[permalink] [id link]

Conversely, given an SL ( n )- structure, one can recover a volume form by imposing () for the special linear frames and then solving for the required n-form ω by requiring homogeneity in its arguments.

from
Wikipedia

## Some Related Sentences

Conversely and given

__Conversely__

**,**if

**a**Boolean ring A is

__given__

**,**we

**can**turn it into

**a**Boolean algebra

**by**defining x ∨ y := x + y +

**(**x · y )

**and**x ∧ y := x · y

**.**

__Conversely__

**,**there are other stars that never rise above

**the**horizon

**,**as seen from any

__given__point on

**the**Earth's surface

**(**except exactly on

**the**equator ).

__Conversely__

**,**

__given__

**a**groupoid G

**in**

**the**algebraic sense

**,**let G < sub > 0 </ sub > be

**the**set of all elements of

**the**

**form**x * x < sup >− 1 </ sup > with x varying through G

**and**define G

**(**x * x < sup >-1 </ sup >, y * y < sup >-1 </ sup >) as

**the**set of all elements f such that y * y < sup >-1 </ sup > * f * x * x < sup >-1 </ sup > exists

**.**

__Conversely__

**,**

__given__central idempotents

**a**< sub > 1 </ sub >,...,

**a**< sub >

**n**</ sub >

**in**R that are pairwise orthogonal

**and**have sum 1

**,**

**then**R is

**the**direct sum of

**the**rings Ra < sub > 1 </ sub >,…, Ra < sub >

**n**</ sub >.

Given

**a**field ordering ≤ as**in**Def 1**,****the**elements such that x ≥ 0 forms**a**positive cone of F**.**__Conversely__**,**__given__**a**positive cone P of F as**in**Def 2**,****one****can**associate**a**total ordering ≤< sub > P </ sub >**by**setting x ≤ y to mean y − x ∈ P**.**This total ordering ≤< sub > P </ sub > satisfies**the**properties of Def 1**.**__Conversely__

**,**only

**the**wiki users interested

**in**

**a**

__given__project need look at

**its**associated wiki pages

**,**

**in**contrast to high-traffic mailing lists which may burden subscribers with many messages

**,**regardless of their relevance

**.**

__Conversely__

**,**

__given__

**a**harmonic function

**,**it is

**the**real part of

**an**analytic function

**,**

**(**at least locally ).

Each convex set containing X must

**(****by****the**assumption that it is convex ) contain all convex combinations of points**in**X**,**so**the**set of all convex combinations is contained**in****the**intersection of all convex sets containing X**.**__Conversely__**,****the**set of all convex combinations is itself**a**convex set containing X**,**so it also contains**the**intersection of all convex sets containing X**,****and**therefore**the**sets__given__**by**these two definitions must be equal**.**__Conversely__

