[permalink] [id link]
Some Related Sentences
Formally and inner
Formally, the integral
is the inner product of
the luminosity function
with the light spectrum
.
Formally and product
Formally, a bifunctor
is a functor whose domain
is a product category
.
Formally, we start
with a category C
with finite products (
i. e. C has
a terminal object 1 and any two objects of C have
a product ).
Formally, a unique factorization domain
is defined to be
an integral domain R in which every non-zero and non-unit x of R can be written as
a product ( including
an empty
product ) of irreducible elements p < sub >
i </ sub > of R and
a unit u:
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, 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, the differential appearing under
the integral behaves exactly as
a differential: thus
, the integration by substitution and integration by parts formulae for Stieltjes integral correspond
, respectively
, to
the chain rule and
product rule for
the differential
.
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, a product term P in
a sum of products
is an implicant of
the Boolean function F if P implies F
. More precisely:
Formally, the Barnes G-function
is defined ( in
the form of
a Weierstrass
product ) as
Formally and space
Formally, a topological
space X
is called compact if each of its open covers has
a finite subcover
.
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, a frame on
a homogeneous
space G / H consists of
a point in
the tautological bundle G → G / H
.
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.
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, 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 set S
is called finite if there exists
a bijection
Formally, the system
is said to have memory
.
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, 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
.
0.193 seconds.