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Page "Word problem for groups" ¶ 37
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:: and Given
:: Example: Given this option to reinstate the contract on its original terms when a plan is proposed, it may be anomalous to require the payment of interest at a market rate while a case is pending.
:: See Committee Note to Interim Rule 8001 ( f ) (" Given the short time limit to file the petition with the circuit clerk, subdivision ( f )( 1 ) provides that entry of a certification on the docket does not occur until an effective appeal is taken under Rule 8003 ( a ) or ( b ).
:: Given the marginalized position of homosexuals in society, the metamessage that flows almost inevitably from excluding same-sex couples from such an important social institution is essentially that society considers such relationships to be less worthy of respect, concern and consideration than relationships involving members of the opposite sex.
:: Given, borrowed, bought, stolen.

:: and recursive
:: then there is a partial recursive function f < sub > P </ sub > such that:
:: To solve the uniform word problem for a class K of groups it is sufficient to find a recursive function f ( P, w ) that takes a finite presentation P for a group G and a word w in the generators of G such that whenever in G ∈ K:

:: and presentation
:: 3 ) Participants perform other activities during a delay between the formed intention and the presentation of the target cue.

:: and P
:: adjective ( A ), adposition ( preposition, postposition, circumposition ) ( P ), adverb ( Adv ), coordinate conjunction ( C ), determiner ( D ), interjection ( I ), noun ( N ), particle ( Par ), pronoun ( Pr ), subordinate conjunction ( Sub ), verb ( V ), etc.
:: Coordinate conjunction ( C ), determiner ( D ), negation ( Neg ), particle ( Par ), preposition ( P ) and prepositional phrase ( PP ), subordinate conjunction ( Sub ), etc.
:: Example: A defendant is entitled to a diminished capacity instruction when he produces expert testimony establishing that he suffered from a mental disorder, and the evidence “ logically and reasonably connects the defendant's alleged mental condition with the ... inability to possess the required level of culpability to commit the crime charged .” State v. Griffin, 100 Wn. 2d 417, 418 – 19, 670 P. 2d 265 ( 1983 ); see also Cienfuegos, 144 Wn. 2d at 227 ; State v. Ellis, 136 Wn. 2d 498, 521, 963 P. 2d 843 ( 1998 ).
:: Concerto in D major, RV 392, P. 166
:: Concerto in D minor, RV 393, P. 289
:: Concerto in D minor, RV 394, P. 288
:: Concerto in D minor, RV 395, P. 287
:: Concerto in A major, RV 396, P. 233
:: Concerto in A minor, RV 397, P. 37
:: Fall after 4: 00 P. M ( October 1 – March 31 )
:: C < sub > 6 </ sub > H < sub > 12 </ sub > O < sub > 6 </ sub > + 2 ADP + 2 P < sub > i </ sub > + 2 NAD < sup >+</ sup > → 2 CH < sub > 3 </ sub > COCOO < sup >−</ sup > + 2 ATP + 2 NADH + 2 H < sub > 2 </ sub > O + 2H < sup >+</ sup >
PL, P. L., Pl, Pl., or. pl may refer to ::
:: 46th Troop Carrier Squadron ( P )
:: 47th Troop Carrier Squadron ( P )
:: 48th Troop Carrier Squadron ( P )
:: w ⊨ P if and only if for some element v of G, it holds that v ⊨ P and w R v.
:: w ⊨ P if and only if for some element v of G, it holds that v ⊨ P.
:: 12th Infantry Col. Russell P. Reeder ( 11 June )

Given and recursive
Given a recursive trie
Given a linearly recursive sequence, let C be the transpose of the companion matrix of its characteristic polynomial, that is
* Given a partial function f from the natural numbers into the natural numbers, f is a partial recursive function if and only if the graph of f, that is, the set of all pairs such that f ( x ) is defined, is recursively enumerable.
The general scenario is the following: Given a class S of computable functions, is there a learner ( that is, recursive functional ) which for any input of the form ( f ( 0 ), f ( 1 ),..., f ( n )) outputs a hypothesis ( an index e with respect to a previously agreed on acceptable numbering of all computable functions ; the indexed function should be consistent with the given values of f ).
Given a recursive formula for producing a series, one can define a transfinite series by transfinite recursion by defining the series at limit ordinals by
Given a Gödel numbering of recursive functions, there is a primitive recursive function s of two arguments with the following property: for every Gödel number p of a partial computable function f with two arguments, the expressions and are defined for the same combinations of natural numbers x and y, and their values are equal for any such combination.

Given and presentation
* Given a recursively enumerable set A of positive integers that has insoluble membership problem, ⟨ a, b, c, d | a < sup > n </ sup > ba < sup > n </ sup > = c < sup > n </ sup > dc < sup > n </ sup >: n ∈ A ⟩ is a finitely generated group with a recursively enumerable presentation whose word problem is insoluble
Given a finite presentation P =
Given that many of the talented young artists had been raised in housing projects and were short on social and dress skills, this Motown department was not only necessary, it created an elegant style of presentation long associated with the label.
Given their role in antigen presentation, HSPs are useful as immunologic adjuvants in boosting the response to a vaccine.
Given the initial presentation of Guellen, Claire's power, the history between Claire and Ill, and the nature of Claire's decree, Ill's death appears almost inevitable.
" Given this presentation, it is hardly surprising that it has been taken to be a retelling of an actual legend ; Gallico writes that " the person and character of the painter are wholly fictional as is the story itself, although I am told that in some quarters the snow goose appearing over Dunkirk has been accepted as legend and I have been compelled to reply to many correspondents that it was sheer invention.
Given a presentation of a group G by generators and relations and a subgroup H of G, the algorithm enumerates the cosets of H on G and describes the permutation representation of G on the space of the cosets.
Given a group presentation by generators and relations, one gets a 2-complex with that fundamental group.
Given the controversy on the etiology of PANDAS ( i. e., whether caused by strep throat ) and the apparent ambiguity in the definitions of the clinical presentation leading to different research results, a new definition was proposed that would clarify the presentation of symptoms to ensure that research studies were studying the same group of children.

Given and P
Given points P < sub > 0 </ sub > and P < sub > 1 </ sub >, a linear Bézier curve is simply a straight line between those two points.
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.
Given the fact that the period P of an object in circular orbit around a spherical object obeys
Given the abundance of such optimization problems in everyday life, a positive answer to the " P vs. NP " question would likely have profound practical and philosophical consequences.
Given any curve C and a point P on it, there is a unique circle or line which most closely approximates the curve near P, the osculating circle at P. The curvature of C at P is then defined to be the curvature of that circle or line.
Given two points P and Q on C, let s ( P, Q ) be the arc length of the portion of the curve between P and Q and let d ( P, Q ) denote the length of the line segment from P to Q.
Given an eclipse, then there is likely to be another eclipse after every period P. This remains true for a limited time, because the relation is only approximate.
: Given any x and y, x = y if, given any predicate P, P ( x ) if and only if P ( y ).
Given to films dealing with science and technology by the Alfred P. Sloan Foundation each year at the Sundance Film Festival.
Given two permutations π and σ of m elements and the corresponding permutation matrices P < sub > π </ sub > and P < sub > σ </ sub >

1.820 seconds.