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Estimate of error bounds in the improved support vector regression

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Progress in Natural Science:Materials International 2004年第4期 76-78页

作者： SUN Yanfeng, LIANG Yanchun, WU Chunguo, YANG Xiaowei, LEE Heow Pueh2 and LIN Wu Zhong (1. College of Computer Science and technology, Jilin university, Changchun 13.012, china 2. Institute of High Performance Computing, Singapore 117528, Singapore 3. {3. of applied mathematics, south china university of technology, guangzhou 510640, china 4. Centre for ACES, {3. of Mechanical Engineering, National university of Singapore, 119260, Singapore) College of Computer Science and technology Jilin UniversityChangchun 130012China College of Computer Science and technology Jilin UniversityChangchun 130012China Institute of High Performance Computing Singapore 117528Singapore department of applied mathematics South China University of TechnologyGuangzhou 510640China Centre for ACES Department of Mechanical EngineeringNational University of Singapore119260Singapore Institute of High Performance Computing Singapore 117528Singapore

An estimate of a generalization error bound of the improved support vector regression (SVR) is provided based on our previous work. The boundedness of the error of the improved SVR is proved when the algorithm is appl... 详细信息

关键词： support vector regression (SVR) generalization error approximation error estimation error.

Free orthodox semigroups and free bands with inverse transversals

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Science china mathematics 2010年第11期53卷 3015-3026页

作者： TANG XiLin department of mathematics, south china university of technology,{3., china 1. department of mathematics South China University of Technology Guangzhou 510640 China

It is well known that the subclass of inverse semigroups and the subclass of completely regular semigroups of the class of regular semigroups form the so called e-varieties of semigroups. However, the class of regular semigroups with inverse transversals does not belong to this variety. We now call this class of semigroups the ist-variety of semigroups, and denote it by IST . In this paper, we consider the class of orthodox semigroups with inverse transversals, which is a special ist-variety and is denoted by OIST . Some previous results given by Tang and Wang on this topic are extended. In particular, the structure of free bands with inverse transversals is investigated. Results of McAlister, McFadden, Blyth and Saito on semigroups with inverse transversals are hence generalized and enriched.

关键词： inverse transversal ist-variety free orthodox semigroup free band

On the Existence of Nontrivial Solutions of Quasi-asymptotically Linear Problem for the P-Laplacian

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Acta Mathematicae Applicatae Sinica 2002年第4期18卷 599-606页

作者： Zhi-hui Chen, Yao-tian Shendepartment of applied mathematics,{3., guangzhou 510640, china department of applied mathematics South China University of Technology Guangzhou 510640 China

In this paper, we study the existence of nontrivial solutions for the following Dirichlet problem for the p-Laplacian (p > 1):where Ω is a bounded domain in Rn (A≥1) and f(x,u) is quasi-asymptotically linear with respect to |u|p-2 u at infinity. Recently it was proved that the above problem has a positive solution under the condition that f(x, s)/sp-1 is nondecrcasing with respect to s for all x ∈Ω and some others. In this paper. by improving the methods in the literature, we prove that the functional corresponding to the above problem still satisfies a weakened version of (P.S.) condition even if f(x, s)/sp-1 isn't a nondecreasing function with respect to s, and then the above problem has a nontrivial weak solution by Mountain Pass Theorem.

关键词： Quasi-asymptotically linear weak solution critical point Palais-Smale type condition

Invariant basis number of the ring of Morita context

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Chinese Science Bulletin 1997年第8期42卷 633-636页

作者： HAO Zhifengdepartment of applied mathematics,{3., guangzhou 510641, china department of applied mathematics South China University of Technology Guangzhou 510641 China

A ring is said to be an IBN ring if for every free left module A,every two bases of A havethe same *** class of such a ring has been applied to alegbraic K-theory and *** free module over the IBN ring can be defined b... 详细信息

关键词： ring of Morita context IBN ring Five Lemma.

Transitional function of DG to CA3.in the hippocampus

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Progress in Natural Science:Materials International 2007年第12期17卷 1436-1444页

作者： Yan Chuankui1 and Liu Shenquan2(1. department of mathematics, Hangzhou Normal university, Hangzhou 3.003.,{3. 2. department of applied mathematics, School of Mathematical Sciences, south china university of technology, guangzhou 510640,{3.) department of mathematics Hangzhou Normal University Hangzhou 310036 China department of applied mathematics School of Mathematical Sciences South China University of Technology Guangzhou 510640 China

Using single cell channel model, the transmission features of CA3.DG network in the hippocampus are investigated. The influence of the stimulation on discharge pattern of pyramidal neurons is analyzed, which shows that it starts with period spiking discharges, followed by period-doubling bifurcation to chaos, and period 3.discharge evolving into chaos, and ultimately a period of bursting discharges. By the synaptic model, the CA3.DG network model is constructed, which analyzes the summation of postsynaptic currents in the network, the influence of postsynaptic current on discharge rhythm as well as the mechanism of bursting discharges. The strong capacity of spatiotemporal encoding in the network indicates the features of CA3.network during the information transmission process in the hippocampus. The modeling result with time delay of the synaptic transmission is in accordance with the experimental phenomena of action potential in the hippocampus.

