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EXISTENCE AND CONVERGENCE RESULTS FOR AN ELASTIC FRICTIONAL CONTACT PROBLEM WITH NONMONOTONE SUBDIFFERENTIAL BOUNDARY CONDITIONS

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Acta Mathematica Scientia 2021年第4期41卷 1151-1168页

作者： Yongjian LIU Stanisiaw MIGÓRSKI Van Thien NGUYEN Shengda ZHENG Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing Yulin Normal UniversityYulin 537000China College of Applied Mathematics Chengdu University of Information TechnologyChengdu 610225China Jagiellonian University in Krakow Chair of Optimization and Controlul.Lojasiewicza 630348 KrakowPoland Departement of Mathematics FPT UniversityEducation ZoneHoa Lac High Tech ParkKm29 Thang Long HighwayThach That WardHanoiVietnam

The goal of this paper is to study a mathematical model of a nonlinear static frictional contact problem in elasticity with the mixed boundary conditions described by a combination of the Signorini unilateral frictionless contact condition,and nonmonotone multivalued contact,and friction laws of subdifferential ***,under suitable assumptions,we deliver the weak formulation of the contact model,which is an elliptic system with Lagrange multipliers,and which consists of a hemivariational inequality and a variational ***,we prove the solvability of the contact ***,employing the notion of H-convergence of nonlinear elasticity tensors,we provide a result on the convergence of solutions under perturbations which appear in the elasticity operator,body forces,and surface tractions.

关键词： Mixed variational-hemi variational inequality H-convergence homogenization Clarke subgradient Lagrange multiplier elasticity operator

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NONSMOOTH INTERVAL-VALUED MULTIOBJECTIVE optimization PROBLEMS AND GENERALIZED VARIATIONAL INEQUALITIES ON HADAMARD MANIFOLDS

Applied Set-Valued Analysis and Optimization

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Applied Set-Valued Analysis and optimization 2023年第1期5卷 69-84页

作者： Upadhyay, B.B. Li, Lijie Mishra, Priyanka Department of Mathematics Indian Institute of Technology Patna Bihar Patna801103 India Guangxi Colleges Universities Key Laboratory of Complex System Optimization and Big Data Processing Yulin Normal University Guangxi Yulin537000 China Mathematics Division School of Advanced Sciences and Languages VIT Bhopal University Bhopal-Indore Highway Kothrikalan Madhya Pradesh Sehore466114 India

In this paper, we study the classes of approximate Minty and Stampacchia type vector variational inequalities along with their local and weak versions on a Hadamard manifold, and a class of nonsmooth interval-valued multiobjective optimization problems, respectively. We obtain the equivalence between the solutions of considered approximate vector variational inequalities and LU-efficient solutions of nonsmooth interval-valued multiobjective optimization problems in which the cost function is assumed to be geodesic approximately LU-convex or geodesic LU-α-convex. ©2023 Applied Set-Valued Analysis and optimization.

关键词： Cost functions

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Analysis of drying characteristics and quality of Star Anise (Illicium verum) using microwave vacuum and hot air combined drying

Journal of Biotech Research

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Journal of Biotech Research 2023年 15卷 386-396页

作者： Liu, Yongfu Zhou, Xiaoting Pan, Xiaoli Fan, Wenyan Yang, Guimei Yu, Wangxin Hong, Weisheng School of Physical and Telecommunication Engineering Yulin Normal University Guangxi Yulin China Yulin Center for Food and Drug Control Guangxi Yulin China Guangxi Colleges and Universities Key Lab of Complex System Optimization and Big Data Processing Yulin Normal University Guangxi Yulin China Center for Applied Mathematics of Guangxi Yulin Normal University Guangxi Yulin China Fangchenggang Agricultural Machinery Service Center Guangxi Fangchenggang China

