(n,k)-星图网络的t/m-诊断度及诊断算法

故障诊断度在衡量多处理机系统可靠性上起着极其重要的作用.t/m-诊断分析是一种能极大提高多处理机系统自我诊断性能的诊断策略,该诊断策略能至多识别t个故障处理机,其中最多包含m个被误诊的无故障处理机.在PMC诊断模型下,证明了(n,k)-星图是n+(m-1)k-2m+1/m-可诊断的,其中2≤m≤4,且给出了复杂度为O(NlogN)的快速诊断算法来识别所有的故障节点,其中N是(n,k)-星图网络节点总数.     

5-一致超图的全横贯

设H=(V,E)是以V为顶点集, E为(超)边集的超图. 如果H的每条边均含有k个顶点, 则称H是k-一致超图. 超图H的点子集T称为它的一个横贯, 如果T 与H 的每条边均相交. 超图H的全横贯是指它的一个横贯T, 并且T还满足如下性质: T中每个顶点均至少有一个邻点在T中. H 的全横贯数定义为H 的最小全横贯所含顶点的数目, 记作\tau_{t}(H). 对于整数k\geq 2, 令b_{k}=\sup_{H\in{\mathscr{H}}_{k}}\frac{\tau_{t}(H)}{n_{H}+m_{H}}, 其中n_H=|V|, m_H=|E|, {\mathscr{H}}_{k} 表示无孤立点和孤立边以及多重边的k-一致超图类. 最近, Bujt\'as和Henning等证明了如下结果: b_{2}=\frac{2}{5}, b_{3}=\frac{1}{3}, b_{4}=\frac{2}{7}; 当k\geq 5 时, 有b_{k}\leq \frac{2}{7}以及b_{6}\leq \frac{1}{4}; 当k\geq 7 时, b_{k}\leq \frac{2}{9}. 证明了对5-一致超图, b_{5}\leq \frac{4}{15}, 从而改进了当k=5 时b_k的上界.     

多维局部平稳高斯过程最大值的联合渐近分布

$\{(X_1(t),\cdots,X_p(t)),0\leq t\leq T\}$为$p$维局部平稳高斯过程, 具有渐近中心化的均值$m_k(t)$和常数的方差, $M_k(T)=\sup\{X_k(t),0\leq t\leq T\},\;k=1,\cdots,p$, 当$T\rightarrow\infty$时, 本文在一定条件下获得了$M(T)=(M_1(T),\cdots,M_p(T))$的联合渐近分布.     

完全对换网络的限制连通度

完全对换网络是基于 Cayley 图模型的一类重要互连网络. 一个图 G 的 k-限制点(边)连通度是使得 G-F 不连通且每个分支至少有 k 个顶点的最小点(边)子集 F 的基数, 记作 \kappa_{k}(\lambda_{k}). 它是衡量网络可靠性的重要参数之一, 也是图的容错性的一种精化了的度量. 一般地, 网络的 k-限制点(边)连通度越大, 它的连通性就越好. 证明了完全对换网络 CT_{n} 的 2-限制点(边)连通度和 3-限制点(边)连通度, 具体来说: 当 n\geq4 时, \kappa_{2}(CT_{n})=n(n-1)-2, \kappa_{3}(CT_{n})=\frac{3n(n-1)}{2}-6; 当 n\geq3 时, \lambda_{2}(CT_{n})=n(n-1)-2, \lambda_{3}(CT_{n})=\frac{3n(n-1)}{2}-4.     

