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A Generalization of Hall-Higman's reduction Theorem

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Acta Mathematica Sinica,English Series 1995年第1期11卷 74-80页

作者： wang yanming {2. of mathematics zhongshan University guangzhou,510275 china harm.showa-u.ac.jp

In this paper,we generalize the Hall-Higman’s reduction theorem by dropping the restrictive hypothesis(丨G丨,丨H丨)=1 and determine the detailed structure of G.

关键词： Hall A Generalization of Hall-Higman’s reduction Theorem

On a problem of Skiba from the Kourovka Notebook

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Science china mathematics 2004年第1期47卷 96-103页

作者： wang yanming & WEI HuaquanLingnan College and School of {2., zhongshan University, guangzhou 510275, china School of {2., zhongshan University, guangzhou 510275, china department of {2., Guangxi Teacher’s College, Nanning 530001, china 1. Lingnan College and School of mathematics Zhongshan University 510275 Guangzhou China 2. School of mathematics Zhongshan University 510275 Guangzhou China 3. department of mathematics Guangxi Teacher’s College 530001 Nanning China

In this paper, we give a positive answer to a recent open problem of Skiba in Kourovka Notebook without using the odd order theorem and other deep theorems. Some of the techniques are improved.

关键词： supersolvable group c-supple merited subgroup complemented subgroup generalized fitting subgroup saturated formation

ON THE MODULI NUMBEr OF pLANE CUrVE SINGULArITIES WITHONE CHArACTErISTIC pAIr

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Chinese Annals of mathematics,Series B 1999年第4期20卷 407-412页

作者： CHEN HAO(department of mathematics, {2. University, guangzhou 510275, china) zhongshan Univ Dept Math Guangzhou 510275 Peoples R China

The author gives another linear-algebraic proof of the famous result of Zariski, Delorme,Briancon- Granger- Maisonobe about the moduli number of plane curve singularities with the same topological type as Xa + Yb = 0 (i.e.,with one characteristic pair). Since the original proof depends very much on the division theorem of Briancon, it cannot be generalized to higher dimensions. It is hopeful that the proof here will be applied to the higher dimensional cases.

关键词： Moduli number plane curve Singularity Characteristic pair

ID-WAVELETS METHOD FOr HAMMErSTEIN INTEGrAL EQUATIONS

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Journal of Computational mathematics 1998年第6期16卷 499-508页

作者： Xian-biao wang Wei Lin (department of {2., zhongshan University, guangzhou 510275, china) zhongshan Univ Dept Math Canton 510275 Peoples R China

The numerical solutions to the nonlinear integral equations of Hammerstein-type y(t) = f(t) + integral(0)(1)k(t, s)g(s, y(s))ds, t is an element of [0,1] are investigated. A degenerate kernel scheme basing on ID-wavelets combined with a new collocation-type method is presented. The Daubechies interval wavelets and their main properties are briefly mentioned. The rate of approximation solution converging to the exact solution is given. Finally we also give two numerical examples.

关键词： nonlinear integral equation interval wavelets degenerate kernel

population-size-dependent branching processes in Markovian random environments

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Chinese Science Bulletin 1998年第8期43卷 635-638页

作者： wang Hanxing 1 and DAI Yonglong 2.1. department of {2., Shanghai University, Shanghai 2.1800, china 2. department of {2., zhongshan University, guangzhou 510275, china department of mathematics Shanghai University Shanghai China department of mathematics Zhongshan University Gunngzhou China

A branching model {Z n} n≥0is considered where the offspring distribution of the population’s evolution is not only dependent on the population size, but also controlled by a Markovian environmental process {ξ n} n≥0. For this model, asymptotic behaviour is studied such as limn→∞Z n and limn→∞Z n/m n in the case that the mean m k, θof the offspring distribution converges to m>1 as the population size k grows to ∞. In the case that {ξ n} n≥0is an irreducible positive recurrent Markov chain, certain extinction (i.e. p(Z n=0 for some n)=1) and noncertain extinction (i.e. p(Z n=0 for some n)re studied.

