关于某类Reinhardt域的Bergman核函数与解析自同构最大群

本文给出了Ｒｅｉｎｈａｒｄｔ域Ｄ＝｛ｚ＝（ｚ１，ｚ２，ｚ３）∈：｜ｚ１｜２ｋ＋｜ｚ２｜＋｜ｚ３｜２＜１，ｋ＞０｝的Ｂｅｒｇｍａｎ核函数，Ｂｅｒｇｍａｎ度量方阵及其解析自同构最大群。     

新题征展(18)

Ａ　题组新编 １．已知ｆ（ｘ）＝　满足ｆ（０）＋ｆ（４）＝Ｆ（ａ＋３）,（１）求ａ的值;（２）当ｆ～（－１）（２Ｘ）＋１＞ｋｆ～（－１）（ｘ）恒成立时,求ｋ的取值范国;（３）若三个互不相等的正数ｍ、ｎ、ｔ成等比数列,问ｆ（ｍ）、ｆ（ｎ）、ｆ（ｔ）能否成等差数列？ ２．设双曲线　　＝１（ａ＞０,ｂ＞０）的 右顶点为Ａ,Ｐ是双曲线上的一个动点（异于顶点）,从Ａ引双曲线的两条渐近线的平行线与直线 ＯＰ分别交于Ｑ和Ｒ两点,则 （１）｜ＯＱ｜、｜ＯＰ｜、｜ＯＲ｜成＿数列; （２）｜ＯＱ｜＋ ｜ＯＲ｜—２｜ＯＰ｜…     

新题征展(3)

题组新编１．（１）设Ｍ＝｛ｘ｜ｆ（ｘ）＝０｝、Ｎ＝｛ｘ｜ｇ（ｘ）＝０｝,则｛ｘ｜ｆ（ｘ）·ｇ（ｘ）＝０｝为（　　）;（Ａ）Ｍ　（Ｂ）Ｎ　（Ｃ）Ｍ∪Ｎ　（Ｄ）以上都不对（２）设ｆ（ｘ）＝ｘ－１ｘ＋３,ｇ（ｘ）＝ｘ＋３ｘ－１,则集合｛ｘ｜ｆ（ｘ）·ｇ（ｘ）＝０｝＝　　;（３）设函数ｆ（ｘ）、ｇ（ｘ）的定义域依次是Ｆ、Ｇ,且Ｍ＝｛ｘ｜ｆ（ｘ）＝０｝、Ｎ＝｛ｘ｜ｇ（ｘ）＝０｝,则｛ｘ｜ｆ（ｘ）·ｇ（ｘ）＝０｝＝　　．２．（１）设ｍ、ｋ∈Ｎ,则Ｃｎｎ＋Ｃｎｎ＋１＋Ｃｎｎ＋２＋…＋Ｃｎｎ＋ｋ＝　　;（２）求…     

关于一道硕士研究生入学试题的修正

关于一道硕士研究生入学试题的修正魏毅强王彩贤（太原工业大学数力系，太原０３００２４）一九九六年全国攻读硕士学位研究生入学考试试题数学（五）中第十题，原题为：设有四阶方阵Ａ满足条件｜３Ｉ＋Ａ｜＝０，ＡＡＴ＝２Ｉ，｜Ａ｜＜０，其中Ｉ是四阶单位阵，求方阵Ａ...     

平均单叶函数的相邻系数

设ｆ（ｚ）＝ｚ＋Σａｎｚ＾ｎ为单位园｜ｚ｜＜１内解析且平均单叶，记其族为Ｍ又设｛ｆ（ｚ）／ｚ｝＾λ＝１＋Σ＾∞ｎ＝１Ｄｎ（λ），λ＞０，本文说明了：定理一 若ｆ∈Ｍ，λ＞０，则：Σ＾∞ｋ＝１｛｜｜Ｄｋ（λ）｜－｜Ｄｋ－１（λ）｜｜／ｄｋ（λ）｝＾２≤Ａｎ，ｎ＝２，３，…其中Ａ为绝对常数。ｄｋ（ｈ）＝ｈ（ｈ＋１）…（ｈ＋ｋ－１）／ｋ！当λ＝１／２，ｆ∈ｓ时为Ｉ．Ｖ．Ｍｉｌｍ所证明。定理二 若ｆ∈Ｍ并     

