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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.

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## Some Related Sentences

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__

**,**this means

**symmetry**under

**a**sub-group

**of**

**the**Euclidean

__group__

**of**

**isometries**in two

**or**three dimensional Euclidean 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__

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__

**,**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 class

__Formally__

**,**this means that

**the**probability density functions

**or**probability mass functions in this

__class__have

**the**form

__Formally__it

**is**precisely in allowing quantification over

__class__variables α

**,**β

**,**etc., that we assume

**a**range

**of**values

**for**these variables to refer to

**.**

__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__

**,**it may even be taken back to Marx's earliest statements about

**a**

__class__becoming conscious

**of**itself and developing

**a**

__class__identity

**.**

__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__established in 1921

**,**

**the**Profintern was intended to act as

**a**counterweight to

**the**influence

**of**

**the**so-called " Amsterdam International ,"

**the**Social Democratic International Federation

**of**Trade Unions

**,**an organization branded as

__class__collaborationist and an impediment to revolution by

**the**Comintern

**.**

__Formally__

**,**

**a**biased graph Ω

**is**

**a**pair

**(**G

**,**B ) where B

**is**

**a**linear

__class__

**of**circles ; this by definition

**is**

**a**

__class__

**of**circles that satisfies

**the**theta-graph property mentioned above

**.**

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