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A new class of generalized quasi-variational inequalities with applications to Oseen problems under nonsmooth boundary conditions

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Science China Mathematics 2024年第2期67卷 315-338页

作者： Shengda Zeng Akhtar A.Khan stanislaw Migórski Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing Yulin Normal UniversityYulin 537000China Faculty of Mathematics and Computer Science Jagiellonian University in Krak´owKrak´ow 30348Poland Center for Applied and Computational Mathematics School of Mathematical SciencesRochester Institute of TechnologyRochesterNY 14623USA College of Sciences Beibu Gulf UniversityQinzhou 535000China

In this paper, we study a generalized quasi-variational inequality (GQVI for short) with twomultivalued operators and two bifunctions in a Banach space setting. A coupling of the Tychonov fixedpoint principle and the Katutani-Ky Fan theorem for multivalued maps is employed to prove a new existencetheorem for the GQVI. We also study a nonlinear optimal control problem driven by the GQVI and givesufficient conditions ensuring the existence of an optimal control. Finally, we illustrate the applicability of thetheoretical results in the study of a complicated Oseen problem for non-Newtonian fluids with a nonmonotone andmultivalued slip boundary condition (i.e., a generalized friction constitutive law), a generalized leak boundarycondition, a unilateral contact condition of Signorini’s type and an implicit obstacle effect, in which themultivalued slip boundary condition is described by the generalized Clarke subgradient, and the leak boundarycondition is formulated by the convex subdifferential operator for a convex superpotential.

关键词： generalized quasi-variational inequality existence theorem optimal control Kakutani-Ky Fan theorem Oseen problem non-Newtonian fluid nonmonotone slip boundary condition

Environmental exposure to cadmium but not lead is associated with decreased semen quality parameters:quality regionalism of sperm properties

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Asian Journal of Andrology 2022年第1期24卷 26-31页

作者： Katarzyna Olszak-Wasik Andrzej Tukiendorf Aleksandra Kasperczyk Artur Wdowiak stanislaw Horak Department of Gynecology Obstetrics and Oncological Gynecology in BytomMedical University of SilesiaSchool of Medicine and Division of Dentistry in ZabrzeBatorego 15Bytom 41-902Poland Department of Public Health Wroclaw Medical UniversityBartla 5Wroclaw 51-618Poland Department of Biochemistry Medical University of SilesiaSchool of Medicine and Division of Dentistry in ZabrzeJordana 19Zabrze 41-808Poland Faculty of Health Sciences Diagnostic Techniques UnitMedical University of LublinStaszica 4/6Lublin 20-081Poland

Environmental factors may negatively contribute to a progressive worsening of semen quality,and differences in semen quality may result from different environmental exposures(regional differences)or lifestyle differences.Heavy metals are factors with a confirmed negative influence on male fertility.Among them,lead and cadmium are commonly found in human surroundings.Thus,we analyzed semen parameters(according to the World Health Organization 2010 recommendations)and semen lead and cadmium concentrations in 188 men from two different regions in Poland,a typical agricultural area and an industrial area,in couples that had been diagnosed with infertility.The assays were performed using flameless electrothermal atomic absorption spectrometry.In the statistical analysis,regional comparisons and then taxonomic comparisons based on three parameters(age,semen concentration,and sperm morphology)were applied.We showed that more cadmium than lead accumulated in semen,a higher cadmium concentration was observed in semen obtained from men from the agricultural region,and better semen quality and lower cadmium concentrations were found in the semen of men from the industrial,more polluted region.We thus showed an existing regionalism in the sperm quality properties.However,semen parameters such as morphology and progressive and nonprogressive motility followed the same trends,regardless of the patient’s age,region,or class.We could conclude that the environment has a minor impact on sperm morphology and progressive and nonprogressive motility and that other existing factors could have an indirect influence on semen quality.

