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Formally and called
Formally, a binary operation on a set S is called associative if it satisfies the associative law:
Formally, a topological space X is called compact if each of its open covers has a finite subcover.
Formally speaking, a collation method typically defines a total order on a set of possible identifiers, called sort keys, which consequently produces a total preorder on the set of items of information ( items with the same identifier are not placed in any defined order ).
Formally, a set S is called finite if there exists a bijection
Formally, these reside in a complex separable Hilbert space-variously called the " state space " or the " associated Hilbert space " of the system-that is well defined up to a complex number of norm 1 ( the phase factor ).
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:
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 called " Willow Township "
Formally, however, a face is any of the lower dimensional boundaries of the polytope, more specifically called an n-face.
Formally, a hypergraph is a pair where is a set of elements called nodes or vertices, and is a set of non-empty subsets of called hyperedges or edges.
Formally, a Lie superalgebra is a ( nonassociative ) Z < sub > 2 </ sub >- graded algebra, or superalgebra, over a commutative ring ( typically R or C ) whose product, called the Lie superbracket or supercommutator, satisfies the two conditions ( analogs of the usual Lie algebra axioms, with grading ):
Formally, a Hopf algebra is a ( associative and coassociative ) bialgebra H over a field K together with a K-linear map S: H → H ( called the antipode ) such that the following diagram commutes:
Formally, an ultrametric space is a set of points with an associated distance function ( also called a metric )
Formally, the group was called Studiengesellschaft für Geistesurgeschichte ‚ Deutsches Ahnenerbe e. V.
Formally the neutral is called the “ grounded conductor ”; as of the 2008 NEC, the terms “ neutral conductor ” and “ neutral point ” have been defined in the Code to record what had been common usage.
Formally, the game ( coalitional game ) consists of a finite set of players, called the grand coalition, and a characteristic function denotes the power set of .</ ref > from the set of all possible coalitions of players to a set of payments that satisfies.
Formally called the Final Declaration of the Stresa Conference, its aim was to reaffirm the Locarno Treaties and to declare that the independence of Austria " would continue to inspire their common policy ".
Formally, a non-empty partially ordered set ( D, ≤) is called a Scott domain if the following hold:
Formally called " the Wigwam ", this immense edifice was located on Girard Avenue between 19th and 20th Streets, across from Philadelphia's Girard College.
Formally, the Ministry of Aeronautics was founded on January 20, 1941 and so its military branch called " National Air Forces ", changed to " Brazilian Air Force " ( Força Aérea Brasileira-FAB ) on May, 22.
Formally called Mills and Boon Classics and Mills and Boon Favourites.
Formally called The Best Of and Collection.
Formally called Modern Romance Extra.

Formally and power
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, 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 declared on October 9, 1970, the Khmer Republic was a right-wing pro-United States military-led government headed by General Lon Nol and Prince Sisowath Sirik Matak that took power in the March 18, 1970 coup against Prince Norodom Sihanouk, then the country's head of state.
Formally, a measurable cardinal is an uncountable cardinal number κ such that there exists a κ-additive, non-trivial, 0-1-valued measure on the power set of κ.
Formally titled ' An Act to protect all Persons in the United States in their Civil Rights, and furnish the Means of their vindication, the Act declared that people born in the United States and not subject to any foreign power are entitled to be citizens, without regard to race, color, or previous condition of slavery or involuntary servitude.
Formally, the power to appoint members of the Vorstand lies with the Aufsichtsrat, which can appoint members with a two-thirds majority vote of approval, or a simple majority if multiple rounds of voting are required in order to reach a decision.
Formally it can be seen just as an ordinary function from X to the power set of Y, written as φ: X → 2 < sup > Y </ sup >.
Formally the power resides with the Plenary Session ; in practice this approves the decisions of the Nomenclature Section.

Formally and house
Other amenities in Saltney include the Corner Pin public house, a post office, Saltney Business Centre, St David's Retail Park ( Farmfoods / Poundstretchers / Ableworld ), an Asda Supermarket ( Formally a Netto store ) and a Morrisons supermarket.

Formally and are
However, shortly after this positive result, Kurt Gödel published On Formally Undecidable Propositions of Principia Mathematica and Related Systems ( 1931 ), showing that in any sufficiently strong axiomatic system there are true statements which cannot be proved in the system.
Formally, as per the 2002 Memorandum of Understanding between the BSI and the United Kingdom Government, British Standards are defined as:
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, both the pattern and searched text are vectors of elements of Σ.
Limits and colimits in a category C are defined by means of diagrams in C. Formally, a diagram of type J in C is a functor from J to C:
Formally, Gaussian integers are the set
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, 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, 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 two parts are given by the following expression, where is the number being encoded:
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, they are known as Ridunians, from the Latin Riduna.
( 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 outcomes Y < sub > i </ sub > are described as being Bernoulli-distributed data, where each outcome is determined by an unobserved probability p < sub > i </ sub > that is specific to the outcome at hand, but related to the explanatory variables.
Formally unnamed icefields are not listed
Formally this approximation is founded on the variational principle, valid for Hamiltonians that are bounded from below.
Formally, an analytic function ƒ ( z ) of the real or complex variables z < sub > 1 </ sub >,…, z < sub > n </ sub > is transcendental if z < sub > 1 </ sub >, …, z < sub > n </ sub >, ƒ ( z ) are algebraically independent, i. e., if ƒ is transcendental over the field C ( z < sub > 1 </ sub >, …, z < sub > n </ sub >).
These are manufactured by Amphenol ( Formally Alcatel Components and ITT Cannon Australia ).
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, the sets of free and bound names of a process in π – calculus are defined inductively as follows.

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