首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 15 毫秒
1.
《Quaestiones Mathematicae》2013,36(1-2):357-378
Abstract

Semi-infinite block Toeplitz operators with rational matrix symbols are inverted explicitly by employing the factorization method. All formulas are based on a special representation of the symbol involving a quintet of matrices, which differs from the ones that have been used earlier.  相似文献   

2.
We discuss the convergence and numerical evaluation of simultaneous quadrature formulas which are exact for rational functions. The problem consists in integrating a single function with respect to different measures using a common set of quadrature nodes. Given a multi-index n, the nodes of the integration rule are the zeros of the multi-orthogonal Hermite–Padé polynomial with respect to (S, α, n), where S is a collection of measures, and α is a polynomial which modifies the measures in S. The theory is based on the connection between Gauss-type simultaneous quadrature formulas of rational type and multipoint Hermite–Padé approximation. The numerical treatment relies on the technique of modifying the integrand by means of a change of variable when it has real poles close to the integration interval. The output of some tests show the power of this approach in comparison with other ones in use.  相似文献   

3.
In analogy to valuation characterizations and kinematic formulas of convex geometry, we develop a combinatorial theory of invariant valuations and kinematic formulas for finite lattices. Combinatorial kinematic formulas are shown to have application to some probabilistic questions, leading in turn to polynomial identities for Möbius functions and Whitney numbers.  相似文献   

4.
Motivated by the resemblance of a multivariate series identity and a finite analogue of Euler's pentagonal number theorem, we study multiple extensions of the latter formula. In a different direction we derive a common extension of this multivariate series identity and two formulas of Lucas. Finally we give a combinatorial proof of Lucas’ formulas.  相似文献   

5.
For an arbitrary rational matrix function, not necessarily analytic at infinity, the existence of a right canonical Wiener-Hopf factorization is characterized in terms of a left canonical Wiener-Hopf factorization. Formulas for the factors in a right factorization are given in terms of the formulas for the factors in a given left factorization. All formulas are based on a special representation of a rational matrix function involving a quintet of matrices.  相似文献   

6.
We investigate the wavelet transforms of tempered distributions in a way that closely links their Fourier transforms and wavelet transforms. Two exchange formulas of the convolution and the multiplication of wavelet transforms of tempered distributions are established. We call these formulas the quasi-exchange formulas for wavelet transforms of distributions, because of the resemblance between these formulas and the well-known exchange formula for Fourier transforms.  相似文献   

7.
8.
This survey is devoted to one of the most general Laplace-type integral transforms, the so-called Obrechkoff integral transform, introduced and studied for the first time by Obrechkoff[25]. It has been modified by Dimovski [5],[6] and used as a basis of a Mikusinski-type operational calculus for the hyper-Bessel differential operators of arbitrary order. Later, in a series of papers Dimovski and Kiryakova [8],[9],[10] have found operational properties, complex and real inversion formulas, Abel-type theorems for the Obrechkoff transform. This theory has been further developed by Kiryakova [16],[17],[18] using the tools of the Meijer's G-functions and of the fractional calculus. Namely, a new definition as a G-transform has been given for the Obrechkoff transform. The hyper-Bessel operators themselves, have given rise to a new generalized fractional calculus and further extensive use of the G-functions. Many other generalized differentiation and integration operators happen to be special cases in this calculus, too. Special cases of the Obrechkoff transform have been "rediscovered" later by many authors. We give examples how their results could be derived from the general ones surveyed here.  相似文献   

9.
Based on the relation of exponential maps and interior products in exterior algebras, some formulas of Pfaffians, including expansion formulas and the Cayley-Jacobi formula for determinants of alternating matrices, are deduced with new proofs. As an application, Pfaffian powers of alternating bilinear forms [O. Loos, Discriminant algebras and adjoints of quadratic forms, Beiträge Algebra Geom. 38 (1997) 33-72] are interpreted in terms of exponential maps in algebras of alternating multi-linear forms.  相似文献   

