry can define the structure, or at least clarify what we mean by an invariant, geometric language in which to discuss it ; this is one way of looking at the Erlangen programme.
Conversely a large cargo, for example in structure relocation, may be disassembled for carriage on multiple vehicles and then reassembled in the correct order at the destination.
Conversely, a wing dam is a structure that only partly restricts a waterway, creating a faster channel that resists the accumulation of sediment.
Conversely, many polymers ( notably flexible vinyl ) are intentionally swelled with plasticizers, which can be leached out of the structure, causing brittleness or other undesirable changes.
Conversely, the sequence of an ancient gene for a given structure may have diverged considerably in different species while at the same time maintaining the same basic structural features.
Conversely, given a Hopf algebra whose coalgebra structure is given above, we can recover a formal group law F from it.
Conversely, one of the characteristics of mental illness is a distorted value structure ; the neurotic does not value things according to their objective merit, in relation to his nature and needs ; he frequently values the very things that will lead him to self-destruction.
Conversely, every incidence structure can be viewed as a hypergraph.
Conversely, all later attempts at land reform by legal means, starting with the 1960s organization of peasant leagues ( Ligas Camponesas ) in Northeastern Brazil which opposed mostly eviction of peasants from rented plots and transformation of plantations into cattle ranches, would be nationally directed by a tendency to counter the existing landed property structure by means of a more rational appeal to the allegedly social function of property.
Conversely, the basic structure of a transitive Japanese sentence is SOV, with the usual syntactic features associated with languages of this typology, including postpositions, that is, grammar particles that appear after the words and phrases to which they apply.
Conversely any bipartite graph with girth at least six can be viewed as the Levi graph of an abstract incidence structure.
Conversely, if the defeasance provisions allow borrowers to provide the actual defeasance collateral to lenders and do not require defeasance deposits, the borrowers ’ defeasance consultant will be able to structure an optimized securities portfolio and hold a competitive auction to ensure best pricing.

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