几类任务到达时间受资源约束的单机排序问题

本研究了任务到达时间受资源影响的，与时间表长有关的几个问题。对问题1|rj=bj-ajuj,∑j=1^nju≤U|Cmax的一种特殊情况给出了求任务的最优排序的算法，对问题1|rj=fj(uj),pj=p,Cmax≤C|∑j=1^nuj给出了最优算法；还给出了问题1|rj=fj(uj)|∑j=1^nujΛCmax的一个算法。     

资源有限的加权总完工时间单机排序问题

本讨论资源有限的加权总工时间单机排序问题，对现在仍为OPEN问题1｜pj=bj-ajuj，∑uj≤U｜∑wjCj给出了一个有关最优解中最优资源分配的重要性质，并利用该性质分别给出了三种情况bj=b,wj=w,aj=a；bj=b,wj=w,uj=u；aj=a,wj=w,uj=u的最优算法。     

一类资源分配与排序问题

给出与研究1 rj=bj-ajuj,∑uj U-∑uj+Cm ax型资源分配与排序问题.对于系统中加工顺序确定的情况给出并证明一个寻求其最优资源分配的多项式算法;就系统参量的某些特殊情况研究系统的最优排序.     

一类非线性抛物方程组解的爆破时间上下界估计

本文研究了一类非线性抛物方程组uj/t=△uj+fj(u)解的爆破时间的估计问题.通过构造恰当的辅助函数和建立一系列微分不等式,获得了此类非线性抛物方程组解的爆破时间上下界的估计.从而将单个方程的结论推广到了方程组的情形.     

关于单机两个客户竞争排序问题1||∑wAjcAj:fBmax≤Q的一个注记

研究了单机两个客户竞争排序问题1||∑wAjcAj:fBmax≤Q,证明了该问题与问题1|MAi|∑wjcj及问题1|hi,pmtn|∑wjcj之间是相互等价的.对wj=pj时的特殊情形,指出了问题1||∑wAjcAj:fBmax≤Q存在近似比为2的最长处理时间优先算法(LPT)且该界是紧的,对wj任意的一般情形,指出了问题1||∑wAjcAj:fBmax≤Q存在近似比为4+ε的近似算法.当客户B的工件数是常数时,对问题1||∑wAjcAj:fBmax≤Q则给出了伪多项式时间的动态规划算法.此外,指出了问题1||∑wAjcAj:∑wBjcBj ≤ Q具有多项式时间近似方案(PTAS).     

带到达时间的单机排序中的资源分配问题

讨论两个单机排序的资源分配问题1｜rj,pj=bj-ajuj,Cmax≤｜∑uj和1｜rj,prec,pj=bj-ajuj C max≤｜∑uj并给出求其最优资源分配的多项式算法.     

单机排序问题|r_j,prmp| ∑w_j(1-e~(-ac_j)) 的动态在线调度

本文首先一般化了可中断的概念,并建立了相应的中断—安装重复模型,然后研究了单机排序问题1|rj,prmp| wj(1-e-acj)在中断—重复和中断—安装重复模型下的动态在线排序问题,给出了只考虑当前可用信息而不是考虑全部任务信息的在线调度规则。     

带权的误工排序问题的最优算法

研究工件有不同的权(重要性)、但是与工件加工时间有反向"一致性"关系,并且在保证工件的一个子集T中的工件必须不误工的前提下,使得带权的误工工件的个数(误工造成损失的费用)为最少的排序问题1∣T,(pi≤pj ) (wi≥wj)∣∑wjUj ;提出该问题的最优算法,证明提出的算法得到的排序是最优排序,而且证明这个最优排序在所有最优排序中不误工工件总的加工时间为最小.     

单机排序问题1|rj,prmp|∑wj(1-e-acj)的动态在线调度

本文首先一般化了可中断的概念,并建立了相应的中断-安装重复模型,然后研究了单机排序问题1 |rj,prmp|∑wj(1-c-acj)在中断-重复和中断-安装重复模型下的动态在线排序问题,给出了只考虑当前可用信息而不是考虑全部任务信息的在线调度规则.     

OPTIMAL SUMMATION INTERVAL AND NONEXISTENCE OF POSITIVE SOLUTIONS TO A DISCRETE SYSTEM

In this paper, we are concerned with properties of positive solutions of the following Euler-Lagrange system associated with the weighted Hardy-Littlewood-Sobolev inequality in discrete form{uj =∑ k ∈Zn u~q_k/(1 + |j|)α(1 + |k- j|)λ(1 + |k|)β,(0.1)vj =∑ k ∈Zn u~p_k/(1 + |j|)β(1 + |k- j|)λ(1 + |k|),where u, v 0, 1 p, q ∞, 0 λ n, 0 ≤α + β≤ n- λ,1p+1λ+αnand1p+1+1q+1≤λ+α+βn:=λˉn. We first show that positive solutions of(0.1) have the optimal summation interval under assumptions that u ∈ lp+1(Zn) and v ∈ lq+1(Zn). Then we show that problem(0.1) has no positive solution if 0 λˉ pq ≤ 1 or pq 1 and max{(n-)(q+1)pq-1,(n-λˉ)(p+1)pq-1} ≥λˉ.     