关键词： cadmium environment lead semen quality taxonomic analysis

TIME PERIODIC SOLUTIONS TO THE EVOLUTIONARY OSEEN MODEL FOR A GENERALIZED NEWTONIAN INCOMPRESSIBLE FLUID

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Acta Mathematica Scientia 2023年第4期43卷 1645-1667页

作者：岑金夏 stanislaw MIGóRSKI Emilio VILCHES 曾生达 School of Mathematical Sciences Zhejiang Normal UniversityJinhua 321004China Jagiellonian University in Krakow Chair of Optimization and Controlul.Lojasiewicza 630348 KrakowPoland Instituto de Ciencias de la Ingenier´ıa Universidad de O’HigginsAv.Libertador Bernardo OHiggins 6112841959 RancaguaChile Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing Yulin Normal UniversityYulin 537000China Department of Mathematics Nanjing University Nanjing 210093China Jagiellonian University in Krakow Faculty of Mathematics and Computer Scienceul.Lojasiewicza 630348 KrakowPoland

In this paper we study a nonstationary Oseen model for a generalized Newtonian incompressible fluid with a time periodic condition and a multivalued,nonmonotone friction law.First,a variational formulation of the model is obtained;that is a nonlinear boundary hemivariational inequality of parabolic type for the velocity field.Then,an abstract first-order evolutionary hemivariational inequality in the framework of an evolution triple of spaces is investigated.Under mild assumptions,the nonemptiness and weak compactness of the set of periodic solutions to the abstract inequality are proven.Furthermore,a uniqueness theorem for the abstract inequality is established by using a monotonicity argument.Finally,we employ the theoretical results to examine the nonstationary Oseen model.

关键词： nonstationary Oseen model Newtonian incompressible fluid hemivariational inequality periodic solution generalized subgradient

Difficulties in post-stroke gait improvement caused by post-stroke depression

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Chinese Medical Journal 2014年第11期127卷 2085-2090页

作者： stanislaw Kijowski Faculty of Physical Education and Physiotherapy Opole University of Technology Ul Prószkowska 76 45-758 Opole Poland

Background Depression is a common problem impeding post-stroke rehabilitation.Up to 70% of patients show depression symptoms during the first twelve months after stroke onset.However,the depression and its effect on functional recovery can be difficult to diagnose.The purpose of this study was to use gait analysis as a tool to compare the recovery after stroke in patients with and without depression and to assess the impact of the initiation time of rehabilitation after stroke onset.Methods One hundred and forty five consecutive patients after first ever stroke admitted for designed rehabilitation program within 2 to 31 months after stroke onset participated.All patients received 4 weeks treatment program included comprehensive rehabilitation consisted of multipurpose activities 5 days a week.These included individual and group exercises,physiotherapy,occupational therapy and gait training.Gait analysis with Kistler force plates was employed to assess gait pattern symmetry before and after the treatment.Gait symmetry was evaluated based on seven gait parameters.Regaining of gait pattern symmetry was assumed as a measure of rehabilitation outcome.Results After rehabilitation program gait symmetry w（）ined in patients without depression.Gait asymmetry remained unchanged in patients diagnosed with depression.No major differences in outcome from rehabilitation were noted in regards to the initiation time of rehabilitation after the stroke onset.Conclusions Depression limits gait recovery after stroke.The time of initiation of rehabilitation after stroke onset does not limit the motor recovery after rehabilitation program.

关键词： stroke depression gait rehabilitation

Uncertainty in public health models treated by differential inclusions

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International Journal of Modeling, Simulation, and Scientific Computing 2020年第4期11卷 224-236页

作者： stanislaw Raczynski Faculty of Engineering Universidad Panamericana Augusto Rodin No.49803920 Mexico CityD.F.Mexico

An application of differential inclusions in the epidemic spread models is presented.Some mostly used epidemic models are discussed here,and a brief survey of epidemic modeling is given.Most of the models are some modifications of the Susceptible–Infected–Recovered model.Simple simulations are carried out.Then,we consider the influence of some uncertain parameters.It is pointed out that the presence of some fluctuating model parameters can be treated by differential inclusions.The solution to such differential inclusion is given in the form of reachable sets for model variables.Here,we focus on the differential inclusion application rather than the model construction.

关键词： Modeling simulation epidemics public health sensitivity differential inclusions.

