Optimal normal bases are special cases of the so-called Gauss periods (Disquisitiones Arithmeticae, Articles 343-366); in particular, optimal normal bases are Gauss periods of type (n,1) for any characteristic and type (n,2) for characteristic 2. We present the multiplication tables and complexities of Gauss periods of type (n, t) for all n and t = 3,4,5 over any finite field and give a slightl...

properties of the hybrid of block-pulse functions and lagrange polynomials based on the legendre-gauss-type points are investigated and utilized to define the composite interpolation operator as an extension of the well-known legendre interpolation operator. the uniqueness and interpolating properties are discussed and the corresponding differentiation matrix is also introduced. the applicabili...

A Gauss paragraph is a combinatorial formulation of a generic closed curve with multiple components on some surface. A virtual string is a collection of circles with arrows that represent the crossings of such a curve. Every closed curve has an underlying virtual string and every virtual string has an underlying Gauss paragraph. A word-wise partition is a partition of the alphabet set of a Gaus...

We study the Gauss map of minimal surfaces in the Heisenberg group Nil3 endowed with a left-invariant Riemannian metric. We prove that the Gauss map of a nowhere vertical minimal surface is harmonic into the hyperbolic plane H. Conversely, any nowhere antiholomorphic harmonic map into H is the Gauss map of a nowhere vertical minimal surface. Finally, we study the image of the Gauss map of compl...

In this paper, we report that we have solved the SVP Challenge over a 128-dimensional lattice in Ideal Lattice Challenge from TU Darmstadt, which is currently the highest dimension in the challenge that has ever been solved. The security of lattice-based cryptography is based on the hardness of solving the shortest vector problem (SVP) in lattices. In 2010, Micciancio and Voulgaris proposed a G...

The development of numerical techniques now permits us to analyze complex structures such as dielectric resonator filters and planar passive elements for coplanar monolithic microwave integrated circuits. In this paper, we describe a novel method for designing dielectric resonator filters. Then a Chebychev band pass filter is designed by coaxially placing high-Q TM01Q dielectric resonators ...

This paper is concerned with the approximation of matrix functionals defined by a large, sparse or structured, symmetric definite matrix. These functionals are Stieltjes integrals with a measure supported on a compact real interval. Rational Gauss quadrature rules that are designed to exactly integrate Laurent polynomials with a fixed pole in the vicinity of the support of the measure may yield...

Department of Mathematics, University of Gaziantep, Gaziantep, Turkey e-mail address : [email protected] Abstract For the practical estimation of the error of Gauss quadrature rules Gauss-Kronrod rules are widely used; but, it is well known that for the generalized Hermite weight function, ωα(x) = |x|2α exp(−x2) over [−∞,∞], real positive Gauss-Kronrod rules do not exist. Among the alternati...

EEG signals contain information directly related to cognitive activity. This paper presents a method classify the images person imagines via provided by signals. The relating objects ‘tree’, ‘house’, ‘plane’ and ‘dog’ have been reconstructed. We used convolutional neural networks obtain reconstruction of genetic algorithm find parameters this network. results obtained evaluated means Chebychev ...

We are concerned with the numerical exact controllability of semilinear wave equation on interval (0, 1). introduce a Picard iterative scheme yielding sequence approximated solutions which converges towards solution null problem, provided that initial data small enough. The boundary control, is applied at endpoint $$x=1$$ , taken in space $$H^1_0(0,T)$$ for $$T=2$$ . For linear part, control in...