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Conversely, let G be any polynomial such that Af.

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## Some Related Sentences

Conversely and let

__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

**.**

We define Thm ( C ) to

**be**the set of all formulas**that**are valid in C**.**__Conversely__**,**if X is a set of formulas**,**__let__Mod ( X )**be**the class of all frames which validate every formula from X**.**__Conversely__

**,**people who generally tend to blame others for negative events

**,**believe

**that**

**such**events will end soon

**,**and do not

__let__

**such**events affect too many aspects of their lives display what is called an optimistic explanatory style

**.**

__Conversely__

**,**

__let__a set S

**be**a neighborhood of x if x is not in the closure of the complement of S

**.**The set of all

**such**neighborhoods can

**be**shown to

**be**a neighborhood system for a pretopology

**.**

Conversely and G

__Conversely__

**,**if F is left adjoint to

__G__

**,**and

__G__is naturally isomorphic to

__G__′ then F is also left adjoint to

__G__′.

As stated earlier

**,**an adjunction between categories C and D gives rise to a family of universal morphisms**,**one for each object in C and one for each object in D**.**__Conversely__**,**if there exists a universal morphism to a functor__G__: C → D from every object of D**,**then__G__has a left adjoint**.**__Conversely__

**,**every Polish space is homeomorphic to a

__G__< sub > δ </ sub >- subset of the Hilbert cube

**.**

__Conversely__

**,**one can show

**that**given a manifold M and a principal H-bundle P over M

**,**and a 1-form η with these properties

**,**then P is locally isomorphic as an H-bundle to the principal homogeneous bundle

__G__→

__G__/ H

**.**

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**.**
Given then a normal extension L of K

**,**with automorphism group Aut ( L / K ) =__G__**,**and containing α**,****any**element g ( α ) for g in__G__will**be**a conjugate of α**,**since the automorphism g sends roots of p to roots of p**.**__Conversely__**any**conjugate β of α is of this form: in other words**,**__G__acts transitively on the conjugates**.**
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__

**,**given a left kG module M

**,**then M is a k vector space

**,**and multiplication with an element g of

__G__yields a k-linear automorphism of M ( since g is invertible in kG ), which describes a group homomorphism

__G__→ GL ( M ).

Conversely and be

__Conversely__

**,**experimenters would consider as impressive

**such**statements as the following

**,**which

**,**if they turned out to

__be__hits

**,**are so unusual as to

__be__really significant:

__Conversely__

**,**the vowel marks of the Tigrinya abugida and the Amharic abugida ( ironically

**,**the original source of the term " abugida ") have been so completely assimilated into their consonants

**that**the modifications are no longer systematic and have to

__be__learned as a syllabary rather than as a segmental script

**.**

__Conversely__

**,**Howard Marshall writes

**that**the speeches were not entirely the inventions of the author and

**,**while they may not

__be__verbatim

**,**nevertheless records the general idea

**.**

__Conversely__

**,**the Belgian Blue's meat tenderness has been argued to

__be__just as tender because there are a large number of smaller muscle fibers

**.**

__Conversely__

**,**certain general principles ( for example

**,**neighbourliness

**,**or charity ) are seen to

__be__universal and consistent

**.**

__Conversely__the equilibrium position is said to

__be__" far to the left " if hardly

**any**product is formed from the reactants

**.**

__Conversely__

**,**in the English language as a whole

**,**singular verb forms can often

__be__used with nouns ending in "- s "

**that**were once considered plural ( for example: " Physics is my favorite academic subject ").

__Conversely__

**,**every point on the line can

__be__interpreted as a number in an ordered continuum which includes the real numbers

**.**

__Conversely__

**,**non-spontaneous electrochemical reactions can

__be__driven forward by the application of a current at sufficient voltage

**.**

__Conversely__

**,**if the data are sparse —

**that**is

**,**if only K out of N Fourier coefficients are nonzero — then the complexity can

__be__reduced to O ( K log N log ( N / K )), and this has been demonstrated to lead to practical speedups compared to an ordinary FFT for N / K > 32 in a large-N example ( N = 2 < sup > 22 </ sup >) using a probabilistic approximate algorithm ( which estimates the largest K coefficients to several decimal places ).

__Conversely__

**,**when one wants to compute an arbitrary number ( N ) of discrete samples of one cycle of a continuous DTFT

**,**it can

__be__done by computing the relatively simple DFT of s < sub > N </ sub >, as defined above

**.**

__Conversely__

**,**one might expect

**that**inertial motions

**,**once identified by observing the actual motions of bodies and making allowances for the external forces (

**such**as electromagnetism or friction ), can

__be__used to define the geometry of space

**,**as well as a time coordinate

**.**

__Conversely__

**,**the symbol width could

__be__set at 8

**,**even if only values 0 and 1 are used ; these data would only require a 2-color table

**.**

__Conversely__

**,**since Imhotep was known as the " Son of Ptah ," his mother was sometimes claimed to

__be__Sekhmet

**,**the patron of Upper Egypt whose consort was Ptah

**.**

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__

**,**every formally real field can

__be__equipped with a compatible total order

**,**

**that**will turn it into an ordered field

**.**

__Conversely__

**,**Walter Burkert suggests

**that**the Hellene cult worship of Poseidon as a horse god may

__be__connected to the introduction of the horse and war-chariot from Anatolia to Greece around 1600 BC

**.**

__Conversely__

**,**Scheme contains multiple coherent subsets

**that**suffice to construct the rest of the language as library macros

**,**and so the language designers do not even bother to say which portions of the language must

__be__implemented as language constructs

**,**and which must

__be__implemented as parts of a library

**.**

Conversely and any

__Conversely__

**,**a subset R defines a binary function if and only if

**,**for

__any__x in X and y in Y

**,**there exists a unique z in Z

**such**

**that**( x

**,**y

**,**z ) belongs to R

**.**

* 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__

**,**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__

**,**a person may feel like he belongs to one state without having

__any__legal relationship to it

**.**

__Conversely__

**,**the interior of the box has a constant

**,**zero potential energy .< ref > Actually

**,**

__any__constant

**,**finite potential can

**be**specified within the box

**.**

__Conversely__

**,**extremely thin jewelry can cause the same tearing in what is commonly referred to as the " cheese cutter effect ", either during sudden torsion or over a long period of wearing

**,**especially if the thin jewelry bears

__any__weight

**.**

__Conversely__

**,**

__any__Hermitian positive semidefinite matrix M can

**be**written as M = A < sup >*</ sup > A ; this is the Cholesky decomposition

**.**

__Conversely__

**,**if a double sharp were added to

__any__other note not containing a sharp or flat as indicated by the key signature then the note will

**be**raised two semitones or a whole step with respect to the chromatic scale

**.**

__Conversely__

**,**supplementation with L-phenylalanine

**,**L-tyrosine

**,**L-DOPA

**,**or

__any__of the cofactors will increase their respective concentrations

**.**

__Conversely__

**,**

__any__choice of μ

**,**full rank matrix U

**,**and positive diagonal entries Λ < sub > i </ sub > yields a non-singular multivariate normal distribution

**.**

__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 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

**.**

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 ).0.523 seconds.