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Generalized Lagrangian Duality in Set-valued Vector Optimization via Abstract Subdifferential

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Acta Mathematicae Applicatae Sinica 2022年第2期38卷 337-351页

作者： Yan-fei CHAI san-yang liu Si-qi WANG Department of Mathematics Xi'an Polytechnic UniversityXi'an 710048China School of Mathematics and Statistics Xidian UniversityXi'an 710071China College of Transportation Engineering Chang'an UniversityXi'an 710064China

In this paper,we investigate dual problems for nonconvex set-valued vector optimization via abstract *** first introduce a generalized augmented Lagrangian function induced by a coupling vector-valued function for set-valued vector optimization problem and construct related set-valued dual map and dual optimization problem on the basic of weak efficiency,which used by the concepts of supremum and infimum of a *** then establish the weak and strong duality results under this augmented Lagrangian and present sufficient conditions for exact penalization via an abstract subdifferential of the object ***,we define the sub-optimal path related to the dual problem and show that every cluster point of this sub-optimal path is a primal optimal solution of the object optimization *** addition,we consider a generalized vector variational inequality as an application of abstract subdifferential.

关键词： Nonconvex set-valued vector optimization abstract subdifferential generalized augmented Lagrangian duality exact penalization sub-optimal path

Globally Proper Saddle Point in Ic-Cone-Convexlike Set-Valued Optimization Problems

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Acta Mathematica Sinica,English Series 2009年第11期25卷 1921-1928页

作者： Guo Lin YU san yang liu Institute of Information and Systems Science The North University for Ethnics Yinchuan 750021 P. R. China Department of Applied Mathematics Xidian University Xi'an 710071 P. R. China

The existence conditions of globally proper efficient points and a useful property of ic- cone-convexlike set-valued maps are obtained. Under the assumption of the ic-cone-convexlikeness, the optimality conditions for globally proper efficient solutions are established in terms of Lagrange multipliers. The new concept of globally proper saddle-point for an appropriate set-valued Lagrange map is introduced and used to characterize the globally proper efficient solutions. The results which are obtained in this paper are proven under the conditions that the ordering cone need not to have a nonempty interior.

关键词： set-valued map ic-cone-convexlikeness globally proper efficiency saddle point

Proximal-Based Pre-correction Decomposition Methods for Structured Convex Minimization Problems

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Journal of the Operations Research Society of China 2014年第2期2卷 223-235页

作者： Yuan-Yuan Huang san-yang liu School of Mathematics and Statistics Xidian UniversityXi’an 710071China

This paper presents two proximal-based pre-correction decomposition methods for convex minimization problems with separable *** methods,derived from Chen and Teboulle’s proximal-based decomposition method and He’s parallel splitting augmented Lagrangian method,remain the nice convergence property of the proximal point method and could compute variables in parallel like He’s method under the prediction-correction *** results are established without additional *** the efficiency of the proposed methods is illustrated by some preliminary numerical experiments.

关键词： Structured convex programming Parallel splitting Proximal point method Augmented Lagrangian Prediction-correction method

Characterization of Day–James Spaces and Generalized Day–James Spaces

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Acta Mathematica Sinica,English Series 2016年第7期32卷 813-820页

作者： Jin Huan LI san yang liu Bo LING School of Mathematics and Statistics Xidian University

In this paper, we introduce the definition of generalized Day-James space on Rn （n 〉 2） and give a characterization of it, which extend some known results. In addition, we provide a sufficient and necessary condition for Day-James space, which reappeared Day＇s construction for any two-dimensional normed space to make Birkhoff orthogonality symmetry.