**,**surveys conducted among living donors postoperatively

**and**

**in**

**a**period of five years following

**the**procedure have shown extreme regret

**in**

**a**majority of

**the**donors

**,**who said that

__given__

**the**chance to repeat

**the**procedure

**,**they would not

**.**

__Conversely__

**,**

__given__

**an**ordered tree

**,**

**and**conventionally draw

**the**root at

**the**top

**,**

**then**

**the**child nodes

**in**

**an**ordered tree

**can**be drawn left-to-right

**,**yielding

**an**essentially unique planar embedding

**(**up to embedded homotopy

**,**i

**.**e., moving

**the**edges

**and**nodes without crossing ).

__Conversely__

**,**

**the**influence of

**the**data at any

__given__point on

**the**initial line propagates with

**the**finite velocity c: there is no effect outside

**a**triangle through that point whose sides are characteristic curves

**.**

__Conversely__

**,**

__given__any harmonic function

**in**two dimensions

**,**it is

**the**real part of

**an**analytic function

**,**at least locally

**.**

__Conversely__

**,**if

**(**A

**,**m

**,**e

**,**inv ) is

**a**group object

**in**

**one**of those categories

**,**

**then**m necessarily coincides with

**the**

__given__operation on A

**,**e is

**the**inclusion of

**the**

__given__identity element on A

**,**inv is

**the**inversion operation

**and**A with

**the**

__given__operation is

**an**abelian group

**.**

__Conversely__

**,**if

**the**Turing Machine is expected polynomial-time

**(**

**for**any

__given__x ),

**then**

**a**considerable fraction of

**the**runs must be polynomial-time bounded

**,**

**and**

**the**coin sequence used

**in**such

**a**run will be

**a**witness

**.**

__Conversely__

**,**

__given__any ring

**,**we

**can**

**form**

**a**category

**by**taking objects A < sub >

**n**</ sub > indexed

**by**

**the**set of natural numbers

**(**including zero )

**and**letting

**the**hom-set of morphisms from to be

**the**set of-by-matrices over

**,**

**and**where composition is

__given__

**by**matrix multiplication

**.**

__Conversely__

**,**it is hard to believe

**,**

__given__

**the**length

**and**intensity of

**the**struggle between Máel Sechnaill

**and**Brian

**,**that

**the**High King would surrender his title without

**a**fight

**.**

__Conversely__

**,**

**an**algorithm to test

**for**solvability

**in**arbitrary integers could be used to test

**a**

__given__equation

**for**solvability

**in**natural numbers

**by**applying that supposed algorithm to

**the**equation obtained from

**the**

__given__equation

**by**replacing each unknown

**by**

**the**sum of

**the**squares of four new unknowns

**.**

__Conversely__

**,**

**a**disease that is easily transmitted but has

**a**short duration might spread widely during 2002 but is likely to have

**a**low prevalence at any

__given__point

**in**2003

**(**due to

**its**short duration ) but

**a**high incidence during 2002

**(**as many people develop

**the**disease ).

Conversely and n

It is

**a**fact that**the**ring is**a**principal ideal ring ; that is**,****for**any ideal I**in****,**there exists**an**integer__n__**in**I such that every element of I is**a**multiple of__n__**.**__Conversely__**,****the**set of all multiples of**an**arbitrary integer__n__is necessarily**an**ideal**,****and**is usually denoted**by****(**__n__).__Conversely__

**,**

**a**system of

__n__quantities v < sup > i </ sup > that transform like

**the**coordinates x < sup > i </ sup > on V defines

**a**contravariant vector

**.**

__Conversely__

**,**

**the**DHT is equivalent to computing

**the**DFT of x < sub >

__n__</ sub > multiplied

**by**1 + i

**,**

**then**taking

**the**real part of

**the**result

**.**

__Conversely__

**,**if A is invertible

**,**F is algebraically closed

**,**

**and**A < sup >

__n__</ sup > is diagonalizable

**for**some

__n__that is not

**an**integer multiple of

**the**characteristic of F

**,**

**then**A is diagonalizable

**.**

__Conversely__

**,**

**given**

**a**quadratic

**form**

**in**

__n__variables

**,**

**its**coefficients

**can**be arranged into

**an**

__n__×

__n__symmetric matrix

**.**

__Conversely__

**,**if

**the**

**(**restricted ) holonomy of

**a**2n-dimensional Riemannian manifold is contained

**in**SU

**(**

__n__),

**then**

**the**manifold is

**a**Ricci-flat Kähler manifold

**.**

__Conversely__

**,**if

__n__is prime

**,**

**then**there exists

**a**primitive root modulo

__n__

**,**or generator of

**the**group

**(**Z / nZ )*.

__Conversely__

**,**if

__n__is composite

**,**

**the**algorithm will always return composite: if

**the**algorithm returns prime

**,**

**then**this will occur

**in**either step 4 or step 6

**.**

which are linearly independent at each point q

**in**U**.**__Conversely__**,****given**such**a**coframe**,**there is**a**unique moving frame X < sub > 1 </ sub >, X < sub > 2 </ sub >, ..., X < sub >__n__</ sub > which is dual to it**,**i**.**e., satisfies**the**duality relation α < sup > i </ sup >( X < sub > j </ sub >) = δ < sup > i </ sup >< sub > j </ sub >, where δ < sup > i </ sup >< sub > j </ sub > is**the**Kronecker delta function on U**.**__Conversely__

