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Short cycle structures for graphs on surfaces and an open problem of Mohar and Thomassen

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Science china mathematics 2006年第2期49卷 212-224页

作者： REN Han & DENG Mo Department of mathematics, East china Normal university, Shanghai 200062, china college of mathematics & information Science, Northwest Normal university, Lanzhou 730070, china Department of mathematics East China Normal University Shanghai China college of mathematics & information Science Northwest Normal University Lanzhou China

In this paper we investigate cycle base structures of a (weighted) graph and show that much information of short cycles is contained in an MCB (i.e., minimum cycle base). After setting up a Hall type theorem for base-transformation, we give a sufficient and necessary condition for a cycle base to be an MCB. Furthermore, we show that the structure of MCB in a (weighted)graph is unique. The property is also true for those having a longest length (although much work has been down in evaluating MCB, little is known for those having a longest length). We use those methods to find out some unknown properties for short cycles sharing particular properties in (unweighted) graphs. As applications, we determine the structures of short cycles in an embedded graph and show that there exist polynomially bounded algorithms in finding a shortest contractible cycle and a shortest two-sided cycle provided such cycles exist. Those answer an open problem of B. Mohar and C. Thomassen.

关键词： cycle base facial cycle graph embedding.

Optimal error bound of restricted Monte Carlo integration on anisotropic Sobolev classes

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Progress in Natural Science:Materials International 2006年第6期16卷 588-593页

作者： GAO Wenhua, YE Peixin and WANG Hui (college of mathematics and System sciences, Xinjiang university, Urumqi 830046, china School of Mathematical sciences and LPMC, Nankai university, Tianjin 300071, china Department of mathematics, Ily Teachers' college, Yining 835000, china college of Science, Hehai university, Nanjing 210098, china) college of mathematics and System sciences Xinjiang University Urumqi 830046 China School of Mathematical sciences and LPMC Nankai University Tianjin 300071 China Department of mathematics Ily Teachers' College Yining 835000 China college of Science Hehai University Nanjing 210098 China

We study the restricted Monte Carlo integration error for anisotropic Sobolev classes. Results prove that with O(log2 n) random bits we have the optimal order for the n-th minimal Monte Carlo integration error with ar... 详细信息

关键词： Monte Carlo integration random bits anisotropic Sobolev classes.

Substrate and Functional Diversity of Protein Lysine Post-translational Modifica

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Genomics, Proteomics & Bioinformatics 2024年第1期22卷 29-49页

作者： Bingbing Hao kaifeng Chen Linhui Zhai Muyin Liu Bin Liu Minjia Tan State Key Laboratory of Drug Research Shanghai Institute of Materia MedicaChinese Academy of SciencesShanghai 201203China university of Chinese Academy of sciences Beijing 100049China Tianjian Laboratory of Advanced Biomedical sciences Institute of Advanced Biomedical SciencesZhengzhou UniversityZhengzhou 450001China Zhongshan Institute for Drug Discovery Shanghai Institute of Materia MedicaChinese Academy of SciencesZhongshan 528400China State Key Laboratory of Pharmaceutical Biotechnology Nanjing UniversityNanjing 210023China Department of Cardiology Shanghai Institute of Cardiovascular DiseasesZhongshan HospitalFudan UniversityShanghai 200032China Jiangsu Key Laboratory of Marine Pharmaceutical Compound Screening College of PharmacyJiangsu Ocean UniversityLianyungang 222005China

Lysine post-translational modifications(PTMs)are widespread and versatile protein PTMs that are involved in diverse biological processes by regulating the fundamental functions of histone and non-histone *** of lysine PTMs is implicated in many diseases,and targeting lysine PTM regulatory factors,including writers,erasers,and readers,has become an effective strategy for disease *** continuing development of mass spectrometry(MS)technologies coupled with antibody-based affinity enrichment technologies greatly promotes the discovery and decoding of *** global characterization of lysine PTMs is crucial for deciphering the regulatory networks,molecular functions,and mechanisms of action of lysine *** this review,we focus on lysine PTMs,and provide a summary of the regulatory enzymes of diverse lysine PTMs and the proteomics advances in lysine PTMs by MS *** also discuss the types and biological functions of lysine PTM crosstalks on histone and non-histone proteins and current druggable targets of lysine PTM regulatory factors for disease therapy.

关键词： Protein lysine PTM Regulatory enzyme PTM crosstalk Drug target Acylation

THE LIMITING CASE OF THIELE'S INTERPOLATING CONTINUED FRACTION EXPANSION

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Journal of Computational mathematics 2001年第4期19卷 433-444页

作者： Jie-qing Tan (Institute of Applied mathematics, college of Science and CAD/CG Division college of Computer & information Hefei, university of Technology, Hefei 230009, china) 中国科学技术大学安徽合肥 230009

By means of the determinantal formulae for inverse and reciprocal differences with coincident data points, the limiting case of Thiele's interpolating continued fraction expansion is studied in this paper and given numerical example shows that the limiting Thiele's continued fraction expansion can be determined once for all instead of carrying out computations for each step to obtain each convergent as done in [3].

关键词： Continued fraction Inverse difference Reciprocal difference Expansion.

Construction of Boolean functions with maximum algebraic immunity and count of their annihilators at lowest degree

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Science china(information sciences) 2010年第4期53卷 780-787页

作者： DU YuSong* & PEI DingYi School of mathematics and information sciences, Guangzhou university, Guangzhou 510006, china School of mathematics and information sciences Guangzhou University Guangzhou China

Boolean functions used in stream ciphers against algebraic attacks are required to have a necessary cryptographic property-high algebraic immunity (AI). In this paper, Boolean functions of even variables with the maximum AI are investigated. The number of independent annihilators at the lowest degree of Boolean functions of even variables with the maximum AI is determined. It is shown that when n is even, one can get an (n + 1)-variable Boolean function with the maximum AI from two n-variable Boolean functions with the maximum AI only if the Hamming weights of the two functions satisfy the given conditions. The nonlinearity of the Boolean functions obtained in this way is computed. Similarly, one can get an (n + 2)-variable Boolean function with the maximum AI from four n-variable Boolean functions with the maximum AI. The nonlinearity of a class of Boolean functions with the maximum AI is determined such that their Hamming weights are either the maximum or the minimum.

