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Some Related Sentences
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 solution
Formally, one has an implication
, not an equivalence
, so
the solution set may get larger
.
Formally, we have for
the approximation to
the full
solution A
, a series in
the small parameter ( here called ), like
the following:

The Knight Foundation (
Formally the Foundation for Law and Government ), offers
a possible
solution –
the " Knight 4000 ".
Formally and matrix
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, 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 singular value decomposition
of an m × n real or complex
matrix M
is a factorization
of the form
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, Aff ( V )
is naturally isomorphic to
a subgroup
of, with V embedded as
the affine plane
, namely
the stabilizer
of this affine plane ;
the above
matrix formulation
is the ( transpose
of )
the realization
of this, with
the ( n × n and 1 × 1 ) blocks corresponding to
the direct sum decomposition
.
Formally, let A be
a real
matrix of which we want to compute
the eigenvalues
, and let A < sub > 0 </ sub >:= A
.
Formally, the Mahalanobis distance
of a multivariate vector from
a group
of values with mean and covariance
matrix is defined as:
Formally, the definition only requires some invertibility
, so we can substitute for Q any
matrix M whose eigenvalues do not include − 1
.
Formally, consider an n × n
matrix A =(
a < sub > i
, j </ sub >).
Formally and equation
Formally it
is defined
by the equation
Formally the self-inductance
of a wire loop would be given
by the above
equation with i
Formally, the equation above defines
the macroscopic neutron cross-section ( for reaction x ) as
the proportionality constant between
a neutron flux incident on
a ( thin ) piece
of material and
the number
of reactions that occur ( per unit volume ) in that material
.
Formally and by

*
Formally appoints
the Prime Minister
of Finland selected
by the Parliament
, and formally appoints
the rest
of the cabinet ( Council
of State ) as proposed
by the Prime Minister
Formally the Prince-Electors elected
a King
of the Romans
, who was elected in Germany but became Holy Roman Emperor only when crowned
by the Pope
.
Formally, these failed when they were rejected
by the Church
of England's General Synod in 1972 ; conversations and co-operation continued
, however
, leading in 2003 to
the signing
of a covenant between
the two churches
.
Formally the " head
of state " can also personally be
the " head
of government " ( ex officio or
by ad hoc cumulation such as an absolute monarch nominating himself ) but otherwise has formal precedence over
the Head
of Government and other ministers
, whether he
is their actual political superior ( absolute monarch
, executive president ) or rather theoretical or ceremonial in character
.

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 named " United Press Associations " for incorporation and legal purposes
, but publicly known and identified as United Press or UP
, it was created
by the 1907 uniting
of three smaller news syndicates
by the Midwest newspaper publisher E
. W
. Scripps
.
Formally, most
of these people were convicted
by NKVD troikas (" triplets ")– special courts martial
.
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, a decision problem
is P-complete ( complete for
the complexity class P ) if it
is in P and that every problem in P can be reduced to it
by using an appropriate reduction
.
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, a transductive support vector machine
is defined
by the following primal optimization problem:
Formally, DFS
is an uninformed search that progresses
by expanding
the first child node
of the search tree that appears and thus going deeper and deeper until
a goal node
is found
, or until it hits
a node that has no children
.
Formally, powers with positive integer exponents may be defined
by the initial condition

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
.
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