A Note on the Approximate Solution of the Cauchy Problem by Number-Theoretic Nets

рябенький, в. с.曾提出用数论网络构造的常微分方程组的解来构造偏微分方程 $\frac{\partial u}{\partial t}=Q(\frac{\partial}{\partial x_1},\cdots,\frac{\partial}{\partial x_s})u,0 \leq t \leq T,-\infty相似文献   

某类$q$差分方程亚纯解的性质

对于一个有穷非零复数$q$, 若下列$q$差分方程存在一个非常数亚纯解$f$, $$f(qz)f(\frac{z}{q})=R(z,f(z))=\frac{P(z,f(z))}{Q(z,f(z))}=\frac{\sum_{j=0}^{\tilde{p}}a_j(z)f^{j}(z)}{\sum_{k=0}^{\tilde{q}}b_k(z)f^{k}(z)},\eqno(\dag)$$ 其中 $\tilde{p}$和$\tilde{q}$是非负整数, $a_j$ ($0\leq j\leq \tilde{p}$)和$b_k$ ($0\leq k\leq \tilde{q}$)是关于$z$的多项式满足$a_{\tilde{p}}\not\equiv 0$和$b_{\tilde{q}}\not\equiv 0$使得$P(z,f(z))$和$Q(z,f(z))$是关于$f(z)$互素的多项式, 且$m=\tilde{p}-\tilde{q}\geq 3$. 则在$|q|=1$时得到方程$(\dag)$不存在亚纯解, 在$m\geq 3$和$|q|\neq 1$时得到方程$(\dag)$解$f$的下级的下界估计.     

The Generalized Riemann^Haseman Problem

In this paper we study the generalized Riemann—Haseman problem which was given by Vekua, I. N. Problem (R-H). Find a sectionally generalized holomorphic function w(z) = {w^+(z), w^-(z)} such that $\frac {\partial w}{\partial \bar z}+B(z)\bar w=0,z\in E$ Here $B(z)\in C_\alpha ^n-1(D^++L),B(z)\in C_\alpha ^n-1(D^- +L),L\in C_\alpha ^n-1,0<\alpha \leq 1,|B(z)|\leq \frac {K}{|z|^1+s}(z\rightarrow \infty),K>0,\varepsilon >0;w(z)$ Satisfies the boundary condition $\sum\limits_{k=0}^n {a_k(t)\frac {\partial ^k w^+}{\partial t^k}|b_k \frac{\bar \partial ^kw^+}{\partial t^k}}_{t=\alpha(z)}-\sum\limits_{k=0}^n{c_k(t)\frac{\partial ^k w^-}{\partial t^k}+d_k(t)\frac{\bar \partial ^kw^-}{\partial t^k}}=f(t),t\in L$, Where a_k(t)、 b_k (t) 、 c_k (t) 、d_k(t)、f(t)\in H;\alpha(t) is a mapping of L into itself, $\alpha'(t)\ne 0$and \alpha [\alpha(t)] \equal t. We study the conditions of the solubility and the number of linearly independent solutions.     

The Estimation for the Multiple de la ValKe Poussin Square Remainders

Let Q_N={\bar x=(x_1,\cdots ,x_N)|-pi \leq x_i <\pi,i=1,\cdots,N} and X(Q_N) denote L(Q_N) and C(Q_N) , The square de la УаДбо Poussin sums of f\in X (Q_N) are defined by $V_n^n+l(f;\bar x)=\frac{1}{\pi ^N}\int _Q_N f(\bar x+\bar t)\prod\limits_{i = 1}^N {(\frac{1}{{l + 1}}} \sum\limits_{v = n}^{n + l} {{D_v}({t_i}))d\bar t(n,l = 0,1,2, \cdots )}$ where D_v(t) =sin(v+1/2)t/2sint/2, - The differences $R_n,l(f;\bar x)=f(\bar x)-V_n^n+l(f;\bar x)$ are called square remainders. We denote by E_k(f)_X the best approximation of the function f\in X(Q_N) by N-multiple trigonometric polynomials of order K. Theorem Let {\varepsilon _k}_k=0^\infty be a sequence such that \varepsilon _n \downarrow \infty(n\rightarrow \infty), the class $X(\varepsilon)={f\in X(Q_N)|E_k(f)_X \leq \varepsilon _k,k=0,1,2,\cdots}$ Then $C_N^'\sum\limits_{v=0}^n+l \frac {\varepsilon_v+nln^N-1(3+v/(l+1))}{v+l+1}\leq sup_{f\in X(\varepsilon)||R_n,l(f)||_X\leq C_N \sum\limits_{v=0}^{n+l}\frac {\varepsilon _v+nln^N-1(3+v/l+1)}{v+l+1}$ where C_N>C'_N>0 are constants depending only on N.     

