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Formally, a state space can be defined as a tuple where:

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## Some Related Sentences

Formally and state

__Formally__

**,**oxidation

__state__is the hypothetical charge that an atom would have if all bonds to atoms of different elements were 100 % ionic.

__Formally__

**,**these reside in

**a**complex separable Hilbert space-variously called the "

__state__

**space**" or the " associated Hilbert

**space**" of the system-that is well

**defined**up to

**a**complex number of norm 1 ( the phase factor ).

__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__

**,**

**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__declared on October 9

**,**1970

**,**the Khmer Republic was

**a**right-wing pro-United States military-led government headed by General Lon Nol and Prince Sisowath Sirik Matak that took power in the March 18

**,**1970 coup against Prince Norodom Sihanouk

**,**then the country's head of

__state__.

__Formally__

**,**the problem

**can**

**be**stated

**as**follows

**:**given

**a**desired property

**,**expressed

**as**

**a**temporal logic formula p

**,**and

**a**structure M with initial

__state__s

**,**decide if.

__Formally__

**,**the Cisalpine Republic was an independent

__state__allied with France

**,**but the treaty of alliance established the effective subalternity of the new republic to France.

__Formally__

**,**an unlabelled

__state__transition system is

**a**

**tuple**( S

**,**→)

**where**S is

**a**set ( of states ) and → ⊆ S × S is

**a**binary relation over S ( of transitions ).

__Formally__

**a**member of the country's collective head of

__state__and

**,**

**as**president of parliament

**,**holder of the third-highest office

**,**he was left with little political influence.

__Formally__

**,**knowing the step response of

**a**dynamical system gives information on the stability of such

**a**system

**,**and on its ability to reach one stationary

__state__when starting from another.

__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__

**,**

**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__known

**as**the Constitution of the Republic of Poland (), it replaced the temporary amendments put into place in 1992 designed to reverse the effects of Communism

**,**establishing the nation

**as**"

**a**democratic

__state__ruled by law and implementing the principles of social justice ".

__Formally__

**,**it was owned by the PWS

__state__aircraft manufacturer

**,**in fact it was subordinated to the PZL.

__Formally__

**,**

**a**

__state__is

**a**set of conditions

**:**

**a**

__state__is represented by the set of conditions that are true in it.

Formally and space

__Formally__

**,**an inner product

__space__is

**a**vector

__space__V over the field together with an inner product

**,**i. e., with

**a**map

__Formally__

**,**

**a**profinite group is

**a**Hausdorff

**,**compact

**,**and totally disconnected topological group

**:**that is

**,**

**a**topological group that is also

**a**Stone

__space__.

__Formally__

**,**this means symmetry under

**a**sub-group of the Euclidean group of isometries in two or three dimensional Euclidean

__space__.

__Formally__

**,**the question of whether the universe is infinite or finite is whether it is an unbounded or bounded metric

__space__.

__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 is

**a**norm

**defined**on the

__space__of bounded linear operators between two given normed vector spaces.

__Formally__

**,**

**a**ringed

__space__( X

**,**O < sub > X </ sub >) is

**a**topological

__space__X together with

**a**sheaf of rings O < sub > X </ sub > on X.

__Formally__

**,**

**a**coalgebra over

**a**field K is

**a**vector

__space__C over K together with K-linear maps Δ

**:**C → C ⊗ C and ε

**:**C → K such that

__Formally__

**,**an ultrametric

__space__is

**a**set of points with an associated distance function ( also called

**a**metric )

__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__

**,**an iterated function system is

**a**finite set of contraction mappings on

**a**complete metric

__space__.

__Formally__

**,**rotational symmetry is symmetry with respect to some or all rotations in m-dimensional Euclidean

__space__.

__Formally__

**,**

**a**complex projective

__space__is the

__space__of complex lines through the origin of an ( n + 1 )- dimensional complex vector

__space__.

Formally and can

__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__

**,**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**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**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 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 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.

__Formally__

**,**the poem

__can__

**be**understood

**as**the combination of two sonnets

**,**though the spacing of the stanzas is irregular.

__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__

**,**the definition only requires some invertibility

**,**so we

__can__substitute for Q any matrix M whose eigenvalues do not include − 1.

__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__

**,**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.

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