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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, 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 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 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, 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, 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.
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, to switch off a p-channel device requires V < sub > GS </ sub > positive.
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 sup
Conversely, a system of n quantities v < sup > i </ sup > that transform like the coordinates x < sup > i </ sup > on V defines a contravariant vector.
Conversely, if A is invertible, F is algebraically closed, and A < sup > n </ sup > is diagonalizable for some n that is not an integer multiple of the characteristic of F, then A is diagonalizable.

Conversely and >
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, 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 25
Conversely, frequencies used for some railway electrification systems were much lower ( e. g. 16. 7 Hz and 25 Hz ) than normal utility frequencies ( 50 – 60 Hz ) for historical reasons concerned mainly with the limitations of early electric traction motors.
Conversely, Eldad ha-Dani argued that the tribe of Simeon had become quite powerful, taking tribute from 25 other kingdoms, some of which were Arabians ; though he names their location, surviving versions of his manuscripts differ as to whether it was the land of the Khazars or of the Chaldeans-Chaldeans would be an anachronism, though it could possibly refer to Buyid Dynasty Persia.
Conversely, traffic joining the M4 from Caerleon can join the M4 eastbound at Junction 25 but to join the M4 westbound traffic must follow the Junction 25A offslip, Heidenheim Drive, Malpas Road route to M4 Junction 26.
Conversely, he also ranked among the top ten in strikeouts and led all American League batters by grounding into 25 double plays.
Conversely, men were only allowed to marry after the age of 25.
Conversely, the GDC may order the attachment of personal property valued up to $ 25, 000, but has no authority to order the attachment of real estate, no matter how low the value.
Conversely, the ABC affiliation moved to WEHT ( channel 25 ) ending its affiliation with CBS after 41 years.

Conversely and >,
Conversely, it is possible to 2-colour a K < sub > 5 </ sub > without creating any monochromatic K < sub > 3 </ sub >, showing that R ( 3, 3 ) > 5.
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.
which are linearly independent at each point q in U. Conversely, given such a coframe, there is a unique moving frame X < sub > 1 </ sub >, X < sub > 2 </ sub >, ..., X < sub > n </ sub > which is dual to it, i. e., satisfies the duality relation α < sup > i </ sup >( X < sub > j </ sub >) = δ < sup > i </ sup >< sub > j </ sub >, where δ < sup > i </ sup >< sub > j </ sub > is the Kronecker delta function on U.
If f is flat, then .< ref > EGA IV < sub > 2 </ sub >, Corollaire 6. 1. 2 .</ ref > Conversely, if this equality holds for all x, X is Cohen-Macaulay, and Y is regular, then f is flat .< ref > EGA IV < sub > 2 </ sub >, Proposition 6. 1. 5.
If X is reduced or normal at x, then Y is reduced or normal, respectively, at f ( x ).< ref > EGA IV < sub > 2 </ sub >, Proposition 2. 1. 13 .</ ref > Conversely, if f is also of finite presentation and f < sup >− 1 </ sup >( y ) is reduced or normal, respectively, at x, then X is reduced or normal, respectively, at x .< ref > EGA IV < sub > 3 </ sub >, Proposition 11. 3. 13 .</ ref >
Conversely, if Y is regular at f ( x ) and f < sup >− 1 </ sup >( f ( x )) is regular at x, then X is regular at x .< ref > EGA IV < sub > 2 </ sub >, Corollaire 6. 5. 2 .</ ref >
Conversely, if Y is normal at f ( x ) and f < sup >− 1 </ sup >( f ( x )) is normal at x, then X is normal at x .< ref > EGA IV < sub > 2 </ sub >, Corollaire 6. 5. 4 .</ ref >
Conversely, if the holonomy group of the Riemannian manifold M is contained in Sp ( k ), choose complex structures I < sub > x </ sub >, J < sub > x </ sub > and K < sub > x </ sub > on T < sub > x </ sub > M which make T < sub > x </ sub > M into a quaternionic vector space.
Conversely if f is a homomorphism from G to K < sub > k </ sub >, then one can color G by using the same color for two vertices in G whenever they are both mapped to the same vertex in K < sub > k </ sub >.
Conversely, when carbon's hybridization changes from sp < sup > 2 </ sup > to sp < sup > 3 </ sup >, the out of plane bending force constants at the transition state increase and an inverse SKIE is observed with typical values of 0. 8 to 0. 9.
Conversely, since the existence of T < sup >∗∗</ sup > implies that that of T < sup >∗</ sup >, which in turn implies T is densely defined.
If f is unramified at a point x, then f is quasi-finite at x. Conversely, if f is quasi-finite at x, and if also, the local ring of x in the fiber f < sup >− 1 </ sup >( f ( x )), is a field and a finite separable extension of κ ( f ( x )), then f is unramified at x .< ref > EGA IV < sub > 4 </ sub >, Théorème 17. 4. 1 .</ ref >

Conversely and Court
Conversely, the Court has approved routine warrantless seizures, for example " where there is probable cause to believe that a criminal offense has been or is being committed.
Conversely, the Supreme Court's denial of a petition for a writ of certiorari is sometimes misunderstood to mean that the Supreme Court approves the decision of the lower court.
Conversely, the State Constitution was amended to provide that no city could elect the majority of the State Assembly, a provision later struck down by the US Supreme Court as violating the Fourteenth Amendment to the United States Constitution.
Conversely, in The Mortgage Specialists, Inc. v. Implode-Explode Heavy Industries, Inc. the New Hampshire Supreme Court adopted a much broader definition of media that applies to blogs and website curators, reiterating that " freedom of the press is a fundamental personal right which is not confined to newspapers and periodicals.
For example, Chern v. Bank of America held that a loan officer ’ s statement over the phone about interest rates was “ advertising .” Conversely, Bank of the West v. Superior Court implied that advertising might require “ widespread promotional activities directed to the public-at-large ” and that mere “ personal solicitations are not advertising .”
Conversely, in National Collegiate Athletic Association v. Smith, the Supreme Court has found that the National Collegiate Athletic Association is not a state actor for the purposes of 28 U. S. C.

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