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Formally, the game ( coalitional game ) consists of a finite set of players, called the grand coalition, and a characteristic function denotes the power set of .</ ref > from the set of all possible coalitions of players to a set of payments that satisfies.

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## Some Related Sentences

Formally and game

__Formally__

**,**

**the**situation has

**the**characteristics

**of**

**a**prisoner's dilemma

__game__

**that**is played repeatedly between

**the**same partners

**,**

**and**in this case " defection "-jumping

**the**queue-would not be advantageous

**.**

Formally and consists

__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__

**,**

**a**deterministic Büchi automaton is

**a**tuple A =

**(**Q

**,**Σ

**,**δ

**,**q < sub

**>**0 </ sub >, F

**)**

**that**

__consists__

**of**

**the**following components:

__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**rigged Hilbert space

__consists__

**of**

**a**Hilbert space H

**,**together with

**a**subspace Φ which carries

**a**finer topology

**,**

**that**is one for which

**the**natural inclusion

__Formally__

**,**

**a**frame on

**a**homogeneous space G / H

__consists__

**of**

**a**point in

**the**tautological bundle G → G / H

**.**

__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__

**,**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__

**,**

**a**graph rewriting system usually

__consists__

**of**

**a**

**set**

**of**graph rewrite rules

**of**

**the**form

**,**with being

**called**pattern graph

**(**or left-hand side

**)**

**and**being

**called**replacement graph

**(**or right-hand side

**of**

**the**rule ).

__Formally__

**,**

**a**signed graph Σ is

**a**pair

**(**G

**,**σ

**)**

**that**

__consists__

**of**

**a**graph G =

**(**V

**,**E

**)**

**and**

**a**sign mapping or signature σ

**from**E

**to**

**the**sign group

__Formally__

**,**

**the**right Kan extension

**of**along

__consists__

**of**

**a**functor

**and**

**a**natural transformation which is couniversal with respect

**to**

**the**specification

**,**in

**the**sense

**that**for any functor

**and**natural transformation

**,**

**a**unique natural transformation is defined

**and**fits into

**a**commutative diagram

Formally and finite

__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__

**,**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__

**,**

**the**question

**of**whether

**the**universe is infinite or

__finite__is whether it is an unbounded or bounded metric space

**.**

__Formally__

**,**an iterated

**function**system is

**a**

__finite__

**set**

**of**contraction mappings on

**a**complete metric space

**.**

__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__

**,**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__

**,**we define

**a**bad field as

**a**structure

**of**

**the**form

**(**K

**,**T ), where K is an algebraically closed field

**and**T is an infinite

**,**proper

**,**distinguished subgroup

**of**K

**,**such

**that**

**(**K

**,**T

**)**is

**of**

__finite__Morley rank in its full language

**.**

__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**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__

**,**assuming our intuition

**from**

**the**

__finite__dimensional case carries over into

**the**infinite dimensional setting

**,**

**the**measure should then be equal

**to**

__Formally__

**,**

**the**upper density

**of**

**a**graph G is

**the**infimum

**of**

**the**values α such

**that**

**the**

__finite__subgraphs

**of**G with density α have

**a**bounded number

**of**vertices

**.**

Formally and set

__Formally__

**,**

**the**

__set__

**of**

**all**context-free languages is identical

**to**

**the**

__set__

**of**languages accepted by pushdown automata

**(**PDA ).

__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__

**,**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__

**,**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__

**,**

**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__

**,**

**the**discrete cosine transform is

**a**linear

**,**invertible

**function**

**(**where

**denotes**

**the**

__set__

**of**real numbers ), or equivalently an invertible N × N square matrix

**.**

__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__

**,**

**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__

**,**

**the**movement is

**a**rondo

**that**acts as

**the**theme for

**a**

__set__

**of**eight variations

**,**capped off by

**a**dramatic coda

**.**

__Formally__

**,**

**the**discrete sine transform is

**a**linear

**,**invertible

**function**F: R < sup

**>**N </ sup

**>**< tt >-></ tt

**>**R < sup

**>**N </ sup

**>**

**(**where R

**denotes**

**the**

__set__

**of**real numbers ), or equivalently an N × N square matrix

**.**

__Formally__

**,**

**the**discrete Hartley transform is

**a**linear

**,**invertible

**function**H: R < sup

**>**n </ sup

**>**< tt >-></ tt

**>**R < sup

**>**n </ sup

**>**

**(**where R

**denotes**

**the**

__set__

**of**real numbers ).

__Formally__

**,**

**a**constraint satisfaction problem is defined as

**a**triple

**,**where is

**a**

__set__

**of**variables

**,**is

**a**domain

**of**values

**,**

**and**is

**a**

__set__

**of**constraints

**.**

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