Simultaneous events, singularity in the space of models and chicken game

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International Journal of Modeling, Simulation, and Scientific Computing 2021年第4期12卷 1-11页

作者： stanislaw Raczynski Facultad de Ingenier´ıa Universidad Panamericana Augusto Rodin 498Ciudad de M´exico 03920M´exico

The discrete event simulation with simultaneous events is discussed.Discrete models are treated as some points in the general space of models.The main topic of this paper is the convergence of sequences of continuous models to the corresponding discrete event model.It is pointed out that the discrete event models may represent some singularities in the space of models.This fact is related to the problem of validity of discrete event simulation.The models presented here are not the topic of the paper.These are known models,used as examples.The model of the“chicken game”and multiple elastic collisions are considered.It is shown that if a discrete event model is some special limit case of a sequence of continuous models with finite event duration,then that limit model is a singularity.It may provide results very different from the expected limit value of the results from the converging sequence of models.

关键词： Simulation discrete events modeling

Gas-dynamic phenomena caused by rock mass tremors and rock bursts

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International Journal of Mining Science and Technology 2020年第3期30卷 413-420页

作者： stanislaw Wasilewski The Strata Mechanics Research Institute of the Polish Academy of Science ul.Reymonta 2730-059 KrakowPoland

Similar to coal, rock and gas ejections, rock mass tremors and rock bursts are among the most serious natural hazards accompanying the underground extraction of coal. Gas-dynamic phenomena caused by rock mass tremors and rock bursts observed as transient states of air parameters in mining headings,are usually generated as a result of a change in the geometry of headings and the release of considerable amounts of gases. Particular significance is attributed to transient states caused by disasters, which are often accompanied by rapid incidents, presenting threats to the life and health of the underground crew.In Polish mining there are known examples of transient states of air parameters recorded during gasdynamic phenomena, e.g. tremors and rock bursts. The paper presents the case studies of rapid seismic incidents to show how records in mine monitoring systems broaden the knowledge about the transient states of air parameters in mining headings generated because of them.

关键词： Rock mass tremors Rock bursts Gas-dynamic phenomena Transient states of air parameters Mine monitoring systems

Lorentz Transformation Leads to Invariance of the Difference between the Electric and Magnetic Field Intensity

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Journal of Modern Physics 2022年第8期13卷 1212-1215页

作者： stanislaw Olszewski Institute of Physical Chemistry Polish Academy of Sciences Warsaw Poland

In course of a direct calculation we demonstrate the activity of parameters of the Lorentz transformation entering the original electric and magnetic field vectors E and H. The validity of the transformation is shown with the aid of the relation E 2- H2 = E'2- H'2 which holds for any suitable pair of the vectors E, H and E', H'. No special geometry of the vector pairs entering (E, H) and (E ', H') is assumed. The only limit applied in the paper concerns the velocity ratio betweeen v and c which should be smaller than unity.

关键词： Electric and Magnetic Intensity Pairs v Denotes the Velocity Ratio be-tween Two Vector Systems

Designing coal panels in the conditions of associated methane and spontaneous fire hazards

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International Journal of Mining Science and Technology 2020年第4期30卷 525-531页

作者： stanislaw Prusek Eugeniusz Krause Jacek Skiba Central Mining Institute Katowice 40-166Poland

An increase in methane,spontaneous fire and bumping hazards in Polish hard coal mines,observed in the last two decades,led to the need to elaborate the tools allowing proper selection of a range of preventive measures to fight them at the stage of designing coal extraction.Designing the production of a coal seams in the conditions of associated methane and spontaneous fires hazards in Polish hard coal mines requires elaboration of the design standards for coal panels in gassy coal seams.This paper presents the guidelines on how to design production in the conditions of associated methane and spontaneous fire hazards.Presented tools and methodology since the very first research were many times verified by daily mining operations in the conditions of associated methane and spontaneous fire hazards,which confirms their significant contribution to the development of safe and economical mining operations.

关键词： Coal exploitation Methane Spontaneous fires Associated hazards Designing coal panels Ventilation