检索结果-南通市图书馆

Estimates for eigenvalues of Laplacian operator with any order

在线全文

学校读者我要写书评

暂无评论

Science china mathematics 2007年第8期50卷 1078-1086页

作者： Fa-en WU~(1+) Lin-fen CAO~2 1 department of mathematics,beijing jiaotong university,beijing 100044,china 2 department of mathematics,Henan Normal university,Xinxiang 453007,china department of mathematics Beijing Jiaotong University Beijing China department of mathematics Henan Normal University Xinxiang China

Let D be a bounded domain in an n-dimensional Euclidean space ? n . Assume that $$0 < \lambda _1 \leqslant \lambda _2 \leqslant \cdots \leqslant \lambda _k \leqslant \cdots $$ are the eigenvalues of the Dirichlet Laplacian operator with any order l: $$\left\{ \begin{gathered} ( - \vartriangle )^l u = \lambda u, in D \hfill \\ u = \frac{{\partial u}}{{\partial \vec n}} = \cdots = \frac{{\partial ^{l - 1} u}}{{\partial \vec n^{l - 1} }} = 0, on \partial D \hfill \\ \end{gathered} \right.$$ . Then we obtain an upper bound of the (k+1)-th eigenvalue λ k+1 in terms of the first k eigenvalues. $$\sum\limits_{i = 1}^k {(\lambda _{(k + 1)} - \lambda _i )} \leqslant \frac{1}{n}[4l(n + 2l - 2)]^{\tfrac{1}{2}} \left\{ {\sum\limits_{i = 1}^k {(\lambda _{(k + 1)} - \lambda _i )^{\tfrac{1}{2}} \lambda _i^{\tfrac{{l - 1}}{l}} \sum\limits_{i = 1}^k {(\lambda _{(k + 1)} - \lambda _i )^{\tfrac{1}{2}} \lambda _i^{\tfrac{1}{l}} } } } \right\}^{\tfrac{1}{2}} $$ . This ineguality is independent of the domain D. Furthermore, for any l ? 3 the above inequality is better than all the known results. Our rusults are the natural generalization of inequalities corresponding to the case l = 2 considered by Qing-Ming Cheng and Hong-Cang Yang. When l = 1, our inequalities imply a weaker form of Yang inequalities. We aslo reprove an implication claimed by Cheng and Yang.

关键词： Dirichlet problem eigenvalue estimate Laplacian operator 35P15 58G25

The genus distributions for a certain type of permutation graphs in orientable surfaces

在线全文

学校读者我要写书评

暂无评论

Science china mathematics 2007年第12期50卷 1748-1754页

作者： Rong-xia HAO~(1+) Wei-li HE~1 Yan-pei LIU~1 Er-ling WEI~2 ~1 department of mathematics,beijing jiaotong university,beijing 100044,china ~2 School of Information,Renmin university of china,beijing 100872,china department of mathematics Beijing Jiaotong University Beijing China School of Information Renmin University of China Beijing China

A circuit is a connected nontrivial 2-regular graph. A graph G is a permutation graph over a circuit C, if G can be obtained from two copies of C by joining these two copies with a perfect matching. In this paper, based on the joint tree method introduced by Liu, the genus polynomials for a certain type of permutation graphs in orientable surfaces are given.

关键词： graph, genus distribution, genus, surfaces

The genus of a type of graph

在线全文

学校读者我要写书评

暂无评论

Science china mathematics 2010年第9期53卷 457-464页

作者： SHAO ZeLing 1 & LIU YanPei 21 department of mathematics, Hebei university of Technology, Tianjin 300401, china 2 department of mathematics, beijing jiaotong university, beijing 100044, china department of mathematics Hebei University of Technology Tianjin China department of mathematics Beijing Jiaotong University Beijing China

Based on the joint tree model introduced by Liu, the genera of further types of graphs not necessary to have certain symmetry can be obtained. In this paper, we obtain the genus of a new type of graph with weak symmetry. As a corollary, the genus of complete tripartite graph K n,n,l (l≥n≥2) is also derived. The method used here is more direct than those methods, such as current graph, used to calculate the genus of a graph and can be realized in polynomial time.

关键词： surface joint tree embedding genus

Number of embeddings of circular and Mbius ladders on surfaces

在线全文

学校读者我要写书评

暂无评论

Science china mathematics 2010年第5期53卷 356-368页

作者： YANG Yan1 & LIU YanPei2 1department of mathematics,Tianjin university,Tianjin 300072,china 2department of mathematics,beijing jiaotong university,beijing 100044,china

There are many results on the flexibility of(general) embeddings of graphs,but few are known about that of strong *** this paper,we study the flexibility of strong embeddings of circular and Mbius ladders on the projective plane and the Klein bottle by using the joint tree model of *** numbers of(nonequivalent) general embeddings and strong embeddings of circular and Mbius ladders on these two nonorientable surfaces are obtained,*** the structures of those strong embeddings are described.

