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The Rate of Convergence of Augmented Lagrangian Method for Minimax.Optimization Problems with Eq.ality Constraints

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Journal of the Operations Research Society of China 2024年第2期12卷 265-297页

作者： Yu-Hong Dai li-Wei Zhang LSEC ICMSECAMSSChinese Academy of SciencesBeijing 100190China Institute of Operations Research and Control Theory School of Mathematical SciencesDalian University of TechnologyDalian 116024China

The augmented Lagrangian function and the corresponding augmented Lagrangian method are constructed for solving a class of minimax.optimization problems with eq.ality *** prove that,under the linear independence constraint q.alification and the second-order sufficiency optimality condition for the lower level problem and the second-order sufficiency optimality condition for the minimax.problem,for a given multiplier vectorμ,the rate of convergence of the augmented Lagrangian method is linear with respect to||μu-μ^(*)||and the ratio constant is proportional to 1/c when the ratio|μ-μ^(*)||/c is small enough,where c is the penalty parameter that ex.eeds a threshold c_(*)>O andμ^(*)is the multiplier corresponding to a local ***,we prove that the seq.ence of multiplier vectors generated by the augmented Lagrangian method has at least q.linear convergence if the seq.ence of penalty parameters(ck)is bounded and the convergence rate is superlinear if(ck)is increasing to ***,we use a direct way to establish the rate of convergence of the augmented Lagrangian method for the minimax.problem with a q.adratic objective function and linear eq.ality constraints.

关键词： Minimax.optimization Augmented Lagrangian method.Rate of convergence Second-order sufficiency optimality

Flocking Effects of the Stochastic Cucker-Smale System with Noise

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Journal of Systems Science & Complex.ty 2024年第5期37卷 1978-1994页

作者： HAN Ning GE Bin li lin School of Mathematical Sciences Harbin Engineering University

In this paper, the flocking behavior of a Cucker-Smale model with a leader and noise is studied in a finite time. The authors present a Cucker-Smale system with two nonlinear controls for a complex.network with stochastic synchronization in probability. Based on the finite-time stability theory of stochastic differential eq.ations, the sufficient conditions for the flocking of stochastic systems in a finite time are obtained by using the Lyapunov function method. Finally, the numerical simulation of the particle system is carried out for the leader and noise, and the correctness of the results is verified.

关键词： Cucker-Smale model flocking behavior leader noise

Synthesis and Catalyzing Behavior of Olefin Polymerization of cis-Cyclopentene Bridged Titanocenes

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Chinese Chemical Letters 2000年第11期11卷 979-980页

作者： li J.S. x.ong C.H. Ma Y.q. li J. Chen x. Inst. of Elemento-Organic Chemistry Nankai University Tianjin 300071 China Department of Chemistry Tianjin Normal University Tianjin 300070 China

Two cis-cyclopentene bridged titanocenes have been synthesized. Two homogeneous Ziegler catalysts prepared by activation of synthesized compounds with methylalumox.ne are active for ethylene polymerization reactions.

关键词： cis Ti Synthesis and Catalyzing Behavior of Olefin Polymerization of cis-Cyclopentene Bridged Titanocenes

Indian monsoon drove the dispersal of the thoracica group of Scytodes spitting spiders

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Zoological Research 2024年第1期45卷 152-159页

作者： Yu-Fa Luo Shu-q.ang li School of life and Environmental Sciences Shaoxing UniversityShaoxingZhejiang 312000China Key Laboratory of Zoological Systematics and Evolution Institute of ZoologyChinese Academy of SciencesBeijing 100101China Southeast Asia Biodiversity Research Institute Chinese Academy of SciencesYezinNay Pyi Taw 05282Myanmar

We ex.mined the global biogeography of the Scytodes thoracica group of spitting spiders based on 23 years of sampling at the species level(61 species in the thoracica group and 84 species of Scytodes)using DNA data from six.*** results indicated that the thoracica group initially dispersed from Southeast Asia to East Africa between 46.5 and 33.0 million years ago,and dispersal events intensified between Southeast/South Asia and East/South Africa from the early to late *** timing of these events indicates that Asian-African faunal ex.hange of the thoracica group was driven by the Indian monsoon,and the pattern of dispersal suggests that colonialization took root when the Indian monsoon shifted from a North-South direction to an East-West direction from the middle Eocene.

