Complementary multiplicative hyperrings

In this paper the complementary hyperstructure obtained from a multiplicative hyperring is considered. Furthermore a characterization for such hyperstructures obtained starting from a strongly distributive multiplicative hyperring is given.     

Strongly distributive multiplicative hyperrings

The aim of this paper is to characterize the strongly distributive multiplicative hyperrings. A non trivial example is provided giving a model for such hyperrings; also a characterization theorem is proved.Dedicated to G. Tallini on the occasion of his 60^th birthday.Research supported by G.N.S.A.G.A. — C.N.R.     

A fundamental relation between predictor identification and power spectrum estimation

Summary An asymptotic linear relation between the FPE (final prediction error) of the predictor obtained by using the least squares estimate of autoreggression coefficients and the integrated relative mean square error of the estimate of power spectrum obtained from the fitted autoregression model is established. This relation provides a link between the predictor identification and the power spectrum estimation and has already been used as a theoretical background of a former paper [3]. The Institute of Statistical Mathematics     

The fundamental theorem on the relation between spin and statistics

The fundamental theorem on the connection of spin and statistics is deduced from the basic symmetry between emission and absorption processes in quantum field theory. The new theorem which prescribes the physical connection of Bose fields with integral spin and Fermi fields with half-integral spin, is valid for all field theories; and it contains Pauli’s theorem as a special case.     

组合优化若干经典问题新进展

组合优化是20世纪中后期发展起来的一个运筹学与计算机科学交叉学科分支, 研究具有离散结构的优化问题解的性质和求解方法. 由于不同离散问题的结构差异, 出现了各种各样的研究手段和技巧. 针对组合优化的若干经典问题, 简述了算法和复杂性理论的研究进展.     

New nonlinear estimates for surfaces in terms of their fundamental forms

We establish several estimates of the distance between two surfaces immersed in the three-dimensional Euclidean space in terms of the distance between their fundamental forms, measured in various Sobolev norms. These estimates, which can be seen as nonlinear versions of linear Korn inequalities on a surface appearing in the theory of linearly elastic shells, generalize in particular the nonlinear Korn inequality established in 2005 by P. G. Ciarlet, L. Gratie, and C. Mardare.     

Exploring students' mathematical performance,metacognitive experiences and skills in relation to fundamental theorem of calculus

Several studies have explored students’ understanding of the relationships between definite integrals and areas under curve(s). So far, however, there has been less attention to students’ understanding of the Fundamental Theorem of Calculus (FTC). In addition, students’ metacognitive experiences and skills whilst solving FTC questions have not previously been explored. This paper explored students’ mathematical performance, metacognitive experiences and metacognitive skills in relation to FTC questions by interviewing nine university and eight Year 13 students. The findings show that several students had difficulty solving questions related to the FTC and that students’ metacognitive experiences and skills could be further developed.     

New relation formula for generating functions

Periodica Mathematica Hungarica - In this paper, we develop a new relation between certain types of generating functions using formal algorithmic methods. As an application, we give a relation...     

Chaos in a four-dimensional system consisting of fundamental lag elements and the relation to the system eigenvalues

A simple system consisting of a second-order lag element (a damped linear pendulum) and two first-order lag elements with piecewise-linear static feedback that has been derived from a power system model is presented. It exhibits chaotic behavior for a wide range of parameter values. The analysis of the bifurcations and the chaotic behavior are presented with qualitative estimation of the parameter values for which the chaotic behavior is observed. Several characteristics like scalability of the attractor and globality of the attractor-basin are also discussed.     

On the fundamental group-scheme

We show that the fundamental group-scheme of a separably rationally connected variety defined over an algebraically closed field is trivial. Let X be a geometrically irreducible smooth projective variety defined over a finite field k admitting a k-rational point. Let {En,σn}_n?0 be a flat principal G-bundle over X, where G is a reductive linear algebraic group defined over k. We show that there is a positive integer a such that the principal G-bundle is isomorphic to E₀, where FX is the absolute Frobenius morphism of X. From this it follows that E₀ is given by a representation of the fundamental group-scheme of X in G.     

On fundamental skew distributions

A new class of multivariate skew-normal distributions, fundamental skew-normal distributions and their canonical version, is developed. It contains the product of independent univariate skew-normal distributions as a special case. Stochastic representations and other main properties of the associated distribution theory of linear and quadratic forms are considered. A unified procedure for extending this class to other families of skew distributions such as the fundamental skew-symmetric, fundamental skew-elliptical, and fundamental skew-spherical class of distributions is also discussed.