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Formally, the two parts are given by the following expression, where is the number being encoded:

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## Some Related Sentences

Formally and two

__Formally__

**,**

**the**Congress serves

__two__functions

**:**to approve changes to

**the**Party constitution regarding policy and to elect a Central Committee

**,**about 300 strong.

__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__

**,**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__

**,**this means symmetry under a sub-group of

**the**Euclidean group of isometries in

__two__or three dimensional Euclidean space.

__Formally__

**,**EMF

**is**classified as

**the**external work expended per unit of charge to produce an electric potential difference across

__two__open-circuited terminals.

__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__

**,**

__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__speaking**,**this then satisfies**the**premises of an axiom of well-founded induction**,**which asserts that these__two__conditions**are**sufficient for**the**proposition to hold for all x.__Formally__

**,**it

**is**a norm defined on

**the**space of bounded linear operators between

__two__

**given**normed vector spaces.

__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**poem can be understood as

**the**combination of

__two__sonnets

**,**though

**the**spacing of

**the**stanzas

**is**irregular.

__Formally__

**,**

**given**

__two__categories C and D

**,**an equivalence of categories consists of a functor F

**:**C → D

**,**a functor G

**:**D → C

**,**and

__two__natural isomorphisms ε

**:**FG → I < sub > D </ sub > and η

**:**I < sub > C </ sub >→ GF.

__Formally__

**,**a vertex cover of a graph G

**is**a set C of vertices such that each edge of G

**is**incident to at least one vertex in C. The set C

**is**said to cover

**the**edges of G. The

**following**figure shows examples of vertex covers in

__two__graphs ( and

**the**set C

**is**marked with red ).

__Formally__

**,**

**given**

__two__partially ordered sets ( S

**,**≤) and ( T

**,**≤), a function f

**:**S → T

**is**an order-embedding if f

**is**both order-preserving and order-reflecting

**,**i. e. for all x and y in S

**,**one has

__Formally__

**,**he says

**,**

**the**piece consists of

__two__

**parts**of nearly equal length

**,**

**the**end of

**the**first section

**being**bars 24 – 28 ( p. 77 ).

__Formally__

**,**

**given**a finite set X

**,**a collection C of subsets of X

**,**all of size n

**,**has Property B if we can partition X into

__two__disjoint subsets Y and Z such that every set in C meets both Y and Z.

__Formally__known as " Brooks Institute of Photography ," Brooks Institute offers four majors

**,**

__two__certificate programs and

__two__graduate programs.

Formally and parts

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__

**,**Mbenga – Mbuti Pygmy music consists of at most only four

__parts__

**,**and can be described as an

**,**" ostinato with variations ," or similar to a passacaglia

**,**in that it

**is**cyclical.

__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__

**,**

**the**1772 Constitution was adopted

**by**

**the**Parliament ( Riksdag ) on 21 August 1772

**,**but this took place as members of

**the**Parliament and

**the**Privy Council were under threat

**by**

**the**royal garrison on order

**by**King Gustav III outside of Stockholm Palace

**,**

**where**

**the**Parliament and Privy Council were assembled in different

__parts__of

**the**palace.

Formally and are

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__

**,**as per

**the**2002 Memorandum of Understanding between

**the**BSI and

**the**United Kingdom Government

**,**British Standards

__are__defined as

**:**

__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__

**,**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.

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__

**,**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__

**,**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__

**,**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**word

**is**applied to persons who

__are__publicly accepted in a recognised capacity

**,**such as professional employment

**,**graduation from a course of study

**,**etc., to give critical commentaries in one or any of a

**number**of specific fields of public or private achievement or endeavour.

__Formally__

**,**

**the**outcomes Y < sub > i </ sub >

__are__described as

**being**Bernoulli-distributed data

**,**

**where**each outcome

**is**determined

**by**an unobserved probability p < sub > i </ sub > that

**is**specific to

**the**outcome at hand

**,**but related to

**the**explanatory variables.

__Formally__this approximation

**is**founded on

**the**variational principle

**,**valid for Hamiltonians that

__are__bounded from below.

__Formally__

**,**an analytic function ƒ ( z ) of

**the**real or complex variables z < sub > 1 </ sub >,…, z < sub > n </ sub >

**is**transcendental if z < sub > 1 </ sub >, …, z < sub > n </ sub >, ƒ ( z )

__are__algebraically independent

**,**i. e., if ƒ

**is**transcendental over

**the**field C ( z < sub > 1 </ sub >, …, z < sub > n </ sub >).

__Formally__most of these approaches

__are__similar to an artificial neural network

**,**as inputs to a node

__are__summed up and

**the**result serves as input to a sigmoid function

**,**e. g., but proteins do often control gene

**expression**in a synergistic

**,**i. e. non-linear

**,**way.

__Formally__

**,**

**the**sets of free and bound names of a process in π – calculus

__are__defined inductively as follows.

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