关键词： embedding strong embedding flexibility circular ladders Mbius ladders

Reliability analysis of M/G/1 queues with general retrial times and server breakdowns

在线全文

学校读者我要写书评

暂无评论

Progress in Natural Science:Materials International 2006年第5期16卷 464-473页

作者： WANG Jinting (department of mathematics, beijing jiaotong university, beijing 100044, china) department of mathematics Beijing Jiaotong University Beijing 100044 China

This paper concerns the reliability issues as well as queueing analysis of M/G/1 retrial queues with general retrial times and server subject to breakdowns and repairs. We assume that the server is unreliable and customers who find the server busy or down are queued in the retrial orbit in accordance with a first-come-first-served discipline. Only the customer at the head of the orbit queue is allowed for access to the server. The necessary and sufficient condition for the system to be stable is given. Using a supplementary variable method, we obtain the Laplace-Stieltjes transform of the reliability function of the server and a steady state solution for both queueing and reliability measures of interest. Some main reliability indexes, such as the availability, failure frequency, and the reliability function of the server, are obtained.

关键词： retrial queues general retrial times reliability server breakdowns and repairs.

Recommendation Method for Contrastive Enhancement of Neighborhood Information

在线全文

同方期刊数据库

学校读者我要写书评

暂无评论

Computers, Materials & Continua 2024年第1期78卷 453-472页

作者： Hairong Wang beijing Zhou Lisi Zhang He Ma School of Computer Science and Engineering North Minzu UniversityNingxia750021China

Knowledge graph can assist in improving recommendation performance and is widely applied in various person-alized recommendation ***,existing knowledge-aware recommendation methods face challenges such as weak user-item interaction supervisory signals and noise in the knowledge *** tackle these issues,this paper proposes a neighbor information contrast-enhanced recommendation method by adding subtle noise to construct contrast views and employing contrastive learning to strengthen supervisory signals and reduce knowledge ***,first,this paper adopts heterogeneous propagation and knowledge-aware attention networks to obtain multi-order neighbor embedding of users and items,mining the high-order neighbor informa-tion of users and ***,in the neighbor information,this paper introduces weak noise following a uniform distribution to construct neighbor contrast views,effectively reducing the time overhead of view *** paper then performs contrastive learning between neighbor views to promote the uniformity of view information,adjusting the neighbor structure,and achieving the goal of reducing the knowledge noise in the knowledge ***,this paper introduces multi-task learning to mitigate the problem of weak supervisory *** validate the effectiveness of our method,experiments are conducted on theMovieLens-1M,MovieLens-20M,Book-Crossing,and Last-FM *** results showthat compared to the best baselines,our method shows significant improvements in AUC and F1.

关键词： Contrastive learning knowledge graph recommendation method

ON THE LINEAR CONVERGENCE OF PC-METHOD FOR ACLASS OF LINEAR VARIATIONAL INEQUALITIES

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Journal of Computational mathematics 1999年第2期17卷 199-208页

作者： Nai-hua Xiu(department of mathematics, Nothern jiaotong university, beijing 100044, china Instituteof Applied mathematics, Chinese Academy Of Sciences, beijing 100080, china) 北方交通大学数学系北京

This paper studies the linear convergence properties of a class of the projection and contraction methods for the affine variational inequalities, and proposes a necessary and sufficient condition under which PC-Metho... 详细信息

关键词： affine variational inequality projection and contraction method linear convergence

Techniques for searching first integrals by Lie group and application to gyroscope system

在线全文

学校读者我要写书评

暂无评论

Science china mathematics 2005年第8期48卷 1135-1143页

作者： HU Yanxia & GUAn Keying department of mathematics, School of Science, beijing jiaotong university, beijing 100044, china department of mathematics School of Science Beijing Jiaotong University Beijing China

In the paper, the methods of finding first integrals of an autonomous system using one-parameter Lie groups are discussed. A class of nontrivial one-parameter Lie groups admitted by the classical gyroscope system is found, and based on the properties of first integral determined by the one-parameter Lie group, the fourth first integral of the gyroscope system in Euler case, Lagrange case and Kovalevskaya case can be obtained in a uniform idea. An error on the fourth first integral in general Kovalevskaya case (A=B=2C,zG=0), which appeared in literature is found and corrected.

关键词： one-parameter Lie group first integral gyroscope system

ON THE SINGLE SERVER RETRIAL QUEUE WITH PRIORITY SUBSCRIBERS AND SERVER BREAKDOWNS

在线全文

学校读者我要写书评

暂无评论

Journal of Systems Science & Complexity 2008年第2期21卷 304-315页

作者： Jinting WANG department of mathematics Beijing Jiaotong University Beijing 100044 China

The author concerned the reliability evaluation as well as queueing analysis of M1, M2/G1, G2/1 retrial queues with two different types of primary customers arriving according to independent Poisson flows. In the case of blocking, the first type of customers can be queued whereas the second type of customers must leave the service area but return after some random period of time to try their luck again. The author assumes that the server is unreliable and it has a service-type dependent, exponentially distributed life time as well as a service-type dependent, generally distributed repair time. The necessary and sufficient condition for the system to be stable is investigated. Using a supplementary variable method, the author obtains a steady-state solution for queueing measures, and the transient as well as the steady-state solutions for reliability measures of interest.

关键词： Priority queues reliability retrial queues server breakdowns.