Star anise, rich in effective active constituents, is extensively employed in the pharmaceutical and food industries. The drying temperature can irreversibly damage these constituents. To enhance the drying quality and efficiency, this study undertook experiments using three drying methods on star anise including microwave vacuum drying, hot air drying, and a combination of microwave vacuum and hot air drying. The research examined the impacts of varying drying conditions on the drying characteristics of star anise, the moisture diffusion coefficient, and the primary component contents (anethole and shikimic acid). Models were separately established for microwave vacuum and hot air thin-layer drying kinetics including Lewis, Weibull distribution, two-term exponential, Wang, and Singh models, and a Weibull distribution model for combined microwave vacuum-hot air drying. The results indicated that drying with microwave vacuum and hot air primarily proceeded in a falling rate drying phase, whereas combined microwave vacuum and hot air drying encompassed both falling rate and constant rate stages. The effective moisture diffusion coefficients (Deff) for microwave vacuum drying and hot air drying of star anise ranged from 3.4423E-07 to 8.8239E-07 m2/s and 2.0386E-08 to 8.8239E-07 m2/s, respectively, while the Deff for combined microwave and hot air drying ranged from 2.8683E-07 to 4.8014E-07 m2/s and 7.9516E-8 to 2.0964E-7 m2/s, respectively. Evidently, segmented combined drying facilitated more convenient moisture diffusion, and both coefficients increased with microwave power and hot air temperature. During the microwave vacuum and hot air drying processes, both the Wang and Singh models and the Weibull distribution models showed good fitting effects. The Weibull distribution model could effectively predict the drying behavior of segmented microwave vacuum and hot air drying of star anise. In comparison with hot air drying time, combined microwave vacuum and hot air dr

关键词： Drying

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FRACTIONAL PARTIAL DIFFERENTIAL VARIATIONAL INEQUALITY

arXiv

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arXiv 2023年

作者： Cen, Jinxia Sousa, Vanterler Da C.J. Wu, Wei School of Mathematical Sciences Zhejiang Normal University Jinhua321004 China Aerospace Engineering PPGEA-UEMA Department of Mathematics DEMATIUEMA MA Sao Luís65054 Brazil Center for Applied Mathematics of Guangxi Guangxi Colleges Universities Key Laboratory of Complex System Optimization and Big Data Processing Yulin Normal University Guangxi Yulin537000 China

In this present paper, we introduce and study a dynamical systems involving fractional derivative operator and nonlocal condition, which is constituted of a fractional evolution equation and a time-dependent variational inequality, and is named as fractional partial differential variational inequality (FPDVI, for short). By employing the estimates involving the one-and two-parameter Mittag-Leffler functions, fixed-point theory for set-value mappings, and non-compactness measure theory, we develop a general framework to establish the existence of smooth solutions to (FPDVI).MSC Codes 47J20, 35R11, 49J40, 35J88, 26A33 Copyright © 2023, The Authors. All rights reserved.

关键词： Dynamical systems

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Drying kinetics characteristics and model fitting of exocarpium citreic grandis microwave vacuum drying

Journal of Biotech Research

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Journal of Biotech Research 2023年 15卷 397-409页

作者： Zhou, Ying Liu, Yongfu Liu, Jiaming Pan, Xiaoli Yang, Guimei Lv, Weiwei Li, Weibin Yulin Center for Food and Drug Control Guangxi Yulin China School of Physical and Telecommunication Engineering China Guangxi Colleges and Universities Key Lab of Complex System Optimization and Big Data Processing China Center for Applied Mathematics of Guangxi Yulin Normal University Guangxi Yulin China Fangchenggang Agricultural Machinery Service Center Guangxi Fangchenggang China Yulin City Food and Drug Certification Evaluation Center Guangxi Yulin China

