串联双路图的亏格分布

计算双路图的亏格分布是拓扑图论关注的一个问题,利用传递矩阵与向量积矩阵,给出了两类由双路图串联构建而成的两类闭链图的亏格分布.     

A-hypergeometric series and the Hasse–Witt matrix of a hypersurface

We give a short combinatorial proof of the generic invertibility of the Hasse–Witt matrix of a projective hypersurface. We also examine the relationship between the Hasse–Witt matrix and certain A-hypergeometric series, which is what motivated the proof.     

On the absolute matrix summability of Fourier series and some associated series

The object of the paper is to study the absolute matrix summability problem of Fourier series, conjugate series and some associated series under a new set of conditions on matrix methods, generalising many known results in the literature.     

A series of Siamese twin designs

A {0,±1}-matrix S is called a Siamese twin design sharing the entries of I if S=I+K−L, where I,K,L are nonzero {0,1}-matrices and both I+K and I+L are incidence matrices of symmetric designs with the same parameters. Let p and 2p+3 be prime powers and . We construct a Siamese twin design with parameters (4(p+1)²,2p²+3p+1,p²+p).     

On (N, p, q) summability factors of infinite series

In this paper a necessary and sufficient condition has been obtained for Σa_n∈_n to be summable |N, q| whenever Σa_n is bounded (N, p, q).     

Matrix summability and uniform convergence of series

Some classical results about uniform convergence of unconditionally convergent series are generalized to weakly unconditionally Cauchy series by means of the matrix summability method for regular matrices.

     

On general summability factor theorem of infinite series

A lower triangular matrix with nonzero principal diagonal entries is called a triangle. In this paper we obtain the sufficient conditions for ∑a_nλ_n to be summable ∣A∣_k whenever ∑a_n is summable ∣T∣_k for a triangle T.     

Optimal control of linear time-varying systems via Fourier series

The optimal control of linear time-varying systems with quadratic cost functional is obtained by Fourier series approximation. The properties of Fourier series are first briefly presented and the operational matrix of backward integration together with the product operational matrix are utilized to reduce the optimal control problem to a set of simultaneous linear algebraic equations. An illustrative example is included to demonstrate the validity and applicability of the technique.     

The spectra of nonnegative integer matrices via formal power series

We characterize the possible nonzero spectra of primitive integer matrices (the integer case of Boyle and Handelman's Spectral Conjecture). Characterizations of nonzero spectra of nonnegative matrices over and follow from this result. For the proof of the main theorem we use polynomial matrices to reduce the problem of realizing a candidate spectrum to factoring the polynomial as a product where the 's are polynomials in satisfying some technical conditions and is a formal power series in . To obtain the factorization, we present a hierarchy of estimates on coefficients of power series of the form to ensure nonpositivity in nonzero degree terms.

     

Universality and summability of trigonometric polynomials and trigonometric series

Periodica Mathematica Hungarica -     

Factorizing multivariate time series operators

Motivated by problems occurring in the empirical identification and modelling of a n-dimensional ARMA time series X(t) we study the possibility of obtaining a factorization (I + a₁B + … + a_pB^p) X(t) = [Π_i=1^p (I ? α_iB)] X(t), where B is the backward shift operator. Using a result in [3] we conclude that as in the univariate case such a factorization always exists, but unlike the univariate case in general the factorization is not unique for given a₁, a₂,…, a_p. In fact the number of possibilities is limited upwards by $\text{(np)!}\text{(n!)}{}^{\mathrm{p}}$, there being cases, however, where this maximum is not reached. Implications for the existence and possible use of transformations which removes nonstationarity (or almost nonstationarity) of X(t) are mentioned.     

Laguerre matrix polynomial series expansion: Theory and computer applications

This paper deals with the expansion of matrix functions in series of Laguerre matrix polynomials of a complex matrix parameter. A new asymptotic expression for positive and large x and n is obtained for this family of matrix polynomials that improves previous existing expressions. This expression is applied to improving the conditions imposed on the matrix function that are to be expanded in a series of non-hermitian Laguerre matrix polynomials, providing a new series expansion theorem that is more general than previous works. An application to solving linear differential systems without matrix exponentials is included.     

On application of matrix summability to Fourier series

Bor has recently obtained a main theorem dealing with absolute weighted mean summability of Fourier series. In this paper, we generalized that theorem for summability method. Also, some new and known results are obtained dealing with some basic summability methods.     

Absolute summability of infinite series

It is shown in [4] that if a normal matrix,A satisfies some conditions then |C,1| _k summability implies |A| _k summability wherek≥1. In the present paper, we consider the converse implication.     

Multivariate power series distributions and Neyman's properties for multinomials

A probelm of J. Neyman (in Classical and Contagious Discrete Distributions (G. P. Patil, Ed.), 1965, pp. 4–14) regarding a characterization of positive and negative multinomial distributions is studied in this paper. Some properties of multivariate power series distributions in general which should be of independent interest are also derived.     

Degree of approximation of functions associated with Hardy-Littlewood series in the generalized Hölder metric

The paper studies the degree of approximation of functions associated with Hardy Littlewood series in the generalized Hölder metric.     

An application of single-term Haar wavelet series in the solution of nonlinear oscillator equations

In this paper, a novel single-term Haar wavelet series (STHWS) method is implemented for the solution of the Duffing equation and Painleve’s transcendents (PI and PII). The results, in the form of a block pulse and a discrete solution, are presented. Unlike classical numerical schemes, the STHWS method has no restrictions on the coefficients of the Duffing equation as regards its solution. PI and PII are analysed as regards their solutions, up to nearest singularities (poles), using the STHWS. Also, an efficient computational implementation shows the remarkable features of wavelet based techniques.