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Formally said, the intersection of each two of them is empty ( the null event ): A and B

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## Some Related Sentences

Formally and said

__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.

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__

**,**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__

**,**a system

**is**

__said__to be observable if

**,**for any possible sequence

**of**state

**and**control vectors

**,**

**the**current state can be determined in finite time using only

**the**outputs

**(**this definition

**is**slanted towards

**the**state space representation ).

Formally and intersection

__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 and each

__Formally__

**,**cl

**(**S ) denotes

**the**smallest subset Y

**of**M that contains S such that for

__each__reaction

**(**

**A**

**,**

**B**)

__Formally__speaking

**,**

**the**strategy pattern defines a family

**of**algorithms

**,**encapsulates

__each__one

**,**

**and**makes

**them**interchangeable.

__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 follows from

**the**convolution theorem in mathematics

**,**which relates

**the**Fourier transform

**of**

**the**power spectrum

**(**

**the**intensity

**of**

__each__frequency ) to its autocorrelation.

__Formally__it consists

**of**three groups

**of**four measure phrases

**of**three to four chords repeated four times

__each__

**,**ABC :|| ABC

**,**which then merges with

**the**next movement

**,**" Floe " with

**the**entrance

**of**

**the**horns.

__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**

**is**reflexive if it

**is**equal to

**the**algebra

**of**bounded operators which leave invariant

__each__subspace left invariant by every operator in

**A**.

__Formally__

**,**Chrétien

**and**Martin have remained publicly respectful

**of**

__each__other ; while much

**of**

**the**verbal sparring was between their supporters.

__Formally__

**,**

**the**use

**of**a reduction

**is**

**the**function that sends

__each__natural number n to

**the**largest natural number m whose membership in

**the**set

**B**was queried by

**the**reduction while determining

**the**membership

**of**n in

**A**.

__Formally__described

**,**it alternates slow sections in a modal F with faster sections

**,**" Neue Kraft fühlend "

**(**with renewed strength ), in D. The slow sections

__each__have

**two**elements

**,**

**(**1 ) a passage reminiscent

**of**

**the**opening

**of**

**the**first movement in which

**the**instruments overlap

__each__other with a brief motive ;

**(**2 ) a chorale

**,**

**the**actual song.

__Formally__

**,**consider an economic model with different mathematical weightings placed on

**the**utilities

**of**

__each__self.

__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__

**,**

__each__

**of**

**the**following definitions defines a concrete category

**,**

**and**every pair

**of**these categories can be shown to be concretely isomorphic.

__Formally__

**,**

**the**city has designations for

__each__

**of**

**the**eight neighborhoods which are represented by neighborhood councils.

__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 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__

**,**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.

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