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A Novel Hybrid Vortex Search and Artificial Bee Colony Algorithm for Numerical Optimization Problems

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Wuhan University Journal of Natural Sciences 2017年第4期22卷 295-306页

作者： WANG Zhaowei WU Guomin WAN Zhongping School of mathematics and Statistics Wuhan University department of mathematics and physics Beijing Institute of Petrochemical Technology

Though vortex search（VS） algorithm has good performance in solving global numerical optimization problems, it cannot fully search the whole space occasionally. Combining the vortex search algorithm and the artificial bee colony algorithm（ABC） which has good performance in exploration, we present a HVS（hybrid vortex search） algorithm to solve the numerical optimization problems. We first use the employed bees and onlooker bees of ABC algorithm to find a solution, and then adopt the VS algorithm to find the best solution. In the meantime, we cannot treat the best solution so far as the center of the algorithm all the time. The algorithm is tested by 50 benchmark functions. The numerical results show the HVS algorithm has superior performance over the ABC and the VS algorithms.

关键词： numerical optimization problems vortex searchalgorithm artificial bee colony algorithm hybrid algorithm

A NONLINEAR SCHRODINGER EQUATION WITH COULOMB POTENTIAL

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Acta Mathematica Scientia 2022年第6期42卷 2230-2256页

作者：苗长兴张军勇郑继强 institute of Applied physics and Computational mathematics Beijing 100088China department of mathematics Beijing Institute of TechnologyBeijing 100081China department of mathematics Cardiff UniversityUK

In this paper,we study the Cauchy problem for the nonlinear Schrodinger equations with Coulomb potential i■_(t)u+△u+k/|x|u=λ/|u|^(p-l)u with 10,and the scattering theory when the Coulomb potential is repulsive,i.e.,when K≤O.The argument is based on the newlyestablished interaction Morawetz-type inequalities and the equivalence of Sobolev norms for the Laplacian operator with the Coulomb potential.

关键词： nonlinear Schrodinger equations long range potential global well-posedness blow-up scattering

Asymmetric Information, Heterogeneous Prior Beliefs and Market Regulation

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Acta Mathematicae Applicatae Sinica 2021年第3期37卷 459-476页

作者： Hong LIU Ying JIANG Huai-nian ZHANG KLAS and School of mathematics and Statistics Northeast Normal UniversityChangchun 130024China department of mathematics and physics Beijing Institute of Petrochemical TechnologyBeijing 102617China

This paper studies the trading behavior of an irrational insider and its influence on the market equilibrium in the presence of market regulation.We find that the market with only one insider with private information is almost close to a strong efficient market,under the condition of market regulation.In the equilibrium,the probability of the insider being caught trading with private information is zero,which shows that the reasonable behavior of the regulator is to essentially give up regulation.But the market efficiency and the irrational trader’s trading intensity all greatly improve because of the existence of the market regulation.

关键词： insider trading market regulation heterogeneous prior beliefs asymmetric information

Stability of the Phase Separation State for Compressible Navier-Stokes/Allen-Cahn System

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Acta Mathematicae Applicatae Sinica 2024年第1期40卷 45-74页

作者： Ya-zhou Chen Hakho Hong Xiao-ding Shi department of mathematics College of Mathematics and PhysicsBeijing University of Chemical TechnologyBeijing100029China institute of mathematics State Academy of SciencesPyongyangKorea

This paper is concerned with the large time behavior of the Cauchy problem for Navier-Stokes/AllenCahn system describing the interface motion of immiscible two-phase flow in 3-D. The existence and uniqueness of global solutions and the stability of the phase separation state are proved under the small initial perturbations. Moreover, the optimal time decay rates are obtained for higher-order spatial derivatives of density,velocity and phase. Our results imply that if the immiscible two-phase flow is initially located near the phase separation state, then under small perturbation conditions, the solution exists globally and decays algebraically to the complete separation state of the two-phase flow, that is, there will be no interface fracture, vacuum, shock wave, mass concentration at any time, and the interface thickness tends to zero as the time t → +∞.