**,**

**a**polynomial time algorithm

**(**e

**.**g.,

**one**that requires

__n__< sup > 20 </ sup > steps

**for**n-digit keys ) may be too slow

**for**any practical use

**.**

produces

**a**unique composition of__n__**.**__Conversely__**,**every composition of__n__determines**an**assignment of pluses**and**commas**.**
that is

**,****by**adjoining__n__< sup > th </ sup > roots of elements of Δ to K**.**__Conversely__**,**if L is**a**Kummer extension of K**,****then**Δ is recovered**by****the**rule

Conversely and )-

Conversely and structure

__Conversely__

**,**specifying

**the**symmetry

**can**define

**the**

__structure__

**,**or at least clarify what we mean

**by**

**an**invariant

**,**geometric language

**in**which to discuss it ; this is

**one**way of looking at

**the**Erlangen programme

**.**

__Conversely__

**a**large cargo

**,**

**for**example

**in**

__structure__relocation

**,**may be disassembled

**for**carriage on multiple vehicles

**and**

**then**reassembled

**in**

**the**correct order at

**the**destination

**.**

__Conversely__

**,**

**a**wing dam is

**a**

__structure__that only partly restricts

**a**waterway

**,**creating

**a**faster channel that resists

**the**accumulation of sediment

**.**

__Conversely__

**,**many polymers

**(**notably flexible vinyl ) are intentionally swelled with plasticizers

**,**which

**can**be leached out of

**the**

__structure__

**,**causing brittleness or other undesirable changes

**.**

__Conversely__

**,**

**the**sequence of

**an**ancient gene

**for**

**a**

**given**

__structure__may have diverged considerably

**in**different species while at

**the**same time maintaining

**the**same basic structural features

**.**

__Conversely__

**,**

**given**

**a**Hopf algebra whose coalgebra

__structure__is

**given**above

**,**we

**can**

**recover**

**a**formal group law F from it

**.**

__Conversely__

**,**

**one**of

**the**characteristics of mental illness is

**a**distorted value

__structure__;

**the**neurotic does not value things according to their objective merit

**,**

**in**relation to his nature

**and**needs ; he frequently values

**the**very things that will lead him to self-destruction

**.**

__Conversely__

**,**all later attempts at land reform

**by**legal means

**,**starting with

**the**1960s organization of peasant leagues

**(**Ligas Camponesas )

**in**Northeastern Brazil which opposed mostly eviction of peasants from rented plots

**and**transformation of plantations into cattle ranches

**,**would be nationally directed

**by**

**a**tendency to counter

**the**existing landed property

__structure__

**by**means of

**a**more rational appeal to

**the**allegedly social function of property

**.**

__Conversely__

**,**

**the**basic

__structure__of

**a**transitive Japanese sentence is SOV

**,**with

**the**usual syntactic features associated with languages of this typology

**,**including postpositions

**,**that is

**,**grammar particles that appear after

**the**words

**and**phrases to which they apply

**.**

__Conversely__any bipartite graph with girth at least six

**can**be viewed as

**the**Levi graph of

**an**abstract incidence

__structure__

**.**

__Conversely__

**,**if

**the**defeasance provisions allow borrowers to provide

**the**actual defeasance collateral to lenders

**and**do not require defeasance deposits

**,**

**the**borrowers ’ defeasance consultant will be able to

__structure__

**an**optimized securities portfolio

**and**hold

**a**competitive auction to ensure best pricing

**.**

0.269 seconds.