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Conversely every positive functional φ gives a corresponding inner product < ƒ, g >< sub > φ </ sub > = φ ( g * ƒ ).

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## Some Related Sentences

Conversely and every

__Conversely__

**,**

__every__point on the line can be interpreted as

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

__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.

__Conversely__

**,**

__every__formally real field can be equipped with

**a**compatible total order

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

__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__

**,**though

__every__president from Washington to John Quincy Adams can be definitely assigned membership in an Anglican or Unitarian body

**,**the significance of these affiliations is often downplayed as unrepresentative of their true beliefs.

__Conversely__

**,**birds of prey-which show distinct reverse sexual dimorphism — tend to be monogamous for long periods or mate for life ; some species like the Snail kite will choose new mates

__every__year

**,**polygyny is noted in many Harriers and polyandry has been observed in the Harris ' Hawk

**(**notable for being the only bird of prey to regularly live and hunt in family and social groups ) and the aforementioned Galapagos hawk.

__Conversely__

**,**

__every__

**positive**semi-definite matrix is the covariance matrix of some multivariate distribution.

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__

**,**if we pick

__every__member of the same population with property and ask " what proportion of these have property?

__Conversely__

**,**

__every__admissible statistical procedure is either

**a**Bayesian procedure or

**a**limit of Bayesian procedures.

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.
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**).**
This ring is the endomorphism ring of A.

__Conversely__**,**__every__ring**(**with identity ) is the endomorphism ring of some object in some preadditive category.__Conversely__

**,**

__every__Polish space is homeomorphic to

**a**G

**<**

**sub**

**>**δ

**</**

**sub**>- subset of the Hilbert cube.

__Conversely__

**,**extra lives are earned by collecting heart points

**,**which are earned by defeating enemies or collecting Hearts

**,**with an extra life earned for

__every__100 points earned.

__Conversely__the building can be recovered from the BN pair

**,**so that

__every__BN pair canonically defines

**a**building.

__Conversely__

**,**the following characterization of derived functors holds: given

**a**family of functors R

**<**sup

**>**i

**</**sup >: A → B

**,**satisfying the above

**,**i. e. mapping short exact sequences to long exact sequences

**,**such that for

__every__injective object I of A

**,**R

**<**sup

**>**i

**</**sup >( I )= 0 for

__every__

**positive**i

**,**then these functors are the right derived functors of R

**<**sup

**>**0

**</**sup >.

Conversely and positive

__Conversely__

**,**in an n-channel enhancement-mode device

**,**

**a**

__positive__gate-to-source voltage is necessary to create

**a**conductive channel

**,**since one does not exist naturally within the transistor.

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__

**,**some have identified low protein intake as

**a**

__positive__factor

**,**protein is among the causes of dietary acidity.

__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__

**,**inserting

**a**tube that is too small can result in inability to achieve effective

__positive__pressure ventilation due to retrograde escape of gas through the glottis and out the mouth and nose

**(**often referred to as

**a**" leak " around the tube

**).**

__Conversely__

**,**

**a**number that is greater than zero is called

__positive__; zero is usually thought of as neither

__positive__nor negative.

"

__Conversely__**,**in the__positive__sense**,**it would refer to " having it both ways " or " having the best of both worlds.__Conversely__

**,**the film did receive notably

__positive__reviews from such critics as Varietys Derek Elley

**,**A. O. Scott of The New York Times

**,**and online critic James Berardinelli.

__Conversely__

**,**by the Riesz representation theorem

**,**each

__positive__linear form on arises as integration with respect to

**a**Radon measure and is thus

**a**continuous

__positive__linear form on.

__Conversely__

**,**recruiting creatures which share

**a**

__positive__predisposition towards each other increases their morale.

__Conversely__

**,**

**a**down period is characterized by the close being lower than the previous period's

**(**note that D is nonetheless

**a**

__positive__number ),

__Conversely__

**,**increasing the external K

**<**sup >+</ sup

**>**concentration raises

**(**more

__positive__) the K

**<**sup >+</ sup

**>**equilibrium potential and produces

**a**

__positive__shift in reversal potential.

__Conversely__

**,**he instituted

__positive__changes

**,**such as longer home leaves and better food and medical / surgical assistance for the troops.

Conversely and functional

__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__

**,**if

**a**white father is paired with

**a**green mother with

__functional__chloroplasts

**,**the progeny will only inherit

__functional__chloroplasts

**,**and will thus be green.

__Conversely__

**,**the density determines the wave function modulo

**a**phase factor

**,**providing the formal foundation of density

__functional__theory.

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