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Page "Stone–von Neumann theorem" ¶ 13
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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 two
) Conversely, it is often helpful to use the geometry of Cartesian coordinates in two or three dimensions to visualize algebraic relationships between two or three of many non-spatial variables.
If neither A nor B includes the idea of existence, then " some A are B " simply adjoins A to B. Conversely, if A or B do include the idea of existence in the way that " triangle " contains the idea " three angles equal to two right angles ", then " A exists " is automatically true, and we have an ontological proof of A's existence.
Conversely, if either of these last two expressions is defined, then so is the other ( and again they are equal ).
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, the two sunniest months of the year ; both in winter-June and July, both receive an abundant daily average of 9. 0 hours of sunshine.
Conversely, if God is incapable of being incapable, then the two inabilities cancel each other out, making God have the capability to do something.
Conversely any two or more states may be superposed to give a new state ...
Conversely, in 2004 the South Korean government charged the Korean High Speed Rail Construction Authority, a public entity, to construct its high speed rail line, 412 km from Seoul to Busan, in two phases.
Conversely, two of the most famous rock musicians from Ontario, Avril Lavigne and Alanis Morissette, are Franco-Ontarian by the second definition but not by the first, since they were born to Franco-Ontarian parents but currently work and live predominantly using the English language ( both currently have residences in Los Angeles ).
Conversely, Francesca Folan played two very different characters: Madeline Bassett in series one and Lady Florence Craye in series four.
Conversely, some view that Sunni jurisprudence falls into two groups: Ahl al-Ra ' i, or people of opinions, due to their emphasis on scholarly judgment and reason ; and Ahl al-Hadith, or people of traditions, due to their emphasis on restricting juristic thought to only what is found in scripture.
Conversely the index theorem for an elliptic complex can easily be reduced to the case of an elliptic operator: the two vector bundles are given by the sums of the even or odd terms of the complex, and the elliptic operator is the sum of the operators of the elliptic complex and their adjoints, restricted to the sum of the even bundles.
Conversely, Y-adapter cables are available that allow two separate joysticks to be connected to a single DA15 game adapter port ; if a joystick connected to one of these Y-adapters has more than two axes or buttons, only the first two of each will work.
Conversely, a connection on E determines a connection on F ( E ), and these two constructions are mutually inverse.
Conversely, in multiprocessor ( or multicore ) systems, there are two or more processing elements working at the same time, and so it is possible that they simultaneously access the same memory location.
Conversely, less than one Yellow Warbler nest in three on average suffers from predation in one way or another, while two out of three Mangrove and Golden Warbler nests are affected.
Conversely, where extra strength but the smooth drive of a smaller pitch is required, the chain may be " siamesed "; instead of just two rows of plates on the outer sides of the chain, there may be three (" duplex "), four (" triplex "), or more rows of plates running parallel, with bushings and rollers between each adjacent pair, and the same number of rows of teeth running in parallel on the sprockets to match.
Conversely, two unitary district councils added the word " county " to their titles to become " Rutland County Council District Council " and " County of Herefordshire District Council ".
Conversely, vocational schools are Government-owned or at least Government-supported institutions, occupy two full years of study, their credits are by and large accepted elsewhere in the academic world and in some instances such as charter academies or magnet schools may take the place of the final years of high school.
Conversely if f is a homomorphism from G to K < sub > k </ sub >, then one can color G by using the same color for two vertices in G whenever they are both mapped to the same vertex in K < sub > k </ sub >.

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