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Formally and for
Formally, there is a clear distinction: " DFT " refers to a mathematical transformation or function, regardless of how it is computed, whereas " FFT " refers to a specific family of algorithms for computing DFTs.
Formally neutral and reluctant to become involved with the great powers except as a last resort, Kuwait turned to the United States, the Soviet Union and Britain for naval protection of its tanker fleet after twenty-one ships were attacked in the gulf since late 1986.
*, see On Formally Undecidable Propositions of Principia Mathematica and Related Systems for details on English translations.
Formally named " United Press Associations " for incorporation and legal purposes, but publicly known and identified as United Press or UP, it was created by the 1907 uniting of three smaller news syndicates by the Midwest newspaper publisher E. W. Scripps.
Formally stated, the FFT is a method for computing the discrete Fourier transform of a sampled signal.
Formally, collective noun forms such as “ a group of people ” are represented by second-order variables, or by first-order variables standing for sets ( which are well-defined objects in mathematics and logic ).
Formally it is precisely in allowing quantification over class variables α, β, etc., that we assume a range of values for these variables to refer to.
Formally, a decision problem is P-complete ( complete for the complexity class P ) if it is in P and that every problem in P can be reduced to it by using an appropriate reduction.
If R is a ring, let R denote the ring of polynomials in the indeterminate X over R. Hilbert proved that if R is " not too large ", in the sense that if R is Noetherian, the same must be true for R. Formally,
Formally, the sequence of partial sums of some infinite summation converges if for every fixed power of X the coefficient stabilizes: there is a point beyond which all further partial sums have the same coefficient.
Formally, a function ƒ is real analytic on an open set D in the real line if for any x < sub > 0 </ sub > in D one can write
Formally, an elliptic function is a function meromorphic on for which there exist two non-zero complex numbers and with ( in other words, not parallel ), such that and for all.
Formally, if is an open subset of the complex plane, a point of, and is a holomorphic function, then is called a removable singularity for if there exists a holomorphic function which coincides with on.
Formally, we have for the approximation to the full solution A, a series in the small parameter ( here called ), like the following:
In late 1900s the day that of the City was founded is Jakin School is a Private School is Formally Part of Jakin School Board was Grades One through Twelve there is no Football field on this school. In 1966 When Jakin School was Closed were Sent to Blakely-Union Elementary, Junior High, and High School ( which later Became Early County High, Middle, and Elementary School ). while Carver school was built for African-American students grades One through Twelve. although late 1960s when Carver school was closed along with Kestler School was based in Damascus were sent to Washington High & Elementary at Blakely. In addition to small farm agriculture, Jakin's early economic growth resulted from turpentine.
Formally, cl ( S ) denotes the smallest subset Y of M that contains S such that for each reaction ( A, B )
Formally, it is a coalition of U. S. and European CEOs, largely from transnational corporations, launched at the urging of former United States Secretary of Commerce Ron Brown in Seville ( Spain ) in late 1995 at a conference attended by CEOs from more than 100 U. S. and EU companies and by top government representatives led by the Commissioners for Trade and Industry and by the U. S. Secretary of Commerce.
Formally, a government would lay out its reasons for going to war, as well as its intentions in prosecuting it and the steps that might be taken to avert it.
Formally, the movement is a rondo that acts as the theme for a set of eight variations, capped off by a dramatic coda.
( Formally speaking, this then satisfies the premises of an axiom of well-founded induction, which asserts that these two conditions are sufficient for the proposition to hold for all x.
Formally, the motion merely calls on parliament to thank the monarch or viceroy for the speech via an Address in Reply.
; Electronics: Formally a fixture in radio shacks, now used for assembly and repair of all sorts of electronic equipment including communication, computer, and home entertainment items.
It has been leased from the National Trust since 1974 by the Somerset Wildlife Trust ( Formally Somerset Trust for Nature Conservation ) and is run as a nature reserve and visitor centre.

Formally and received
Formally nominated on December 11, 1851, Curtis was confirmed by the United States Senate on December 20, 1851, and received his commission the same day.
Formally nominated on January 3, 1820, Bland was confirmed by the United States Senate on January 5, 1820, and received his commission the same day.
Formally trained in music composition, Dargel studied with Oliveros, John Luther Adams, and Lewis Nielson, and received a B. A.
Formally nominated on January 5, 1950, he was confirmed by the United States Senate on February 8, 1950, and received his commission on February 10, 1950.

Formally and words
Formally, if f is a harmonic function, then f cannot exhibit a true local maximum within the domain of definition of f. In other words, either f is a constant function, or, for any point inside the domain of f, there exist other points arbitrarily close to at which f takes larger values.

Formally and let
Formally, let S and T be finite sets and let F =
Formally, let P be an expression in which the variable x is free.
Formally, let
Formally, let be a surjective homomorphism.
Formally, let be a stochastic process and let represent the cumulative distribution function of the joint distribution of at times.
Formally, let f: < sup > n </ sup > → be the cost function which must be minimized.
Formally, let P and Q be abelian categories, and let
Formally, let A be a real matrix of which we want to compute the eigenvalues, and let A < sub > 0 </ sub >:= A.
Formally, let G be a Coxeter group with reduced root system R and k < sub > v </ sub > a multiplicity function on R ( so k < sub > u </ sub > = k < sub > v </ sub > whenever the reflections σ < sub > u </ sub > and σ < sub > v </ sub > corresponding to the roots u and v are conjugate in G ).
Formally, let p ( x, y ) be a complex polynomial in the complex variables x and y.
Formally, let p and q be two nonzero polynomials, respectively of degree m and n. Thus:
Formally, let P be a poset ( partially ordered set ), and let F be a filter on P ; that is, F is a subset of P such that:
Formally, let denote the pairwise score for against.
Formally, let X be any scheme and S be a sheaf of graded-algebras ( the definition of which is similar to the definition of-modules on a locally ringed space ): that is, a sheaf with a direct sum decomposition

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