关于面积平均p叶函数（Ⅱ）

假设ｆ（ｚ）＝ｚ＾ｐ（１＋Σ＾∞ｎ＝１ａｎ＾ｚ＾ｎｋ）是△＝｛｜ｚ｜＜１｝内面积平均ｐ叶的（如果必要，△＝｛｜ｚ｜＜１｝＼（－１，０］）。本文的主要结论是：（１）如果设Ｍ（ｒ）＝ｍａｘ｜ｆ（ｚ）｜，则（１－ｒ）２ｐ／ｋＭ（ｒ）→αｋ≤１（ｒ→１），αｋ＝１的充要条件是ｆ（ｚ）＝ｚ＾ｐ（１－ｘｚ＾ｋ）＾－２ｐ／ｋ，｜ｘ｜＝１。进一步，如果１≤ｋ＜４ｐ，我们有｜ａｎ｜ｎ＾１－２ｐ／ｋ→αｋГ（２ｐ／ｋ     

关于模N的原根及其整除性

设整数ｎ≥３存在原根，对给定的正整数１＜ｋ＜ｎ且（ｋ，ｎ）＝１，本文证明了如下的结论：当ｎ充分大时一定存在模ｎ的二个原根ｒ及ｓ使得ｒｓ≡１（ｍｏｄｎ）且ｋ｜ｒ＋ｓ。     

布尔矩阵行空间基数的存在点

设 Ｂｎ 表示所有的ｎ 阶布尔矩阵的集合, Ｒ（ Ａ）表示 Ａ∈ Ｂｎ 的行空间,｜ Ｒ（ Ａ）｜表示 Ｒ（ Ａ）的基数．设ｍ ,ｎ,ｋ 为正整数,本文证明了当ｎ≥９, ｎ＋ ５２ ≤ｋ≤ｎ－ ３ 时,对任意的 ｍ ,２ｋ≤ｍ ≤２ｋ＋ ２ｎ－ ｋ＋ ２＋ ２ｎ－ ｋ＋ １ ＋ …＋ ２３,存在 Ａ∈ Ｂｎ,使得｜ Ｒ（ Ａ）｜＝ ｍ ．     

半值环的两个交换结果

定理１设Ｒ是半值环，ｎ为固定的正整数，如果Ｒ满足条件：存在依赖于(?)_ｘ，ｙ的两个字ｋ（Ｘ，Ｙ），ｔ（Ｘ，Ｙ），其中｜ｋ｜_X＞１，｜ｔ｜_X＝１，｜ｋ｜_Y≥｜ｔ｜_Y，｜ｔ｜_Y≤ｎ，使ｋ（ｘ，ｙ）－ｔ（ｘ，ｙ）∈Ｉ（Ｒ），则Ｒ是交换环。定理２设Ｒ是半值环，如果Ｒ满足条件：存在正整数ｍ＝ｍ（ｘ，ｙ）＞１，ｎ＝ｎ（ｙ），使得（ｘ^ｎｙ）^m－ｘ     

k－Bounded Space On－line装箱中AFB_k算法的界

Ｊ．Ｃｓｉｒｉｋ与Ｄ．Ｓ．Ｊｏｈｎｓｏｎ针对带ｋ－箱限制的在线装箱问题提出了四种装入和关闭法则，并利用这些法则给出了四种相应的算法．其中ＢＢＦｋ，ＮｋＦ和ＡＢＦｋ算法的紧界在文［１－３］中分别进行了很好的研究．但对算法ＡＦＢｋ来讲，其紧界仍是一个公开问题．本文给出了ＡＦＢｋ算法性能比的一个上界，即．同时，本文提出了一个新的关闭法则，对ＡＦＢｋ算法进行了修改，使修改后的算法ＡＦＢｋ的性能比不超过１．７（ｋ３）     

The first K shortest unique-arc walks in a traffic-light network

In this article, we present an algorithm to find the first K shortest unique-arc walks in a traffic-light network. Each node of the present network is associated with a repeated sequence of different windows to model operations of traffic signals and intersection movements. Unlike conventional simple or looping paths, we refer to the paths in this paper as unique-arc walks because they may include repeated nodes but will exclude repeated arcs. Using the heap structure, we develop an algorithm to find the first K shortest unique-arc walks in time O(Kr|V|³|A|), where |V| is the number of nodes, |A| is the number of arcs, and r represents the number of different windows associated with a node.     

