宏观因素影响下的系统中元件重要性研究

为研究复杂系统在工作环境中其组成元件对系统安全运行的重要性,将汪培庄先生的因素空间理论与笔者提出的空间事故树理论相结合,构造了一套元件重要性研究方法.构建系统T={U,C,D},将元件作为研究对象集合U,系统工作的宏观环境作为因素集C,元件重要性排序集作为D.对宏观环境中的工作时间a1和温度a_2进行划分形成不同的状态区域S_q,计算在S_q中元件xj的失效权重γ(AS_q(x_j))和在S_q中系统T的失效权重δ(AS_q(T))),从而得到x_j在S状态下的等效失效权重Z(AS_q(x_j)),研究状态S_q下的原件重要性排序D_η,及元件x_j失效性对a_1及a_2的敏感性.使用一个实际的电气系统维修情况统计资料,使用上述方法进行了研究,结果表明:不同工作环境下元件对系统的重要程度是不同的.元件对温度和使用时间是敏感的,并得到了在10³0°且5030°且50⁷5d环境下工作系统可靠性是最高的结论.在给定工作环境下,重要性大的元件多储备,重要性小的元件少储备,以满足系统维修需要,并指导实际工程.     

On the local semiconcavity of the solutions of the eikonal equation

We show that if the Hamiltonian is locally semiconvex with respect to the state variables and strictly convex with respect to the gradient then every viscosity solution of the eikonal equation is locally semiconcave. Furthermore, in the 1D case, we show that every viscosity solution of the eikonal equation is semiconcave if and only if the Hamiltonian is Lipschitz continuous with respect to the state variable.     

On the numerical approach of the enthalpy method for the Stefan problem

In this article an error bound is derived for a piecewise linear finite element approximation of an enthalpy formulation of the Stefan problem; we have analyzed a semidiscrete Galerkin approximation and completely discrete scheme based on the backward Euler method and a linearized scheme is given and its convergence is also proved. A second‐order error estimates are derived for the Crank‐Nicolson Galerkin method. In the second part, a new class of finite difference schemes is proposed. Our approach is to introduce a new variable and transform the given equation into an equivalent system of equations. Then, we prove that the difference scheme is second order convergent. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004     

On the analyticity and the almost periodicity of the solution to the Euler equations with non-decaying initial velocity

The Cauchy problem of the Euler equations in the whole space is considered with non-decaying initial velocity in the frame work of . It is proved that if the initial velocity is real analytic then the solution is also real analytic in spatial variables. Furthermore, a new estimate for the size of the radius of convergence of Taylor's expansion is established. The key of the proof is to derive the suitable estimates for the higher order derivatives of the bilinear terms. It is also shown the propagation of the almost periodicity in spatial variables.     

On the determination of the control parameters of the optimal can-order policy

This paper considers the well-known class of can-order policies. This type of coordinated replenishment policies accounts for a joint set-up cost structure, where a major set-up cost is incurred for any order and an individual minor set-up cost is charged for each item in the replenishment. Recent comparative studies have pointed out that the performance of the optimal can-order policy is poor, compared to other coordinated replenishment strategies, when the major set-up cost is high. This paper shows that it is the approximate decomposition method to calculate the optimal canorder parameters which performs bad in such situations and not the policy itself. Attention is focused to a subclass of can-order policies, which is close to the optimal can-order policy for high major set-up costs. A solution procedure is developed to calculate the optimal control parameters of this policy. It is shown that a properly chosen combination of the solution procedures to calculate can-order parameters leads to a can-order strategy which performs as well as other coordinated replenishment policies.     

Acceleration of the convergence of the Laguerre series in the problem of inverting the Laplace transform

When the Laplace transform is inverted numerically, the original function is sought in the form of a series in the Laguerre polynomials. To accelerate the convergence of this series, the Euler-Knopp method is used. The techniques for selecting the optimal value of the parameter of the transform on the real axis and in the complex plane are proposed.     

