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Formally this approximation is founded on the variational principle, valid for Hamiltonians that are bounded from below.

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## Some Related Sentences

Formally and approximation

__Formally__

**,**we have

**for**

**the**

__approximation__to

**the**full solution A

**,**a series in

**the**small parameter ( here called ), like

**the**following:

__Formally__

**,**an nth order

__approximation__

**is**one where

**the**order of magnitude of

**the**error

**is**at most

**,**or in terms of big O notation

**,**

**the**error

**is**

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 founded

In late 1900s

**the**day**that**of**the**City was__founded__**is**Jakin School**is**a Private School**is**__Formally__Part of Jakin School Board was Grades One through Twelve there**is**no Football field**on****this**school**.**In 1966 When Jakin School was Closed were Sent to Blakely-Union Elementary**,**Junior High**,**and High School ( which later Became Early County High**,**Middle**,**and Elementary School ). while Carver school was built**for**African-American students grades One through Twelve**.**although late 1960s when Carver school was closed along with Kestler School was based in Damascus were sent to Washington High & Elementary at Blakely**.**In addition to small farm agriculture**,**Jakin's early economic growth resulted**from**turpentine**.**__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__

**,**

**the**Ministry of Aeronautics was

__founded__

**on**January 20

**,**1941 and so its military branch called " National Air Forces ", changed to " Brazilian Air Force " ( Força Aérea Brasileira-FAB )

**on**May

**,**22

**.**

__Formally__introduced in 1991

**,**Gut Recordings was

__founded__by Guy Holmes

**,**who had been Head of Promotions at Island Records

**.**

__Formally__

__founded__by

**the**Virginia General Assembly in 1823

**,**

**the**Library of Virginia organizes

**,**cares

**for**

**,**and manages

**the**state's collection of books and official records

**,**many of which date back to

**the**early colonial period

**.**

__Formally__

**,**

**the**party was

__founded__in 1973 as

**the**Women's Free Deputies ( Kvinnenes Frie folkevalgte ).

Formally and on

__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 ).

*

**,**see On__Formally__Undecidable Propositions of Principia Mathematica and Related Systems**for**details__on__English translations**.**__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 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__

**,**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__

**,**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__

**,**if

**is**an open subset of

**the**complex plane

**,**a point of

**,**and

**is**a holomorphic function

**,**then

**is**called a removable singularity

**for**if there exists a holomorphic function which coincides with

__on__

**.**

__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 ).

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 center of gravity

**is**an application point of

**the**resultant gravitational force

__on__

**the**body

**.**

__Formally__named The King's College of Our Lady and Saint Nicholas in Cambridge

**,**

**the**college lies

__on__

**the**River Cam and faces out onto King's Parade in

**the**centre of

**the**city

**.**

__Formally__

**,**a statistic s

**is**a measurable function of X ; thus

**,**a statistic s

**is**evaluated

__on__a random variable X

**,**taking

**the**value s ( X ), which

**is**itself a random variable

**.**

__Formally__educated African Americans

**,**

__on__

**the**other hand

**,**either disregarded black minstrelsy or openly disdained it

**.**

__Formally__

**,**

**the**motion merely calls

__on__parliament to thank

**the**monarch or viceroy

**for**

**the**speech via an Address in Reply

**.**

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