变截面功能梯度棒的一维全约束热应力

求解了变截面功能梯度棒的一维全约束热应力问题.假设棒在热膨胀主轴上没有剪应力只有纵向应变,且沿热膨胀的主轴,棒的线膨胀系数和弹性模量呈幂函数变化.材料力学观点下计算了棒自由时的缩短量和棒受未知拉力时的伸长量,并借助全约束假设令其相等,确定未知拉力值,进一步得到棒沿热膨胀主轴上热应力分布的解析解.结果进行退化后可得到与均匀棒相关问题完全一致的结果.数值算例详细的分析了圆孔半径以及功能梯度参数等对热应力的影响.     

求总极值的区间压缩方法

对求解无约束最优化问题 ,本文给出了一个区间压缩方法 .应用此方法能使函数值按几何级数收敛于 f (x)的极小值 ,并且计算量远小于郑权等人方法的计算量     

一类发烟装液弹装填率的数学模型

装液弹的装填率对弹的安全可靠性极其重要 .如果装液弹的装填率不合理 ,不是造成弹腔容积的浪费 ,就会造成弹内压过大 ,易于破坏密封性能引起渗漏甚至破裂而造成损失和危险 .本文通过对一类发烟装液炮弹弹内压力分析 ,得出了弹内压力计算公式 .在分析压力诸因素时 ,我们运用了固体热膨胀理论 ;考虑了液体的压缩性 .这是本文区别于以往压力计算的两个特点 .通过这类发烟装液炮弹内压压力曲线的分析 ,导出了装液 (炮 )弹弹腔空隙率合理选定最后的数学模型 (PLT方程——可由此确定合理的装填率 ) ,由此所计算的空隙率数据与国外文献值相符 ,并引入了“预极限温度”的概念 .可以相信 ,所谓“预极限温度”,将是装液 (炮 )弹 (或任何装液容器 )设计者必须认真考虑的问题     

关于集中载荷下圆板非线性弯曲问题的解析电算求解*

本文获得了求解中心承受集中载荷的圆板大挠度问题迭代解析解的递推公式的计算程序,使之能便于计算执行。同时,通过对此方法收敛性的研究,得到了关于载荷值P收敛的一个上界值。这为解析电算法的应用提供了一个有用的判据。     

迁移理论中的一个扰动问题

§1.前言在反应堆理论和应用中,临界参数的计算是一个十分重要的问题.反应堆在运转过程中会发生一些微小的变化,例如热膨胀引起反应堆几何的变化,燃耗引起成分的变化等等.一般说来,这些变化对系统反应性的影响可以用微扰理论找出.本文的主要目的是讨论反应堆几何变化对临界参数的影响,所基于的简单模型是均匀介质、各向同性散射单速迁移方程     

带层次结构效用可转移合作对策的Shapley值及其简化计算方法

从分配式角度引入了带层次结构效用可转移合作对策的Shapley值,因此该值的商对策性质就成了一个很自然的推论.为了方便计算,文章还引入了该值的联盟式描述及简化联盟式描述.最后,给出了利用简化联盟式描述来计算该值的具体过程.     

光波导研究的最陡下降逼近理论

本文应用最陡下降逼近方法,发展了一套计算波导本征值和本征函数的新方法.该方法既能避免微扰法对于参考模式的无限求和,又能逐级迭代计算逼近体系精确的本征值与本征函数,以较少的计算工作量使模场分布与传播常数的计算达到很高的精度.     

铋系超导体反常晶格膨胀X射线衍射研究

本文利用变温X射线衍射方法研究了室温至液氮温度区间铋系超导体晶格热膨胀与畸变特性.在从正常态向超导态转变过程中,铋系2223相和2212相均在高温区和低温区发生反常热膨胀.发生在超导转变前的晶格反常热膨胀与Mossbauer谱和超声内耗测量得到晶格软化温度相对应,这种结构上的反常行为是超导转变的前驱效应.     

复合二项对偶模型中的周期性分红问题

该文主要在有界红利率的条件下讨论复合二项对偶模型的周期性分红问题.通过对值函数进行变换,得到了最优红利策略的一些性质,并且证明了最优值函数是一个HJB方程的唯一解.从而得到了最优策略和最优值函数的一个简单计算方法.根据最优红利策略的一些性质,该文还得到了最优值函数的可无限逼近的上界和下界.最后提供一些数值计算实例来说明该算法.     

基于方案综合评价值和效用值偏差的多属性决策方法

研究了属性权重未知、方案偏好为效用值的多属性决策问题,提出了一种多属性决策模型.首先,分析了部分文献中利用方案属性值与效用值的偏差建模求出属性权重的不合理性,以及根据方案综合评价值与效用值的偏差建模得到属性权重的合理性.然后,通过最小化方案综合评价值与效用值的偏差,建立了一个规划模型,计算出属性权重,进而利用方案综合评价值实现方案的排序择优.最后,通过一个实例说明了方法的可行性.     

