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Some Related Sentences
Conversely and any
Conversely, let G
be any polynomial such that Af
.
Conversely,
any algebra whose associator is alternating is clearly alternative
.
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,
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 planar
Conversely, given an ordered tree, and conventionally draw the root at the top, then the child nodes
in an ordered tree
can be drawn left-to-right, yielding an essentially unique
planar embedding ( up to embedded homotopy, i
. e., moving the edges and nodes without crossing ).
Conversely and graph
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, if R is
a symmetric relation over
a set X, one
can interpret it as describing an undirected
graph with the elements of X as the vertices and the pairs
in R as the edges
.

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,
any median
graph can be represented as the set of solutions to
a 2-satisfiability instance
in this way.
Conversely, as Lefschetz shows, whenever
a graph G has
a set of cycles with
this property, they necessarily form the face cycles of an embedding of the
graph onto the sphere
.
Conversely any bipartite
graph with girth at least six
can be viewed as the Levi
graph of an abstract incidence structure
.
Conversely, every abstract frame matroid is the frame matroid of some biased
graph.
Conversely, the histogram for
a very bright image with few dark areas and / or shadows will have most of its data points on the right side and center of the
graph.

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 and can
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,
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, existing DSN antennas
can split time among more missions
.
Conversely, non-spontaneous electrochemical reactions
can be driven forward by the application of
a current at sufficient voltage
.
Conversely, badly managed food aid
can create problems by disrupting local markets, depressing crop prices, and discouraging food production
.
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, rifle bullets
can pierce light armor and are easier to shoot accurately, but even
a carbine such as the Colt M4 is larger and / or longer than
a submachine gun, making it harder to maneuver
in close quarters
.
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, languages that grammaticalise aspect
can have tense as
a secondary use of an aspect
.
Conversely,
a high pH, low CO < sub > 2 </ sub >, or low 2, 3 BPG favors the relaxed form which
can better bind oxygen
.
Conversely,
a very severe bit,
in the right hands,
can transmit subtle commands that cause no pain to the horse
.

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, every formally real field
can be equipped with
a compatible total order, that will turn it into an ordered field
.
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 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, 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, specifying the symmetry
can define the structure, or at least clarify what we mean by an invariant, geometric language
in which to discuss it ;
this is one
way of looking at the Erlangen programme
.
Conversely, water deep
in the ocean near geothermal vents
can reach temperatures of hundreds of degrees and remain liquid
.
Conversely, AES is sensitive to the lighter elements, and unlike X-ray fluorescence, Auger peaks
can be detected for elements as light as lithium ( Z = 3 ).
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