逆谱理论新方法中A-函数和势函数依赖关系的稳定性研究

对于一维Schrdinger算子,本文基于Simon给出的惟—性定理(势函数由A-函数惟一确定)证明了势函数连续依赖于A-函数;反过来,若势函数q∈L~1(0,∞),给出了A-函数也连续依赖于势函数的结论.     

On the fallacy of the likelihood principle

By using the direct and inverse binomial experiments it is shown that there is a situation where Birnbaum's basic axiom of mathematical equivalence and the likelihood principle is a tautology. This observation disqualifies Birnbaum's proof of the likelihood principle based on the axioms of mathematical equivalence and conditionality. The implication of this disproof of Birnbaum's argument for Bayesian statistics is briefly discussed.     

On the algorithm of the solution of the signorini problem

An algorithm is proposed for solving the Signorini problem /1/ in the formulation of a unilateral variational problem for the boundary functional in the zone of possible contact /2/. The algorithm is based on a dual formulation of Lagrange maximin problems for whose solution a decomposition approach is used in the following sense: a Ritz process in the basis functions that satisfy the linear constraint of the problem, the differential equation in the domain, is used in solving the minimum problem (with fixed Lagrange multipliers); the maximum problem is solved by the method of descent (a generalization of the Frank-Wolf method) under convexity constraints on the Lagrange multipliers. The algorithm constructed can be conisidered as a modification of the well-known algorithm to find the Udzawa-Arrow-Hurwitz saddle points /3, 4/. The convergence of the algorithm is investigated. A numerical analysis of the algorithm is performed in the example of a classical contact problem about the insertion of a stamp in an elastic half-plane under approximation of the contact boundary by isoparametric boundary elements. The comparative efficiency of the algorithm is associated with the reduction in the dimensionality of the boundary value problem being solved and the possibility of utilizing the calculation apparatus of the method of boundary elements to realize the solution.     

不忽略一次项损失时望大特性质量损失函数设计

田口先生提出的质量特性损失函数是用二次项来表示的,对于望大特性而言,质量特性实际上不可能达到无穷大。讨论了不能忽略一次项损失时,望大特性质量损失函数应采用二次式表示。研究了二次式损失函数中一次项损失系数和二次项损失系数确定的方法。比较分析了二次式损失函数中一次项损失和二次项损失的大小。本文的研究结果显示,田口先生经典的二次项损失函数是二次式损失函数的一种形式。实际问题也验证了本文的研究成果。     

ON THE SPACES OF THE MAXIMAL POINTS

For a continuous domain D, some characterization that the convex powerdomain CD is a domain hull of Max(CD) is given in terms of compact subsets of D. And in this case, it is proved that the set of the maximal points Max(CD) of CD with the relative Scott topology is homeomorphic to the set of all Scott compact subsets of Max(.D) with the topology induced by the Hausdorff metric derived from a metric on Max(D) when Max(D) is metrizable.     

On the combinatorial lower bound for the extension complexity of the Spanning Tree polytope

This paper concerns the extension complexity of the Minimum Spanning Tree problem on a complete graph with  $n$ nodes. The best known lower bound is the trivial bound, $\Omega \left(n^2\right)$, the best known upper bound is the extended formulation size $O\left(n^3\right)$ (Wong 1980, Martin 1991). We give a nondeterministic communication protocol with cost ${log}_2(n^{2}logn)+O\left(1\right)$ for the support of the spanning tree slack matrix.     

The numerical analysis of the influence of the blankholder force and the friction coefficient on the value of the drawing force

In this paper the numerical analysis of the drawing process with the blankholder is presented. The influence of the value of the blankholder force on the value of the drawing force and drawpiece height is examined. A different friction coefficient of the sheet metal for die and blankholder is considered. A defect at the lack of the blankholder is presented. The analysis in the system ANSYS/LS-DYNA is passed. The material model with the mixed hardening, isotropic and isothermal is used. Technological parameters of the sheet-metal to drawing, the die, the stamp and the blankholder from the literatures are chosen. Examples results of computer simulations are presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

From the Boundary of the Convex Core to the Conformal Boundary

If N is a hyperbolic 3-manifold with finitely generated fundamental group, then the nearest point retraction is a proper homotopy equivalence from the conformal boundary of N to the boundary of the convex core of N. We show that the nearest point retraction is Lipschitz and has a Lipschitz homotopy inverse and that one may bound the Lipschitz constants in terms of the length of the shortest compressible curve on the conformal boundary.     

