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Batalin-Vilkovisky algebra structures on Hochschild cohomology of generalized weyl algebras

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Frontiers of mathematics in China 2022年第5期17卷 915-941页

作者： Liyu LIU wen ma School of mathematical Sciences Yangzhou UniversityYangzhou 225002China

we devote to the calculation of Batalin–Vilkovisky algebra structures on the Hochschild cohomology of skew Calabi–Yau generalized weyl *** first establish a Van den Bergh duality at the level of *** based on the results of Solotar et al.,we apply Kowalzig and Krähmer's method to the Hochschild homology of generalized weyl algebras,and translate the homological information into cohomological one by virtue of the Van den Bergh duality,obtaining the desired Batalin–Vilkovisky algebra ***,we apply our results to quantum weighted projective lines and Podleśquantum spheres,and the Batalin–Vilkovisky algebra structures for them are described completely.

关键词： Hochschild cohomology Batalin-Vilkovisky algebra Van den Bergh duality generalized weyl algebra

Number of fixed points for unitary T^n-1-manifold

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Frontiers of mathematics in China 2019年第4期14卷 819-831页

作者： Shiyun wen Jun ma School of mathematical Sciences Capital Normal University Beijing 100048 China College of mathematics Taiyuan University of Technology Taiyuan 030024 China

Let M be a 2n-dimensional closed unitary manifold with a T^n-1- action with only isolated fixed points. In this paper, we first prove that the equivariant cobordism class of a unitary T^n-1-manifold M is just determined by the equivariant Chern numbers C^Tn-1/ω[M], where ω=(i1,i2,…,i6)are the multi-indexes for all i1,i2,…,i6∈N. Then we show that if M does not bound equivariantly, then the number of fixed points is greater than or equal to [n/6]+ 1, where [n/6] denotes the minimum integer no less than n/6.

关键词： Unitary torus manifold equivariant Chern number cobordism localization theorem

二氢杨梅素分子结构与性质的密度泛函理论研究

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原子与分子物理学报 2025年第1期42卷 29-34页

作者：辛国鹏毛敏刘信平马文涛马杰张煜湖北民族大学化学与环境工程学院恩施445000

本文基于密度泛函理论(DFT),采用B3LYP泛函结合6-31G基组上对二氢杨梅素的分子几何结构进行了优化,在此基础上以水为溶剂计算二氢杨梅素分子的活性位点以及红外光谱进行分析.静电势结果表明二氢杨梅素的亲核活性位点位于酚羟基氢原子(H... 详细信息

本文基于密度泛函理论(DFT),采用B3LYP泛函结合6-31G基组上对二氢杨梅素的分子几何结构进行了优化,在此基础上以水为溶剂计算二氢杨梅素分子的活性位点以及红外光谱进行分析.静电势结果表明二氢杨梅素的亲核活性位点位于酚羟基氢原子(H23)附近;而亲电活性位点位于氧原子(O32)及其附近.前线分子轨道研究结果表明二氢杨梅素分子的最高占据轨道(HOMO)都位于酮基氧(O32)和羟基氧(O20)附近,说明这些位点易与亲电试剂反应.而最低空轨道(LUMO)位于碳原子(C12、C13、C14)区域,表明这些区域可与亲核试剂反应.简缩福井函数(f)结果证实了位于C-O-C键中的氧原子的f-值的亲电活性较其他位点氧原子大;而位于C8碳原子的f^(+)值较大,因此该位点亲核活性较强.通过理论计算所得到的二氢杨梅素的红外光谱数据与实验所得到的红外光谱数据相差不大,这就说明理论计算结果是较为可靠的.从而为实验和理论研究二氢杨梅素结构与性质的关系提供了一定的理论参考.

关键词：二氢杨梅素密度泛函理论反应活性位点量子化学计算

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Lump solutions to a generalized Hietarinta-type equation via symbolic computation

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Frontiers of mathematics in China 2020年第3期15卷 435-450页

作者： Sumayah BATwA wen-Xiu ma Department of mathematics King Abdulaziz UniversityJeddahSaudi Arabia Department of mathematics Zhejiang Normal UniversityJinhua 321004China Department of mathematics and Statistics University of South FloridaTampaFL 33620USA School of mathematics South China University of TechnologyGuangzhou 510640China

Lump solutions are one of important solutions to partial differential equations,both linear and *** paper aims to show that a Hietarinta-type fourth-order nonlinear term can create lump solutions with second-order linear dispersive *** key is a Hirota bilinear *** solutions are constructed via symbolic computations with maple,and specific reductions of the resulting lump solutions are *** illustrative examples of the generalized Hietarinta-type nonlinear equations and their lumps are presented,together with three-dimensional plots and density plots of the lump solutions.