Exocarpium citreic grandis is the immature outer peel of grapefruit and contains active ingredients such as naringin and rhoifolin. The drying temperature can have a significant effect on the constituents. In order to explore the rules of moisture and quality changes in exocarpium citreic grandis during microwave vacuum drying, this study investigated the effects of different microwave intensities (0.75, 1.25, 1.50, 1.75, 2.00 W/g) on the drying characteristics and main component content of exocarpium citreic grandis. The results showed that, at a microwave intensity of 0.75 W/g, the drying process was controlled by a constant speed stage. At microwave intensities of 1.25 W/g and 1.50 W/g, the drying process was divided into three parts including acceleration stage, constant speed stage, and deceleration stage. When the microwave intensity increased to 1.75 W/g and 2.00 W/g, the drying process was divided into acceleration and deceleration stages with no constant speed drying stage. The resulted data suggested that the thin-layer drying kinetics model of exocarpium citreic grandis was fitted. The selection principle of the model was analyzed from four aspects including modification of the original model, transformation of dependent and independent variables, complex model, and initial and terminal conditions. Lewis, Page, Two-term exponential, and Weibull distribution models were selected for fitting analysis. The optimal thin-layer drying models were the Page model and the Weibull distribution model. The scale parameter α of the Weibull distribution function decreased with the increase in microwave intensity. The shape parameter β underwent slight changes with moisture migration mechanisms being the combined effect of surface moisture evaporation and internal moisture diffusion. The effective moisture diffusion coefficient Deff was increasing with the increase in microwave intensity. The activation energy Ea for microwave vacuum drying of exocarpium citreic grandis

关键词： Weibull distribution

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On second order differential inclusion driven by quasi-variational–hemivariational inequalities

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Nonlinear Analysis: Real World Applications 2024年 77卷

作者： Liang, Yunshui Ceng, Lu-Chuan Yao, Jen-Chih Zeng, Shengda Department of Mathematics Shanghai Normal University Shanghai200234 China Center for Fundamental Science Kaohsiung Medical University Kaohsiung807 Taiwan Department of Applied Mathematics National Sun Yat-sen University Kaohsiung804 Taiwan Center for Applied Mathematics of Guangxi and Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing Yulin Normal University Guangxi Yulin537000 China Jagiellonian University in Krakow Faculty of Mathematics and Computer Science ul. Lojasiewicza 6 Krakow30-348 Poland

In this paper we investigate an evolution problem (SDQHVI) which constitutes of the second order differential inclusion driven by a quasi-variational–hemivariational inequality (QHVI) with perturbation operator in Banach spaces. Unlike the existing literature on differential inclusions, on the one hand, the second order differential operator is not assumed to be compact;on the other hand, the solvability of the inequality is proved under non-coercive condition. More precisely, first, it is shown that the solution set of the QHVI with perturbation operator is nonempty, bounded, closed and convex under the KKM theorem and the Minty formulation. Then, an associated multivalued map with the solution set of the QHVI with perturbation operator is introduced, and we prove that it is upper semicontinuous and measurable. Finally, by utilizing Kakutani–Fan–Glicksberg fixed point theorem, a weak topology technique and properties of strong continuous cosine operators, we prove the existence of mild solutions for SDQHVI. © 2023 Elsevier Ltd

关键词： Banach spaces

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A Spectral Efficient Hybrid Precoding Algorithm for MmWave MIMO systems 8

A Spectral Efficient Hybrid Precoding Algorithm for MmWave M...

引用

8th International Conference on Identification, Information and Knowledge in the Internet of Things, IIKI 2019

作者： Li, Tingting Zhao, Feng Key Laboratory of Cognitive Radio and Information Processing Guilin University of Electronic Technology Guilin541004 China Guangxi Colleges Universities Key Laboratory of Complex System Optimization and Big Data Processing Yulin Normal University Yulin China

Millimeter-wave MIMO will use hybrid precoding to improve the spectral efficiency. In this paper, we propose a spectral efficient hybrid precoding algorithm. In order to maximize the projection of hybrid precoding matrix on the optimal precoding matrix, we design the analog precoding matrix by selecting an optimal combination from the candidate matrix. Then, we regard the channel matrix and the obtained analog precoding matrix as an equivalent channel matrix, and use regularized zero-forcing to acquire the digital precoding matrix. Finally, we present simulation results of the proposed hybrid precoding algorithm and show that the algorithm approaches the optimal precoding. © 2020 The Authors. Published by Elsevier B.V.

