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Formally and frame
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, this effect is referred to as and is a process whereby the capture frame rate of the camera changes over time.

Formally and on
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 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, if M is a set, the identity function f on M is defined to be that function with domain and codomain M which satisfies
*, see On Formally Undecidable Propositions of Principia Mathematica and Related Systems for details on English translations.
Formally a random variable is considered to be a function on the possible outcomes.
Formally, in the finite-dimensional case, if the linear map is represented as a multiplication by a matrix A and the translation as the addition of a vector, an affine map acting on a vector can be represented as
Formally, a detailed balanced process is the one on which the probability to be in the state x and transit to x ' must be the same as to be in the state x ' and transit to x.
Formally, Gaussian curvature only depends on the Riemannian metric of the surface.
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, 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 ).
Informally, G has the above presentation if it is the " freest group " generated by S subject only to the relations R. Formally, the group G is said to have the above presentation if it is isomorphic to the quotient of a free group on S by the normal subgroup generated by the relations R.
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 WPAZ, the station changed its call letters and name on October 28th, 2011.
Formally, the Sachs – Hornbostel is modeled on the Dewey Decimal classification.
Formally, a center of gravity is an application point of the resultant gravitational force on the body.
Formally named The King's College of Our Lady and Saint Nicholas in Cambridge, the college lies on the River Cam and faces out onto King's Parade in the centre of the city.
Formally, start with a set Ω and consider the sigma algebra Σ on Ω consisting of all subsets of Ω.
Formally, a statistic s is a measurable function of X ; thus, a statistic s is evaluated on a random variable X, taking the value s ( X ), which is itself a random variable.
Formally educated African Americans, on the other hand, either disregarded black minstrelsy or openly disdained it.
Formally, the motion merely calls on parliament to thank the monarch or viceroy for the speech via an Address in Reply.

Formally and space
Formally, a topological space X is called compact if each of its open covers has a finite subcover.
Formally, an inner product space is a vector space V over the field together with an inner product, i. e., with a map
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, 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, this means symmetry under a sub-group of the Euclidean group of isometries in two or three dimensional Euclidean space.
Formally, the question of whether the universe is infinite or finite is whether it is an unbounded or bounded metric space.
Formally, we start with a metric space M and a subset X.
Formally, Minkowski space is a four-dimensional real vector space equipped with a nondegenerate, symmetric bilinear form with signature < tt >(−,+,+,+)</ tt > ( Some may also prefer the alternative signature < tt >(+,−,−,−)</ tt >; in general, mathematicians and general relativists prefer the former while particle physicists tend to use the latter.
Formally, it is a norm defined on the space of bounded linear operators between two given normed vector spaces.
Formally, a ringed space ( X, O < sub > X </ sub >) is a topological space X together with a sheaf of rings O < sub > X </ sub > on X.
Formally, a coalgebra over a field K is a vector space C over K together with K-linear maps Δ: C C ⊗ C and ε: C K such that
Formally, an ultrametric space is a set of points with an associated distance function ( also called a metric )
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, an iterated function system is a finite set of contraction mappings on a complete metric space.
Formally, a state space can be defined as a tuple where:
Formally, rotational symmetry is symmetry with respect to some or all rotations in m-dimensional Euclidean space.
Formally, a complex projective space is the space of complex lines through the origin of an ( n + 1 )- dimensional complex vector space.

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