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Formally and is
Formally organized vocational programs supported by federal funds allow high school students to gain experience in a field of work which is likely to lead to a full-time job on graduation.
Formally, a binary operation on a set S is called associative if it satisfies the associative law:
Formally, their designation is the letter Ž and the number.
Formally, a topological space X is called compact if each of its open covers has a finite subcover.
Formally, the set of all context-free languages is identical to the set of languages accepted by pushdown automata ( PDA ).
Formally, the derivative of the function f at a is the limit
More rigorously, the divergence of a vector field F at a point p is defined as the limit of the net flow of F across the smooth boundary of a three dimensional region V divided by the volume of V as V shrinks to p. Formally,
Formally, the base is known as Naval Support Facility Diego Garcia ( the US activity ) or Permanent Joint Operating Base ( PJOB ) Diego Garcia ( the UK's term ).
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, oxidation state is the hypothetical charge that an atom would have if all bonds to atoms of different elements were 100 % ionic.
Formally, a bifunctor is a functor whose domain is a product category.
Formally, a set S is called finite if there exists a bijection
Formally, the system is said to have memory.
Formally, an inner product space is a vector space V over the field together with an inner product, i. e., with a map
Formally, if M is a set, the identity function f on M is defined to be that function with domain and codomain M which satisfies
* Formally, when working over the reals, as here, this is accomplished by considering the limit as ε → 0 ; but the " infinitesimal " language generalizes directly to Lie groups over general rings.
Formally, a profinite group is a Hausdorff, compact, and totally disconnected topological group: that is, a topological group that is also a Stone space.
Formally, this sharing of dynamics is referred to as universality, and systems with precisely the same critical exponents are said to belong to the same universality class.
Formally, a frame is defined to be a lattice L in which finite meets distribute over arbitrary joins, i. e. every ( even infinite ) subset
Formally, Φ = kx − ωt is the phase.

Formally and take
Formally, the verbal noun ( VN, still retaining verbal characteristics ) takes okurigana, as is usual for verbs, while the deverbal noun ( DVN, without verbal characteristics ) does not take okurigana, as is usual for nouns.

Formally and integral
Formally, the Lebesgue integral provides the necessary analytic device.
Formally, a unique factorization domain is defined to be an integral domain R in which every non-zero and non-unit x of R can be written as a product ( including an empty product ) of irreducible elements p < sub > i </ sub > of R and a unit u:
Formally, the integral is the inner product of the luminosity function with the light spectrum.
Formally, the differential appearing under the integral behaves exactly as a differential: thus, the integration by substitution and integration by parts formulae for Stieltjes integral correspond, respectively, to the chain rule and product rule for the differential.

Formally and defining
Formally, the statement that " value decreases over time " is given by defining the linear differential operator as:

Formally and inverse
Formally, two variables are inversely proportional ( or varying inversely, or in inverse variation, or in inverse proportion or in reciprocal proportion ) if one of the variables is directly proportional with the multiplicative inverse ( reciprocal ) of the other, or equivalently if their product is a constant.
Formally, the probit function is the inverse of, denoted.

Formally and Fourier
Formally stated, the FFT is a method for computing the discrete Fourier transform of a sampled signal.
Formally, this follows from the convolution theorem in mathematics, which relates the Fourier transform of the power spectrum ( the intensity of each frequency ) to its autocorrelation.

Formally and transform
Formally, the discrete cosine transform is a linear, invertible function ( where denotes the set of real numbers ), or equivalently an invertible N × N square matrix.
Formally, the discrete sine transform is a linear, invertible function F: R < sup > N </ sup > < tt >-></ tt > R < sup > N </ sup > ( where R denotes the set of real numbers ), or equivalently an N × N square matrix.
Formally, the discrete Hartley transform is a linear, invertible function H: R < sup > n </ sup > < tt >-></ tt > R < sup > n </ sup > ( where R denotes the set of real numbers ).

idea and is
The general acceptance of the idea of governmental ( i.e., societal ) responsibility for the economic well-being of the American people is surely one of the two most significant watersheds in American constitutional history.
The dweller at p is last to hear about a new cure, the slowest to announce to his neighbors his urgent distresses, the one who goes the farthest to trade, and the one with the greatest difficulty of all in putting over an idea or getting people to join him in a cooperative effort.
And it is clearly argued by Lord Percy of Newcastle, in his remarkable long essay, The Heresy Of Democracy, and in a more general way by Voegelin, in his New Science Of Politics, that this same Rousseauan idea, descending through European democracy, is the source of Marx's theory of the dictatorship of the proletariat.
As a Humanist, Dr. Huxley interests himself in the possibilities of human development, and one thing we can say about this suggestion, which comes from a leading zoologist, is that, so far as he is concerned, the scientific outlook places no rigid limitation upon the idea of future human evolution.
The idea here is one of discharge but this must stand in opposition to a second view, Plato's notion of the arousal of emotion.
A third idea is that artistic literature serves to reduce emotional conflicts, giving a sense of serenity and calm to individuals.
It is possible that the idea of enrichment of emotion is a fifth idea.
It is true that this distinction between style and idea often approaches the arbitrary since in the end we must admit that style and content frequently influence or interpenetrate one another and sometimes appear as expressions of the same insight.
At this point a working definition of idea is in order, although our first definition will have to be qualified somewhat as we proceed.
Outstanding among these is the idea of human nature itself, including the many definitions that have been advanced over the centuries ; ;
An idea, of the sort that we have in mind, although of necessity readily available to imagination, is more general in connotation than most poetic or literary images, especially those appearing in lyric poems that seek to capture a moment of personal experience.
Finally we may note that the idea appears in educational theory where its influence is at present widespread.
namely, is the idea that there were Saxon mercenaries in England at all reasonable??
And to do this requires first of all the kind of information about people which is provided by the scientists in industrial anthropology and consumer research, who, for example, tell Courtenay that three days is the `` optimum priming period for a closed social circuit to be triggered with a catalytic cue-phrase '' -- which means that an effective propaganda technique is to send an idea into circulation and then three days later reinforce or undermine it.
He mentions the beats only once '', when he refers to their having revived through mere power and abandonment and the unwillingness to, commit death in life some idea of a decent equivalent between verbal expression and actual experience,, but the entire narrative, is written in the tiresome vocabulary `` of '' that lost `` and '' dying cause, `` and in the '' `` sprung syntax that is supposed to supplant, our mother, tongue.
The trouble is that at first glance the idea looks like such a good one.
Although Mr. Brown was not himself its inventor ( it was a French idea ), it is typical that his intuition first conceived the importance of mass producing this basic tool for general use.

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