关键词： Markov chains in random environments stochastic population models branching processes.

Drogue detection for autonomous aerial refueling via hybrid pigeon-inspired optimized color opponent and saliency aggregation

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Chinese Journal of Aeronautics 2024年第5期37卷 27-38页

作者： Tongyan WU Haibin DUAN yanming FAN State Key Laboratory of Virtual reality Technology and Systems School of Automation Science and Electrical EngineeringBeihang UniversityBeijing 100083China Virtual reality Fundamental research Laboratory Department of Mathematics and TheoriesPeng Cheng LaboratoryShenzhen 518000China AVIC Shenyang Aircraft Design and research Institute Shenyang 110035China

Drogue detection is one of the challenging tasks in autonomous aerial refueling due to the requirement for accuracy and *** detection based on image intrinsic cues can achieve fast detection,but with poor *** studies reveal that optimization-based methods provide accurate and quick solutions for saliency *** paper presents a hybrid pigeon-inspired optimization method,the optimized color opponent,that aims to adjust the weight of color opponent channels to detect the drogue *** can optimize the weights in the selected aerial refueling scene offline,and the results are applied for drogue detection in the scene.A novel algorithm aggregated by the optimized color opponent and robust background detection is presented to provide better precision and *** results on benchmark datasets and aerial refueling images show that the proposed method successfully extracts the saliency region or drogue and exhibits superior performance against the other saliency detection methods with intrinsic *** algorithm designed in this paper is competent for the drogue detection task of autonomous aerial refueling.

关键词： Autonomous aerial refueling Drones Hybrid pigeon-inspired optimization Color opponent Saliency detection Saliency aggregation

The Isotone Mappings on Ockham Algebras

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Acta Mathematica Sinica,English Series 1996年第1期12卷 43-48页

作者： Fang Jie department of mathematics {2. University guangzhou, 510275 china 中山大学数学系广东广州

In this paper we shall describe some algebraic concepts of Ockham algebras. We show that, if L, M∈K1,1 then H（S（L）,S（M））≌S（H（L,M））.

关键词： Isotone (Ockham) Isomorphism

T1 theorem for Besov and Triebel-Lizorkin spaces

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Science china mathematics 2005年第5期48卷 657-665页

作者： DENG Donggao & HAN Yongsheng department of mathematics, {2. University, guangzhou 510275, china department of mathematics, Auburn University, Alabama, 36849, USA Dept. of Math. Zhongshan Univ. Guangzhou 510275 China Dept. of Math. Auburn Univ. Alabama 36849 United States

Using the discrete Calderon type reproducing formula and the plancherelpolya characterization for the Besov and Triebel-Lizorkin spaces, the T1 theorem for the Besov and Triebel-Lizorkin spaces was proved.

关键词： T1 theorem Besov and Triebel-Lizorkin spaces Calderon reproducing formula plancherel-polya inequalities.

Twisting products of Hopf algebras and quantum double

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Chinese Science Bulletin 1999年第4期44卷 309-312页

作者： HU Guoquandepartment of mathematics, {2. University, guangzhou 510275, china department of mathematics Zhongshan University Guangzhou China

Let σ be a skew pairing on the pair (B, H) of Hopf algebras, and A a left(B, H) bicomodule algebra. A new algebra A_σ, called the twisting product of A, is obtained by alternating the multiplication of A using σ and the coactions on A by B and H. σ induces a skew pairing on (B B,H H), and the regular comodule structures of B and H induce a left (B B,H H) bicomodule algebra structure on B H, and the associated twisting product (B H)is a Hopf algebra, with the tensor coalgebra structure; moreover, A_σ remains a left (B H),comodule algebra. In particular,a description of the Drinfeld double is obtained from the twisting point of view. In addition, smash products appear as special cases. Dually, the construction of twisting coproducts is introduced by using copairings, and the Drinfeld quantum codouble and some smash coproducts are described.

关键词： skew (co)pairing twisting (co)products (co)quantum double.