关键词： Navier-Stokes/Allen-Cahn system existence uniqueness large time behavior decay rate

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具有淹没分支的有理函数的性质（英文）

Chinese Quarterly Journal of mathematics 2019年第1期34卷 29-42页

作者：庄伟 department of mathematics and physics Beijing Institute of Petrochemical Technology

Let R(z) be an NCP map with buried components of degree d = degf ≥ 2 on the complex sphere ■, and HD denotes the Hausdorff dimension. In this paper we prove that if R_n→ R algebraically, and R_n and R topologically conjugate for all n >> 0, then R_n is an NCP map with buried components for all n >> 0, and for some C > 0,d_H(J(R), J(R_n)) ≤ C(dist(R, R_n))^(1/d),where d_H denotes the Hausdorff distance, and HD(J(R_n)) → HD(J(R)).In this paper we also prove that if the Julia set J(R) of an NCP map R(z) with buried components is locally connected, then any component J_i(R) is either a real-analytic curve or HD(J_i(R)) > 1.

关键词： Julia set Buried components Net Hausdorff dimension

THE LOW MACH NUMBER LIMIT FOR ISENTROPIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH A REVISED MAXWELL'S LAW

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Acta Mathematica Scientia 2023年第3期43卷 1239-1250页

作者：胡玉玺王召 department of mathematics China University of Mining and TechnologyBeijing100083China institute of Applied physics and Computational mathematics Beijing100088China

We investigate the low Mach number limit for the isentropic compressible NavierStokes equations with a revised Maxwell's law(with Galilean invariance) in R^(3). By applying the uniform estimates of the error system, it is proven that the solutions of the isentropic Navier-Stokes equations with a revised Maxwell's law converge to that of the incompressible Navier-Stokes equations as the Mach number tends to zero. Moreover, the convergence rates are also obtained.

关键词： isentropic compressible Navier-Stokes equations low Mach number limit revised Maxwell's law

Single-molecule surface-enhanced Raman scattering of R6G in aqueous environment under non-resonance conditions

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Chinese Optics Letters 2011年第8期9卷 86-89页

作者：谭恩忠殷鹏刚李丽东郭林 School of Chemistry and Environment Beijing University of Aeronautics and Astronautics department of mathematics and physics Beijing Institute of Technology Petrochemical

The single-molecule surface-enhanced Raman scattering （SERS） spectra of Rhodamine 6G （R6G） in an aqueous environment under non-resonance conditions are studied. Series of spectra are recorded in time- mapping mode, and intensity fluctuations of SERS signals and spectral diffusion are observed. The corre- lations between the presence frequency of SERS spectra and number of hot spots as well as the quantity of molecules in scattering volume are examined thoroughly. The results indicate that only molecules located at hot spots produce good signal-to-noise ratio Raman spectra and the origin of fluctuating SERS signals are mainly ascribed to the movement of hot spots.

关键词： Molecules Raman spectroscopy Resonance Scattering Signal to noise ratio

A NONLINEAR SCHR?DINGER EQUATION WITH COULOMB POTENTIAL

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Acta Mathematica Scientia 2022年第6期42卷 2230-2256页

作者：苗长兴张军勇郑继强 institute of Applied physics and Computational mathematics department of mathematics Beijing Institute of Technology department of mathematics Cardiff University

In this paper,we study the Cauchy problem for the nonlinear Schr?dinger equations with Coulomb potential i?tu+Δu+K/|x|u=-λ|u|p-1u with 1 0,and the scattering theory when the Coulomb potential is repulsive,i.e.,when K <0.The argument is based on the newlyestablished interaction Morawetz-type inequalities and the equivalence of Sobolev norms for the Laplacian operator with the Coulomb potential.

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On the Equality of Hausdorff Dimensions and Conformal Measures of Parabolic Maps

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Chinese Quarterly Journal of mathematics 2013年第2期28卷 206-213页

作者： ZHUANG Wei department of mathematics and physics Beijing Institute of Petrochemical Technology Beijing 102617China ) '

Let f, g be two parabolic maps of degree ≥ 2. HD(J) denotes the Hausdorff dimension of the Julia set J and m f and m g denote the t-conformal measure supported on the Julia set J(f) and J(g) respectively. In this paper we show that if J(f) and J(g) are locally connected and f and g topologically conjugate, then HD(J(f)) = HD(J(g)), mg = mfoh-1 .

关键词： Julia set net conformal measure Hausdorff dimension