随机利率下的Erlang(2)风险模型

本文主要对索赔记数过程是Erlang(2)过程,随机利率为一个L啨vy过程的风险模型进行了讨论.首先导出了破产概率满足的积分方程,估计了其上下界,然后针对随机利率为布朗运动以及漂移布朗运动的情况导出了破产概率满足的具体积分方程,最后讨论了罚金函数,并写出了罚金函数满足的积分方程以及在特殊情况下满足的积分微分方程.     

具有较小交换子群的限p-群I

研究了具有性质P的一类有限p-群,即:设G为有限p-群,M为其任一交换子群且满足|MZ(G)/Z(G)|≤p,则称群G满足性质P,得到了和满足性质P的群G同倾的群,以及群G满足性质P的一些充分或必要条件.     

满足任务要求的航材库存限额确定方法

针对航材需求不确定性大、保障经费紧张导致难以全面充分满足航材保障需求的问题,提出了航空兵团日常训练任务航材需求量和外地驻训任务航材携行量的确定方法.以满足日常训练任务的航材需求量为库存下限,满足日常训练任务和外地驻训任务的航材需求量为库存上限,确定了满足任务要求的航材库存限额标准,为实现航材精确保障提供了决策依据.最后结合实例验证了方法的可行性和有效性.     

关于满足ACC的*-λ-半环

从满足ACC的任何偏序集是pre-CPO出发,研究了满足ACC的偏序集上的定向集,并由此给出满足ACC的＊-λ-半环的一些性质.证明了S是满足ACC的＊-λ-半环,则S是局部闭＊-半环和连续＊-半环.进一步得到任何满足ACC的＊-λ-半环是对称＊-λ-半环。     

可拓逻辑的可满足性问题研究

可满足性是逻辑语义理论的基本概念.在分析基元命题内部的逻辑形式的基础上,研究了可拓逻辑的语法及语义理论,给出了可拓逻辑中的可满足性定义.讨论了矛盾问题的可拓逻辑表示,并给出了基于可满足性概念的矛盾问题定义和表示实例.     

一类完全重构滤波器的精度条件

本文研究了如何构造满足精度条件的小波滤波器.利用频域分析方法,给出了关于尺度函数精度条件的新结果以及满足精度条件的几个例子.     

时变参数动力系统的两种跟踪性质

在时变参数动力系统中引入链传递,伪轨跟踪以及渐进伪轨跟踪的概念,并通过这些概念讨论时变参数动力系统的伪轨跟踪和渐进伪轨跟踪的性质.证明了扩张的时变参数动力系统满足伪轨跟踪性质蕴含其满足渐近伪轨跟踪性质;论证了时变参数动力系统的积系统满足伪轨跟踪和渐进伪轨跟踪性质的充要条件是其每一个分系统也满足相应的性质.最后构造出了一个时变参数动力系统的例子:(∑∞X,F),证明了(∑∞X,F)是拓扑传递的,并且满足渐近伪轨跟踪性质.     

不动点迭代法的一点注记

对于迭代函数不满足收敛定理假定条件的情况 ,提出了一种简单方法 .此方法对于迭代函数满足收敛定理假定条件的情况 ,可以加速序列收敛 .最后给出了实例和程序 .     

自相似集的质量分布原理与Hausdorff测度及其应用

本文提出了满足开集条件的自相似集的质量分布原理.作为应用,得到了计算一类满足开集条件的自相似集的Hausdorff测度的准确值的方法,并举例说明了此方法对于计算一类满足开集条件的自相似集的Hausdorff测度的准确值是行之有效的.     

二维双曲守恒律的大时间步长Godunov方法(英文)

考虑了关于二维守恒律的大时间步长Godunov方法.该方法是关于一维问题的自然推广.证明了文中给出的数值流函数下,该方法是守恒的.进一步还给出了近似Riemann解应满足的条件,并且证明了利用满足这些条件的近似Riemann解的大时间步长Godunov方法守恒.最后,补充证明了满足这些条件的近似Riemann解是满足熵条件的.     

Orderings and Probability Functionals Consistent with Preferences

This paper unifies the classical theory of stochastic dominance and investor preferences with the recent literature on risk measures applied to the choice problem faced by investors. First, we summarize the main stochastic dominance rules used in the finance literature. Then we discuss the connection with the theory of integral stochastic orders and we introduce orderings consistent with investors' preferences. Thus, we classify them, distinguishing several categories of orderings associated with different classes of investors. Finally, we show how we can use risk measures and orderings consistent with some preferences to determine the investors' optimal choices.     