Long range dependence of point processes, with queueing examples

Possible definitions of the long range dependence (LRD) of a stationary point process are discussed. Examples from the standard queueing literature are considered and shown to be amenable to yielding processes with long range count dependence. In particular the effect of the single-server queueing operator, whereby one point process is transformed into another via the mechanism of a simple queue, is examined for possible long range dependence of both the counting and interval properties of the output process. For an infinite server queue, the output is long range count dependent if and only if the input is long range count dependent.     

一类循环图中的Eulerian定向数

一般的图中Eulerian定向数的计数是#P-完全问题,但对于某些特殊图中的Eulerian定向数给出精确计数是完全有可能的.通过拆分解构的方法可以找到与一类循环图中Eulerian定向数有关的递推关系,从而给出该数的精确计数.前人的工作在于给出了一些近似估计.     

(IGa-Exp)模型下二行动线性决策问题的抽样信息期望值

二行动线性决策问题是一类常见而重要的决策问题.指数分布在排队论和可靠性理论等领域应用广泛.本文讨论了逆Γ分布共轭于指数分布的决策模型下的二行动线性决策问题的抽样信息期望值的计算公式及应用价值.     

A Counting Formula for Labeled, Rooted Forests

Given a power series, the coefficients of the formal inverse may be expressed as polynomials in the coefficients of the original series. Further, these polynomials may be parameterized by certain ordered, labeled forests. There is a known formula for the formal inverse, which indirectly counts these classes of forests, developed in a non-direct manner. Here, we provide a constructive proof for this counting formula that explains why it gives the correct count. Specifically, we develop algorithms for building the forests, enabling us to count them in a direct manner.     

Numerical algorithm for solving diffusion equations on the basis of multigrid methods

A new effective algorithm based on multigrid methods is proposed for solving parabolic equations. The algorithm preserves implicit-scheme advantages (such as stability, accuracy, and conservativeness) while it involves a considerably reduced amount of arithmetic operations at every time level. The absolute stability, conservativeness, and convergence of the algorithm is proved theoretically using one- and two-dimensional initial-boundary value model problems for the heat equation. The error of the solution is estimated. The good accuracy of the method is demonstrated using two-dimensional model problems, including ones with discontinuous coefficients.     

Teaching young children decomposition strategies to solve addition problems: An experimental study

The ability to count has traditionally been considered an important milestone in children's development of number sense. However, using counting (e.g., counting on, counting all) strategies to solve addition problems is not the best way for children to achieve their full mathematical potential and to prepare them to develop more complex and advanced computational skills. In this experimental study, we demonstrated that it was possible to teach children aged 5-6 to use decomposition strategy and thus reduced their reliance on counting to solve addition problems. The study further showed that children’ ability to adopt efficient strategies was related to their systematic knowledge of the part-part-whole relationship of the numbers 1-10.     

Efficiently computing the permanent and Hafnian of some banded Toeplitz matrices

We present a new efficient method for computing the permanent and Hafnian of certain banded Toeplitz matrices. The method covers non-trivial cases for which previous known methods do not apply. The main idea is to use the elements of the first row and column, which determine the entire Toeplitz matrix, to construct a digraph in which certain paths correspond to permutations that the permanent and Hafnian count. Since counting paths can be done efficiently, the permanent and Hafnian for those matrices is easily obtainable.     

Optimal proportional reinsurance with common shock dependence

In this paper, we consider the optimal proportional reinsurance strategy in a risk model with multiple dependent classes of insurance business, which extends the work of Liang and Yuen (2014) to the case with the reinsurance premium calculated under the expected value principle and to the model with two or more classes of dependent risks. Under the criterion of maximizing the expected exponential utility, closed-form expressions for the optimal strategies and value function are derived not only for the compound Poisson risk model but also for the diffusion approximation risk model. In particular, we find that the optimal reinsurance strategies under the expected value premium principle are very different from those under the variance premium principle in the diffusion risk model. The former depends not only on the safety loading, time and interest rate, but also on the claim size distributions and the counting processes, while the latter depends only on the safety loading, time and interest rate. Finally, numerical examples are presented to show the impact of model parameters on the optimal strategies.     

Morse homology for the heat flow

We use the heat flow on the loop space of a closed Riemannian manifold—viewed as a parabolic boundary value problem for infinite cylinders—to construct an algebraic chain complex. The chain groups are generated by perturbed closed geodesics. The boundary operator is defined by counting, modulo time shift, heat flow trajectories between geodesics of Morse index difference one. By Salamon and Weber (GAFA 16:1050–138, 2006) this heat flow homology is naturally isomorphic to Floer homology of the cotangent bundle for Hamiltonians given by kinetic plus potential energy.     

Enumeration of labelled chain graphs and labelled essential directed acyclic graphs

A chain graph is a digraph whose strong components are undirected graphs and a directed acyclic graph (ADG or DAG) G is essential if the Markov equivalence class of G consists of only one element. We provide recurrence relations for counting labelled chain graphs by the number of chain components and vertices; labelled essential DAGs by the number of vertices. The second one is a lower bound for the number of labelled essential graphs. The formula for labelled chain graphs can be extended in such a way, that allows us to count digraphs with two additional properties, which essential graphs have.