关键词： Birkhoff orthogonality Day James space generalized Day-James space

Hausdorff-type Measures of the Sample Path of Gaussian Random Fields

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Acta Mathematicae Applicatae Sinica 2005年第4期21卷 623-636页

作者： Zhen-long Chen san-yang liu School of Statistics and Computation Science Zhejiang Gongshang University Hangzhou 310035 China Department of Applied Mathematics Xidian University Xi'an 710071 China

Let φ be a Hausdorff measure function and A be an infinite increasing sequence of positive integers. The Hausdorff-type measure φ - mA associated to φ and A is studied. Let X（t）（t ∈ R^N） be certain Gaussian random fields in R^d. We give the exact Hausdorff measure of the graph set GrX（[0, 1]N）, and evaluate the exact φ - mA measure of the image and graph set of X（t）. A necessary and sufficient condition on the sequence A is given so that the usual Hausdorff measure function for X（[0, 1] ^N） and GrX（[0, 1]^N） are still the correct measure functions. If the sequence A increases faster, then some smaller measure functions will give positive and finite （ φ A）-Hausdorff measure for X（[0, 1]^N） and GrX（[0, 1]N）.

关键词： Gaussian random fields image graph Hausdorff-type measure

Design of weak current measurement system and research on temperature impact

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Nuclear Science and Techniques 2024年第4期35卷 46-56页

作者： Chu-Xiang Zhao san-Gang Li Rong-Rong Su Li yang Ming-Zhe liu Qing-Yue Xue Shan Liao Zhi Zhou Qing-Shan Tan Xian-Guo Tuo Yi Cheng College of Nuclear Technology and Automation Engineering Chengdu University of Technology1#DongsanluErxianqiaoChengdu 610059China Applied Nuclear Technology in Geosciences Key Laboratory of Sichuan Province Chengdu University of Technology1#DongsanluErxianqiaoChengdu 610059China University of Science and Technology of China Hefei 230026China School of Physics and Electronic Engineering Sichuan University of Science and EngineeringZigong 643000China

A dedicated weak current measurement system was designed to measure the weak currents generated by the neutron ionization *** system incorporates a second-order low-pass filter circuit and the Kalman filtering algorithm to effectively filter out noise and minimize interference in the measurement *** conducted under normal temperature conditions has demonstrated the system's high precision ***,it was observed that temperature variations can affect the measurement *** were collected across temperatures ranging from -20 to 70℃,and a temperature correction model was established through linear regression fitting to address this *** feasibility of the temperature correction model was confirmed at temperatures of -5 and 40℃,where relative errors remained below 0.1% after applying the temperature *** research indicates that the designed measurement system exhibits excellent temperature adaptability and high precision,making it particularly suitable for measuring weak currents.

关键词： Weak current measurement system Neutron ionization chamber Kalman filter algorithm Temperature correction model

Coupling Co-Ni phosphides for energy-saving alkaline seawater splitting

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Nano Research 2024年第6期17卷 4797-4806页

作者： Weijia liu Wenxian liu Tong Hou Junyang Ding Zhigui Wang Ruilian Yin Xingyuan san Ligang Feng Jun Luo Xijun liu State Key Laboratory of Featured Metal Materials and Life-cycle Safety for Composite Structures Guangxi Key Laboratory of Processing for Nonferrous Metals and Featured MaterialsMOE Key Laboratory of New Processing Technology for Nonferrous Metals and MaterialsSchool of ResourcesEnvironment and MaterialsGuangxi UniversityNanning 530004China College of Materials Science and Engineering Zhejiang University of TechnologyHangzhou 310014China Hebei Key Laboratory of Optic-electronic Information and Materials the College of Physics Science and TechnologyHebei UniversityBaoding 071002China School of Chemistry and Chemical Engineering Yangzhou UniversityYangzhou 225002China ShenSi Lab Shenzhen Institute for Advanced StudyUniversity of Electronic Science and Technology of ChinaShenzhen 518110China

