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Formally and process
Formally, a Markov chain is a random process with the Markov property.
Formally, the appointment remains a royal one made on the advice of the Lord Chancellor, but he / she no longer comments on individual applications, and merely supervises the process and reviews the panel's recommendations in general terms ( satisfying himself / herself that the process as operated is fair and efficient ).
Formally, the process is one of progressive development, divided into three stages of increasingly complexity.
Formally, this effect is referred to as and is a process whereby the capture frame rate of the camera changes over time.
Formally, let be a stochastic process and let represent the cumulative distribution function of the joint distribution of at times.
Formally, the sets of free and bound names of a process in π – calculus are defined inductively as follows.
Formally, it is the process of eliciting information from the government.
Formally, a deterministic algorithm computes a mathematical function ; a function has a unique value for any given input, and the algorithm is a process that produces this particular value as output.

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 one
Formally, one has an implication, not an equivalence, so the solution set may get larger.
Formally one defines
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, 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, they are partial derivatives of the option price with respect to the independent variables ( technically, one Greek, gamma, is a partial derivative of another Greek, called delta ).
Formally known as the Kingfisher Pier, the Pier at Garden City is one of the most renowned attractions in Garden City, SC.
Formally, the word is applied to persons who are publicly accepted in a recognised capacity, such as professional employment, graduation from a course of study, etc., to give critical commentaries in one or any of a number of specific fields of public or private achievement or endeavour.
Formally speaking, the strategy pattern defines a family of algorithms, encapsulates each one, and makes them interchangeable.
Formally, the symphony is one of Mahler's most outwardly conventional.
Formally, however, there is an examination board consisting of a candidate's teachers / examiners, the headmaster / headmistress and one external Vorsitzende ( r ) ( head ), usually a high-ranking school official or the head of another school.
Formally, one may connect the kernel and the cokernel by the exact sequence
Formally, one inserts under the trace for each degree of freedom
Formally, an nth order approximation is one where the order of magnitude of the error is at most, or in terms of big O notation, the error is
Formally a congruence subgroup is one that contains Γ ( N ) for some N, and the least such N is the level or Stufe of the subgroup.
Formally, a rigged Hilbert space consists of a Hilbert space H, together with a subspace Φ which carries a finer topology, that is one for which the natural inclusion
Formally, a generative grammar is defined as one that is fully explicit.
Formally, if R is a Noetherian ring and I is a principal, proper ideal of R, then I has height at most one.
Formally, knowing the step response of a dynamical system gives information on the stability of such a system, and on its ability to reach one stationary state when starting from another.
Formally, a vertex cover of a graph G is a set C of vertices such that each edge of G is incident to at least one vertex in C. The set C is said to cover the edges of G. The following figure shows examples of vertex covers in two graphs ( and the set C is marked with red ).
Formally, given complex-valued functions f and g of a natural number variable n, one writes
Formally dedicated " as a memorial to the boys that were " on October 30, 1915, Alumni Field and its distinctive " maroon goal-posts on a field of green " were hailed in that evening's edition of the Boston Saturday Evening Transcript as " one of the sights in Boston.
Formally, given two partially ordered sets ( S, ≤) and ( T, ≤), a function f: S → T is an order-embedding if f is both order-preserving and order-reflecting, i. e. for all x and y in S, one has

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