We obtain randomized algorithms for factoring degree n univariate polynomials over Fq that use O(n + n log q) field operations, when the characteristic is at most n. When log q < n, this is asymptotically faster than the best previous algorithms (von zur Gathen & Shoup (1992) and Kaltofen & Shoup (1998)); for log q ≥ n, it matches the asymptotic running time of the best known algorithms. The im...

We obtain randomized algorithms for factoring degree n univariate polynomials over Fq requiring O(n1.5+o(1) log q + n1+o(1) logq) bit operations. When log q < n, this is asymptotically faster than the best previous algorithms [J. von zur Gathen and V. Shoup, Comput. Complexity, 2 (1992), pp. 187–224; E. Kaltofen and V. Shoup, Math. Comp., 67 (1998), pp. 1179– 1197]; for log q ≥ n, it matches th...

abstract. in this paper we study some relations between the power andquotient power graph of a finite group. these interesting relations motivateus to find some graph theoretical properties of the quotient power graphand the proper quotient power graph of a finite group g. in addition, weclassify those groups whose quotient (proper quotient) power graphs areisomorphic to trees or paths.

In this paper we treat some fractal and statistical features of the DNA sequences. First, a fractal record model of DNA sequence is proposed by mapping DNA sequences to integer sequences, followed by R/S analysis of the model and computation of the Hurst exponents. Second, we consider transition between the four kinds of bases within DNA. The transition matrix analysis of DNA sequences shows th...

we prove that for $p>7$ there are‎ ‎[‎ ‎p^{4}+2p^{3}+20p^{2}+147p+(3p+29)gcd (p-1,3)+5gcd (p-1,4)+1246‎ ‎] ‎groups of order $p^{8}$ with exponent $p$‎. ‎if $p$ is a group of order $p^{8}$‎ ‎and exponent $p$‎, ‎and if $p$ has class $c>1$ then $p$ is a descendant of $‎p/gamma _{c}(p)$‎. ‎for each group of exponent $p$ with order less than $‎p^{8} $ we calculate the number of descendants of o...

We present a non-perturbative solution of large N matrix models modified by terms of the form g(TrΦ4)2, which add microscopic wormholes to the random surface geometry. For g < gt the sum over surfaces is in the same universality class as the g = 0 theory, and the string susceptibility exponent is reproduced by the conventional Liouville interaction ∼ eα+φ. For g = gt we find a different univers...

The sandpile group of a connected graph is the group of recurrent configurations in the abelian sandpile model on this graph. We study the structure of this group for the case of regular trees. A description of this group is the following: Let T (d, h) be the d-regular tree of depth h and let V be the set of its vertices. Denote the adjacency matrix of T (d, h) by A and consider the modified La...

We use molecular-dynamics computer simulations to study the dynamics of amorphous (Na2O)2(SiO2). We find that the Na ions move in channels embedded in a SiO2 matrix. The characteristic distance between these channels gives rise to a prepeak in the structure factor at q approximately equal to 0.95 A(-1). The dynamics of sodium is given by a fast process which can be seen in the incoherent scatte...

Oscillatory matrices were introduced in the seminal work of Gantmacher and Krein. An n × matrix A is called oscillatory if all its minors are nonnegative there exists a positive integer k such that positive. The smallest for which this holds exponent . Krein showed always smaller than or equal to − 1 important nontrivial problem determine exact value exponent. Here we use successive elementary ...