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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 ).

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## Some Related Sentences

Formally and system

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__known as

**the**" Six

**and**A Half Point Pole " form

**,**

**this**

**is**

**the**second

**to**last form

**of**

**the**

__system__.

__Formally__

**,**HPGCC

**is**

**a**cross-compiler ; it compiles code

**for**

**the**ARM-based HP calculators

**,**but runs on

**a**PC rather than

**the**target

__system__.

__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__

**,**an iterated function

__system__

**is**

**a**

**finite**set

**of**contraction mappings on

**a**complete metric

**space**.

__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__

**,**let G

**be**

**a**Coxeter group with reduced root

__system__R

**and**k < sub > v </ sub >

**a**multiplicity function on R

**(**so k < sub > u </ sub > = k < sub > v </ sub > whenever

**the**reflections σ < sub > u </ sub >

**and**σ < sub > v </ sub > corresponding

**to**

**the**roots u

**and**v are conjugate

**in**G

**).**

__Formally__

**,**

**a**squeeze preserves

**the**hyperbolic metric expressed

**in**

**the**form ;

**in**

**a**different coordinate

__system__.

__Formally__

**,**an Hamiltonian

__system__

**is**

**a**dynamical

__system__completely described by

**the**scalar function

**,**

**the**Hamiltonian.

__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__

**,**Transnistria has

**a**multi-party

__system__

**and**an unicameral parliament

**,**called

**the**Supreme Council.

__Formally__

**,**

**a**redistribution

**of**all agents ’ initial endowments

**of**goods among all agents

**in**

**the**

__system__

**is**

**a**core allocation

**if**no group

**of**agents

**can**redistribute their own initial endowments among themselves so as

**to**improve

**the**satisfaction

**of**someone

**in**

**the**group without impairing that

**of**

**any**other

**in**

**the**group.

__Formally__known as

**the**" Eastern Division

**of**Surrey " or " Surrey Eastern ", it elected two MPs by

**the**bloc vote

__system__.

__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__

__system__networks correspond

**to**type lattices

**in**formal lattice theory

**,**although they are occasionally erroneously mistaken

**for**flowcharts or directed decision trees.

__Formally__known as

**the**Federal Reserve Wire Network

**,**Fedwire

**is**

**a**Real Time Gross Settlement Funds Transfer

__system__operated by

**the**United States Federal Reserve Banks that enables financial institutions

**to**electronically transfer funds between its more than 9

**,**289 participants

**(**as

**of**March 19

**,**2009

**).**

Formally and is

__Formally__organized vocational programs supported by federal funds allow high school students

**to**gain experience

**in**

**a**field

**of**work which

__is__likely

**to**lead

**to**

**a**full-time job on graduation.

__Formally__

**,**

**the**set

**of**all context-free languages

__is__identical

**to**

**the**set

**of**languages accepted by pushdown automata

**(**PDA

**).**

More rigorously

**,****the**divergence**of****a**vector field F at**a**point p__is__defined as**the**limit**of****the**net flow**of**F across**the**smooth boundary**of****a**three dimensional region V divided by**the**volume**of**V as V shrinks**to**p.__Formally__**,**__Formally__

**,**

**the**base

__is__known as Naval Support Facility Diego Garcia

**(**

**the**US activity ) or Permanent Joint Operating Base

**(**PJOB ) Diego Garcia

**(**

**the**UK's term

**).**

__Formally__

**,**there

__is__

**a**clear distinction: " DFT " refers

**to**

**a**mathematical transformation or function

**,**regardless

**of**how it

__is__computed

**,**whereas " FFT " refers

**to**

**a**specific family

**of**algorithms

**for**computing DFTs.

__Formally__

**,**oxidation

**state**

__is__

**the**hypothetical charge that an atom would have

**if**all bonds

**to**atoms

**of**different elements were 100 % ionic.

__Formally__

**,**an inner product

**space**

__is__

**a**vector

**space**V over

**the**field together with an inner product

**,**i. e., with

**a**map

__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__**,**when working over**the**reals**,**as here**,****this**__is__accomplished by considering**the**limit as ε → 0 ; but**the**" infinitesimal " language generalizes directly**to**Lie groups over general rings.__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**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.

__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 and said

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 and be

__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__

**,**

**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__

**,**

**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__

**,**

**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**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.

If R

**is****a**ring**,**let R denote**the**ring**of**polynomials**in****the**indeterminate X over R. Hilbert proved that**if**R**is**" not too large ",**in****the**sense that**if**R**is**Noetherian**,****the**same must__be__true**for**R.__Formally__**,**__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__

**,**

**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__

**,**

**a**government would lay out its reasons

**for**going

**to**war

**,**as well as its intentions

**in**prosecuting it

**and**

**the**steps that might

__be__taken

**to**avert it.

__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.

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