Dirac定理的局部化与Hamilton图

设Ｇ为一个ｎ阶２－连通图，ｎ≥３．若｜Ｄ_ｎ／２（Ｋ_１，３）｜≥２且满足下述条件之一：ｉ）｜Ｄ_ｎ／２（Ｋ_１，３＋ｅ）｜≥２，ii）若Ｋ_１，３＋ｅ→Ｇ，ｘｙ(?)Ｅ（Ｋ_１，３＋ｅ），则ｍａｘ｛ｄＧ（ｘ），ｄＧ（ｙ）｝≥ｎ／２，则Ｇ是一个Ｈａｍｉｌｔｏｎｉａｎ图或其闭包为ｓＰ|⊕Ｈ，这里ｓＰ⊕Ｈ是一类极小２－边连通图．     

图K_nH_((5n/2)-4)的升分解

Ａｌａｖｉ等人给出了图的升分解的概念并猜测任何一个有正数条边的图都可以升分解．Ｆａｕｄｒｅｅ等１９８７年证明了当完全图Ｋｎ的子图Ｈ至多有ｎ—１条边时，Ｋｎ－Ｈ可以升分解．马克杰等１９９７年证明了当Ｈ至多含有ｎ条边时，Ｋｎ－Ｈ可以升分解．作者１９９９年证明了当Ｈ的边数小于３ｎ／２时，Ｋｎ－Ｈ可以升分解．本文将证明当Ｈ的边数小于（５ｎ／２）－４时Ｋｎ－Ｈ有升分解．     

关于Kn—H2n＋1的升分解

［１］中猜想：任意有正数条边的图都可以升分解．本文证明了Ｋｎ－Ｈ２ｎ＋１可以升分解,其中Ｈ２ｎ＋１表示至多有ｎ个顶点和２ｎ＋１条边的图,ｎ≥７．     

关于图升分解为独立边集问题

Ａｌａｖｉ［１］给出了图的升分解概念，并猜想每一图都可升分解．本文证明了边数为（?）的图Ｇ当边色数Ｘ＇（Ｇ）≤（ｎ＋２）／２时可升分解为{G_i}, 1≤i≤n, G_i≈iK₂．     

若干广义Ramsey数

本文讨论了关于树对完全图删去一些相交的三阶路的广义Ｒａｍｓｅｙ数Ｒ（Ｔ_ｍ，Ｋ_n－ｔＰ₃）和关路对完全图删去一些不相交的三阶完全图的广义Ｒａｍｓｅｙ数Ｒ（Ｐ_ｍ，Ｋ_n－ｔＫ₃），获得如下结果：1．如果m≥3,n≥3，那么Ｒ（Ｔ_ｍ，Ｋ_n－ｔＰ₃）=(m-1)(n-t-1)+1,0≤t≤[n/3].２．若m≥4,n,T≥1，则Ｒ（P_ｍ，Ｋ_n－ｔK₃）=(m-1)(n+2t-1)+1.从而，这两个结果部分地回答了１９８３年Ｒ．Ｊ．Ｇｏｕｌｄ和Ｍ．Ｓ．Ｊａｃｏｂｓｏｎ在［１］中提出的未解决问题．     

MATCH（14，3，1）－设计的一个构造法

一个ＭＡＴＣＨ（ｎ，ｋ，λ）－设计就是完全图Ｋ_n的一个ｋ－匹配集合，使得Ｋ_n的每一对独立边恰好出现在λ个ｋ－匹配中。本文构造了一个ＭＡＴＣＨ（１４，３，１）－设计，解决了文献［１］中一个尚未解决的问题，同时还得到一个ＭＡＴＣＨ（４２，３，１）－设计。     

Grassmann流形上Pontrjagin示性式的积分式公式

命Ｇ_n+m,n是一个Ｇｒａｓｓｍａｎｎ流形，Ｚ_2k＝是Ｇ_n+m,n的一个Ｓｃｈｕｂｅｒｔ流形。命Ｅ是Ｇ_n+m,n上的规范矢丛，ＥＣ是Ｅ的变化，Ｅ是ＥＣ的相配酉（ｎ－２ｋ）－标架丛，并且Ｅ′是ＥＣ的一个矢丛，本文证明了下列积分公式：其中ｃ_4k是Ｇ_n+m,n的４ｋ链，Ｐ_k（Ω）是Ｇ_n+m,n的第ｋ个Ｐｏｎｔｒｊａｇｉｎ示性式，是定义在Ｅ和Ｅ′上的（４ｋ－１）－形式。     

关于二部图K(m,n)-2的色唯一性

设Ｋ（ｍ，ｎ）－２表示从完全二部图Ｋ（ｍ，ｎ）中删去任意２条边所得之图．本文证明了：１．若ｎ≥ｍ≥３，且ｎ＋ｍ＞(（ｎ－ｍ）^２＋８)^1/2＋１/２（ｎ－ｍ）^２＋４，则Ｋ（ｍ，ｎ）－２是色唯一图；２．当ｍ≥３时，Ｋ（ｍ，ｍ）－２，Ｋ（ｍ，ｍ＋１）－２和Ｋ（ｍ，ｍ＋２）－２均是色唯一图．     

