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Formally, the sets of free and bound names of a process in π – calculus are defined inductively as follows.

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## Some Related Sentences

Formally and sets

__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__

**,**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__

**,**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

Many interior

__sets__were built at**the**Castle Brae Business Centre (__Formally__**the**Castlebrae High School )**in**Edinburgh**.**__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__

**,**

**a**quantization predicate QUA can be

**defined**

**as**

**follows**

**,**where is

**the**universe

**of**discourse

**,**

**and**is

**a**variable over

__sets__

**,**

**and**is

**a**mereological part structure on with < math > < _p </ math >

**the**mereological part-of relation

**.**

__Formally__

**,**

**a**Markov partition is used to provide

**a**finite cover for

**the**smooth system ; each set

**of**

**the**cover is associated with

**a**single symbol

**,**

**and**

**the**sequences

**of**symbols result

**as**

**a**trajectory

**of**

**the**system moves from one

**of**

**the**covering

__sets__to another

**.**

__Formally__

**,**propositional models can be represented by

__sets__

**of**propositional variables ; namely

**,**each model is represented by

**the**set

**of**propositional variables it assigns to true

**.**

Formally and free

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__known

**as**

**the**Inverurie Parish Church

**,**

**a**split

**in**Church

**of**Scotland over

**the**appointment

**of**ministers

**in**1843 ( The Disruption ) led to

**the**creation

**of**

**the**West Parish Church ( known locally

**as**" The West Kirk ") which was founded

**as**

**a**Free Church (

**a**church

__free__from Edinburgh control ) thus causing

**the**Inverurie Parish Church to change its name

**.**

Formally and bound

__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 and process

__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

**.**

__Formally__

**,**

**the**appointment remains

**a**royal one made on

**the**advice

**of**

**the**Lord Chancellor

**,**but he / she no longer comments on individual applications

**,**

**and**merely supervises

**the**

__process__

**and**reviews

**the**panel's recommendations

**in**general terms ( satisfying himself / herself that

**the**

__process__

**as**operated is fair

**and**efficient ).

__Formally__

**,**

**the**

__process__is one

**of**progressive development

**,**divided into three stages

**of**increasingly complexity

**.**

__Formally__

**,**this effect is referred to

**as**

**and**is

**a**

__process__whereby

**the**capture frame rate

**of**

**the**camera changes over time

**.**

__Formally__

**,**let be

**a**stochastic

__process__

**and**let represent

**the**cumulative distribution function

**of**

**the**joint distribution

**of**at times

**.**

__Formally__

**,**

**a**deterministic algorithm computes

**a**mathematical function ;

**a**function has

**a**unique value for any given input

**,**

**and**

**the**algorithm is

**a**

__process__that produces this particular value

**as**output

**.**

Formally and –

__Formally__

**,**arbitrage transactions have negative skew

__–__prices can get

**a**small amount closer ( but often no closer than 0 ), while they can get very far apart

**.**

__Formally__inaugurated

**in**March 2004

**,**

**the**Global Leadership Foundation works to " promote good governance

__–__democratic institutions

**,**open markets

**,**human rights

**and**

**the**rule

**of**law

__–__

**and**to contribute to

**the**prevention

**and**resolution

**of**conflict through mediation

**.**

__Formally__designated

**as**

**the**Manhattan Engineer District

**,**it refers specifically to

**the**period

**of**

**the**project from 1941

__–__1946 under

**the**control

**of**

**the**U

**.**S

**.**Army Corps

**of**Engineers

**,**under

**the**administration

**of**General Leslie R

**.**Groves

**.**

__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**complexity class MA is

**the**set

**of**decision problems that can be decided

**in**polynomial time by an Arthur

__–__Merlin protocol where Merlin's only move precedes any computation by Arthur

**.**

__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__trained specialists recognized by

**the**American Dental Association undergo

**a**minimum

**of**2

__–__3 years full-time rigorous education program after dental school graduation

**.**

__Formally__

**,**

**the**issue is that interfertile " able to interbreed " is not

**a**transitive relation

__–__if A can breed with B

**,**

**and**B can breed with C

**,**it does not follow that A can breed with C

__–__

**and**thus does not define an equivalence relation

**.**

__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

**.**

The Knight Foundation (

__Formally__**the**Foundation for Law**and**Government ), offers**a**possible solution__–__**the**" Knight 4000 ".

Formally and calculus

__Formally__

**,**

**the**bounded Borel functional

__calculus__

**of**

**a**self adjoint operator T on Hilbert space H is

**a**mapping

**defined**on

**the**space

**of**bounded complex-valued Borel functions f on

**the**real line

**,**

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__

**,**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__

**,**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__

**,**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__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__

**,**

**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

**.**

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