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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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## Some Related Sentences

Formally and case

__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**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__

**,**assuming our intuition from

**the**finite dimensional

__case__carries over into

**the**infinite dimensional setting

**,**

**the**measure should then

**be**equal to

Formally and where

__Formally__

**,**

**the**theorem

**is**stated as follows: There exist unique integers q and r

**such**

**that**

**a**= qd + r and 0 ≤ r < | d |,

__where__| d | denotes

**the**absolute value

**of**d

**.**

__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__

**,**

**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

**.**

__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__

**,**

**a**hypergraph

**is**

**a**pair

__where__

**is**

**a**set

**of**elements called nodes or vertices

**,**and

**is**

**a**set

**of**non-empty subsets

**of**called hyperedges or edges

**.**

__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__

**,**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__

**,**

**the**principle

**of**subsidiarity applies to those areas

__where__

**the**Community

**does**

**not**

**have**exclusive competence

**,**

**the**principle delineating those areas

__where__

**the**Community should and should

**not**act

**.**

__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__

**,**an antihomomorphism between X and Y

**is**

**a**homomorphism

**,**

__where__equals Y as

**a**set

**,**but has multiplication reversed: denoting

**the**multiplication

**on**Y as and

**the**multiplication

**on**as

**,**we

**have**

**.**

__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__

**,**

**the**1772 Constitution was adopted by

**the**Parliament

**(**Riksdag

**)**

**on**21 August 1772

**,**but this took place as members

**of**

**the**Parliament and

**the**Privy Council were

**under**threat by

**the**royal garrison

**on**order by King Gustav III outside

**of**Stockholm Palace

**,**

__where__

**the**Parliament and Privy Council were assembled

**in**different parts

**of**

**the**palace

**.**

__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__accepted as

**a**candidate for

**the**Franciscan Order at Christ House

**in**Lafayette

**,**New Jersey

**,**

**in**1970

**,**

**the**following year he entered

**the**novitiate

**of**

**the**Order at St

**.**Francis Friary

**in**Brookline

**,**Massachusetts

**,**

__where__he professed his first vows

**in**1972

**.**

Formally and only

__Formally__

**the**Prince-Electors elected

**a**King

**of**

**the**Romans

**,**who was elected

**in**Germany but became Holy Roman Emperor

__only__when crowned by

**the**Pope

**.**

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__

**the**euro

**is**

**the**

__only__legal tender

**in**Büsingen

**;**however

**,**

**the**Swiss franc

**is**far more popular

**in**everyday use as shopping

**is**generally done

**in**nearby Schaffhausen instead

**of**across

**the**border

**(**s

**)**

**in**Germany

**.**

__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__

**,**

**a**cardinal number κ

**is**λ-unfoldable if and

__only__if for every transitive model M

**of**cardinality κ

**of**ZFC-minus-power set

**such**

**that**κ

**is**

**in**M and M contains all its sequences

**of**length less than κ

**,**there

**is**

**a**non-trivial elementary embedding j

**of**M into

**a**transitive model with

**the**critical

**point**

**of**j being κ and j

**(**κ

**)**≥ λ

**.**

__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__

**,**

**the**definition

__only__requires some invertibility

**,**so we

**can**substitute for Q any matrix M

**whose**eigenvalues do

**not**include − 1

**.**

__Formally__Roman Kalyn

**is**now

**the**

__only__member

**of**

**the**group

**,**but de-facto GreenJolly exists

**in**name

__only__

**.**

__Formally__

**,**

**a**number n

**is**colossally abundant if and

__only__if there

**is**an ε > 0

**such**

**that**for all k > 1

**,**

__Formally__

**,**

**a**natural number n

**is**called highly abundant if and

__only__if for all natural numbers m < n

**,**

__Formally__this mission was declared to

**be**

__only__

**in**pursuit

**of**

**the**Russian vessels and ammunition taken to Anzali by

**the**White Russian counter-revolutionary General Denikin

**,**who had

**been**given asylum by British forces

**in**Anzali

**.**

__Formally__known as Crown Point Airport

**,**

**the**airport was renamed

**the**Arthur Napoleon Raymond Robinson International Airport

**on**May 19

**,**2011

**in**honour

**of**

**the**

__only__Prime Minister and President from

**the**island

**of**Tobago

**.**

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