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Formally, this means symmetry under a sub-group of the Euclidean group of isometries in two or three dimensional Euclidean space.

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## Some Related Sentences

Formally and means

__Formally__

**,**

**this**

__means__that

**the**probability density functions

**or**probability mass functions

**in**

**this**class have

**the**form

Limits and colimits

**in****a**category C are defined by__means__**of**diagrams**in**C**.**__Formally__**,****a**diagram**of**type J**in**C is**a**functor from J to C:__Formally__

**,**

**this**

__means__that

**,**for some function f

**,**

**the**image f ( D )

**of**

**a**directed set D ( i

**.**e

**.**

**the**set

**of**

**the**images

**of**each element

**of**D ) is again directed and has as

**a**least upper bound

**the**image

**of**

**the**least upper bound

**of**D

**.**One could also say that f preserves directed suprema

**.**

__Formally__

**,**

**this**

__means__classifying finitely generated groups with their word metric up to quasi-isometry

**.**

__Formally__

**,**however

**,**

**the**role also carries

**the**title

**of**" Klingon supreme commander " ( TNG's " Reunion "), which presumably

__means__commander-in-chief

**of**

**the**military

**.**

Formally and symmetry

__Formally__

**,**

**a**frieze

**group**is

**a**class

**of**infinite discrete

__symmetry__groups for patterns on

**a**strip ( infinitely wide rectangle ), hence

**a**class

**of**groups

**of**

**isometries**

**of**

**the**plane

**,**

**or**

**of**

**a**strip

**.**

__Formally__

**,**rotational

__symmetry__is

__symmetry__with respect to some

**or**all rotations

**in**m-dimensional

**Euclidean**

**space**

**.**

Formally and under

__Formally__

**,**

__under__Henry IV

**,**Arundel served twice as Lord Chancellor

**,**first

**in**1399 and again from 1407 to 1410

**.**

__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

**.**

* General Headquarters United Nations Command ( Korea ) ( UNC ) —

__Formally__activated 10 July 1950**,**before then Allied forces were formally__under__American operational control**.**__Formally__

**,**

**the**city remained

__under__Italian sovereignty until September 15

**,**1947 ( Paris Peace Treaties ).

__Formally__designated as

**the**Manhattan Engineer District

**,**it refers specifically to

**the**period

**of**

**the**project from 1941 – 1946

__under__

**the**control

**of**

**the**U

**.**S

**.**Army Corps

**of**Engineers

**,**

__under__

**the**administration

**of**General Leslie R

**.**Groves

**.**

__Formally__

**a**vassal

**of**

**the**Persians

**,**he secured

**the**northern borders by subjugating

**the**Caucasian mountaineers

**,**and brought

**the**adjacent western and southern Georgian lands

__under__his control

**.**

__Formally__

**,**

**the**differential appearing

__under__

**the**integral behaves exactly as

**a**differential: thus

**,**

**the**integration by substitution and integration by parts formulae for Stieltjes integral correspond

**,**respectively

**,**to

**the**chain rule and product rule for

**the**differential

**.**

__Formally__

**,**if

**the**equilibrium strategy profile

__under__

**the**mechanism maps to

**the**same goods allocation as

**a**social choice function

**,**

Dick Smith Electronics has also long been known for its " home brand " range

**of**electronics which fall__under__**the**brand name " Dick Smith " (__Formally__called DSE**,****a**commonly used abbreviation**of**Dick Smith Electronics ).__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__

**the**Greyhound Cafe

**,**" The Entry " opened its door

**in**March 1980

__under__

**the**club Sam's as

**a**venue that catered to more local bands

**.**

__Formally__

__under__

**the**command

**of**Poniatowski was Major General Józef Orłowski

**,**

**the**commander

**of**

**the**fortress

**of**Kamieniec Podolski

**.**

__Formally__

**,**for any dimension

**,**

**the**orientation

**of**

**the**image

**of**an object

__under__

**a**direct isometry with respect to that object is

**the**linear part

**of**that isometry

**.**

Formally and Euclidean

__Formally__

**,**

**in**

__Euclidean__

**space**

**,**

**the**wave front set

**of**ƒ is defined as

**the**complement

**of**

**the**set

**of**all pairs ( x < sub > 0 </ sub >, v ) such that there exists

**a**test function with φ ( x < sub > 0 </ sub >) ≠ 0 and an open cone Γ containing v such that

**the**estimate

Formally and group

__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__

**,**collective noun forms such as “

**a**

__group__

**of**people ” are represented by second-order variables

**,**

**or**by first-order variables standing for sets ( which are well-defined objects

**in**mathematics and logic ).

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**ring is an Abelian

__group__( R

**,**+), together with

**a**second binary operation * such that for all

**a**

**,**b and c

**in**R

**,**

* Blades ( hip-hop

__group__) (__Formally__Blades Of Hades ), Australian hip hop__group__from Newcastle**,**New South Wales__Formally__

**,**

**the**

__group__was called Studiengesellschaft für Geistesurgeschichte ‚ Deutsches Ahnenerbe e

**.**V

**.**

__Formally__

**,**

**the**Mahalanobis distance

**of**

**a**multivariate vector from

**a**

__group__

**of**values with mean and covariance matrix is defined as:

__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__

**,**define

**the**set

**of**lines

**in**

**the**plane P as L ( P ); then

**a**rigid motion

**of**

**the**plane takes lines to lines –

**the**

__group__

**of**rigid motions acts on

**the**set

**of**lines – and one may ask which lines are unchanged by an action

**.**

__Formally__Roman Kalyn is now

**the**only member

**of**

**the**

__group__

**,**but de-facto GreenJolly exists

**in**name only

**.**

__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__

**,**

**this**meant that

**the**whole peloton finished out

**of**time limits

**,**but

**the**referees understandably used

**a**rule saying that they could give clemency to any

__group__

**of**more than 20 %

**of**

**the**stage's starting riders

**,**officially citing

**the**weather conditions as their reason to do so

**.**

__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__

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