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Some Related Sentences
Conversely and any
Conversely, let G be
any polynomial such that Af
.
Conversely, any algebra for which this
is true
is clearly alternative.
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 the equilibrium position
is said to be " far to the left " if hardly
any product
is formed from the reactants
.

* 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, corresponding to
any partition of X
, there exists an equivalence relation ~ on X
.
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 any planar graph can be formed from a map in this way
.
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 in rings with unity
, any simple left R module arises this way
.
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, in the absence of spatial continuity can take
any value
.
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 ).
Conversely and algebra
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, many theorems that hold in universal
algebra do not generalise all the way to category theory
.
Conversely, once a basis for A has been chosen
, the products of basis elements can be set arbitrarily
, and then extended in a unique way to a bilinear operator on A
, i
. e., so the resulting multiplication satisfies the
algebra laws
.
Conversely, for
any topology the clopen ( i
. e
. closed and open ) subsets yield a Boolean
algebra.
Conversely, given a Hopf
algebra whose coalgebra structure
is given above
, we can recover a formal group law F from it
.
Conversely, given
any topological space X
, the collection of subsets of X that are clopen ( both closed and open )
is a Boolean
algebra.
Conversely, symmetric tensors are defined as invariants: given the natural action of the symmetric group on the tensor
algebra, the symmetric tensors are the subspace on which the symmetric group acts trivially
.
Conversely, the normed division algebras immediately give rise to trialities by taking each V < sub > i </ sub > equal to the division
algebra, and using the inner product on the
algebra to dualize the multiplication into a trilinear form
.
Conversely, given a generalized Cartan matrix
, one can recover its corresponding Lie
algebra.
Conversely, given
any Lie
algebra with a direct sum decomposition satisfying these three conditions
, the linear map σ
, equal to the identity on and minus the identity on
, is an involutive automorphism
.
Conversely and whose
Conversely, the existence of Bletchley Park
, and of the decrypting achievements there
, was never officially shared with the Soviet Union
, whose war effort would have greatly benefited from regular decrypting of German messages relating to the Eastern Front
.
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
.
Conversely, there have been a number of popes
whose reign lasted less than a month
.
Conversely, citizens may find themselves ineligible because they do not currently reside within the United States ; exceptions apply for children of military parent ( s ) who were born overseas
, were disabled or became blind overseas
, or first applied for benefits overseas and for students studying abroad who were eligible for SSI in the month prior to leaving the US
, whose absence will be for less than 1 year
, and who are studying to enhance their ability to perform substantial gainful activity
, sponsored by an educational institution in the US
, and would not be available to the individual in the US
.
Conversely, nominating the party leader
whose party maintains a plurality and who are already familiar with their party manifesto facilitates a smoother nomination process
.

Equipped with this notion of length
, a Riemannian manifold
is a metric space
, meaning that it has a distance function d ( p
, q )
whose value at a pair of points p and q
is the distance from p to q
. Conversely, the metric tensor itself
is the derivative of the distance function ( taken in a suitable manner ).
Conversely, nominating the party leader
whose party maintains a plurality and who are already familiar with their party manifesto facilitates a smoother nomination process
.

*
Conversely, a wave
whose phase drifts quickly will have a short coherence time
.
Conversely, the valuation on a discrete valuation ring can be extended to a valuation on the quotient field giving a discrete valued field
, whose associated discrete valuation ring
is just
.
Conversely this book
, whose discovery
is touted in 2 Kings
, was therefore believed to have been of an early enough authorship to validate
, not only its inclusion
, but the book's ultimate placement as the 5th of the " Five Books of Moses ".
Conversely, Clover points out that the villain of slasher films
is often a male
whose masculinity
, and sexuality more generally
, are in crisis
.

To a graph G there corresponds a signed complete graph Σ on the same vertex set
, whose edges are signed negative if in G and positive if not in G
. Conversely, G
is the subgraph of Σ that consists of all vertices and all negative edges
.
Conversely, in the United States Navy
, the term " shipmate " can be the derogatory term used by officers and senior enlisted to refer to a sailor
whose name they have not bothered to remember or read off of their uniform ( Example: Hey!
0.180 seconds.