关键词： Soliton equation lump solution symbolic computation Hirota derivative dispersion relation

身体还是认知努力的损害?抑郁症努力奖赏动机评估及计算模型应用

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心理科学进展 2025年第1期33卷 107-122页

作者：温秀娟马毓璟谭斯祺李芸刘文华广州医科大学附属脑科医院广州510370 广州医科大学卫生管理学院广州511436

动机损害是抑郁症的常见特征,患者常表现出异常的奖励评估或体验等行为。理解抑郁症患者努力奖赏动机活动中不愿意付出努力的类型——是不愿意付出身体努力还是不愿意付出认知努力,对帮助患者恢复社会功能活动具有重要作用。然而,当前... 详细信息

动机损害是抑郁症的常见特征,患者常表现出异常的奖励评估或体验等行为。理解抑郁症患者努力奖赏动机活动中不愿意付出努力的类型——是不愿意付出身体努力还是不愿意付出认知努力,对帮助患者恢复社会功能活动具有重要作用。然而,当前缺少研究探讨努力类型(身体或认知努力)对研究认识的影响,同时,计算模型方法具有能够精细评估动机相关变量的优势,这一方法在该领域中并未得到普及应用。通过实验方法区分评估抑郁症患者“认知努力”和“身体努力”这两种不同的努力决策,并结合计算模型的数据分析方式,从努力奖赏动机这一角度探索抑郁症动机损害行为,对揭示这一损害潜在的认知神经基础具有促进作用。

关键词：抑郁症快感缺失动机损害身体努力认知努力计算模型

A refined invariant subspace method and applications to evolution equations

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Science China mathematics 2012年第9期55卷 1769-1778页

作者： ma wen-Xiu Department of mathematics and Statistics University of South Florida Tampa FL 33620-5700 USA

The invariant subspace method is refined to present more unity and more diversity of exact solutions to evolution equations. The key idea is to take subspaces of solutions to linear ordinary differential equations as invariant subspaces that evolution equations admit. A two-component nonlinear system of dissipative equations is analyzed to shed light oi1 the resulting theory, and two concrete examples are given to find invariant subspaces associated with 2nd-order and 3rd-order linear ordinary differentii equations and their corresponding exact solutions with generalized separated variables.

关键词： invariant subspace generalized separation of variables evolution equation

Stochastic Approximation for Expensive One-Bit Feedback Systems

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Tsinghua Science and Technology 2017年第3期22卷 317-327页

作者： Xiaoqin Zhang Huimin ma Jinghuan wen Department of Electronic Engineering Tsinghua UniversityBeijing 100084China

One-bit feedback systems generate binary data as their output and the system performance is usually measured by the success rate with a fixed parameter combination. Traditional methods need many executions for parameter optimization. Hence, it is impractical to utilize these methods in Expensive One-Bit Feedback Systems （EOBFSs）, where a single system execution is costly in terms of time or money. In this paper, we propose a novel algorithm, named Iterative Regression and Optimization （IRO）, for parameter optimization and its corresponding scheme based on the maximum Likelihood Estimation （MLE） method and Particle Swarm Optimization （PSO） method, named MLEPSO-IRO, for parameter optimization in EOBFSs. The IRO algorithm is an iterative algorithm, with each iteration comprising two parts： regression and optimization. Considering the structure of IRO and the Bernoulli distribution property of the output of EOBFSs, MLE and a modified PSO are selected to implement the regression and optimization sections, respectively, in MLEPSO-IRO. we also provide a theoretical analysis for the convergence of MLEPSO-IRO and provide numerical experiments on hypothesized EOBFSs and one real EOBFS in comparison to traditional methods. The results indicate that MLEPSO-IRO can provide a much better result with only a small amount of system executions.

关键词： stochastic approximation parameter optimization one-bit feedback system regression maximumLikelihood Estimation (MLE)

Optimization of the Occlusion Strategy in Visual Tracking

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Tsinghua Science and Technology 2016年第2期21卷 221-230页

作者： Jinghuan wen Huimin ma Xiaoqin Zhang Department of Electronic Engineering Tsinghua University

Interference and anti-interference are two opposite and important issues in visual tracking. Occlusion interference can disguise the features of a target and can also be used as an effective benchmark to determine whether a tracking algorithm is reliable. In this paper, we proposed an inner Particle Swarm Optimization （PSO） algorithm to locate the optimal occlusion strategy under different tracking conditions and to identify the most effective occlusion positions and direction of movement to allow a target to evade tracking. This algorithm improved the standard PSO process in three ways. First, it introduced a death process, which greatly reduced the time cost of optimization. Second, it used statistical data to determine the fitness value of the particles so that the fitness more accurately described the tracking. Third, the algorithm could avoid being trapped in local optima, as the fitness changes with time. Experimental results showed that this algorithm was able to identify a global optimal occlusion strategy that can disturb the tracking machine with 86.8% probability over more than 10 000 tracking processes. In addition, it reduced the time cost by approximately 80%, compared with conventional PSO algorithms.

关键词： particle swarm optimization virtual tracking occlusion interference death process statistical fitnessfunction

AN ABLOwITZ-LADIK INTEGRABLE LATTICE HIERARCHY wITH MULTIPLE POTENTIALS

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Acta mathematica Scientia 2020年第3期40卷 670-678页

作者： wen-Xiu ma School of mathematics South China University of TechnologyGuangzhou 510640China Department of mathematics King Abdulaziz UniversityJeddahSaudi Arabia Department of mathematics and Statistics University of South FloridaTampaFL 33620USA Department of mathematics Zhejiang Normal UniversityJinhua 321004China College of mathematics and Systems Science Shandong University of Science and TechnologyQingdao 266590China Department of mathematical Sciences North-West UniversityMafikeng CampusMmabatho 2735South Africa

within the zero curvature formulation,a hierarchy of integrable lattice equations is constructed from an arbitrary-order matrix discrete spectral problem of Ablowitz-Ladik *** existence of infinitely many symmetries and conserved functionals is a consequence of the Lax operator algebra and the trace *** the involved two potential vectors are scalar,all the resulting integrable lattice equations are reduced to the standard Ablowitz-Ladik hierarchy.

关键词： Integrable lattice discrete spectral problem symmetry and conserved functional