Introduction: Epilepsy is a clinical syndrome in which seizures have a tendency to recur. Sodium valproate is the most effective drug in the treatment of all types of generalized seizures. Finding the optimal dosage (the lowest effective dose) of sodium valproate is a real challenge to all neurologists. In this study, a new approach based on Adaptive Neuro-Fuzzy Inference System (ANFIS) was pre...

Three approaches are currently used for devising identitybased encryption schemes. They respectively build on pairings, quadratic residues (QR), and lattices. Among them, the QR-based scheme proposed by Cocks in 2001 is notable in that it works in standard RSA groups: its security relies on the standard quadratic residuosity assumption. But it has also a number of deficiencies, some of them hav...

Article history: Received 3 October 2014 Accepted 17 February 2015 Available online 9 March 2015 Submitted by J.F. Queiro MSC: 90C22 15A39 90C20

The problem of moments has been studied for more than a century. This paper discusses a practical issue related to the problem of moments namely the bounding of a distribution based on a given number of moments. The presented approach is unified in the sense that all measures of interests are provided as a quadratic expression of the same Hankel-matrix. Application examples indicate the importa...

In this paper, we prove that there does not exist a set with more than 98 nonzero polynomials in Z[X], such that the product of any two of them plus a quadratic polynomial n is a square of a polynomial from Z[X] (we exclude the possibility that all elements of such set are constant multiples of a linear polynomial p ∈ Z[X] such that p2|n). Specially, we prove that if such a set contains only po...

We consider quadratic eigenproblems (

We focus on a very specific case of the Uniform Boundedness Conjecture, namely, bounding the number of possible c such that the quadratic polynomial φc(z) = z2 + c has quadratic periodic points of some small period. We show that there are infinitely many rational c with quadratic 4-cycles, with all such c completely understood; and only finitely many rational c with quadratic 5-cycles (we conje...

In this paper we prove a function field version of a theorem by Rudnick and Soundararajan about lower bounds for moments of quadratic Dirichlet L–functions. We establish lower bounds for the moments of quadratic Dirichlet L–functions associated to hyperelliptic curves of genus g over a fixed finite field Fq in the large genus g limit.

A sampling-based optimization method for quadratic functions is proposed. Our method approximately solves the following n-dimensional quadratic minimization problem in constant time, which is independent of n: z∗ = minv∈Rn〈v, Av〉 + n〈v,diag(d)v〉 + n〈b,v〉, where A ∈ Rn×n is a matrix and d, b ∈ R are vectors. Our theoretical analysis specifies the number of samples k(δ, ) such that the approximat...

A new quasi-Newton scheme for updating a low rank positive semi-definite Hessian approximation is described, primarily for use in sequential quadratic programming methods for nonlinear programming. Where possible the symmetric rank one update formula is used, but when this is not possible a new rank two update is used, which is not in the Broyden family, although invariance under linear transfo...