模糊数值函数的微分和梯度及其应用

基于Goetschel-Voxman所定义的序关系(Goetschel Jr R,Voxman W.Elementaryfuzzy calculus.Fuzzy Sets and Systems,1986,18:31-43),讨论了模糊数值函数的可微性,并利用梯度讨论了定义在n-维空间上的无约束条件模糊规划的最优性条件以及有约束条件的模糊规划取得最优解的必要条件—Kuhn-Tucker条件.同时,对于凸模糊规划问题,给出了其取得最优解的充分条件和算例.     

Revisiting Chiral Extrapolation by Studying a Lattice Quark Propagator

The quark propagator in the Landau gauge is studied on the lattice, including the quenched and the unquenched results. No obvious unquenched effects are found by comparing the quenched quark propagator with the dynamical one. For the quenched and unquenched configurations, the results with different quark masses have been computed. For the quark mass function, a nonlinear chiral extrapolating behavior is found in the infrared region for both the quenched and dynamical results.     

函数单调性的求解思维策略

函数单调性是函数的重要性质．对于常见的函数单调性问题，比如函数单调性的判断、证明等问题明确指明研究方向，解题过程有章可循，易于掌握．但是，对于有些数学问题，题型上比较新颖，题目表述不够直接，往往使学生不知所措，甚至看不懂题，无从下手．这类题目需要进行合理转化，数学思维具有一定的跳跃性．     

注重函数模型构建,探究实际应用问题

随着社会科技的发展,数学与其他学科的联系日趋密切,数学的应用越来越广泛,因此构建数学模型、解决实际问题已成为近几年的考试热点之一.这类问题贴近生活,贴近社会,有利于体现数学的人文价值和社会价值,有利于考查学生分析、猜想、建模和综合应用等各方面的能力.     

探讨罗列法与函数法判断仪表刻度均匀的优劣

随着社会的发展,越来越多的先进仪器、表盘进入我们的生活中,如汽车里的油量表、速度盘,市场上的电子秤,工厂车间里监控着机器运转的各种仪表等;它们与生活息息相关.这些仪表上的刻度有     

ON THE EXPECTED DISCOUNTED PENALTY FUNCTION IN A MARKOV-DEPENDENT RISK MODEL WITH CONSTANT DIVIDEND BARRIER

This article considers a Markov-dependent risk model with a constant dividend barrier. A system of integro-differential equations with boundary conditions satisfied by the expected discounted penalty function, with given initial environment state, is derived and solved. Explicit formulas for the discounted penalty function are obtained when the initial surplus is zero or when all the claim amount distributions are from rational family. In two state model, numerical illustrations with exponential claim amounts are given.