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Conversely if a Kleinian group has no nontrivial torsion elements then it is the fundamental group of a hyperbolic 3-manifold.
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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 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 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 group
Conversely, if ( A, m, e, inv ) is a group object in one of those categories, then m necessarily coincides with the given operation on A, e is the inclusion of the given identity element on A, inv is the inversion operation and A with the given operation is an abelian group.
Conversely, discretionary behavior is motivated by internal values and is seen as more cooperative and therefore ideal within a group.
Conversely, other British acts such as Wang Chung, Breathe and Murray Head, as well as the Anglo-Australian duo Air Supply, are one-hit wonders in the UK but not in the US, and the American group 3T, best known in their homeland as being the three sons of Tito Jackson of The Jackson 5, along with other bands such as Blind Melon and Deep Blue Something, are one-hit wonders in the US but not in the UK.
Conversely, a group may also devolve to an earlier stage if unable to resolve outstanding issues in a particular stage.
Conversely, it is a consequence of the subsequent conclusions of the theorem that any compact Lie group is isomorphic to a matrix group.
Conversely, any affine linear transformation extends uniquely to a projective linear transformations, so the affine group is a subgroup of the projective group.
Conversely, if n is prime, then there exists a primitive root modulo n, or generator of the group ( Z / nZ )*.
* Conversely, a letter or group of letters can correspond to different phonemes in different contexts ( as th does in English ; originally this stood for a single phoneme, which then split ).
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.
Conversely, given a Hopf algebra whose coalgebra structure is given above, we can recover a formal group law F from it.
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, Austereo's Triple M group of stations have suffered heavily from increased competition from new station Vega 95. 3 and Vega 91. 5 in Sydney and Melbourne respectively, with the stations in Melbourne and Sydney recording some of their lowest ratings of all time.
Conversely, if one pottery-type suddenly replaces a great diversity of pottery types in an entire region this might be interpreted as a new group migrating in with this new style.
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, symmetric tensors are defined as invariants: given the natural action of the symmetric group on the tensor algebra, the symmetric tensors are the subspace on which the symmetric group acts trivially.
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.
Conversely, the conservative group Americans for Constitutional Action stated Mathias agreed with their positions only 16 % of the time.
To summarize, M is a symmetric space G / K with a compact isotropy group K. Conversely, symmetric spaces with compact isotropy group are Riemannian symmetric spaces, although not necessarily in a unique way.
Conversely and has
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, a standard line on which voice service has been unsubscribed ( such as an ADSL dry loop ) may still accept calls to the 958 test exchange but not allow calls to standard numbers.
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, the defensive team will know that the offense has to cover a good deal of ground in a single play, will expect a forward pass, and will know from earlier study something of the propensities of the offense they face.
Conversely, Clausewitz has also been seen as " The preeminent military and political strategist of limited war in modern times.
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, 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, in the bleak Orwellian world of " The High Ones "— where the Soviets have won the Third World War and gained control of the whole world — the dissidents still have some hope, precisely because space flight has not been abandoned.
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, Baptists are underrepresented, a reflection of their quite recent expansion in numbers ; there has been only one Roman Catholic president, although they are currently the largest single denomination, and there have been no Lutheran, Pentecostal, or Latter Day Saint presidents.
Conversely, birds of prey-which show distinct reverse sexual dimorphism — tend to be monogamous for long periods or mate for life ; some species like the Snail kite will choose new mates every year, polygyny is noted in many Harriers and polyandry has been observed in the Harris ' Hawk ( notable for being the only bird of prey to regularly live and hunt in family and social groups ) and the aforementioned Galapagos hawk.
Conversely, ska and reggae, popular among traditionalist skinheads, has influenced several punk musicians.
Conversely, once the hardware and software for an anti-lock braking system has been designed to meet its required deadlines, no further performance gains are obligatory.
Conversely, the southern part has tended to sink to compensate, causing flooding of the Low Countries and Denmark.
Conversely, Slam poetry movement founder Marc Smith has been critical of the commercially successful Def Poetry television and Broadway live stage shows produced by Russell Simmons, decrying it as " an exploitive entertainment that diminished the value and aesthetic of performance poetry ".
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, Sinhalese has also borrowed from the original Vedda language, words and grammatical structures, differentiating it from its related Indo-Aryan languages.
Conversely, Elijah Delmedigo ( c. 1458 – c. 1493 ), in his Bechinat ha-Dat endeavored to show that the Zohar could not be attributed to Shimon bar Yochai, arguing that if it were his work, the Zohar would have been mentioned by the Talmud, as has been the case with other works of the Talmudic period, that had bar Yochai known by divine revelation the hidden meaning of the precepts, his decisions on Jewish law from the Talmudic period would have been adopted by the Talmud, that it would not contain the names of rabbis who lived at a later period than that of Simeon ; and that if the Kabbalah was a revealed doctrine, there would have been no divergence of opinion among the Kabbalists concerning the mystic interpretation of the precepts.
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.
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.