[permalink] [id link]

Conversely, a connection on E determines a connection on F ( E ), and these two constructions are mutually inverse.

from
Wikipedia

## Some Related Sentences

Conversely and connection

That is

**,**the motivational internalist believes that there is an internal**,**necessary__connection__between one's conviction that X ought to be done**and**one's motivation to do X**.**__Conversely__**,**the motivational externalist**(**or moral externalist ) claims that there is no necessary**,**internal__connection__between moral convictions**and**moral motives**.**__Conversely__

**,**using the last line as

**a**definition one shows that the expression so defined is

**a**

__connection__compatible with the metric

**,**i

**.**e

**.**is

**a**Levi-Civita

__connection__

**.**

__Conversely__

**,**if

**a**suitable notion of parallel transport is available

**,**then

**a**corresponding

__connection__can be obtained by differentiation

**.**

__Conversely__

**,**any operator satisfying the above properties defines

**a**

__connection__

**on**

**E**

**and**

**a**

__connection__in this sense is also known as

**a**covariant derivative

**on**

**E**

**.**

__Conversely__

**,**if ∇ is

**a**

__connection__

**on**

**E**

**and**A is

**a**one-form

**on**M with values in End

**(**

**E**

**),**then ∇+ A is

**a**

__connection__

**on**

**E**

**.**

The principal

__connection__α**on**Q can be recovered from the form η by taking Q to be the associated bundle P ×< sub > H </ sub > G**.**__Conversely__**,**the form η can be recovered from α by pulling back along the inclusion P ⊂ Q**.**__Conversely__

**,**an Ehresmann

__connection__H ⊂ TP

**(**or v: TP → V )

**on**P defines

**a**principal G-connection ω if

**and**only if it is G-equivariant in the sense that

**.**

A section Γ of dπ: TP / G → TM such that Γ: TM → TP / G is

**a**linear morphism of vector bundles over M**,**can be identified with**a**principal__connection__in P**.**__Conversely__**,****a**principal__connection__as defined above gives rise to such**a**section Γ of TP / G**.**__Conversely__

**,**the Roman

__connection__introduced foreign influence beyond the control of local rulers

**,**but also allowed rulers to display themselves

**on**

**a**wider

**,**European stage

**,**

**and**to seek out more powerful sources of legitimacy

**.**

where it is understood that d

**and**ω refer to the exterior derivative**and****a**matrix of 1-forms**,**respectively**,**acting**on**the components of ξ**.**__Conversely__**,****a**matrix of 1-forms ω is**a**priori sufficient to completely determine the__connection__locally**on**the open set over which the basis of sections e is defined**.**__Conversely__

**,**it has also been said that the

__connection__between virtual crimes

**and**real crimes

**are**" tenuous at best: It is the link between

**a**brutal rape

**and**

**a**fictional story of

**a**brutal rape

**.**

Conversely and on

__Conversely__

**,**

**a**standard line

__on__which voice service has been unsubscribed

**(**such as an ADSL dry loop ) may still accept calls to the 958 test exchange but not allow calls to standard numbers

**.**

__Conversely__

**,**paintings which came out of his workshop that were not necessarily physically worked

__on__by Cuyp but merely overseen by him technically

**,**were marked with A

**.**C

**.**to show that it was his instruction which saw the paintings ’ completion

**.**

__Conversely__

**,**modern biological sciences

**(**including even concepts such as molecular ecology )

**are**intimately entwined

**and**dependent

__on__the methods developed through biotechnology

**and**what is commonly thought of as the life sciences industry

**.**

__Conversely__

**,**Fleet Captain Honoré Ganteaume later reported the cause as an explosion

__on__the quarterdeck

**,**preceded by

**a**series of minor fires

__on__the main deck among the ship's boats

**.**

* The spectrum of any bounded linear operator

__on__**a**Banach space is**a**nonempty compact subset of the complex numbers C**.**__Conversely__**,**any compact subset of C arises in this manner**,**as the spectrum of some bounded linear operator**.**__Conversely__

**,**if ƒ: C → C is

**a**function which is differentiable when regarded as

**a**function

__on__R < sup > 2 </ sup >, then ƒ is complex differentiable if

**and**only if the Cauchy – Riemann equations hold

**.**

__Conversely__the car is stopped by releasing pressure

__on__the cable

**(**with or without completely detaching )

**and**applying the brakes

**.**

__Conversely__

**,**every point

__on__the line can be interpreted as

**a**number in an ordered continuum which includes the real numbers

**.**

__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__

**,**any surjection between sets

**determines**

**a**partition

__on__its domain

**,**the set of preimages of singletons in the codomain

**.**

__Conversely__

**,**Derek Bickerton

**and**others argue that the advent of abstract words provided

**a**mental basis for analyzing higher-order relations

**,**

**and**that any communication system that remotely resembles human language utterly relies

__on__cognitive architecture that co-evolved alongside language

**.**

"

