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An adaptive improvement on PageRank algorithm

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Applied Mathematics(A Journal of Chinese Universities) 2013年第1期28卷 17-26页

作者： liu gui-mei School of Computer & Computing Science Zhejiang University City College

In this article, we introduce the Google＇s method for quality ranking of web page in a formal mathematical format, use the power iteration to improve the PageRank, and also discuss the effect of different q to the Pa... 详细信息

关键词： PageRank power method adjacency matrix Google matrix.

A Nontrivial Product of Filtration s+5 in the Stable Homotopy of Spheres

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Acta Mathematica Sinica,English Series 2007年第3期23卷 385-392页

作者： Xiu gui liu Department of Mathematics and LPMC Nankai University Tianjin 300071 P. R. China

In this paper, some groups Ext A^s.t （Zp, Zp） with specialized s and t are first computed by the May spectrM sequence. Then we make use of the Adams spectral sequence to prove the existence of a new nontrivial family of filtration s＋5 in the stable homotopy groups of spheres πpnq＋（s＋3）pq＋（s＋1）q-5S which is represented （up to a nonzero scalar） by β＋2bohh∈ExtA^s＋5,P^nq＋（n＋3）pq＋（n＋1）q＋s（Zp, Zp） in the Adams spectral sequence, where p ≥ 5 is a prime number, n ≥3, 0≤ s 〈 p - 3, q = 2（p - 1）.

关键词： Stable homotopy of spheres Adams spectral sequence Toda Smith spectrum May spectral sequence

On the Convergence of Products _sh_1h_n in the Adams Spectral Sequence

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Acta Mathematica Sinica,English Series 2007年第6期23卷 1025-1032页

作者： Xiu gui liu School of Mathematical Sciences and LPMC Nankai University Tianjin 300071 P.R. China

Abstract Let A be the mod p Steenrod algebra and S the sphere spectrum localized at p, where p is an odd prime. In 2001 Lin detected a new family in the stable homotopy of spheres which is represented by （b0hn-h1bn-1）∈ ExtA^3,（p^n＋p）q（Zp,Zp） in the Adams spectral sequence. At the same time, he proved that i.（hlhn） ∈ExtA^2,（p^n＋P）q（H^＊M, Zp） is a permanent cycle in the Adams spectral sequence and converges to a nontrivial element ξn∈π（p^n＋p）q-2M. In this paper, with Lin＇s results, we make use of the Adams spectral sequence and the May spectral sequence to detect a new nontrivial family of homotopy elements jj′j^-γsi^-i′ξn in the stable homotopy groups of spheres. The new one is of degree p^nq ＋ sp^2q ＋ spq ＋（s - 2）q ＋ s - 6 and is represented up to a nonzero scalar by hlhnγ-s in the E2^s＋2,＊-term of the Adams spectral sequence, where p ≥ 7, q = 2（p - 1）, n ≥ 4 and 3 ≤ s 〈 p.

关键词： stable homotopy groups of spheres Adams spectral sequence May spectral sequence

New Upper Bounds on Linear Coloring of Planar Graphs

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Acta Mathematica Sinica,English Series 2012年第6期28卷 1187-1196页

作者： Bin liu gui Zhen liu Department of Mathematics Ocean University of China School of Mathematics Shandong University

A proper vertex coloring of a graph G is linear if the graph induced by the vertices of any two color classes is the union of vertex-disjoint paths. The linear chromatic number lc（G） of the graph G is the smallest number of colors in a linear coloring of G. In this paper, it is proved that every planar graph G with girth g and maximum degree A has （1） lc（G） ≤ △ ＋ 21 if △ ≥ 9; （2） lc（G） ≤[△/2]＋ 7 if g≥5; （3） lc（G） ≤ [△/2]＋2ifg≥7and△ ≥7.

