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Formally, if there exists some B ≥ 0 such that

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## Some Related Sentences

Formally and if

__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__

**,**

__if__d is the dimension of the parameter

**,**and n is the number of samples

**,**

__if__as and as

**,**then the model is semi-parametric.

__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 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.

If R is a ring

**,**let R denote the ring of polynomials in the indeterminate X over R. Hilbert proved**that**__if__R is " not too large ", in the sense**that**__if__R is Noetherian**,**the same must be true for R.__Formally__**,**__Formally__

**,**a hypothesis is compared against its opposite or null hypothesis ("

__if__I release this ball

**,**it will not fall to the floor ").

__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__

**,**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__

**,**

__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__

**,**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.

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.__Formally__

**,**

__if__we write F < sub > Δ </ sub >( x ) to mean the f-polynomial of Δ

**,**then the h-polynomial of Δ is

__Formally__

**,**a cardinal κ is defined to be weakly compact

__if__it is uncountable and for every function f: < sup > 2 </ sup > →

Formally and there

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__

**,**

__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__

**,**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.

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__

**,**however

**,**

__there__is an examination board consisting of a candidate's teachers / examiners

**,**the headmaster / headmistress and one external Vorsitzende ( r ) ( head ), usually a high-ranking school official or the head of another school.

__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__

**,**assuming the axiom of choice

**,**cardinality of a set X is the least ordinal α

**such**

**that**

__there__is a bijection between X and α.

__Formally__

**,**a cardinal number κ is λ-unfoldable

**if**and only

**if**for every transitive model M of cardinality κ of ZFC-minus-power set

**such**

**that**κ is in M and M contains all its sequences of length less than κ

**,**

__there__is a non-trivial elementary embedding j of M into a transitive model with the critical point of j being κ and j ( κ )

**≥**λ.

__Formally__

**,**

**if**

__there__is a utility function

**that**describes preferences over L commodities

**,**the expenditure function

__Formally__

**,**

**if**f is a harmonic function

**,**then f cannot exhibit a true local maximum within the domain of definition of f. In other words

**,**either f is a constant function

**,**or

**,**for any point inside the domain of f

**,**

__there__exist other points arbitrarily close to at which f takes larger values.

__Formally__

**,**however

**,**

__there__is an examination board consisting of a candidate ’ s teachers / examiners

**,**the headmaster / headmistress and a Vorsitzende ( r ) ( head ), usually a high-ranking school official or the head of another school.

__Formally__

**,**a number n is colossally abundant

**if**and only

**if**

__there__is an ε >

**0**

**such**

**that**for all k > 1

**,**

__Formally__

**,**in Euclidean space

**,**the wave front set of ƒ is defined as the complement of the set of all pairs ( x < sub >

**0**</ sub >, v )

**such**

**that**

__there__

**exists**a test function with φ ( x < sub >

**0**</ sub >) ≠

**0**and an open cone Γ containing v

**such**

**that**the estimate

__Formally__

**,**at least

**,**the European Commission has primarily a monitoring role ; in practice

**,**however

**,**

__there__is considerable scope for it to help set the policy agenda and persuade reluctant Member States to implement agreed policies.

__Formally__

**,**a market is complete with respect to a trading strategy

**,**

**,**

**if**

__there__

**exists**a self-financing trading strategy

**,**

**such**

**that**at any time

**,**the returns of the two strategies

**,**and are equal.

Formally and exists

__Formally__Roman Kalyn is now the only member of the group

**,**but de-facto GreenJolly

__exists__in name only.

Formally and some

__Formally__

**,**bending modulus is defined as the energy required to deform a membrane from its intrinsic curvature to

__some__other curvature.

__Formally__

**,**this means

**that**

**,**for

__some__function f

**,**the image f ( D ) of a directed set D ( i. e. the set of the images of each element of D ) is again directed and has as a least upper bound the image of the least upper bound of D. One could also say

**that**f preserves directed suprema.

__Formally__a congruence subgroup is one

**that**contains Γ ( N ) for

__some__N

**,**and the least

**such**N is the level or Stufe of the subgroup.

By 1912

**,**the Social Democrats**,**with an explicitly anti-antisemitic program**,**were the largest party in the German Reichstag**,**and the Progressives ran very strongly as well ...__Formally__**,**at least**,**the Jews had been fully emancipated with the establishment of the German Empire**,**although they were kept out of certain influential occupations**,**enjoyed extraordinary prosperity ... Germans intermarried with Jews: in the 1930s__some__50**,**000 Jews were living in mixed German-Jewish marriages**,**so at least 50**,**000 Germans**,**and presumably parts of their families**,**had familial contact with the Jews.__Formally__

**,**we begin by considering

__some__family of distributions for a random variable X

**,**

**that**is indexed by

__some__θ.

__Formally__

**,**Liouville numbers and elementary numbers contain the algebraic numbers

**,**and they include

__some__but not all transcendental numbers.

__Formally__

**,**rotational symmetry is symmetry with respect to

__some__or all rotations in m-dimensional Euclidean space.

__Formally__

**,**the definition only requires

__some__invertibility

**,**so we can substitute for Q any matrix M whose eigenvalues do not include − 1.

__Formally__

**,**all members of the Ghelani family are Hindu Leuva Patel

**,**although

__some__have since chosen other religious beliefs.

Bābak Khorram-Din (

__Formally__known as " Pāpak " meaning " Young Father ") (, alternative spelling: Bābak Xorramdin ; 795**,**according to__some__other sources 798 — January 838 ) was one of the main PersianArmenian historian Vardan Areweltsʻi**,**ca.__Formally__

**,**a strongly continuous semigroup is a representation of the semigroup ( R < sub >+</ sub >,+) on

__some__Banach space X

**that**is continuous in the strong operator topology.

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