Abelian class group Cl(D) of imaginary quadratic order with odd squarefree discriminant D is used in public key cryptosystems, based on discrete logarithm problem in class group and in cryptosystems, based on isogenies of elliptic curves. Discrete logarithm problem in Cl(D) is hard if #Cl(D) is prime or has large prime divisor. But no algorithms for generating such D are known. We propose proba...

the aim of the present study was the estimation of (co) variance components and genetic parameters for body weight of moghani sheep, using random regression models based on b-splines functions. the data set included 9165 body weight records from 60 to 360 days of age from 2811 moghani sheep, collected between 1994 to 2013 from jafar-abad animal research and breeding institute, ardabil province,...

We present a quadratic outer approximation scheme for solving general convex integer programs, where suitable quadratic approximations are used to underestimate the objective function instead of classical linear approximations. As a resulting surrogate problem we consider the problem of minimizing a function given as the maximum of finitely many convex quadratic functions having the same Hessia...

in cite{p}, park introduced the quadratic $rho$-functional inequalitiesbegin{eqnarray}&& |f(x+y)+f(x-y)-2f(x)-2f(y)| && qquad le  left|rholeft(2 fleft(frac{x+y}{2}right) + 2 fleft(frac{x-y}{2}right)- f(x) -  f(y)right)right|,  nonumberend{eqnarray}where $rho$ is a fixed complex number with $|rho|andbegin{eqnarray}&& left|2 fleft(frac{x+y}{2}right) + 2 fleft(frac{x-y}{2}r...

Definition 1.1. Suppose that R is a commutative ring (possibly a field) and that A, B and C are R-modules. A function f : A× B → C is bilinear if • f (a1 + a2, b) = f (a1, b) + f (a1, b), • f (a, b1 + b2) = f (a, b1) + f (a, b2), and • f (ra, b) = f (a, rb) = r f (a.b). 1.2. The most basic examples of bilinear functions are the functions R×R→ R given by homogeneous quadratic polynomials of degr...

This paper examines with elementary proofs some interesting properties of numbers in the binary quadratic form a + ab+ b, where a and b are non-negative integers. Key findings of this paper are (i) a prime number p can be represented as a + ab + b if and only if p is of the form 6k + 1, with the only exception of 3, (ii) any positive integer can be represented as a +ab+ b if and only if its all...

has an Euler product and gave an explicit formulation for the Euler product. In this paper we develop the theory of binary quadratic forms in order to determine the Euler product for ∑∞ n=1 a(n)n −s, and other similarly defined Dirichlet series, in a completely elementary and natural manner. Let N, Z, R and C be the sets of natural numbers, integers, real numbers and complex numbers respectivel...

The Walsh transform Q̂ of a quadratic function Q : Fpn → Fp satisfies |Q̂(b)| ∈ {0, pn+s 2 } for all b ∈ Fpn , where 0 ≤ s ≤ n−1 is an integer depending on Q. In this article, we study the following three classes of quadratic functions of wide interest. The class C1 is defined for arbitrary n as C1 = {Q(x) = Trn( ∑b(n−1)/2c i=1 aix 2i+1) : ai ∈ F2}, and the larger class C2 is defined for even n a...