On the Uniqueness Solutions of Nonlinear Degenerate Parabolic Equations (in English)

本文证明，在条件$a(s)>0(s>0),a(0)=0,b(s)=O(a(s)^\lambda)(s \geq 0,0 \leq \lambda \geq 1/2),s^\mu=O(a(s))(s \geq 0, \mu >0$之下，混合问题 ${u_t} = {(a(u){u_x})_x} + b(u){u_x},(x,t) \in R = \{ (x,t)| - 1 < x < 1,0 < t < T\} $ $u(x,0)=u_0(x)(\geq0),-1 \leqx \leq 1$ $u(-1,0)=\psi_1(t)(\geq0),u(1,t)=\psi _w(t)(\geq 0),0 \leq t \leq T$ 当$\mu<1,\lambda \geq0$或$\mu \geq1,2\lambda+1/ \mu>1$时，解为唯一的，这改善了[1,2]的结果。     

交比和Poincare度量在平面拟共形映射下的偏差

研究(1)若f是 R²到 R²上的k -拟共形映射, 则对任意x₁,x₂,x₃,x_4∈R²有16^{\frac1k-1}(|(x₁,x_2, x₃,x₄)|+1)^{\frac1k}&;\leq&; \left|\left(f(x_1), f(x_2),f(x_3),f(x_4)\right)\right|+1\\&; \leq&; 16^{k-1}\left(|(x_1,x_2,x_3,x_4)|+1\right)^{k}; \end{eqnarray*}(2)若f是R²到R²上的k -拟共形映射, D是R²中的任一真子域,则对任意x₁,x₂∈D有\begin{eqnarray*}\frac1k\lambda_D(x_1,x_2)+4(\frac1k-1)\log2&;\leq&; \lambda_{f(D)} (f(x_1),f(x_2))\\&;\leq &;k\lambda_D(x_1,x_2)+4(k-1)\log2.\end{eqnarray*}了交比和Poincar\'e度量在平面拟共形映射下的偏差估计, 得到了如下两个结果.     

变更图的直径

P(t,n)和C(t,n)分别表示在阶为n的路和圈中添加t条边后得到的图的最小直径；f(t,k)表示从直径为k的图中删去t条边后得到的连通图的最大直径．这篇文章证明了t≥4且n≥5时,P(t,n)≤(n-8)/(t 1) 3；若t为奇数,则C(t,n)≤(n-8)/(t 1) 3；若t为偶数,则C(t,n)≤(n-7)/(t 2) 3．特别地,「(n-1)/5」≤P(4,n)≤「(n 3)/5」,「n/4」-1≤C(3,n)≤「n/4」．最后,证明了：若k≥3且为奇数,则f(t,k)≥(t 1)k-2t 4．这些改进了某些已知结果．     

关于Banach空间一阶非线性脉冲积分-微分方程初值问题解存在性的注记

设m(t)∈C[Jk,R ](k=1,2,…,m),且满足不等式m(t)<(L1 L2t)∫tn(s)ds L3t∫a m(s)ds ∑o0满足KaLs(eδ(L1 aL2)-1)相似文献   

2-satisfiability and diagnosing faulty processors in massively parallel computing systems

A fault diagnosis model for multiprocessor computers is proposed. Under normal operating mode each processor executes its own data. When an error occurs, the system is switched to the diagnostic mode. Previous input data for each processor is shifted to a different unit, to obtain a set of comparison results. We show that analysis of the test data to diagnose or locate faulty processors is equivalent to a 2-satisfiability problem. Under the assumption that discrepancy in a comparison result occurs if and only if at least one of the processors (being compared) is faulty, we prove that all the faulty processors can be diagnosed in O(n²) time, where n denotes the number of processors in the system.     