关键词： Spectrum efficiency

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A new class of history-dependent quasi variational-hemivariational inequalities with constraints

arXiv

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arXiv 2023年

作者： Migórski, Stanislaw Bai, Yunru Zeng, Shengda College of Applied Mathematics Chengdu University of Information Technology Sichuan Province Chengdu610225 China School of Science Guangxi University of Science and Technology Guangxi Province Liuzhou545006 China Jagiellonian University in Krakow Faculty of Mathematics and Computer Science ul. Lojasiewicza 6 Krakow30348 Poland Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing Yulin Normal University Guangxi Province Yulin537000 China

In this paper we consider an abstract class of time-dependent quasi variational-hemivariational inequalities which involves history-dependent operators and a set of unilateral constraints. First, we establish the existence and uniqueness of solution by using a recent result for elliptic variational-hemivariational inequalities in reflexive Banach spaces combined with a fixed-point principle for history-dependent operators. Then, we apply the abstract result to show the unique weak solvability to a quasistatic viscoelastic frictional contact problem. The contact law involves a unilateral Signorini-type condition for the normal velocity and the nonmonotone normal damped response condition while the friction condition is a version of the Coulomb law of dry friction in which the friction bound depends on the accumulated *** Codes 35J87, 47J20, 49J40, 49J45, 74G30, 74M15 © 2023, CC BY.

关键词： Friction

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A NEW CLASS OF EVOLUTION MULTIVALUED QUASI-VARIATIONAL INEQUALITIES I: EXISTENCE AND NONSMOOTH OPTIMAL CONTROL

arXiv

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arXiv 2024年

作者： Zeng, Shengda Radulescu, Vicentiu D. Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing Yulin Normal University Guangxi Yulin537000 China Jagiellonian University in Krakow Faculty of Mathematics and Computer Science ul. Lojasiewicza 6 Krakow30-348 Poland Faculty of Applied Mathematics AGH University of Kraków Kraków30-059 Poland Department of Mathematics University of Craiova Craiova200585 Romania Simion Stoilow Institute of Mathematics The Romanian Academy Bucharest010702 Romania

In this paper, we consider a new kind of evolution multivalued quasi-variational inequalities with feedback effect and a nonlinear bifunction which contain several (evolution) quasi-variational/hemivariational inequalities as special cases. The main contribution of this paper is twofold. The first goal is to establish a novel framework for proving the existence of solutions and the compactness of solution set to the evolution multivalued quasi-variational inequalities, under quite mild assumptions. Whereas, the second contribution is to introduce and study a nonlinear and nonsmooth optimal control problem governed by an evolution multivalued quasi-variational inequality, and then to obtain the sufficient conditions for guaranteeing the solvability of the nonlinear and nonsmooth optimal control problem under consideration. Such nonlinear and nonsmooth optimal control problem could as a useful model to explore the simultaneous distributed-boundary optimal control problems driven by evolution multivalued quasi-variational inequalities, and optimal parameters identification for evolution multivalued quasi-variational inequalities. Copyright © 2024, The Authors. All rights reserved.

关键词： Optimal control systems

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Geometric analysis and onset of chaos for the resonant nonlinear Schrödinger system

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The European Physical Journal Special Topics 2021年第11期231卷 2133-2142页

作者： Lai, Ting Feng, Chunsheng Liu, Yongjian Liu, Aimin School of Mathematics and Computational Science Xiangtan University Xiangtan People’s Republic of China Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing Yulin Normal University Yulin People’s Republic of China

In this paper, Jacobi stability of a resonant nonlinear Schrödinger (RNS) system is studied by the KCC theory, which is also called differential geometric method. The RNS system is transformed into an equivalent planar differential system by traveling wave transformation, then the Lyapunov stability of equilibrium points of the planar system is analyzed. By constructing geometric invariants, we analyze and discuss the Jacobi stability of three equilibrium points. The results show that the zero point is always Jacobi stable, while the Jacobi stability of the other nonzero equilibrium points are determined by the values of the parameters. In addition, the focusing tendency towards trajectories around the equilibrium points are studied by the dynamical behavior of deviation vector. Finally, numerical results show that the system presents quasi-periodic and chaotic phenomena under periodic disturbances.

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