10.
Divided differences provide an efficient method for computing with functions of several variables.In this note, we use them to generalize the Newton interpolation formula, and obtain an orthogonality relation (3.3). From this, we deduce two inversion formulas (3.4) and (3.8) involving two infinite sets of variables.The generating functions (1.1) to (1.4) of Carlitz and Howard are obtained by a mere specialization of variables in the preceding inversion formulas.As an illustration, we show how to recover several identities due to Carlitz and Lehmer, and we give a newq-analog of the generating series of the Howard numbers (formulas 4.22 and 4.23).
  相似文献   

11.
Explicit formulas for triangular factors of Cauchy and Vandermonde matrices and their inverses in terms of entries of these matrices are presented.  相似文献   

12.
用保险精算法,在标的资产价格服从分数跳-扩散过程,且风险利率、波动率和期望收益率为时间的非随机函数的情况下,给出了欧式复合期权的定价公式.结果推广了Gukhal以及Li等关于传统跳-扩散模型下的欧式复合期权的定价公式.  相似文献   

13.
We study Minkowski contents and fractal curvatures of arbitrary self-similar tilings (constructed on a feasible open set of an IFS) and the general relations to the corresponding functionals for self-similar sets. In particular, we characterize the situation, when these functionals coincide. In this case, the Minkowski content and the fractal curvatures of a self-similar set can be expressed completely in terms of the volume function or curvature data, respectively, of the generator of the tiling. In special cases such formulas have been obtained recently using tube formulas and complex dimensions or as a corollary to results on self-conformal sets. Our approach based on the classical Renewal Theorem is simpler and works for a much larger class of self-similar sets and tilings. In fact, generator type formulas are obtained for essentially all self-similar sets, when suitable volume functions (and curvature functions, respectively) related to the generator are used. We also strengthen known results on the Minkowski measurability of self-similar sets, in particular on the question of non-measurability in the lattice case.  相似文献   

14.
本文介绍的一组计算煤炭低位发热量公式,是在收集了我国各个不同地区、不同煤种的煤样3000多个的基础上,对其进行分类,采用回归分析的方法得到。与国内外现行公式比较,具有使用简单,计算快捷,更为精确的特点。  相似文献   

15.
A formula ?(x) in the one non-logical symbol ? with one free variable x is Russell if the sentence Vχ(χ ? τ ? Φ (χ)) is logically valid. This note describes a pattern common to the classical examples of Russell formulas, adds a couple of new ones, and constructs many formulas that are near-Russell.  相似文献   

16.
We derive left and right quotient representations for central q × q matrix-valued Carathéodory functions. Moreover, we obtain recurrent formulas for the matrix polynomials involved in the quotient representations. These formulas are the starting point for getting recurrent formulas for those matrix polynomials which occur in the Arov-Krein resolvent matrix for the nondegenerate matricial Carathéodory problem.  相似文献   

17.
Starting from recent formulas for calculating the permanents of some sparse circulant matrices, we obtain more general formulas expressing the permanents of a wider class of matrices as a linear combination of appropriate determinants.  相似文献   

18.
19.
This paper continues the recent work of the authors’ [R.-C. Li, W. Zhang, The rate of convergence of GMRES on a tridiagonal Toeplitz linear system, Numer. Math. 112 (2009) 267-293 (electronically published on 19 December 2008)] on the rate of convergence of GMRES for a tridiagonal Toeplitz linear system Ax=b. Much simpler formulas than the earlier ones for GMRES residuals when b is the first or the last column of the identity matrix are established, and these formulas allow us to confirm the rate of convergence that was conjectured but only partially proven earlier. Simpler and sharper bounds than earlier ones when all b’s entries, except its first and last ones, are zeros are also obtained.  相似文献   

20.
The Padua points are a family of points on the square [−1, 1]2 given by explicit formulas that admits unique Lagrange interpolation by bivariate polynomials. Interpolation polynomials and cubature formulas based on the Padua points are studied from an ideal theoretic point of view, which leads to the discovery of a compact formula for the interpolation polynomials. The L p convergence of the interpolation polynomials is also studied. S. De Marchi and M. Vianello were supported by the “ex-60%” funds of the University of Padua and by the INdAM GNCS (Italian National Group for Scientific Computing). Y. Xu was partially supported by NSF Grant DMS-0604056.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号