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Formally, given complex-valued functions f and g of a natural number variable n, one writes
Some Related Sentences
Formally and given
Formally given to bishop Philip of Senj, the permission to use the Glagolitic liturgy ( the Roman Rite conducted in Slavic language instead of Latin, not the Byzantine rite ), actually extended to all Croatian lands, mostly along the Adriatic coast.
Formally, we are given a set of hypotheses and a set of manifestations ; they are related by the domain knowledge, represented by a function that takes as an argument a set of hypotheses and gives as a result the corresponding set of manifestations.
Formally, the statement that " value decreases over time " is given by defining the linear differential operator as:
Formally, it is a norm defined on the space of bounded linear operators between two given normed vector spaces.
Formally, the problem can be stated as follows: given a desired property, expressed as a temporal logic formula p, and a structure M with initial state s, decide if.
Formally, given two categories C and D, an equivalence of categories consists of a functor F: C → D, a functor G: D → C, and two natural isomorphisms ε: FG → I < sub > D </ sub > and η: I < sub > C </ sub >→ GF.
Formally, an absolute coequalizer of a pair in a category C is a coequalizer as defined above but with the added property that given any functor F ( Q ) together with F ( q ) is the coequalizer of F ( f ) and F ( g ) in the category D. Split coequalizers are examples of absolute coequalizers.
Formally, given a partially ordered set ( P, ≤), then an element g of a subset S of P is the greatest element of S if
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, 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
Formally, given a finite set X, a collection C of subsets of X, all of size n, has Property B if we can partition X into two disjoint subsets Y and Z such that every set in C meets both Y and Z.
Formally, given a graph G, a vertex labeling is a function mapping vertices of G to a set of labels.
Formally this mission was declared to be only in pursuit of the Russian vessels and ammunition taken to Anzali by the White Russian counter-revolutionary General Denikin, who had been given asylum by British forces in Anzali.
Formally, a married or widowed woman can be called by the given name of her husband ( Madame ( given name of husband ) family name or Madame veuve ( given name of husband ) family name ); this is now slightly out of fashion.
Formally and complex-valued
Formally, the bounded Borel functional calculus of a self adjoint operator T on Hilbert space H is a mapping defined on the space of bounded complex-valued Borel functions f on the real line,
Formally and functions
Formally, the Congress serves two functions: to approve changes to the Party constitution regarding policy and to elect a Central Committee, about 300 strong.
Formally, this means that the probability density functions or probability mass functions in this class have the form
Formally, an algebraic function in n variables over the field K is an element of the algebraic closure of the field of rational functions K ( x < sub > 1 </ sub >,..., x < sub > n </ sub >).
Formally, if we denote the set of stable functions by S ( D ) and the stability radius by r ( f, D ), then:
Formally and f
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, a cardinal κ is defined to be weakly compact if it is uncountable and for every function f: < sup > 2 </ sup > →
Formally, this means that, for some function f, the image f ( D ) of a directed set D ( i. e. the set of the images of each element of D ) is again directed and has as a least upper bound the image of the least upper bound of D. One could also say that f preserves directed suprema.
Formally, f < sub > X, Y </ sub >( x, y ) is the probability density function of ( X, Y ) with respect to the product measure on the respective supports of X and Y.
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 g
Formally, if T is a complete sufficient statistic for θ and E ( g ( T )) = τ ( θ ) then g ( T ) is the minimum-variance unbiased estimator ( MVUE ) of τ ( θ ).
Formally most of these approaches are similar to an artificial neural network, as inputs to a node are summed up and the result serves as input to a sigmoid function, e. g., but proteins do often control gene expression in a synergistic, i. e. non-linear, way.
Formally and natural
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, the use of a reduction is the function that sends each natural number n to the largest natural number m whose membership in the set B was queried by the reduction while determining the membership of n in A.
Formally, a natural number n is called highly abundant if and only if for all natural numbers m < n,
Formally, citizen science has been defined as " the systematic collection and analysis of data ; development of technology ; testing of natural phenomena ; and the dissemination of these activities by researchers on a primarily avocational basis ".
Formally, the right Kan extension of along consists of a functor and a natural transformation which is couniversal with respect to the specification, in the sense that for any functor and natural transformation, a unique natural transformation is defined and fits into a commutative diagram