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Formally, a product term P in a sum of products is an implicant of the Boolean function F if P implies F. More precisely:

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## Some Related Sentences

Formally and product

__Formally__

**,**

**an**inner

__product__space

**is**

**a**vector space V over

**the**field together with

**an**inner

__product__

**,**i

**.**e., with

**a**map

__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 and term

__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__

**,**

**the**case where only

**a**subset

**of**parameters

**is**defined

**is**still

**a**composite hypothesis ; nonetheless

**,**

**the**

__term__point hypothesis

**is**often applied

**in**such cases

**,**particularly where

**the**hypothesis test can be structured

**in**such

**a**way that

**the**distribution

**of**

**the**test statistic (

**the**distribution under

**the**null hypothesis ) does not depend on

**the**parameters whose values have not been specified under

**the**point null hypothesis

**.**

__Formally__

**,**they are appointed by

**the**President for five-year terms coinciding with

**the**

__term__

**of**

**the**House

**of**Representatives

**.**

Formally and P

__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__

**,**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**partially ordered set (

__P__

**,**≤)

**is**bounded complete

**if**

**the**following holds for any subset S

**of**

__P__

**:**

__Formally__

**,**define

**the**set

**of**lines

**in**

**the**plane

__P__as L (

__P__); then

**a**rigid motion

**of**

**the**plane takes lines to lines –

**the**group

**of**rigid motions acts on

**the**set

**of**lines – and one may ask which lines are unchanged by

**an**action

**.**

__Formally__

**,**

__P__

**is**

**a**symmetric polynomial

**,**

**if**for any permutation σ

**of**

**the**subscripts 1

**,**2

**,**..., n one has

__P__( X < sub > σ ( 1 )</ sub >, X < sub > σ ( 2 )</ sub >, …, X < sub > σ ( n )</ sub >) =

__P__( X < sub > 1 </ sub >, X < sub > 2 </ sub >, …, X < sub > n </ sub >).

__Formally__

**,**let

__P__be

**a**poset ( partially ordered set ), and let

**F**be

**a**filter on

__P__; that

**is**

**,**

**F**

**is**

**a**subset

**of**

__P__such that

**:**

Formally and sum

__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__

**,**

**a**cumulativity predicate CUM can be defined as follows

**,**where capital X

**is**

**a**variable over sets

**,**U

**is**

**the**universe

**of**discourse

**,**p

**is**

**a**mereological part structure on U

**,**and

**is**

**the**mereological

__sum__operation

**.**

__Formally__

**,**let X be any scheme and S be

**a**sheaf

**of**graded-algebras (

**the**definition

**of**which

**is**similar to

**the**definition of-modules on

**a**locally ringed space ): that

**is**

**,**

**a**sheaf with

**a**direct

__sum__decomposition

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__

**,**

**the**set

**of**all context-free languages

__is__identical to

**the**set

**of**languages accepted by pushdown automata ( PDA ).

**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__

**,**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__

**,**

**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

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