Remarks on Rational Approximations of Multiple Power Series

The z-transform supplies a definition of rational approximationsto multiple power series similar to Watson's (1974) using thealgorithm. We discuss the properties of these approximants andwe give some examples in particular for accelcrating convergencein quadrature problems.     

Some Aspects of Degeneracy in Rational Approximations

The phenomenon of degeneracy in rational approximations is shownto be related to the vanishing of the coefficient of the highestpower in either numerator or denominator. Using this fact andsome theorems proved about the behaviour of best rational approximationsin a neighbourhood of a pole of the approximating function,it is shown that various known examples of degeneracy are readilypredictable and that the methods introduced can be used to predictother instances of degeneracy.     

New Rational Interpolation Basis Functions on the Unbounded Intervals and Their Applications

Based on the rational system of Legendre rational functions, we construct two set of new interpolation basis functions on the unbounded intervals. Their explicit expressions are derived, and fast and stable algorithms are provided for computing the new basis functions. As applications, new rational collocation methods based on these new basis functions are proposed for solving various second-order differential equations on the unbounded domains. Numerical experiments illustrate that our new methods are more effective and stable than the existing collocation methods.     

Strong Approximations of Martingale Vectors and Their Applications in Markov-Chain Adaptive Designs

The strong approximations of a class of R~d-valued martingales are considered.The conditions usedin this paper are easier to check than those used in [3] and [9].As an application,the strong approximation ofa class of non-homogenous Markov chains is established,and the asymptotic properties are established for themulti-treatment Markov chain adaptive designs in clinical trials.     

On Inhomogeneous Diophantine Approximations with Rational Terms and Applications to Elliptic and Trigonometric Functions

We investigate inhomogeneous diophantine approximation problems of the type ¦qθ ? p t- α¦. Lower bounds for the error terms are proved in the case of arbitrarily chosen rational α’s. Applications are given to elliptic and trigonometric functions extending former results of the author and others.     

Renewal Approximations of the Switched Poisson Processes and Their Applications to Queueing Systems

The switched Poisson process (SPP), also known as the doubly stochastic Poisson process, has been widely used in the modelling of point processes whose rates vary subject to some random mechanism. The class of SPP includes a wide range of both renewal and non-renewal processes with squared coefficients of variation being larger than one. In this paper, we survey various approaches to approximate a non-renewal process by a renewal process. We derive the expressions for the first two moments of the inter-renewal time of a renewal process that approximates the SPP. We illustrate the quality of these approximations with numerical results in queueing applications. We believe that our approximations have potential applications in areas such as reliability, inventory control, telecommunications and maintenance.     

New Integral Transformations and Their Applications to Some Boundary-Value Problems of Mathematical Physics

We construct new integral transformations and present their applications to the construction of exact solutions of some boundary-value problems of mathematical physics. We solve the problem of diffraction of acoustic waves in a circular cone truncated by two spherical surfaces. We also solve the initial boundary-value problem of the theory of heat conduction for the same truncated cone under nonzero initial conditions.     

关于单形的几个不等式及其应用

Using theory of distance geometry and analytic method, the problem on relations about the volumes of some simplices is studied, and some new inequalities for the volumes of simplices are established. As special cases, an inequality for the volume of the pedal simplex of a simplex and other inequalities for simplices are gotten.     

Uniform Continuity of Generalized Rational Approximations

In this paper, it is shown that there are no uniformly continuous multiplicative $\varepsilon $ -selections from $C[0;1]$ on the set of generalized rational fractions of sufficiently general form for small $\varepsilon $ .     

一类微分从属性及其应用

记△={|z|<1}.设函数(?):C~2×△→C在区域D(?)C中解析,G是△中的单叶解析函数.若△中的解析函数p(z)满足微分从属关系(?)(p(z),zp’(z);z)(?)G(z),z∈△,则可确定(?)和G的某些条件使之Re p(z)>p(z∈△),并且给出这些结果的某些应用.     

某些组合弹性结构的数学模型及其有限元逼近

§1.引言 自70年代后期冯康教授提出组合弹性结构的数学理论及其有限元方法以来,已经有了进一步的理论工作及大量的应用.近年来P.G.Ciarlet等开展了一系列的研究工作。 本文根据中提出的方法详细考虑了一个简单的3维—2维组合结构的数学模型及其有限元逼近.在最后一节,考虑其他的3维—2维弹性结构.     

Rational Approximations of Riemann--Liouville and Weyl Fractional Integrals

We obtain exact rational approximation orders for functions expressible as Riemann--Liouville and Weyl fractional integrals. New results and the strengthening and generalization of theorems due to Popov, Petrusheva, Pekarskii, Rusak, and the author, which are well known in the theory of rational approximation of differentiable functions, are obtained as consequences of theorems due to Pekarskii related to rational approximation of functions from the Hardy--Sobolev classes in the unit disk.     

Asymptotic Two-Point Approximations by Rational Function

Continuous functions in 0 ≤ s ≤ ∞ with asymptotic power expansions both for t → +0 and t → +∞ are approximated by rational functions, being generalized Padé approximants both for s → +0 and s → +∞. The existence and the uniform convergence of such approximants are proved. As examples, piecewise rational functions, square roots of rational functions, and a modified error function are considered.     

Euler Approximations of Solutions of Abstract Equations and Their Applications in the Theory of Semigroups

Using the Euler approximations of solutions of abstract differential equations, we obtain new approximation formulas for C ₀-semigroups and evolution operators.     

几种新的截集及其应用

本文从“邻域”和“重域”的观点出发引入了三种新的截集：下截集，下重截集和上重截集。我们给出这些截集的性质及相应的分解定理，表现定理和扩展原理，作为应用，我们讨论了两方面的内容；一是利用落影表现理论，将一个模糊集看作“重云”的落影，然后用下生截集和落影表现理论来定义模糊集的运算，得到了与“２”一致的结果。     

Piecewise Rational Approximations of Real Algebraic Curves

1.IntroductionAnaJgebraicplanecurveCofdegreedinn2isimplicitlydefinedbyasinglepolynomialequationf(x,y)=Oofdegreedwithcoefficientsinn.Arationalalgebraiccurveofdegreedinn2canadditionaJlybedefinedbyrationalparametricequationswhicharegivenas(x=G1(u),y=G2(u)),whereG1andG2arerationalfunctionsinuofdegreed,i.e-,eachisaquotientofpolynomiaJ8inuofmtalmumdegreedwithcoefficientsinn.ffetionalcurvesaxeonlyasubsetofimplicitalgebraiccurvesofdegreed+1.Whi1eaJldegreetwocurves(conics)arerational,oIilyasubsetof…     

关于有限与无限级数的新的反演级数关系及应用

Some new series inversion formulas of the general form.