关键词： Geological event Climate change Ballooning organism Faunal ex.hange Species distribution

Curvature-induced noncommutativity of two different components of momentum for a particle on a hypersurface

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Communications in Theoretical Physics 2021年第2期73卷 73-77页

作者： Z li x.Yang q.H liu School for Theoretical Physics School of Physics and ElectronicsHunan UniversiyChangsha 410082China School of Materials Science and Engineering Guilin University of Electronic TechnologyGuilin541004China Synergetice Innovation Center for q.antum Efects and Applications(SICq.A) Hunan Normal UniversityChangsha 410081China

As a nonrelativistic particle constrained to remain on an(N−1)-dimensional((N≥2))hypersurface embedded in an N-dimensional Euclidean space,two different components pi and pj(i,j=1,2,3,...N)of the Cartesian momentum of the particle are not mutually commutative,and ex.licitly commutation relations[p^(^)_(i),p^(^)_(j)](≠0) depend on products of positions and momenta in uncontrollable *** generalized Dupin indicatrix.of the hypersurface,a local analysis techniq.e,is utilized to ex.lore the dependence of the noncommutativity on the curvatures around a local point of the *** first finding is that the noncommutativity can be grouped into two categories;one is the product of a sectional curvature and the angular momentum,and another is the product of a principal curvature and the *** second finding is that,for a small circle lying a tangential plane covering the local point,the noncommutativity leads to a rotation operator and the amount of the rotation is an angle anholonomy;and along each of the normal sectional curves centering the given point the noncommutativity leads to a translation plus an additional rotation and the amount of the rotation is one half of the tangential angle change of the arc.

关键词： constrained motion q.antization hypersurface Dirac brackets geometric momentum

Spatial Dynamics of Chickenpox.Outbreaks in Rapidly Developing Regions:Implications for Global Public Health

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Biomedical and Environmental Sciences 2024年第7期37卷 687-697页

作者： li Wang Miaomiao Wang Chengdong x. Peihan Wang Meiying You Zihan li x.nmei Chen x.nyu liu x.dong li Yuanyuan Wang Yuehua Hu Dapeng Yin College of Geography and Environmental Science Henan UniversityKaifeng 475001HenanChina State Key Laboratory of Resources and Environmental Information System Institute of Geographic Science and Natural Resource ResearchChinese Academy of SciencesBeijing 100101BeijingChina Key Laboratory of Geospatial Technology for the Middle and Lower Yellow River Regions(Henan University) Ministry of EducationKaifeng 475001HenanChina Office of Epidemiology Chinese Center for Disease Control and PreventionBeijing 102206BeijingChina University of Chinese Academy of Sciences(UCAS) Beijing 100101BeijingChina Weifang Municipal Center for Disease Control and Prevention Weifang 261061ShandongChina Hainan Center for Disease Control and Prevention Haikou 570203HainanChina

Objective The occurrence of chickenpox.in rapidly developing areas poses substantial seasonal risk to ***,certain factors influencing local chickenpox.outbreaks have not been ***,we ex.mined the relationship between spatial clustering,heterogeneity of chickenpox.outbreaks,and socioeconomic factors in Southern *** We assessed chickenpox.outbreak data from Southern China between 2006 and 2021,comprising both relatively fast-growing parts and slower sub-regions,and provides a representative sample of many developing *** analyzed the spatial clustering attributes associated with chickenpox.outbreaks using Moran’s I and local indicators of spatial association and q.antified their socioeconomic determinants using Geodetector q.*** There were significant spatial heterogeneity in the risk of chickenpox.outbreaks,with strong correlations between chickenpox.risk and various factors,particularly demographics and living ***,interactive effects among specific are factors,such as population density and per capita residential building area,percentage of households with toilets,percentage of rental housing,ex.ibited q.statistics of 0.28,0.25,and 0.24,*** This study provides valuable insights into the spatial dynamics of chickenpox.outbreaks in rapidly developing regions,revealing the socioeconomic factors affecting disease *** implications ex.end the formulation of effective public health strategies and interventions to prevent and control chickenpox.outbreaks in similar global contex.s.

关键词： Chickenpox Spatial dynamics Socioeconomic factors

Monogamy and polygamy for the generalized W-class states using unified-(q.s)entropy

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Science China(Physics,Mechanics & Astronomy) 2024年第1期67卷 10-22页

作者： Bo li Bing x.e Zhanjun Zhang Heng Fan School of Computer and Computing Science Hangzhou City UniversityHangzhou 310015China Department of Mathematics East China University of TechnologyNanchang 330013China School of Information&Electronic Engineering(Sussex.Artificial Intelligence Institute) Zhejiang Gongshang UniversityHangzhou 310018China Institute of Physics Chinese Academy of SciencesBeijing 100190China

We describe the entanglement distribution and restricted shareability of the multipartite generalized W-class states and their reduced density matrix.under arbitrary partitions by using monogamy and polygamy relation based on the unified-(q.s)***,we provide an analytical formula of unified-(q.s)entanglement(UE)and an analytical lower bound of unified-(q.s)entanglement of assistance(UEo A)for a reduced density matrix.of a generalized W-class ***,we use these two analytical formulas to derive the monogamy and polygamy ineq.alities for a reduced density matrix.of a q.dit generalized W-class(GW)*** establish two partition-dependent residual entanglements based on the new monogamy relation,which is helpful to obtain a comprehensive analysis of entanglement dynamics of generalized W-class ***,we investigate tighter monogamy and polygamy relations based on the power ofαth(α≥0)for UE andβth(β≥0)for UEo A,*** results show that the entanglement distribution characteristics of generalized W-class states satisfying stronger constraints can be described more accurately.