The coupling of energy-saving small molecule conversion reactions and hydrogen evolution reaction(HER)in seawater electrolytes can reduce the energy consumption of seawater electrolysis and mitigate chlorine corrosion ***,the fabrication of efficient multifunctional catalysts for this promising technology is of great ***,a heterostructured catalyst comprising CoP and Ni_(2)P on nickel foam(CoP/Ni_(2)P@NF)is reported for hydrazine oxidation(HzOR)-assisted alkaline seawater *** coupling of CoP and Ni_(2)P optimizes the electronic structure of the active sites and endows excellent electrocatalytic performance for HzOR and ***,the two-electrode HzOR-assisted alkaline seawater splitting(OHzS)cell based on the CoP/Ni_(2)P@NF required only 0.108 V to deliver 100 mA·cm^(−2),much lower than 1.695 V for alkaline seawater electrolysis ***,the OHzS cell exhibits satisfactory stability over 48 h at a high current density of 500 mA·cm^(−2).Furthermore,the CoP/Ni_(2)P@NF heterostructured catalyst also efficiently catalyzed glucose oxidation,methanol oxidation,and urea oxidation in alkaline seawater *** work paves a path for high-performance heterostructured catalyst preparation for energy-saving seawater electrolysis for H_(2) production.

关键词： seawater splitting heterostructure electrocatalysis hydrazine oxidation reaction hydrogen evolution reaction

Nondifferentiable Multiobjective Programming under Generalized d-ρ-(η,θ)-Type I Univexity

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Journal of Mathematical Research and Exposition 2011年第4期31卷 655-664页

作者： Chun Feng WANG san yang liu Department of Mathematical Sciences Xidian University Shaanxi 710071 P. R. China College of Mathematics and Information Henan Normal University Henan 453007 P. R. China

In this puper, on the basis of notions of d-p-（η, θ）-invex function, type I function and univex function, we present new classes of generalized d-p-（η, θ）-type I univex functions. By using these new concepts, we obtain several sufficient optimality conditions for a feasible solution to be an efficient solution, and derive some Mond-Weir type duality results.

关键词： multiobjective programming generalized d-p-(η, θ)-type I univexity duality optimality.

Mechanism and control of nonuniform phase transformation of microalloyed dual-phase steel during cooling process after hot rolling

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Journal of Iron and Steel Research(International) 2024年第2期31卷 428-441页

作者： Wen-quan Sun Sheng-yi Yong Tie-heng Yuan Chao liu san-bao Zhou Rui-chun Guo Meng-xia Tang National Engineering Research Center for Advanced Rolling and Intelligent Manufacturing University of Science and Technology BeijingBeijing100083China Strip Production Plant Xichang Steel and Vanadium Corporation of Pangang GroupXichang615000SichuanChina

After cooling in the hot rolling process,the metallographic structure of microalloyed dual-phase steel is nonuniform along the rolling direction,while the thickness fluctuation of microalloyed dual-phase steel with a nonuniform metallographic structure will occur during cold *** mechanism of nonuniform phase transformation of microalloyed dual-phase steels was studied during the cooling process after hot rolling,and the nonuniform phase transformation of microalloyed dual-phase steel was regulated during the cooling process after hot rolling through process ***,the empirical equation of phase transformation temperature was measured by a dilatometer considering thermal ***,the phase field and temperature field of laminar cooling process were calculated to provide initial boundary conditions for the finite element *** that,the coupling finite element model of the temperature phase transformation of the strip steel in coiling transportation process was *** simulation results show that the different thermal contact conditions of the microalloyed dual-phase steel during coil transportation lead to uneven cooling of the coil,which leads to nonuniform transformation of the coil along the rolling *** addition,by prolonging the time interval from coiling to unloading,the phenomenon of nonuniform phase transformation of microalloyed dual-phase steel can be effectively *** simulation results are applied to industrial *** application results show that prolonging the time interval from coiling to unloading can effectively improve the nonuniform phase transformation of microalloyed dual-phase steel in the cooling process after hot rolling.

关键词： Microalloyed dual-phase steel Thickness fluctuation Cooling Heat conduction Nonuniform phase transition Finite element method