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692.
Yossi Moshe 《Journal d'Analyse Mathématique》2006,99(1):267-294
Let λ be the upper Lyapunov exponent corresponding to a product of i.i.d. randomm×m matrices (X
i)
i
0/∞
over ℂ. Assume that theX
i's are chosen from a finite set {D
0,D
1...,D
t-1(ℂ), withP(X
i=Dj)>0, and that the monoid generated byD
0, D1,…, Dq−1 contains a matrix of rank 1. We obtain an explicit formula for λ as a sum of a convergent series. We also consider the case
where theX
i's are chosen according to a Markov process and thus generalize a result of Lima and Rahibe [22].
Our results on λ enable us to provide an approximation for the numberN
≠0(F(x)n,r) of nonzero coefficients inF(x)
n.(modr), whereF(x) ∈ ℤ[x] andr≥2. We prove the existence of and supply a formula for a constant α (<1) such thatN
≠0(F(x)n,r) ≈n
α for “almost” everyn.
Supported in part by FWF Project P16004-N05 相似文献
693.
Moshe Schwartz 《Physics letters. A》1985,107(5):199-203
A new approach to quenched random problems, based on constructing an equivalent annealed system, is presented. The difficulties with the existing solutions of the random field problem are discussed. The new approach is applied to the random field problem yielding a different new result for the dimensionality shift. A by-product of this result is that the lower critical dimension is 2 for the Ising model. 相似文献
694.
695.
Moshe Rosenfeld 《Israel Journal of Mathematics》1975,21(1):24-30
A study is made of the non-regular planar 3-connected graphs with constant weight. 相似文献
696.
697.
Pavol Hell Moshe Rosenfeld 《Journal of Algorithms in Cognition, Informatics and Logic》1983,4(4):303-309
Given a tournament with n vertices, we consider the number of comparisons needed, in the worst case, to find a permutation υ1υ2…υn of the vertices, such that the results of the games υ1υ2, υ2υ3,…, υn−1υn match a prescribed pattern. If the pattern requires all arcs to go forwrd, i.e., υ1 → υ2, υ2 → υ3,…, υn−1 → υn, and the tournament is transitive, then this is essentially the problem of sorting a linearly ordered set. It is well known that the number of comparisons required in this case is at least cn lg n, and we make the observation that O(n lg n) comparisons suffice to find such a path in any (not necessarily transitive) tournament. On the other hand, the pattern requiring the arcs to alternate backward-forward-backward, etc., admits an algorithm for which O(n) comparisons always suffice. Our main result is the somewhat surprising fact that for various other patterns the complexity (number of comparisons) of finding paths matching the pattern can be cn lgαn for any α between 0 and 1. Thus there is a veritable spectrum of complexities, depending on the prescribed pattern of the desired path. Similar problems on complexities of algorithms for finding Hamiltonian cycles in graphs and directed graphs have been considered by various authors, [2, pp. 142, 148, 149; 4]. 相似文献
698.
699.
Moshe Roitman 《Linear algebra and its applications》1978,19(1):87-89
Let F be an infinite field and n?12. Then the number of conjugacy classes of the upper triangular nilpotent matrices in Mn(F) under action by the subgroup of GLn(F) consisting of all the upper triangular matrices is infinite. 相似文献
700.
Arye Friedman 《International Journal of Theoretical Physics》1994,33(2):307-338
An extension of the quantum logical approach to the axiomatization of quantum mechanics usingnonstandard analysis methods is proposed. The physical meaning of a quantum logic as a lattice of propositions is conserved by its nonstandard extension. But not only the usual Hubert space formalism of quantum mechanics can be derived from the nonstandard extended quantum logic. Also the Dirac bra-ket quantum mechanics can be derived as a consequence of such an extended quantum logic. 相似文献