关键词： hippocampus CA3.DG period-doubling bifurcation chaos.

Microwave peak absorption frequency of liquid

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Science china(Physics,Mechanics & Astronomy) 2008年第9期51卷 1254-1263页

作者： HAN GuangZe1 & CHEN MingDong2 1 department of Physics,south china {3. of technology,guangzhou 510640,china 2 guangzhou Auto College,south china {3. of technology,guangzhou 510800,china 1. department of Physics South China University of Technology Guangzhou 510640 China 2. guangzhou Auto College South China University of Technology Guangzhou 510800 China

Microwave-assisted extraction is a new effective method which has practical ap-plications in many fields. Microwave heating is one of its physical mechanisms,and it also has the characteristic of selectivity. When the applied microwave fre-quency equals a certain absorption frequency of the material (or specific compo-nent),the material will intensively absorb microwave energy. This is also known as resonant absorption,and the frequency is called the peak absorption frequency which depends on the physical structure of the material. In this work,dynamic hy-drogen bond energy was included in molecular activation energy; with the liquid cell model,the expression of interaction energy between dipolar molecules was derived. The rotational relaxation time was gotten from the Eyring viscosity formula. Then based on the relationship between dielectric dissipation coefficient and re-laxation time,the expression of microwave peak absorption frequency as a func-tion of the material physical structure,rotational inertia and electrical dipole mo-ment of molecules was established. These theoretical formulas were applied to water and benzene,and the calculated results agree fairly well with the experi-mental data. This work can not only deepen the study of the interaction between microwave and material,but also provide a possible guide for the experiment of microwave-assisted extraction.

关键词： microwave-assisted extraction microwave heating relaxation time liquid viscosity peak absorption fre-quency

Normality and shared values concerning differential polynomials

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Science china mathematics 2010年第3期53卷 749-754页

作者： LEI ChunLin 1 & FANG MingLiang 2, 1 department of applied mathematics, {3. china Agricultural university, guangzhou 510642, china 2 Institute of applied mathematics, {3. china Agricultural university, guangzhou 510642, china 1. department of applied mathematics South China Agricultural University Guangzhou 510642 China2. Institute of Applied Mathematics South China Agricultural University Guangzhou 510642 China

Let F be a family of functions meromorphic in a domain D, let P be a polynomial with either deg P≥3.or deg P = 2 and P having only one distinct zero, and let b be a finite nonzero complex number. If, each pair of fun... 详细信息

关键词： meromorphic function normality shared value

Periodic blow-up solutions and their limit forms for the generalized Camassa-Holm equation

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Progress in Natural Science:Materials International 2008年第3期18卷 259-266页

作者： Zhengrong Liu a, Boling Guob a School of Mathematical Sciences, south china university of technology, guangzhou 510640, china b Institute of {3. Physics and Computational mathematics, Beijing 100088, china School of Mathematical Sciences South China University of Technology Guangzhou 510640 China Institute of applied Physics and Computational mathematics Beijing 100088 China

In this paper, we consider the generalized Camassa-Holm equation ut+2kux-uxxt+ au~2ux=2uxuxx+uuxxxUnder substitution ξ=x-ct, some new explicit periodic wave solutions and their limit forms are presented through some special phase orbits. These periodic wave solutions tend to infinity on ξ-u plane periodically. Thus we call them periodic blow-up solutions. To our knowledge, such periodic blow-up solutions have not been found in any other equations.

关键词： Generalized Camassa–Holm equation Explicit solutions Periodic blow-up

Two new types of bounded waves of CH-γ equation

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Science china mathematics 2005年第12期48卷 1618-1630页

作者： GUO Boling & LIU Zhengrong Institute of applied Physics and Computational mathematics, Beijing 100088, china School of Mathematical Sciences and Center for Nonlinear Science Studies,{3., guangzhou 510640, china 1. Institute of applied Physics and Computational mathematics 100088 Beijing China 2. School of Mathematical Sciences and Center for Nonlinear Science Studies South China University of Technology 510640 Guangzhou China

In this paper, the bifurcation method of dynamical systems and numerical approach of differential equations are employed to study CH-γ equation. Two new types of bounded waves are found. One of them is called the compacton. The other is called the generalized kink wave. Their planar graphs are simulated and their implicit expressions are given. The identity of theoretical derivation and numerical simulation is displayed.

关键词： CH-γ equation,compactons,generalized kink waves.