关于Buchsbaum环的注记

本文证明了下述结论，设Ａ是一个级数为ｄ的Ｂｕｃｈｓｂａｕｍ环，（ａ₁，ａ₂，…，ａ_n）是Ａ的一个参数系统，则任何正整数ｎ，Ａ／（ａ₁，ａ₂，…，ａ_k）ⁿ（１≤ｋ≤ｄ）仍是ｄ－ｋ维的Ｂｕｃｈｓｂａｕｍ环．     

几类可升分解的图

Ａｌａｖｉ等人在文献［１］中定义了图的一种新分解，即“升分解”，并且猜想：任意有正数条边的图都可升分解。本文证明了下面三类图可升分解，并得到了一些有意义的推论。１设Ｒｎ是一个至多含有ｎ个顶点和至多含有ｎ条边的图，Ｋｎ－Ｒｎ可升分解（ｎ≥５）；２对称图可升分解；３对称图Ｇ的混合积（Ｇ；ｋ）可升分解。     

Some results for the queues Mx/M/c and GIx/ G/c

We develop for the queue M^x/M/c an upper bound for the mean queue length and lower bounds for the delay probabilities (that of an arrival group and that of an arbitrary customer in the arrival group). An approximate formula is also developed for the general bulk-arrival queue GI^x/G/c. Preliminary numerical studies have indicated excellent performance of the results.     

关于环Fpm+uFpm+u2Fpm上循环码的注记

本文研究了环F_p^m+uF_p^m+u²F_p^m上长度为p^s的循环码分类.通过建立环F_p^m+uF_p^m+u²F_p^m到环F_p^m+uF_p^m的同态,给出了环F_p^m+uF_p^m+u²F_p^m上长度为p^s的循环码的新分类方法.应用这种方法,得到了环F_p^m+uF_p^m+u²F_p^m长度为p^s的循环码的码词数.     

Large-time asymptotics for the Gt/Mt/st+GIt many-server fluid queue with abandonment

We previously introduced and analyzed the G _t /M _t /s _t +GI _t many-server fluid queue with time-varying parameters, intended as an approximation for the corresponding stochastic queueing model when there are many servers and the system experiences periods of overload. In this paper, we establish an asymptotic loss of memory (ALOM) property for that fluid model, i.e., we show that there is asymptotic independence from the initial conditions as time t evolves, under regularity conditions. We show that the difference in the performance functions dissipates over time exponentially fast, again under the regularity conditions. We apply ALOM to show that the stationary G/M/s+GI fluid queue converges to steady state and the periodic G _t /M _t /s _t +GI _t fluid queue converges to a periodic steady state as time evolves, for all finite initial conditions.     

M/G/1/MLPS compared to M/G/1/PS

Multilevel processor sharing scheduling disciplines have recently been resurrected in papers that focus on the differentiation between short and long TCP flows in the Internet. We prove that, for M/G/1 queues, such disciplines are better than the processor sharing discipline with respect to the mean delay whenever the hazard rate of the service time distribution is decreasing.     

Une question sur les équations xm ? ym = Rzn (A Question on the Equations xm ? ym = Rzn)

Let m and n be integers at least two and R be a nonzero natural number. In this paper, we study the problem of the determination of the proper solutions of the Diophantine equation x ^m – y ^m equals; Rz ⁿ . We raise a question concerning the existence of any proper nontrivial solution of this equation, in case some precise conditions are satisfied by the triple (m, n, R). We prove some results about it.     

On the asymptotic behavior of xn+1=anxn/xn−1

We investigate the asymptotic behavior of solutions of a separable difference equation of the form

     

The least squares problem of the matrix equation A1X1B1^T ＋ A2X2B2^T = T

The matrix least squares （LS） problem minx ｜｜AXB^T--T｜｜F is trivial and its solution can be simply formulated in terms of the generalized inverse of A and B. Its generalized problem minx1,x2 ｜｜A1X1B1^T ＋ A2X2B2^T - T｜｜F can also be regarded as the constrained LS problem minx=diag（x1,x2） ｜｜AXB^T -T｜｜F with A = [A1, A2] and B = [B1, B2]. The authors transform T to T such that min x1,x2 ｜｜A1X1B1^T＋A2X2B2^T -T｜｜F is equivalent to min x=diag（x1 ,x2） ｜｜AXB^T - T｜｜F whose solutions are included in the solution set of unconstrained problem minx ｜｜AXB^T - T｜｜F. So the general solutions of min x1,x2 ｜｜A1X1B^T ＋ A2X2B2^T -T｜｜F are reconstructed by selecting the parameter matrix in that of minx ｜｜AXB^T - T｜｜F.     

Ueber das volle Formensystem der tern?ren biquadratischen Formf=x13x2+x23x3+x33x1

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