关键词： Boolean function algebraic attack algebraic immunity annihilator nonlinearity

Non-wandering points and the depth for graph maps

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Science china mathematics 2007年第12期50卷 1818-1824页

作者： Jie-hua MAI~1 Tai-xiang SUN~(2+) ~1 Institute of mathematics,Shantou university,Shantou 515063,china ~2 college of mathematics and information sciences,Guangxi university,Nanning 530004,china Institute of mathematics Shantou University Shantou China college of mathematics and information sciences Guangxi University Nanning China

Let G be a graph and f:G→G be *** by R(f) andΩ(f) the set of recurrent points and the set of non-wandering points of f ***Ω_0(f) = G andΩ_n(f)=Ω(f|_(Ω_(n-1)(f))) for all n∈*** minimal m∈NU {∞} such thatΩ_m(f)=Ω_(m+1)(f) is called the depth of *** this paper,we show thatΩ_2 (f)=(?) and the depth of f is at most ***,we obtain some properties of non-wandering points of f.

关键词： graph map, non-wandering point, the depth of a graph map

Optical responses of metallic plasmonic arrays under the localized excitation

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Nano Research 2024年第3期17卷 1571-1577页

作者： Sen Yan Hao Ma Yi-Fan Bao Maofeng Cao Chuan Liu kaifeng Zhang Xiaowei Wu Jianbo He Xiang Wang Bin Ren State Key Laboratory of Physical Chemistry of Solid Surfaces Department of ChemistryCollege of Chemistry and Chemical EngineeringXiamen UniversityXiamen 361005China Innovation Laboratory for sciences and Technologies of Energy Materials of Fujian Province(IKKEM) Xiamen 361005China Research&Development Group HitachiLtd.Yokohama 244-0817KanagawaJapan Department of Electronic Science and Engineering Kyoto UniversityKyoto 615-8510Japan

The metallic plasmonic array that can support both propagating surface plasmon polaritons(PSPPs)and localized surface plasmon resonance(LSPR)possesses rich optical properties and remarkable optical performance,making it a powerful platform for applications in photonics,chemistry,and *** practical applications,the excitation spot is usually smaller than the area of metal *** is thus imperative to address“how many array units are enough?”towards a rational design of plasmonic ***,we employed focused ion beam(FIB)to precisely fabricate a series of plasmonic array structures with increased unit *** utilizing photoluminescence(PL)and surface-enhanced Raman spectroscopy(SERS),we found that the array units outside the excitation spot still have a significant impact on the optical response within the *** with the numerical simulation,we found that the boundary of the finite array leads to the loss of PSPP outside the excitation point,which subsequently affects the coupling of PSPP and LSPR in the excitation spot,leading to variations in PL and SERS *** on the findings,we further tuned the LSPR mode of the metal arrays by electrodeposition to obtain strong near-field enhancement without any influence on the PSPP *** work advances the understanding of near-field and far-field optical behavior in finite-size array structures and provides guidance for designing highly-efficient photonic devices.

关键词： plasmonic periodic array finite-size effects dark field scattering surface-enhanced Raman spectroscopy(SERS)

A characterization for a graphic sequence to be potentially C_r-graphic

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Science china mathematics 2010年第11期53卷 2893-2905页

作者： YIN JianHua Department of mathematics, college of information Science and Technology, Hainan university, Haikou 570228, china Department of mathematics College of Information Science and Technology Hainan University Haikou China

Let r 3, n r and π = (d1, d2, . . . , dn) be a graphic sequence. If there exists a simple graph G on n vertices having degree sequence π such that G contains Cr (a cycle of length r) as a subgraph, then π is said to be potentially Cr-graphic. Li and Yin (2004) posed the following problem: characterize π = (d1, d2, . . . , dn) such that π is potentially Cr-graphic for r 3 and n r. Rao and Rao (1972) and Kundu (1973) answered this problem for the case of n = r. In this paper, this problem is solved completely.

关键词： graph cycle degree sequence

D(β)-vertex-distinguishing total coloring of graphs

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Science china mathematics 2006年第10期49卷 1430-1440页

作者： ZHANG Zhongfu,LI Jingwen,CHEN Xiang’en,YAO Bing, WANG Wenjie & QIU Pengxiang Institute of Applied Mathematic, Lanzhou Jiaotong university, Lanzhou 730070, china college of mathematics and information Science, Northwest Normal university, Lanzhou 730070, china college of information and Electrical Engineering, Lanzhou Jiaotong university, Lanzhou 730070, china Institute of Applied Mathematic Lanzhou Jiaotong University Lanzhou China college of mathematics and information Science Northwest Normal University Lanzhou China college of information and Electrical Engineering Lanzhou Jiaotong University Lanzhou China

A new concept of the D(β)-vertex-distinguishing total coloring of graphs, i.e., the proper total coloring such that any two vertices whose distance is not larger than β have different color sets, where the color set of a vertex is the set composed of all colors of the vertex and the edges incident to it, is proposed in this paper. The D(2)-vertex-distinguishing total colorings of some special graphs are discussed, meanwhile, a conjecture and an open problem are presented.

关键词： graph, total coloring, D(β)-vertex-distinguishing total coloring, D(β)-vertexdistinguishing total chromatic number.