一类步数为2(k+1)的次黎曼流形上测地线的研究

构造了一类步数为2(k+1)的次黎曼流形,给出其上连接原点和t轴上一点测地线的条数和相应测地线的长度,同时得到其中最短的测地线.     

Geodesic Ham-Sandwich Cuts

Let P be a simple polygon with m vertices, k of which are reflex, and which contains r red points and b blue points in its interior. Let n = m + r + b. A ham-sandwich geodesic is a shortest path in P between two points on the boundary of P that simultaneously bisects the red points and the blue points. We present an O(n log k)-time algorithm for finding a ham-sandwich geodesic. We also show that this algorithm is optimal in the algebraic computation tree model when parameterizing the running time with respect to n and k.     

Finding K shortest looping paths with waiting time in a time–window network

A time-constrained shortest path problem is a shortest path problem including time constraints that are commonly modeled by the form of time windows. Finding K shortest paths are suitable for the problem associated with constraints that are difficult to define or optimize simultaneously. Depending on the types of constraints, these K paths are generally classified into either simple paths or looping paths. In the presence of time–window constraints, waiting time occurs but is largely ignored. Given a network with such constraints, the contribution of this paper is to develop a polynomial time algorithm that finds the first K shortest looping paths including waiting time. The time complexity of the algorithm is O(rK²|V₁|³), where r is the number of different windows of a node and |V₁| is the number of nodes in the original network.     

On k-critical 2k-connected graphs

A graph G is called an (n, k)-graph if k(G - S) = n - |S| for any S V(G) with |S| ≤ k, where k.(G) denotes the connectivity of G. Mader conjectured that for k ≥ 3 the graph K2k+2 - (1-factor) is the unique (2k, k)-graph. Kriesell has settled two special cases for k = 3, 4. We prove the conjecture for the general case k ≥ 5.     

Some Existence Theorems on Path Factors with Given Properties in Graphs

A path factor of G is a spanning subgraph of G such that its each component is a path.A path factor is called a P≥_n-factor if its each component admits at least n vertices. A graph G is called P≥_n-factor covered if G admits a P≥_n-factor containing e for any e ∈ E(G), which is defined by[Discrete Mathematics, 309, 2067–2076(2009)]. We first define the concept of a(P≥_n, k)-factor-critical covered graph, namely, a graph G is called(P≥_n, k)-factor-critical covered if G-D is P≥_n-factor covered for any D ? V(G) with |D| = k. In this paper, we verify that(i) a graph G with κ(G) ≥ k + 1 is(P≥2, k)-factor-critical covered if bind(G) 2+k/3;(ii) a graph G with |V(G)| ≥ k + 3 and κ(G) ≥ k + 1 is(P≥3, k)-factor-critical covered if bind(G) ≥4+k/3.     

Shortest path algorithms for knapsack type problems

The group knapsack and knapsack problems are generalised to shortest path problems in a class of graphs called knapsack graphs. An efficient algorithm is described for finding shortest paths provided that arc lengths are non-negative. A more efficient algorithm is described for the acyclic case which includes the knapsack problem. In this latter case the algorithm reduces to a known algorithm.     

Finding a minimum independent dominating set in a permutation graph

We give a linear time reduction of the problem of finding a minimum independent dominating set in a permutation graph, into that of finding a shortest maximal increasing subsequence. We then give an O(n log²n)-time algorithm for solving the second (and hence the first) problem. This improves on the O(n³)-time algorithm given in [4] for solving the problem of finding a minimum independent dominating set in a permutation graph.