具有不同失效率和修理率的n中连续取k的可修系统

研究了具有不同失效率和修理率的,2中连续取k的可修系统．在假设失效部件的修理规则为后到先修,且修复如新的条件下,得到了具有不同失效率和修理率的n中连续取k的可修系统各状态的概率,并进一步获得了这类可修系统的一些重要的可靠性指标或者其Laplace变换．     

逐步增加Ⅱ型截尾下n中取m串连续k失效系统的可靠性评估

在逐步增加Ⅱ型截尾样本下,研究不可修n中取m串连续k失效系统(简记为k(m)/n系统)的可靠性评估问题.利用Bayes方法与极大似然估计法,得到了部件失效率、系统可靠度及平均寿命等可靠性指标的经验Bayes估计.最后利用随机模拟例子说明了本文方法的正确性和可行性.     

m（n）相依样本k近邻回归函数估计的一致强相合性

对一大类非参数回归函数，基于m（n）相依样本构造了回归函数的近邻估计并在合适的条件下获得了估计的一致强相合性及收敛速度．     

独立元件组成的n中取k系统剩余寿命的年龄性质

研究了独立元件组成的n中取k系统的剩余寿命长度的年龄性质,该系统在时刻t＜0有n-k个元件失效.对于几类寿命分布元件,讨论了元件仅仅独立的情形下,n中取k个系统剩余寿命的特征.     

"魔(n,k)方"的广义Fibonacci数列解

文 [1 ]将文 [2 ]中的“魔八方”问题推广为“魔(ｎ,ｋ)方”问题 ,研究不定方程ｘ2 +ｘｙ-ｙ2 +ｋ=0　　 (1 )的广义Ｆｉｂｏｎａｃｃｉ数列解 .结束时 ,提出可以证明“魔 (ｎ ,2 )方”和“魔 (ｎ ,3 )方”不可实现 ,未能方便地给出证明 ,也未能很好地实现进一步的探讨 .本文将在文 [1 ]的基础上 ,得出广义Ｆｉｂｏｎａｃｃｉ数列解的首项的充要条件 ,并应用这个充要条件进行简便求解和证明 ,最后对ｋ进行分类讨论 .为了本文叙述的连贯性 ,先摘录文 [1 ]中的 2个定义和定理 1 .1　广义Ｆｉｂｏｎａｃｃｉ数列和“魔 (ｎ ,ｋ)方”问题定义 1…     

“魔（n,k）方”与广义Fibonacci数列

文 [1 ]讨论“魔八方”问题 ,证明了符合条件的ｎ等于ｘ ｙ ,ｘ,ｙ为满足不定方程ｘ2 ｘｙ-ｙ2 1 =0的任一组正整数解 ,并找到了方程的Ｆｉｂｏｎａｃｃｉ解 .结束时提出方程是否只有Ｆｉｂｏｎａｃｃｉ解的问题 .本文将Ｆｉｂｏｎａｃｃｉ数列与“魔八方”问题进行了推广 ,在此基础上对该文作者的问题作了彻底的回答 .1　Ｆｉｂｏｎａｃｃｉ数列的推广Ｆｉｂｏｎａｃｃｉ数列是指下面的数列1 ,1 ,2 ,3,5,8,1 3,2 1 ,34,55,89,1 44 ,…… .此数列可以用递推公式表示如下ａ1 =1 ,ａ2 =1ａｎ =ａｎ- 1 ａｎ- 2 ,ｎ≥ 3. (1 )为了本文的讨…     

离散时间冲击下的k/n(G)系统的可靠性分析

研究了一类离散时间冲击下的k/n(G)系统.冲击到达间隔服从几何发布,冲击的量服从一般发布,每次冲击对系统中工作的部件独立产生影响.假设每一部件受冲击后以一定的概率发生故障,各次冲击独立地对系统造成损失,直到工作部件数少于k系统故障为止.基于上述假设,我们求得了系统的离散时间寿命的分布,进而得到系统的可靠度、平均寿命等可靠性指标.作为k/n(G)系统在k=n和k=1时的特例,还得到n部件串联、并联系统在离散时间冲击下的可靠性指标.最后,给出了数值算例.     

线形(n,f,k)系统和系统的可靠度计算新方法

本文应用两端同时进行的有限马尔可夫链嵌入法给出了具有复合失效准则的(n,f,k)系统和系统可靠度计算公式及公式中连接矩阵的结构特点。数值计算结果表明,随着构成系统的单元个数的增加,应用两端同时进行的有限马尔可夫链嵌入法比应用传统的有限马尔可夫链嵌入法计算可靠度能节省大量运算时间,特别是对于具有对称结构的(n,f,k)和系统效果更加明显。     

修理设备可更换的k/n(G)表决可修系统

研究了修理设备可更换的k/n(G)表决可修系统,其中修理设备在修理故障部件时可能发生失效.假定部件和修理设备的寿命服从负指数分布,故障部件的修理时间和修理设备的更换时间服从一般分布的条件下,利用马尔可夫更新过程理论和拉普拉斯变换(Laplace-Stieltjes变换),分别讨论了系统首次故障前的平均时间,可用度,故障频度及修理设备的不可用度和失效频度,获得了相关指标的递推表达式.在此基础上,给出了1/2(G)表决可修系统和(n-1)/n(G)表决可修系统相关可靠性指标的表达式.     

