The implications of costs, capacity, and competition on product line selection

We consider a situation in which a manufacturer has to select the product(s) to sell as well as the selling price and production quantity of each selected product. There are two substitutable products in the consideration set, where product 2 has a higher quality and reservation price than that of product 1. By considering the cannibalization effect that depends on the selling price of each product, the manufacturer needs to evaluate the profit function associated with three different product line options: sell both products or only one of the 2 products. In order to examine the impact of costs, capacity, and competition on the optimal product line selection, optimal price, and optimal production quantity analytically, we present a stylized model in this paper so that we can determine the conditions under which a particular option is optimal.     

The gerber-shiu expected discounted penalty function for Lévy insurance risk processes

In this paper,we study a general Lévy risk process with positive and negative jumps.A renewal equation and an infinite series expression are obtained for the expected discounted penalty function of this risk model.We also examine some asymptotic behaviors for the ruin probability as the initial capital tends to infinity.     

小时滞梯度系统的动力学行为

该文研究下列具有小时滞的一般非线性梯度型发展方程_tu+Au=f(u(t),u(t-τ)).证明了当时间趋于无穷大时,时滞方程的每一个有界解将收敛于某一个平衡点,只要时滞足够小,这意味着时滞系统的行为非常类似非时滞系统.这里的方法主要是基于梯度系统不变集的Morse结构和发展方程的几何理论.这个结果的证明分两步完成:首先,在梯度系统和有限个孤立平衡点的假设下,证明了一定存在一个足够小的时滞使得时滞方程的任一个有界解将会最终进入并停留在某一个平衡点的邻域里面;其次,在双曲平衡点的假设下,运用指数二分性和一系列的估计,证明了一定存在ε0和足够小的τ0使得任一个落于某个平衡点ε-邻域内的解最终收敛于该平衡点,当时间趋于无穷大时.     

熵极小动力系统的复杂性

设X是一个紧致度量空间,f:X→X是一个连续映射,(X,f)是熵极小的.该文首先证明了f是强遍历的;另外,如果还假设X中存在f的一个真的(拟)弱几乎周期点,则得到f具有正拓扑熵且对任意的n1,f~n是遍历敏感依赖的.因此,f在Li-Yorke和Takens-Ruelle意义下是混沌的.该文所得结论改进和推广了最近的一些结论.     

Matrix inverse problem and its optimal approximation problem for R-skew symmetric matrices

Let R ∈ C^n×n be a nontrivial involution, i.e., R² = I and R ≠ ±I. A matrix A ∈ C^n×n is called R-skew symmetric if RAR = −A. The least-squares solutions of the matrix inverse problem for R-skew symmetric matrices with R∗ = R are firstly derived, then the solvability conditions and the solutions of the matrix inverse problem for R-skew symmetric matrices with R∗ = R are given. The solutions of the corresponding optimal approximation problem with R∗ = R for R-skew symmetric matrices are also derived. At last an algorithm for the optimal approximation problem is given. It can be seen that we extend our previous results [G.X. Huang, F. Yin, Matrix inverse problem and its optimal approximation problem for R-symmetric matrices, Appl. Math. Comput. 189 (2007) 482-489] and the results proposed by Zhou et al. [F.Z. Zhou, L. Zhang, X.Y. Hu, Least-square solutions for inverse problem of centrosymmetric matrices, Comput. Math. Appl. 45 (2003) 1581-1589].     

On the nonexistence of a global nontrivial subsonic solution in a 3D unbounded angular domain

In this paper, under some assumptions on the flow with a low Mach number, we study the nonexistence of a global nontrivial subsonic solution in an unbounded domain Ω which is one part of a 3D ramp. The flow is assumed to be steady, isentropic and irrotational, namely, the movement of the flow is described by the potential equation. By establishing a fundamental a priori estimate on the solution of a second order linear elliptic equation in Ω with Neumann boundary conditions on Ω and Dirichlet boundary value at some point of Ω, we show that there is no global nontrivial subsonic flow with a low Mach number in such a domain Ω.     

Asymptotically optimal dividend policy for regime-switching compound Poisson models

This work develops asymptotically optimal dividend policies to maximize the expected present value of dividends until ruin.Compound Poisson processes with regime switching are used to model the surplus and the switching（a continuous-time controlled Markov chain） represents random environment and other economic conditions.Assuming the switching to be fast varying together with suitable conditions,it is shown that the system has a limit that is an average with respect to the invariant measure of a related Markov chain.Under simple conditions,the optimal policy of the limit dividend strategy is a threshold policy.Using the optimal policy of the limit system as a guide,feedback control for the original surplus is then developed.It is demonstrated that the constructed dividend policy is asymptotically optimal.     

Uniform estimate for the tail probabilities of randomly weighted sums

Several authors have studied the uniform estimate for the tail probabilities of randomly weighted sumsa.ud their maxima. In this paper, we generalize their work to the situation thatis a sequence of upper tail asymptotically independent random variables with common distribution from the is a sequence of nonnegative random variables, independent of and satisfying some regular conditions. Moreover. no additional assumption is required on the dependence structureof {θi,i≥ 1）.     

天然气消费量的偏最小二乘支持向量机预测

结合偏最小二乘法和支持向量机的优缺点,提出基于偏最小二乘支持向量机的天然气消费量预测模型。首先,利用偏最小二乘法确定影响天然气消费量的新综合变量,建立以新综合变量为输入,天然气消费量为输出的支持向量机模型,对天然气消费量进行了预测;然后,与多元回归、偏最小二乘回归、普通支持向量机做误差检验比较,验证该方法的可行性与正确性。结果表明,此天然气消费量预测模型具有较高的精确度和应用价值。     

Interactions of delta shock waves for the relativistic Chaplygin Euler equations with split delta functions

In this article, we are concerned with the interactions of delta shock waves with contact discontinuities for the relativistic Euler equations for Chaplygin gas by using split delta functions method. The solutions are obtained constructively and globally when the initial data consists of three piecewise constant states. The global structure and large time‐asymptotic behaviors of the solutions are analyzed case by case. During the process of the interaction, the strengths of delta shock waves are computed completely. Moreover, it can be found that the Riemann solutions are stable for such small perturbations with special initial data by letting perturbed parameter ε tends to zero. Copyright © 2014 John Wiley & Sons, Ltd.