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Conversely, if dφ < sub > x </ sub > is an isomorphism then there is an open neighborhood U of x such that φ maps U diffeomorphically onto its image.

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## Some Related Sentences

Conversely and if

__Conversely__

**,**

__if__statistics were uncovered which contradicted a cherished theory

**,**the sources were denounced as faulty

**.**

__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__

**,**

__if__he gives a heavy rating to his own reading

**,**and finds more accurate facts in it than in the others

**,**a point

**is**chalked up for the intrinsic

**,**objective meaningfulness

**of**this type

**of**mediumistic material

**.**

__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

**.**

__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__

**,**

__if__the second theory

**is**correct

**,**

**then**the Athenians were merely reacting to the Persians attacking them

**.**

__Conversely__the equilibrium position

**is**said to be " far to the left "

__if__hardly any product

**is**formed from the reactants

**.**

__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__

**,**

__if__the amount

**of**fat

**is**increased

**,**increasing the number

**of**calories ingested will only add weight

**.**

__Conversely__

**,**

__if__the source

**of**waves

**is**moving away from the observer

**,**each wave

**is**emitted from a position farther from the observer than the previous wave

**,**so the arrival time between successive waves

**is**increased

**,**reducing the frequency

**.**

__Conversely__every partition

**of**comes from

**an**equivalence relation in this way

**,**according to which

__if__and only

__if__and belong to the same set

**of**the partition

**.**

If neither A nor B includes the idea

**of**existence**,****then**" some A are B " simply adjoins A to B**.**__Conversely__**,**__if__A or B do include the idea**of**existence in the way**that**" triangle " contains the idea " three angles equal to two right angles ",**then**" A exists "**is**automatically true**,**and we have**an**ontological proof**of**A's existence**.**__Conversely__

**,**

__if__the measured potential

**is**negative

**,**the electrode

**is**more oxidizing than the SHE (

**such**as Zn in ZnSO

**<**

**sub**

**>**4

**</**

**sub**

**>**where the standard electrode potential

**is**− 0

**.**76 V ).

__Conversely__

**,**

__if__the firm

**is**able to get bulk discounts

**of**

**an**input

**,**

**then**it could have economies

**of**scale in some range

**of**output levels even

__if__it has decreasing returns in production in

**that**output range

**.**

__Conversely__

**,**daylight stock shot in daylight will look normal

**,**but orange

__if__shot under tungsten lights

**.**

__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 and <

__Conversely__

**,**some elements do not maintain distinct allotropes in different phases – for example phosphorus has numerous solid allotropes

**,**which all revert to the same P

__<__

**sub**

**>**4

**</**

**sub**

**>**form when melted to the liquid state

**.**

__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__

**,**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__

**,**a high pH

**,**low CO

__<__

**sub**

**>**2

**</**

**sub**>, or low 2

**,**3 BPG favors the relaxed form which can better bind oxygen

**.**

__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**>.

__Conversely__we have a b

**if**and only

**if**a

__<__b or a ~ b

**.**This

**is**the reason for using the notation ""; "≤" can be confusing for a preorder

**that**

**is**not anti-symmetric

**,**it may suggest

**that**a ≤ b implies

**that**a

__<__b or a

__Conversely__every positive functional

**φ**gives a corresponding inner product

__<__ƒ

**,**g ><

**sub**

**>**

**φ**

**</**

**sub**

**>**=

**φ**( g * ƒ ).

__Conversely__

**,**

**if**M

**is**positive definite

**,**it has

**an**eigendecomposition P

__<__sup >− 1

**</**sup

**>**DP where P

**is**unitary

**,**D diagonal

**,**and all diagonal elements

**of**D are real and positive

**.**

__Conversely__

**,**any Hermitian positive semidefinite matrix M can be written as M = A

__<__sup >*</ sup

**>**A ; this

**is**the Cholesky decomposition

**.**

__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__

**,**for the previous range from 2

__<__sup

**>**51

**</**

**sub**

**>**to 2

__<__sup

**>**52

**</**

**sub**>, the spacing

**is**0

**.**5

**,**etc

**.**

Conversely and 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 and >

__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 and x

__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__

**,**every preorder

**is**the reachability relationship

**of**a directed graph ( for instance

**,**the graph

**that**has

**an**edge from

__x__to y for every pair (

__x__

**,**y ) with

__x__≤ y ).

)

__Conversely__**,**a critical point__x__**of**f can be analysed by considering the second derivative**of**f at__x__:

Conversely and is

__Conversely__

**,**

**an**adiabatic process

**that**

__is__irreversible and extracts no work

__is__in

**an**isenthalpic process

**,**

**such**as viscous drag

**,**progressing towards a nonnegative change in entropy

**.**

__Conversely__

**,**British English favours fitted as the past tense

**of**fit generally

**,**whereas the preference

**of**American English

__is__more complex: AmEng prefers fitted for the metaphorical sense

**of**having made

**an**object " fit " ( i

**.**e., suited ) for a purpose ; in spatial transitive contexts

**,**AmEng uses fitted for the sense

**of**having made

**an**object conform to

**an**unchanged object

**that**it surrounds ( e

**.**g., " fitted X around Y ") but fit for the sense

**of**having made

**an**object conform to

**an**unchanged object

**that**surrounds it ( e

**.**g., " fit X into Y "); and for the spatial senses ( both intransitive and transitive )

**of**having been matching with respect to contour

**,**with no alteration

**of**either object implied

**,**AmEng prefers fit (" The clothes fit

**.**

__Conversely__the use

**of**true brass seems to have declined in Western Europe during this period in favour

**of**gunmetals and other mixed alloys but by the end

**of**the first Millennium AD brass artefacts are found in Scandinavian graves in Scotland

**,**brass was being used in the manufacture

**of**coins in Northumbria and

**there**

__is__archaeological and historical evidence for the production

**of**brass in Germany and The Low Countries areas rich in calamine ore which would remain important centres

**of**brass making throughout the medieval period

**,**especially Dinant – brass objects are still collectively known as dinanterie in French

**.**

__Conversely__

**,**because space

__is__expanding

**,**and more distant objects are receding ever more quickly

**,**light emitted by us today may never " catch up " to very distant objects

**.**

__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__

**,**the islands do not receive the upwellings ( cold streams )

**that**affect the West African coast

**,**so the air temperature

__is__cooler than in Senegal

**,**but the sea

__is__actually warmer

**,**because the orographic relief

**of**some islands

**,**as Sao Miguel with steep mountains

**,**cover it with rich woods and luxuriant vegetation where the dense moisture condense and soak the plants

**,**rocks

**,**soil

**,**logs

**,**moss etc

**.**

__Conversely__in francophone Canada

**,**one hundredth

**of**a Canadian dollar

__is__informally called a sou ( penny ), though cent

__is__official in both English and French

**.**

__Conversely__

**,**

**an**absence

**of**secure cycle-parking

__is__a recurring complaint by cyclists from cities with low modal share

**of**cycling

**.**

* 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**.**0.157 seconds.