关键词： monogamy polygamy multiq.dit unified entropy

Effects of hysteresis of static contact angle (HSCA) and boundary slip on the hydrodynamics of water striders

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Acta Mechanica Sinica 2017年第1期33卷 40-61页

作者： J. Zheng B. S. Wang W. q. Chen x. Y. Han C. F. li J. Z. Zhang K. P. Yu School of Energy and Power Engineering Jiangsu UniversityZhenjiang 212013 China China Ship Scientific Research Center Wuxi 200482 China School of Astronautics Harbin Institute of TechnologyHarbin 150001 China

It is known that contact lines keep relatively still on solids until static contact angles ex.eed an interval of hysteresis of static contact angle (HSCA), and contact angles keep changing as contact lines relatively slide on the solid. Here, the effects of HSCA and boundary slip were first distinguished on the micro-curvature force (MCF) on the seta. Hence, the total MCF is partitioned into static and dynamic MCFs correspondingly. The static MCF was found proportional to the HSCA and related with the asymmetry of the micro-meniscus near the seta. The dynamic MCF, ex.rting on the relatively sliding contact line, is aroused by the boundary slip. Based on the Blake-Haynes mechanism, the dynamic MCF was proved important for water walking insects with legs slower than the minimum wave speed . As insects brush the water by laterally swinging legs backwards, setae on the front side of the leg are pulled and the ones on the back side are pushed to cooperatively propel bodies forward. If they pierce the water surface by vertically swinging legs downwards, setae on the upside of the legs are pulled, and the ones on the downside are pushed to cooperatively obtain a jumping force. Based on the dependency between the slip length and shear rate, the dynamic MCF was found correlated with the leg speed U, as , where and are determined by the dimple depth. Discrete points on this curve could give fitted relations as (Suter et al., J. Ex.. Biol. 200, 2523-2538, 1997). Finally, the ax.al torq.e on the inclined and partially submerged seta was found determined by the surface tension, contact angle, HSCA, seta width, and tilt angle. The torq.e direction coincides with the orientation of the spiral grooves of the seta, which encourages us to surmise it is a mechanical incentive for the formation of the spiral morphology of the setae of water striders.

关键词： Seta Water strider Hysteresis of static contact angle (HSCA) Boundary slip

Shear resistance characteristics and influencing factors of root-soil composite on an alpine metal mine dump slope with different recovery periods

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Journal of Mountain Science 2024年第3期21卷 835-849页

作者： PANG Jinghao liANG Shen liU Yabin li Shengwei WANG Shu ZHU Haili li Guorong HU x.asong Department of Geological Engineering Qinghai UniversityXining 810016China Key Laboratory of Genozoic Resource&Environment in North Margin of the Tibetan Plateau Xining 810016China

Artificial vegetation restoration is the main measure for vegetation restoration and soil and water conservation in alpine mine dumps on the q.nghai-Tibet Plateau,***,there are few reports on the dynamic changes and the influencing factors of the soil reinforcement effect of plant species after artificial vegetation restoration under different recovery *** selected dump areas of the Delni Copper Mine in q.nghai Province,China to study the relationship between the shear strength and the peak displacement of the root-soil composite on the slope during the recovery period,and the influence of the root traits and soil physical properties on the shear resistance characteristics of the root-soil composite via in situ direct shear *** results indicate that the shear strength and peak displacement of the rooted soil initially decreased and then increased with the increase of the recovery *** shear strength of the rooted soil and the recovery period ex.ibited a q.adratic function *** is no significant function relationship between the peak displacement and the recovery *** positive correlations(Px.sts between the shear strength of the root-soil composite and the root biomass density,root volume density,and root area ratio,and they show significant linear correlations(P0.05)between the shear strength of the root-soil composite and the root length density,and the root volume ratio of the coarse roots to the fine roots.A significant negative linear correlation(Px.sts between the peak displacement of the rooted soil and the coarse-grain content,but no significant correlations(P>0.05)with the root traits,other soil physical property indices(the moisture content and dry density of the soil),and slope *** coarse-grain content is the main factor controlling the peak displacement of the rooted soil.

关键词： Alpine mine dump Artificial vegetation restoration period Rooted soil Shear resistance characteristics Root traits Soil physical properties