Let n ≥ 1 and F an algebraic closure of a finite field of characteristic p > n + 1. Let ρ : GQ → GL(n,F) be a Galois representation that is isomorphic to a direct sum of a collection of characters and an odd mdimensional representation τ . We assume that m = 2 or m is odd, and that τ is attached to a homology class in degree m(m−1)/2 of a congruence subgroup of GL(m,Z) in accordance with the ma...

Let O be a conic in the classical projective plane PG(2, q), where q is an odd prime power. With respect to O, the lines of PG(2, q) are classified as passant, tangent, and secant lines, and the points of PG(2, q) are classified as internal, absolute and external points. The incidence matrices between the secant/passant lines and the external/internal points were used in [5] to produce several ...

We investigate a class QNC(ADD) that is QNC with gates for addition of two binary numbers, where QNC is a class consisting of quantum operations computed by constant-depth quantum circuits. We show that QNC(ADD) = QAC(PAR) = QAC(MUL), where QAC(PAR) and QAC(MUL) are QAC with gates for parity and multiplication respectively, and where QAC is QNC with Toffoli gates of arbitrary fan-in. In the cla...

in this paper, we present a fourth order method for computing simple roots of nonlinear equations by using suitable taylor and weight function approximation. the method is based on weerakoon-fernando method [s. weerakoon, g.i. fernando, a variant of newton's method with third-order convergence, appl. math. lett. 17 (2000) 87-93]. the method is optimal, as it needs three evaluations per ite...

the aim of the present study was to estimate the genetic parameters and genetic trends of somatic cell score (scs) in the first 3 lactations of iranian holstein cows by random regression (rr) animal model by using restricted maximum likelihood (reml) method. the data set used in this analysis included observations of 340318 test-day records of 41526 cows in 288 herds; 89969 test-day of 11750 co...

we present an approach to design of fault tolerant computing systems. in this paper, a technique is employed that enable the combination of several codes, in order to obtain flexibility in the design of error correcting codes. code combining techniques are very effective, which one of these codes are turbo codes. the algorithm-based fault tolerance techniques that to detect errors rely on the c...

We will now consider the problem of creating a set of bitstrings such that the bits are almost k-wise independent. Our method consists of two steps. In the first step we create a set of bitstrings such that parity on every fixed index set is almost even. In the second step we present a method to convert such a set into a set where the bits are almost k-wise independent. For presentational reaso...

Let A(n, d) denote the greatest number of codewords possible in a binary block code of length n and distance d. Plotkin gave a simple counting argument which leads to an upper bound B(n, d) for A(n, d) when d ≥ n/2. Levenshtein proved that if Hadamard’s conjecture is true then Plotkin’s bound is sharp. Though Hadamard’s conjecture is probably true, its resolution remains a difficult open questi...