Page "Riemann–Roch theorem" ¶ 34
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## Some Related Sentences

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 you do have a better product suddenly you have these businesses that grow like topsy.
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, negative chemotaxis occurs if the movement is in the opposite direction.
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 same is done with the left hand, a left-handed system results.
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, if no advantage is gained from kicking the ball, play should continue.
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 sequence
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.
Conversely, the sequence of an ancient gene for a given structure may have diverged considerably in different species while at the same time maintaining the same basic structural features.
Conversely, there is no parallel concept of secondary or tertiary sequence.
Conversely, any sequence that satisfies a linear recurrence determines a rational function when used as the coefficients of a Taylor series.
Conversely, retaining a series ' original title sequence can allow a producer to change many key elements within a programme itself, without losing the show's on-screen identity.
Conversely, given any ordered sequence of natural numbers,
Conversely, if is a two-sided sequence of complex numbers ( that is, its indices range from negative infinity to positive infinity ) such that
Conversely, the sequence components are generated from the analysis equations

Conversely and way
Conversely, the end of the Cold War marked by the fall of the Berlin Wall in 1989 resulted in a reduction in the duration of Cold War civil wars of 92 % or, phrased another way, a roughly ten-fold increase in the rate of resolution of Cold War civil wars.
Conversely any planar graph can be formed from a map in this way.
Conversely, modern social democracy emphasises a program of gradual legislative reform of capitalism in order to make it more equitable and humane, while the theoretical end goal of building a socialist society is either completely forgotten or redefined in a pro-capitalist way.
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, the object-side numerical aperture is related to the f-number by way of the magnification ( tending to zero for a distant object ):
Conversely, many theorems that hold in universal algebra do not generalise all the way to category theory.
Conversely in rings with unity, any simple left R module arises this way.
Conversely, cartridge names often reflect nothing related to the cartridge in any obvious way ; for example, the. 218 Bee uses a bullet of 224 / 1000-inch diameter, fired through a. 22-in bore, etc.
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, records which originate from a common source ( or fonds ) should be kept together – preferably physically, but, where that is not practicable, certainly intellectually in the way in which they are catalogued and arranged in finding aids – in accordance with what is sometimes termed the principle of archival integrity.
Conversely, any topology can be induced in this way by the correct choice of closure operator.
Conversely, how do the latter achieve superior societal health while having little in the way of the religious values or institutions?
Conversely, the emergence of energy shots has gone the opposite way with much smaller packaging.
Conversely, less than one Yellow Warbler nest in three on average suffers from predation in one way or another, while two out of three Mangrove and Golden Warbler nests are affected.
Conversely, every method for evaluating conditionals can be seen as a way for performing revision.
Conversely, any median graph can be represented as the set of solutions to a 2-satisfiability instance in this way.
Conversely, other-for-me describes the way in which others incorporate my perceptions of them into their own identities.
Conversely, since it is a type of formal third-party certification, museums using this name space obtain a way to assure visitors of the site's validity.
Conversely, a swing seat is one that could easily swing either way.
Conversely, the topological charge only makes sense in the ordered phase and not at all in the disordered phase, because in some hand-waving way there is a " topological condensate " in the disordered phase which randomizes the field from point to point.
Conversely, Eric only seems to find Jackie attractive when not hearing her voice in any way, stating at one point: " Good God, she is hot!
Conversely, every cograph can be represented in this way by a cotree.

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