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Brown Corpus
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, let Q
be any orthogonal matrix which does not have − 1 as an eigenvalue ; then
Conversely, let A
be a self-adjoint operator on a Hilbert space H
. Then

C
. Conversely, if X is a set of formulas
, let Mod ( X )
be the
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
.

where e is the identity in
G. Conversely, given a section s one defines a trivialization Φ by
Conversely, G protein-coupled receptors are neither excitatory nor inhibitory
.
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 withdrawal syndrome may also
be a trigger for relapse
.
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, function application is considered to
be left-associative
, so
that is equivalent to
.
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 any planar graph can
be formed from a map in this way
.
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, 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
.

* 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 ).
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