On Stability and Convergence of the Finite Difference Methods for the Nonlinear Pseudo-Parabolic System

In this paper, we deal with the finite difference method for the initial boundary value problem of the nonlinear pseudo-parabolic system $(-1)^Mu_t+A(x,t,u,u_x,\cdots,u_x 2M-1)u_x2M_t=F(x,t,u,u_x,\cdots,u_x 2M)$,$u_xk(o,t)=\psi_{0k}(t), u_xk(L,t)=\psi_{1k}(t),k=0,1,\cdots,M-1,u(x,0)=\phi (x)$ in the rectangular domain $D=[0\leq X\leq L,0\leq t\leq T]$, where $u(x,t)=(u_1(x,t),u_2(x,t),\cdots,u_m(x,t)),\phi (x),\psi_{0k}(t),\psi_{1k}(t),F(x,t,u,u_x,\cdots,u_x 2M)$ are $m$-dimensional vector functions, and $A(x,t,u,u_x,\cdots,u_x2M-1)$ is an $m\times m$ positive definite matrix. The existence and uniqueness of solution for the finite difference system are proved by fixed-point theory. Stability, convergence and error estimates are derived.     

一个素变量丢番图问题

设k和r是满足k≥3及r≥Ψ(k)+1的正整数,这里当3≤k≤4时,Ψ(k)=2~(k-1);而当k≥5时,Ψ(k)=1/2k(k+1).假定δ和ε是给定的足够小的正数,λ_1,λ_2,…,λ_(r+1)是不全同号且两两之比不全为有理数的非零实数.对于任意实数η与0σ2~(1-2k)/r-1,证明了:存在一个正数序列X→+∞,使得不等式|λ_1p_1~k+λ_2p_2~k+···+λ_rp_r~k+λ_(r+1)p_(r+1)+η|(max(1≤j≤r+1)p_j)~(-σ)有》■X~(■-(2~(1-2k))/(r-1)+ε组素数解(p_1,p_2,…,p_(r+1)),这里(δX)~(1/k)≤p_j≤X~(1/k)(1≤j≤r)及δX≤p_(r+1)≤X.这改进了之前的结果.     

CYCLES EMBEDDING ON FOLDED HYPERCUBES WITH FAULTY NODES

Let FF_v be the set of faulty nodes in an n-dimensional folded hypercube FQ_n with |FF_v| ≤ n-1 and all faulty vertices are not adjacent to the same vertex. In this paper, we show that if n ≥ 4, then every edge of FQn-FF_v lies on a fault-free cycle of every even length from 6 to 2~n-2|FF_v|.     

An Extension of the Win Theorem: Counting the Number of Maximum Independent Sets

Win proved a well-known result that the graph G of connectivity κ(G) withα(G) ≤κ(G) + k-1(k ≥ 2) has a spanning k-ended tree, i.e., a spanning tree with at most k leaves. In this paper, the authors extended the Win theorem in case when κ(G) = 1 to the following: Let G be a simple connected graph of order large enough such that α(G) ≤ k + 1(k ≥ 3) and such that the number of maximum independent sets of cardinality k + 1 is at most n-2k-2. Then G has a spanning k-ended tree.     

具$p$-Laplacian 算子的多点边值问题迭代解的存在性

利用单调迭代技巧和推广的Mawhin定理得到下述带有p-Laplacian算子的多点边值问题迭代解的存在性,{(Фp(u'))' f(t,u, Tu)=0, 0(≤)t(≤)1,u(0)=q-1∑i=1γiu(δi),u(1)=m-1∑i=1ηiu(ξi),其中Фp(s)=|s|p-2s,p＞1;0＜δi＜1,γi＞0,1(≤)i(≤)q-1;0＜ξi＜1,ηi(≥)0,1(≤)i(≤)m-1且q-1∑i=1γi＜1,m-1∑i=1ηi(≤)1;Tu(t)=∫t0k(t,s)u(s)ds,k(t,s)∈C(I×I,R ).