__Conversely__**,**Pat Graham of Chicago Reader disliked the mix of horror**and**comedy**,**writing in his review that " The pop-up humor**and**smirkiness suggest Raimi's aspiring to the fashionable company of the brothers Coen**,**though__on__the basis of this strained effort I'd say he's overshot the mark**.**__Conversely__

**,**in functional code

**,**the output value of

**a**function depends only

__on__the arguments that

**are**input to the function

**,**so calling

**a**function f twice with the same value for an argument x will produce the same result f

**(**x ) both times

**.**

__Conversely__

**,**the blood vessels in the lower legs

**are**under great pressure

**(**because of the weight of fluid pressing down

__on__them ).

__Conversely__

__on__occasions he attracted criticism for dogmatically pursuing schemes favoured by the right of his party

**,**notably the privatisation of British Rail

**,**

**and**for closing down most of the coal industry in advance of privatisation

**.**

__Conversely__

**,**some areas which were merely roadside suburbs in the 1950s

**are**now valuable urban land

__on__which original structures

**are**being removed through gentrification

**and**the land used for other purposes

**.**

__Conversely__

**,**the cultural divergence at the border became sharper: in theory

**,**

**a**uniform French identity extends from the Atlantic coast to the Rhine

**,**

**and**

__on__the other bank of the Rhine

**,**

**a**uniform German identity begins

**.**

__Conversely__

**,**the gravity of the satellite

__on__the bulges applies torque

__on__the primary

**and**speeds up its rotation

**.**

__Conversely__

**,**if the odds of drawing

**a**winning card

**are**numerically lower than the pot odds

**,**the call has

**a**negative expectation

**,**

**and**you can expect to win less money

__on__average than it costs to call the bet

**.**

__Conversely__

**,**from

**a**partial order

__on__

**a**partition of

**a**set S one can construct

**a**preorder

__on__S

**.**There is

**a**1-to-1 correspondence between preorders

**and**pairs

**(**partition

**,**partial order ).

Conversely and E

A hypergraph H may be represented by

**a**bipartite graph BG as follows: the sets X**and**__E__**are**the partitions of BG**,****and****(**x < sub > 1 </ sub >, e < sub > 1 </ sub >)**are**connected with an edge if**and**only if vertex x < sub > 1 </ sub > is contained in edge e < sub > 1 </ sub > in H**.**__Conversely__**,**any bipartite graph with fixed parts**and**no unconnected nodes in the second part represents some hypergraph in the manner described above**.**__Conversely__

**,**

**a**function u:

__E__< sub > 1 </ sub > →

__E__< sub > 2 </ sub > defined

**on**

**a**basis of

__E__< sub > 1 </ sub > can be uniquely extended to

**a**linear function

**.**

*

__Conversely__**,**if is such that**and****are**purely inseparable extensions**,**then__E__is purely inseparable over**F****.**__Conversely__

**,**during the same dispute

**,**the late

__E__

**.**Pierce Marshall sided with his father

**,**Charles Koch

**and**David Koch

**.**

__Conversely__

**,**some fannish terms have been made obsolete by changes in technology

**(**the decline of the mimeograph has doomed corflu for " correction fluid "), cultural changes

**(**

**a**femmefan fan is no longer unusual ) or the mere passage of time

**(**slan shack for "

**a**house where

**a**bunch of fans live together " has faded

**,**since fewer young fans have read Slan by A

**.**

__E__

**.**van Vogt ).

Conversely and determines

__Conversely__

**,**mapping the data flow between the components

__determines__the logical topology of the network

**.**

__Conversely__

**,**

**a**normal subgroup of index p

__determines__

**a**non-trivial map to up to

**a**choice of " which coset maps to which shows that this map is

**a**bijection

**.**

__Conversely__

**,**minimal compliance with

**a**safety statute does not always absolve

**a**defendant if the trier of fact

__determines__that the reasonable person should have taken actions beyond

**and**in excess of what the statute required

**.**

__Conversely__

**,**any sequence that satisfies

**a**linear recurrence

__determines__

**a**rational function when used as the coefficients of

**a**Taylor series

**.**

Any point x gives rise to

**a**continuous function p < sub > x </ sub > from the one element topological space 1**(**all subsets of which**are**open ) to the space X by defining p < sub > x </ sub >( 1 ) = x**.**__Conversely__**,**any function from 1 to X clearly__determines__one point: the element that it " points " to**.**
produces

**a**unique composition of n**.**__Conversely__**,**every composition of n__determines__an assignment of pluses**and**commas**.**__Conversely__

**,**

**a**decomposition with

**these**extra properties

__determines__an involution

**on**that is

**on**

**and**

**on**

**.**

__Conversely__

**,**when local politics

__determines__that it is no longer

**a**crime

**,**they may be decriminalized

**.**

__Conversely__

**,**the density

__determines__the wave function modulo

**a**phase factor

**,**providing the formal foundation of density functional theory

**.**

0.226 seconds.