修正的IPA算法的建立及在不等式约束凸优化问题中的应用

本文首先对IPA算法进行了修正，并证明了修正IPA算法的收敛性，然后将修正后的IPA应用到不等式约束凸优化问题中得到新的内点算法，并与传统的障碍函数法作了比较，从理论上体现了新算法的优势，并给出了其工程解求解法以及收敛性的证明．     

The catwalk task: Reflections and synthesis: Part 2

In this article we recount our experiences with a series of encounters with the catwalk task and reflect on the professional growth that these opportunities afforded. First, we individually reflect on our own mathematical work on the catwalk task. Second, we reflect on our experiences working with a group of community college students on the catwalk task and our interpretations of their mathematical thinking. In so doing we also detail a number of innovative and novel student-generated representations of the catwalk photos. Finally, we each individually reflect on the entire experience with the catwalk problem, as mathematics learners, as teachers, and as professionals.     

Viscosity solutions for second order integro-differential equations without monotonicity condition: the probabilistic approach

In this paper, we establish a new existence and uniqueness result of a continuous viscosity solution for integro-partial differential equation (IPDE in short). The novelty is that we relax the so-called monotonicity assumption on the driver which is classically assumed in the literature of viscosity solutions of equation with non-local terms. Our method strongly relies on the link between IPDEs and backward stochastic differential equations with jumps for which we already know that the solution exists and is unique for general drivers. In the second part of the paper, we deal with the IPDE with obstacle and we obtain similar results.     

机械臂运动路径设计

采用D-H方法推导出了机械臂角度姿态与指尖空间位置的关系,以距离偏差为目标,建立了给定位置求机械臂参数的优化模型,并提出了二分步长接近式搜索算法求解该模型.进一步从实际工程精度要求出发,提出了确定精度求指令的方法.针对按照确定曲线运行的问题,采取了离散曲线而且相邻离散点之间一条指令可达的方法,并用改进的二分步长接近式搜索算法来求解.提出了解决避障问题的启发式算法和位姿空间变换法.还对机械臂结构进行了理论分析及论证,根据分析结果,针对旋转角度范围、角度量化、杆长选择等方面提出了一些建议.     

Positive solutions for ratio-dependent predator-prey interaction systems

In this paper, we study the dynamics of predator-prey interaction systems between two species with ratio-dependent functional responses. First we provide sufficient and necessary conditions for positive steady-state solutions, and then we investigate the relationships between positive equilibria and positive solutions of the system over a large domain. Furthermore, we deal with the uniqueness and the stability of positive steady-states solutions with some assumptions. In addition, we discuss the extinction and the persistence results of time-dependent positive solutions to the system.     

Stochastic integral with respect to set-valued square integrable martingales

In this paper, we shall firstly illustrate why we should consider integral of a stochastic process with respect to a set-valued square integrable martingale. Secondly, we shall prove the representation theorem of set-valued square integrable martingale. Thirdly, we shall give the definition of stochastic integral of a stochastic process with respect to a set-valued square integrable martingale and the representation theorem of this kind of integrals. Finally, we shall prove that the stochastic integral is a set-valued sub-martingale.     

General construction of symmetric parabolic structures

First we introduce a generalization of symmetric spaces to parabolic geometries. We provide construction of such parabolic geometries starting with classical symmetric spaces and we show that all regular parabolic geometries with smooth systems of involutive symmetries can be obtained in this way. Further, we investigate the case of parabolic contact geometries in great detail and we provide the full classification of those with semisimple groups of symmetries without complex factors. Finally, we explicitly construct all non-trivial contact geometries with non-complex simple groups of symmetries. We also indicate geometric interpretations of some of them.     

On the Theoretical and Numerical Control of a One-Dimensional Nonlinear Parabolic Partial Differential Equation

This paper deals with the analysis of the internal and boundary control of a one-dimensional parabolic partial differential equation with nonlinear diffusion. First, we prove a local null controllability result with distributed controls, locally supported in space. The proof relies on local inversion (more precisely, we use Liusternik’s Inverse Function Theorem), together with some appropriate specific estimates. We also establish a similar result with controls on one side of the boundary. Then, we consider an iterative algorithm for the computation of null controls, we prove the convergence of the iterates, and we perform some numerical experiments.     

Baskakov算子加权逼近的收敛阶

本文讨论了Ｂａｓｋａｋｏｖ算子加Ｊａｃｏｂｉ权逼近的收敛性，首先指出了按通常的加权范数，Ｂａｓｋａｋｏｖ算子是无界的。然后引入一种新的范数，在此范数下Ｂａｓｋａｋｏｖ算子具有压缩性，最后借助于Ｋ－泛函，我们着重讨论了它的特征刻划问题。