On Initial-boundary-value Problems for a Class of Systems of Quasi-linear Evolution Equations

In this paper the initial-boundary-value problems for pseudo-hyperbolic system of quasi-linear equations: {(-1)^Mu_{tt} + A(x, t, U, V)u_x^{2M}_{tt} = B(x, t, U, V)u_x^{2M}_{t} + C(x, t, U, V)u_x^{2M} + f(x, t, U, V) u_x^k(0,t) = ψ_{0k}(t), \quad u_x^k(l,t) = ψ_{lk}(t), \quad k = 0,1,…,M - 1 -u(x,0) = φ_0(x), \quad u_t(x,0) = φ_1(x) is studied, where U = (u_1, u_x,…,u_x^{2M - 1}) V = (u_t, u_{xt},…,u_x^{2M - 1_t}), A, B, C are m × m matrices, u, f, ψ_{0k}, ψ_{1k}, ψ_0, ψ_1 are m-dimensional vector functions. The existence and uniqueness of the generalized solution (in H² (0, T; H^{2M} (0, 1))) of the problems are proved.     

Consecutive-(r,f,k)out-of-n:F和Consecutive(f,g)-out-of-(r,n):F线性系统的可靠性

Consecutive-(r,f,k)-out-of-n:F系统由n个单元顺序连结而成,仅当在连续的r个单元中,至少有f个失效或者至少连续k个失效,整个系统才失效;而Consecutive-(f,g)-out-of-(r,n):F系统由n个单元顺序连结而成,仅当在整个系统中至少有f个失效或者在连续的r个单元中,至少有g个失效,整个系统才失效。本文运用马氏链嵌入方法,在单元之间相互独立以及单元之间马氏相关这两种情况下,给出线性系统的可靠性。     

线性和环型Consecutive-k-out-of-r-from-n:F系统可靠性的精确解

本文利用马氏链嵌入法给出了工程上被称为Consecutive k out of r from n :F系统的可靠性精确解。这种方法适用于较复杂的系统可靠性计算 ,且易于在计算机上实现。     

关于多维线性系统的逆

本文给出了多维线性系统求逆的新方法,与以前的方法相比,该方法将高阶矩阵的求逆转化为逐次求低阶矩阵的规范形,而且计算更简单、有效和程序化．本文进一步讨论了多维线性系统的降阶逆系统,并分别通过选取可观测空间和不可观测空间的特殊基,得到了比以往降阶逆系统的阶数更加低的降阶逆系统,揭示了原系统的可观测性对逆系统的阶的影响．     

Lifetime distribution and estimation problems of consecutive-k-out-of-n:F systems

Explicit formula is given for the lifetime distribution of a consecutive-k-out-of-n:F system. It is given as a linear combination of distributions of order statistics of the lifetimes of n components. We assume that the lifetimes are independent and identically distributed. The results should make it possible to treat the parametric estimation problems based on the observations of the lifetimes of the system. In fact, we take up, as some examples, the cases where the lifetimes of the components follow the exponential, the Weibull, and the Pareto distributions, and obtain feasible estimators by moment method. In particular, it is shown that the moment estimator is quite good for the exponential case in the sense that the asymptotic efficiency is close to one.This research was partially supported by the ISM Cooperative Research Program (94-ISM-CRP-5).     

On the best parametrization

The numerical solution to a system of nonlinear algebraic or transcendental equations with several parameters is examined in the framework of the parametric continuation method. Necessary and sufficient conditions are proved for choosing the best parameters, which provide the best condition number for the system of linear continuation equations. Such parameters have to be sought in the subspace tangent to the solution space of the system of nonlinear equations. This subspace is obtained if the original system of nonlinear equations is solved at the various parameter values from a given set. The parametric approximation of curves and surfaces is considered.     

关于微分方程组解的m-非允许分量

在本文里，我们给出了微分方程组解的非允许分量之定义，探讨了一类微分方程组解的m-非允许分量的存在性问题，得到了几个结果。它是文[9]的进—步讨论．     

Active redundancy allocation for a k-out-of-n:F system of dependent components

We characterize active redundancy through compensator transform and use the reverse rule of order 2 (RR₂) property between compensator processes to investigate the problem of where to allocate a spare in a k-out-of-n:F system of dependent components through active redundancy.     

Categorical Abstract Algebraic Logic: Partially Ordered Algebraic Systems

An extension of parts of the theory of partially ordered varieties and quasivarieties, as presented by Pałasińska and Pigozzi in the framework of abstract algebraic logic, is developed in the more abstract framework of categorical abstract algebraic logic. Algebraic systems, as introduced in previous work by the author, play in this more abstract framework the role that universal algebras play in the more traditional treatment. The aim here is to build the generalized framework and to formulate and prove abstract versions of the ordered homomorphism theorems in this framework. To Don Pigozzi and Kate Pałasińska.