A Parallel Algorithm for the Estimation of the Global Error in Runge–Kutta Methods

The object of this work is the estimate of the global error in the numerical solution of the IVP for a system of ODE's. Given a Runge–Kutta formula of order q, which yields an approximation y _n to the true value y(x _n ), a general, parallel method is presented, that provides a second value y _n ^* of order q+2; the global error e _n =y _n –y(x _n ) is then estimated by the difference y _n –y _n ^*. The numerical tests reported, show the very good performance of the procedure proposed. A comparison with the code GEM90 is also appended.     

Exact Analysis of the State-Dependent Polling Model

We consider a polling model in which a number of queues are served, in cyclic order, by a single server. Each queue has its own distinct Poisson arrival stream, service time, and switchover time (the server's travel time from that queue to the next) distribution. A setup time is incurred if the polled queue has one or more customers present. This is the polling model with State-Dependent service (the SD model). The SD model is inherently complex; hence, it has often been approximated by the much simpler model with State-Independent service (the SI model) in which the server always sets up for a service at the polled queue, regardless of whether it has customers or not. We provide an exact analysis of the SD model and obtain the probability generating function of the joint queue length distribution at a polling epoch, from which the moments of the waiting times at the various queues are obtained. A number of numerical examples are presented, to reveal conditions under which the SD model could perform worse than the corresponding SI model or, alternately, conditions under which the SD model performs better than a corresponding model in which all setup times are zero. We also present expressions for a variant of the SD model, namely, the SD model with a patient server.     

Extreme Value Asymptotics for Multivariate Renewal Processes

For a sequence of partial sums ofd-dimensional independent identically distributed random vectors a corresponding multivariate renewal process is defined componentwise. Via strong invariance together with an extreme value limit theorem for Rayleigh processes, a number of weak asymptotic results are established for thed-dimensional renewal process. Similar theorems for the estimated version of this process are also derived. These results are suggested to serve as simultaneous asymptotic testing devices for detecting changes in the multivariate setting.     

On the third and fourth power moments of Fourier coefficients of cusp forms

The asymptotic formulae for the third and fourth power moments of Fourier coefficients of cusp forms are proved in this paper.     

A note on repeated games with non-monotonie value

We show that even when the information structure is independent of the state of nature, the value of then-stage zero-sum game with incomplete information is not necessarily monotonie with respect to the length of the game. More precisely, we give an example of such ann-stage game in whichV ₁ >V ₂ <V ₃.I am very grateful to Ehud Lehrer who introduced this question to me.     

Dead cores of singular Dirichlet boundary value problems with ϕ-Laplacian

The paper discusses the existence of positive solutions, dead core solutions and pseudodead core solutions of the singular Dirichlet problem (ϕ(u′))′ = λf(t, u, u′), u(0) = u(T) = A. Here λ is the positive parameter, A > 0, f is singular at the value 0 of its first phase variable and may be singular at the value A of its first and at the value 0 of its second phase variable. This work was supported by grant no. A100190703 of the Grant Agency of the Academy of Sciences of the Czech Republic and by the Council of Czech Government MSM 6198959214.     

矩阵奇异值分解理论在中文文本分类中的应用

用改进的截断与转换的矩阵奇异值分解算法,设计实现了基于字频特征的中文文本分类器.理论分析与实验结果表明,采用的方法提高了数值计算精度,降低了文本集特征空间的维数,简化了文本分类算法的时间复杂度,提高了文本分类准确率.     

带p-Laplacian算子的奇异脉冲微分方程正解的存在性

运用不动点指数理论,我们研究一类带p-Laplacian算子的奇异脉冲微分方程两点边值问题正解的存在性.     

亚纯函数的正规族与分担值

根据Nevanlinna理论讨论了一族亚纯函数中每个函数与其k(k为任一正整数)阶导数单向分担3个有限复值时的正规性,并举例说明这一结果是精确的.     

Pricing under quality of service uncertainty: Market segmentation via statistical QoS guarantees

This article examines how performance-contingent pricing schemes with long-term statistical performance guarantees can be applied to many IT services. We study two forms of performance-contingent pricing, with rebate proportional to failure rate and fixed rebate for below-threshold performance. We show that threshold-performance contingency pricing can increase both profits and fairness (customers who receive higher benefits pay higher effective price) relative to standard pricing. But an even better solution is to offer a menu of performance guarantees: this can increase the firm’s profit and segment the market. Only service providers whose performance level is sufficiently better than the industry standard can benefit from this pricing mechanism.