关键词： Linear coloring planar graph girth

PARALLEL COMPOUND METHODS FOR SOLVING PARTITIONED STIFF SYSTEMS

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Journal of Computational Mathematics 2001年第6期19卷 639-650页

作者： Li-rong Chen De-gui liu Beijing Inst Comp Applicat & Simulat Technol Beijing 100854 Peoples R China

Deals with the solution of partitioned systems of nonlinear stiff differential equations. Discussion on parallel compound methods; Nonstiff equations; Order conditions of the parallel compound methods (PCM); Numerical... 详细信息

关键词： parallel compound methods stiff systems order conditions convergence stability

On Double Degenerate Quasilinear Parabolic Variational Inequalities

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Acta Mathematicae Applicatae Sinica 2013年第4期29卷 861-868页

作者： gui-fang liu Yi-liang liu Department of Mathematics Hunan City University College of Sciences Guangxi University for Nationalities

We deal with the existence of weak solutions of double degenerate quasilinear parabolic inequalities with a Signorini-Dirichlet-Neumann type mixed boundary condition, which may degenerate in certain subset of the boundary or on a segment in the interior of the domain and in time. The main tools in our study are the maximM monotone property of the derivative operator with zero-initial valued conditions and the theory of pseudomonotone perturbations of maximal monotone mappings.

关键词： double degeneration quasilinear parabolic variational inequalities existence results

Reactor protection system testing for the solid fuel thorium molten salt reactor

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Nuclear Science and Techniques 2016年第5期27卷 238-246页

作者： Zhen-Bao liu Ye liu gui-Min liu Jie Hou Shanghai Institute of Applied Physics Chinese Academy of Sciences Jiading campus Shanghai 201800 China University of Chinese Academy of Sciences Beijing 100049China

Safety system testing is one of the most rigorous and time-consuming requirements in the verification and validation process for reactor protection systems(RPSs).This paper presents the development of a test system for the fully digital and field-programmable gate array-based RPS of the solid fuel(SF) thorium-breeding molten salt pebble bed fluoride salt-cooled reactor(TMSR),denoted as the TMSR-SF1 project,developed by the Chinese Academy of *** test system is applied to the RPS to ensure that it fully meets its designed functions and system *** first introduce the testing principles and ***,the hardware component designs and the software program development of the test system are ***,the test process and test results are discussed and summarized.

关键词：反应堆保护系统试验过程固体燃料熔盐现场可编程门阵列测试系统钍设计功能

The Connectivity and Minimum Degree of Circuit Graphs of Matroids

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Acta Mathematica Sinica,English Series 2010年第2期26卷 353-360页

作者： Ping LI gui Zhen liu ematics and System Sciences Shandong University Ji'nan 250100 P. R. China School of Mathematics and System Sciences Shandong University Ji'nan 250100 P. R. China

Let G be the circuit graph of any connected matroid M with minimum degree 5（G）. It is proved that its connectivity κ（G） ≥2｜E（M） - B（M）｜ - 2. Therefore 5（G） ≥ 2｜E（M） - B（M）｜ - 2 and this bound is t... 详细信息

关键词： matroid circuit graph of matroid connectivity

f-Colorings of Some Graphs of f-Class 1

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Acta Mathematica Sinica,English Series 2008年第5期24卷 743-748页

作者： Xia ZHANG gui Zhen liu College of Mathematics Science Shandong Normal University Ji'nan 250014 P. R. China School of Mathematics and System Sciences Shandong University Ji'nan 250100 P. R. China School of Mathematics and System Sciences Shandong University Ji'nan 250100 P. R. China

An f-coloring of a graph G is an edge-coloring of G such that each color appears at each vertex v V（G） at most f（v） times. The minimum number of colors needed to f-color G is called the f-chromatic index of G and is denoted by X′f（G）. Any simple graph G has the f-chromatic index equal to △f（G） or △f（G）＋ 1, where △f（G） =max v V（G）{[d（v）/f（v）]}. If X′f（G） = △f（G）, then G is of f-class 1; otherwise G is of f-class 2. In this paper, a class of graphs of f-class 1 are obtained by a constructive proof. As a result, f-colorings of these graphs with △f（G） colors are given.

关键词： simple graph edge-coloring f-coloring classification of graphs f-chromatic index