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Formally, powers with positive integer exponents may be defined by the initial condition

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## Some Related Sentences

Formally and powers

__Formally__neutral and reluctant to become involved

**with**

**the**great

__powers__except as a last resort

**,**Kuwait turned to

**the**United States

**,**

**the**Soviet Union and Britain for naval protection of its tanker fleet after twenty-one ships were attacked in

**the**gulf since late 1986.

Formally and with

__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__

**,**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__introduced in September 1979

**,**Initial samples were released in February 1980

**,**

__with__production chips available over

**the**counter in November.

__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__

**,**according to

**the**Constitution

**,**citizens of Turkmenistan have

**the**right to set up political parties and other public associations

**,**acting within

**the**framework of

**the**Constitution and laws

**,**and public associations and groups of citizens have

**the**right to nominate their candidates in accordance

__with__

**the**election law.

__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__

**,**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__

**,**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.

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__

**,**they are partial derivatives of

**the**option price

__with__respect to

**the**independent variables ( technically

**,**one Greek

**,**gamma

**,**is a partial derivative of another Greek

**,**called delta ).

__Formally__

**,**

**the**problem of supervised pattern recognition can

**be**stated as follows: Given an unknown function (

**the**ground truth ) that maps input instances to output labels

**,**along

__with__training data assumed to represent accurate examples of

**the**mapping

**,**produce a function that approximates as closely as possible

**the**correct mapping.

__Formally__

**the**work is operatic

**,**

__with__

**the**plot advanced entirely through dialogue sung

__with__accompanying music.

__Formally__

**,**

**the**President is elected

**by**

**the**National People's Congress in accordance

__with__Article 62 of

**the**Constitution.

Formally and positive

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__established in 1922

**,**over

**the**decades Woodcraft Rangers has modified Seton ’ s original emphasis on outdoor life to incorporate activities that meet

**the**needs of an increasingly urban population

**,**but

**the**goal of changing behavior and encouraging

__positive__outcomes through interaction and education remains central to its mission today.

Formally and may

__Formally__

**,**

**the**convex hull

__may__

**be**

**defined**as

**the**intersection of all convex sets containing X or as

**the**set of all convex combinations of points in 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

__may__even

**be**taken back to Marx's earliest statements about a class becoming conscious of itself and developing a class identity.

__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__

**,**a deterministic finite automaton

__may__

**be**

**defined**

**by**

**the**tuple where is

**the**set of states of

**the**automaton

**,**is

**the**set of input symbols

**,**is

**the**transition function that takes a state and an input symbol to a new state

**,**is

**the**

**initial**state of

**the**automaton

**,**and is

**the**set of accepting or final states of

**the**automaton.

__Formally__

**,**a party in honor of

**the**bride-to-be is never hosted

**by**

**the**bride-to-be

**,**although she

__may__participate in its planning.

Formally and be

__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__

**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.

__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.

__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.

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 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__

**,**a government would lay out its reasons for going to war

**,**as well as its intentions in prosecuting it and

**the**steps that might

__be__taken to avert it.

__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.

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