Existence and Comparison Results for First Order Periodic Implicit Difference Equations with Maxima

In this paper, we establish comparison results (maximum principles) which allow us to use the monotone method and the method of upper and lower solutions in order to build convergent sequences to the solutions of difference equations of the type j u k = f k , u k +1 , max l ] { k m h +1,…, k +1} u l , k ] I , u 0 = u T , with j u k = u k +1 m u k , I ={0,1,…, T m 1} and f ] C ( I 2 R 2 R , R ).     

Existence of Positive Solutions for N-term Non-autonomous Fractional Differential Equations

Existence of positive solutions for the nonlinear fractional differential equation D ^αu = f(x,u), 0 < α < 1 has been given (S. Zhang. J. Math. Anal. Appl. 252 (2000), 804–812) where D ^α denotes Riemann–Liouville fractional derivative. In the present work we extend this analysis for n-term non autonomous fractional differential equations. We investigate existence of positive solutions for the following initial value problem

奇数阶边值问题正解的存在性与多重性

利用锥拉伸锥压缩不动点定理,证明了在一定条件下,下列非线性奇数阶方程(-1)q+1u(2q+1)(t)=λa(t)f(u(t)),0 t 1,(-1)q+1u(2q+1)(t)=λa(t)f(u(t)),0 t 1,u(0)=u′(τ)=u″(1)=0u(2j+1)(0)=u(2j+1)(1)=0,j=1,2,…,q-1.单个和多个正解的存在性,其中λ>0,12<τ<1,q∈N.得到了λ的区间Λ,对一切λ∈Λ,该问题至少有一个正解,同样也得到了该问题至少有两个正解λ相应的区间.     

Asymptotic Behavior of Solutions of Some Linear Difference Equations with Oscillatory Decreasing Coefficients

We investigate the asymptotic behavior of solutions of the system x ( n +1)=[ A + B ( n ) V ( n )+ R ( n )] x ( n ), n S n 0 , where A is an invertible m 2 m matrix with real eigenvalues, B ( n )= ~ j =1 r B j e i u j n , u j are real and u j p ~ (1+2 M ) for any M ] Z , B j are constant m 2 m matrices, the matrix V ( n ) satisfies V ( n ) M 0 as n M X , ~ n =0 X Á V ( n +1) m V ( n ) Á < X , ~ n =0 X Á V ( n ) Á 2 < X , and ~ n =0 X Á R ( n ) Á < X . If AV ( n )= V ( n ) A , then we show that the original system is asymptotically equivalent to a system x ( n +1)=[ A + B 0 V ( n )+ R 1 ( n )] x ( n ), where B 0 is a constant matrix and ~ n =0 X Á R 1 ( n ) Á < X . From this, it is possible to deduce the asymptotic behavior of solutions as n M X . We illustrate our method by investigating the asymptotic behavior of solutions of x 1 ( n +2) m 2(cos f 1 ) x 1 ( n +1)+ x 1 ( n )+ a sin n f n g x 2 ( n )=0 x 2 ( n +2) m 2(cos f 2 ) x 2 ( n +1)+ x 2 ( n )+ b sin n f n g x 1 ( n )=0 , where 0< f 1 , f 2 < ~ , 1/2< g h 1, f 1 p f 2 , and 0< f <2 ~ .     

Integral manifolds and a reduction principle in stability theory. II

In this work we prove reduction theorems, according to which the problem of stability of the zero solution of a system of differential equationsdx/dt=A(t)x+B(t)z+g(t, x, z), dz/dt=C(t)z+h(t, x, z) reduces to the problem of stability of the zero solution of the equationdx/di=A(t)x+B(t) (t,x)+g(t, x, (t, x)), in which the vector function y=(t,x) defines the local or the nonlocal integral manifold that contains the graph of the zero solution.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 10, pp. 1315–1321, October, 1990.     

Cahn-Hilliard方程的动力学稳定性

考虑Cahn－Hilliard方程且a2p-1＞0）的初边值问题,证明了系统在H1－H3中关于f系数的状动于H2中Hausdoorff半距离下稳定的全局吸引子的存在性．     

Structure of multiple solutions for nonlinear differential equations

Based on the eigensystem {λj,φj}of -Δ, the multiple solutions for nonlinear problem Δu f(u) =0 in Ω, u=0 on Ω are approximated. A new search-extension method (SEM), which consists of three steps in three level subspaces, is proposed. Numerical simulations for several typical nonlinear cases, i.e. f(u) = u~3,u~2(u-p),u~2(u~2 -p),     

奇异(n-1,1)共轭边值问题的多重正解

利用锥映射不动点指数定理证明了非线性(n-1,1)共轭边值问题u(n)+a(t)[f(u)+m2u]=0,u(j)(0)=u(1)=0,0≤j≤n-2至少存在两个正解.本文允许a(t)在[0,1]两端点处具有奇性,并允许a(t)在[0,1]某些子区间上恒为零.     

Path-Integral Calculations for the First Excited State of Hydrogen Atom

Consider a path-integral which is the solution to a diffusion version of the generalized Schro¨dinger's equation . Here , where A is an infinitesimal generator of a strongly continuous Markov Semigroup corresponding to the diffusion process . For and V replaced by one obtains , which represents a quantum mechanical Hamiltonian corresponding to a particle of mass 1 (in atomic units) subject to interaction with potential V. This paper is concerned with computer calculations of the second eigenvalue of by generating a large number of trajectories of an ergodic diffusion process.     

A two-point problem for systems of hyperbolic equations

Developing a numerical-analytic method, conditions are determined for the existence of solutions of two-point problems for systems of hyperbolic equations of the form .Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 12, pp. 1657–1663, December, 1990.