Uniqueness and nonuniqueness of the solution to the problem of determining the source in the heat equation

An initial–boundary value problem for the two-dimensional heat equation with a source is considered. The source is the sum of two unknown functions of spatial variables multiplied by exponentially decaying functions of time. The inverse problem is stated of determining two unknown functions of spatial variables from additional information on the solution of the initial–boundary value problem, which is a function of time and one of the spatial variables. It is shown that, in the general case, this inverse problem has an infinite set of solutions. It is proved that the solution of the inverse problem is unique in the class of sufficiently smooth compactly supported functions such that the supports of the unknown functions do not intersect. This result is extended to the case of a source involving an arbitrary finite number of unknown functions of spatial variables multiplied by exponentially decaying functions of time.     

用模糊数学方法刻划公众对天气预报的感受度

气象部门将6小时的降雨按降雨量划分为无雨、小雨、中雨、大雨、暴雨、大暴雨及特大暴雨七个级别进行预报,这与公众感受认可这些降雨量级别的程度是有差异的.即使气象部门预报的很准,这种差异有可能使公众感受到降雨级别的程度和预报的级别不符,从而认为预报得不准确,用模糊数学的方法对公众的感受度进行了刻划,给出了计算预报数据与公众感受度差异的数值公式及方法.     

From the matrix-geometric to the matrix-exponential

We consider the single server queuesN/G/1 andGI/N/1 respectively in which the arrival process or the service process is a Neuts Process, and derive the matrix-exponential forms of the solution of relevant nonlinear matrix equations for such queues. We thereby generalize the matrix-exponential results of Sengupta forGI/PH/1 and of Neuts forMMPP/G/1 to substantially more general models. Our derivation of the results also establishes the equivalence of the methods of Neuts and those of Sengupta. A detailed analysis of the queueGI/N/1 is given, and it is noted that not only the stationary distribution at arrivals but also at an arbitrary time is matrix-geometric. Matrix-exponential steady state distributions are established for the waiting times in the queueGI/N/1. From this, by appealing to the duality theorem of Ramaswami, it is deduced that the stationary virtual and actual waiting times in aGI/PH/1 queue are of phase type.     

On the spectrum for the artificial compressible system

Stability of stationary solutions of the incompressible Navier–Stokes system and the corresponding artificial compressible system is considered. Both systems have the same sets of stationary solutions and the incompressible system is obtained from the artificial compressible one in the zero limit of the artificial Mach number ? which is a singular limit. It is proved that if a stationary solution of the incompressible system is asymptotically stable and the velocity field of the stationary solution satisfies an energy-type stability criterion by variational method with admissible functions being only potential flow parts of velocity fields, then it is also stable as a solution of the artificial compressible one for sufficiently small ?. The result is applied to the Taylor problem.     

On the kernel of the Magnus representation of the Torelli group

From our previous paper, it is known that the Magnus representation of the Torelli group is not faithful. In this paper, we characterize the kernel of its representation for a certain kind of elements.

     

Hydroelastic phenomena in the neighborhood of the bifurcation of the aorta

The mechanical behavior of the vessels and the blood near a bifurcation is analyzed. A single-layer homogeneous shell is taken as a model of the aorta on the assumption that the intima is much less stiff than the other layers. In analyzing the blood flow in large vessels, the blood is treated as a viscous Newtonian liquid, whose motion is described by the Navier-Stokes equations and the continuity equation.Zhukovskii Air Force Engineering Academy, Moscow; Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 164–166, January–February, 1971.