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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.
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Conversely and if
Conversely, if statistics were uncovered which contradicted a cherished theory, the sources were denounced as faulty.
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, if he gives a heavy rating to his own reading, and finds more accurate facts in it than in the others, a point is chalked up for the intrinsic, objective meaningfulness of this type of mediumistic material.
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, 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, if the second theory is correct, then the Athenians were merely reacting to the Persians attacking them.
Conversely the equilibrium position is said to be " far to the left " if hardly any product is formed from the reactants.
Conversely, if the amount of fat is increased, increasing the number of calories ingested will only add weight.
Conversely, if the source of waves is moving away from the observer, each wave is emitted from a position farther from the observer than the previous wave, so the arrival time between successive waves is increased, reducing the frequency.
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.
If neither A nor B includes the idea of existence, then " some A are B " simply adjoins A to B. Conversely, if A or B do include the idea of existence in the way that " triangle " contains the idea " three angles equal to two right angles ", then " A exists " is automatically true, and we have an ontological proof of A's existence.
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 firm is able to get bulk discounts of an input, then it could have economies of scale in some range of output levels even if it has decreasing returns in production in that output range.
Conversely, daylight stock shot in daylight will look normal, but orange if shot under tungsten lights.
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 and ƒ
Conversely every positive functional φ gives a corresponding inner product < ƒ, g >< sub > φ </ sub > = φ ( g * ƒ ).
** Conversely, if ƒ: I → R is absolutely continuous and thus differentiable almost everywhere, and satisfies | ƒ ′( x )| ≤ K for almost all x in I, then ƒ is Lipschitz continuous with Lipschitz constant at most K.
Conversely, if F has characteristic zero, then given an homogeneous polynomial ƒ of degree n on V, the polarization of ƒ is a multilinear function on the n-th Cartesian product of V. The polarization is defined by
for all compactly supported functions ƒ and h. Conversely, () characterizes Δ completely, in the sense that it is the only operator with this property.
Conversely and C
Conversely, paintings which came out of his workshop that were not necessarily physically worked on by Cuyp but merely overseen by him technically, were marked with A. C. to show that it was his instruction which saw the paintings ’ completion.
* 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.
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.
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, by the inverse function theorem, there can be at most one value for σ that, when applied as an input to, will result in a particular value for C.
Conversely, July is the warmest month, with an average temperature of 21. 4 C. The annual temperature ranges between-12 C as an annual low to an annual high of 38 C.
Conversely, Oymyakon on July 28, 2010 recorded a record high temperature of, yielding a temperature range of 105. 8 ° C ( 190. 4 ° F ).
Conversely, if a program adheres to standards such as POSIX and ANSI C, it will be easier to port to the USS environment.
Conversely, CPython applications that depend on extensions to the language that are implemented in C ( e. g. NumPy ) are not compatible with IronPython, although a commercially-supported open source project to address this is underway.
Conversely two widely recognized standards for industrial RTDs IEC 6075 and ASTM E-1137 specify an alpha of 0. 00385 ohms / ohm /° C.
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.
Conversely, several cable news channels exist that carry news information specifically geared toward a particular metropolitan area, state or region such as NY1 in New York City, Ohio News Network ( which is based in Columbus, Ohio, but is carried throughout the state of Ohio ), Bay News 9 in Tampa, Florida and NewsChannel 8 in Washington, D. C.
Conversely, the V. C. s, all colonists from different worlds, often used the term ' earthworm ' to describe Smith and his compatriots.
Conversely and →
Conversely, starting from this equivalence we can recover U as the composite Rel → Sup → Set of the forgetful functor for Sup with this embedding of Rel in Sup.
Conversely, a complete variety is close to being a projective variety: Chow's lemma states that if X is a complete variety, there is a projective variety Z and a birational morphism Z → X.
Conversely, a function u: E < sub > 1 </ sub > → E < sub > 2 </ sub > defined on a basis of E < sub > 1 </ sub > can be uniquely extended to a linear function.
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.
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, an Ehresmann connection H ⊂ TP ( or v: TP → V ) on P defines a principal G-connection ω if and only if it is G-equivariant in the sense that.
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 ).
Suppose S is an immersed submanifold of M. If the inclusion map i: S → M is closed then S is actually an embedded submanifold of M. Conversely, if S is an embedded submanifold which is also a closed subset then the inclusion map is closed.
Conversely, given any element u ∈ F ( A ) we may define a natural transformation Φ: Hom ( A ,–) → F via
Conversely, if G contains a proper non-trivial normal subgroup N, then the composition of the natural surjective group homomorphism G → G / N with the regular representation of G / N produces a representation π of G which has kernel N. Taking χ to be the character of some non-trivial subrepresentation of π, we have a character satisfying the hypothesis in the direct statement above.