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Negative Index Materials and Their Applications:Recent Mathematics Progress(Dedicated to Ham Brezis for his 70th birthday with esteem)

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Chinese Annals of Mathematics,Series B 2017年第2期38卷 601-628页

作者： Hoai-Minh nguyen EPFl SB MATHAA CAMA Station 8CH-1015 LausanneSwitzerland

Negative index materials are artificial structures whose refractive index has negative value over some frequency range. These materials were first investigated theoretically by Veselago in 1946 and were confirmed experimentally by Shelby, Smith, and Schultz in2001. Mathematically, the study of negative index materials faces two difficulties. Firstly,the equations describing the phenomenon have sign changing coefficients, hence the ellipticity and the compactness are lost in general. Secondly, the localized resonance, i.e.,the field explodes in some regions and remains bounded in some others as the loss goes to 0, might appear. In this survey, the author discusses recent mathematics progress in understanding properties of negative index materials and their applications. The topics are reflecting complementary media, superlensing and cloaking by using complementary media, cloaking a source via anomalous localized resonance, the limiting absorption principle and the well-posedness of the Helmholtz equation with sign changing coefficients.

关键词： Negative index materials, localized resonance, Cloaking, Superlensing

A Hybrid Grey DEMATEl and PlS-SEM Model to Investigate COVID-19 Vaccination Intention

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Computers, Materials & Continua 2022年第9期72卷 5059-5078页

作者： Phi-Hung nguyen Department of Business Management National Taipei University of TechnologyTaipei10608Taiwan Faculty of Business FPT UniversityHanoi100000Vietnam

The main objective of this study is to comprehensively investigate individuals’vaccination intention against COVID-19 during the second wave of COVID-19 spread in Vietnam using a novel hybrid ***,the Decision-Making Trial and Evaluation laboratory based on Grey Theory(DEMATEl-G)was employed to explore the critical factors of vaccination intention among ***,Partial least Squares-Structural Equation Modeling(PlS-SEM)was applied to test the hypotheses of individual behavioral intention to get the vaccine to prevent the outbreak of COVID-19.A panel of 661 valid respondents was collected from June 2021 to July 2021,and confidentiality was maintained for all data *** results identified that perception of COVID-19 vaccination and trust in vaccination strategy directly associated with individuals’COVID-19 ***,the perceived severity of COVID-19 has an indirect impact on COVID-19 vaccination intentions via the perception of the COVID-19 *** findings indicated that the government’s information about vaccines is necessary for the new phase of vaccination intervention strategies in ***,the study suggests that the government needs to give complete information about the role of vaccines prioritizes transparency in official information about COVID-19 vaccines to allay concerns about side effects,allowing for the most appropriate policy formulation and implementation to encourage public *** studies can apply PlS-SEM and other MCDM models with the fuzzy,hesitant numbers to re-evaluate the feasibility,validity and reliability of this research’s proposed model.

关键词： COVID-19 vaccination immunization intervention PlS-SEM DEMATEl grey theory vietnam

Study of relationship between motion of mechanisms in gas operated weapon and its shock absorber

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Defence Technology（防务技术） 2024年第3期33卷 42-54页

作者： Jiri Balla Roman Vitek Dung nguyen Van Zbynek krist Hung nguyen Van Department of Weapons and Ammunition University of Defence BrnoCzech Republic Department of Weapons Le Quy Don Technical UniversityHanoiViet Nam Department of Design and Special Engineering Alexander Dubcek University of TrencinSlovakia

The article deals with the motion of the breech block carrier and the weapon casing of an automatic weapon mounted on a flexible carriage and the base of the *** works,which did not consider the dynamic properties of the base of the weapon,did not allow to reconcile the calculated and experimental results of the weapon casing displacement when shooting from firing *** the analysis of the motion of individual parts,the methods of mathematical modelling and firing experiments using a high-speed camera were *** show the best accord with experiment when modelling the system with 4 degrees of *** oscillation of the system regarding the movement of the breech block carrier and the weapon casing was investigated under changed conditions of rate of fire,the use of a muzzle brake and different types of shock *** velocities and displacements of the weapon casing and the breech block carrier at different values of the impulse of the gases to the breech block carrier were determined.

关键词： Shock absorber Gas-operated weapon Force-impulse diagram Recoil system Breech block carrier

Asymptotic Expansions of Backward Equations for Two-time-scale Markov Chains in Continuous Time

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Acta Mathematicae Applicatae Sinica 2009年第3期25卷 457-476页

作者： Dung Tien nguyen Department of Mathematics Wayne State University

This work develops asymptotic expansions for solutions of systems of backward equations of time- inhomogeneous Maxkov chains in continuous time. Owing to the rapid progress in technology and the increasing complexity in modeling, the underlying Maxkov chains often have large state spaces, which make the computa- tional tasks ihfeasible. To reduce the complexity, two-time-scale formulations are used. By introducing a small parameter ε〉 0 and using suitable decomposition and aggregation procedures, it is formulated as a singular perturbation problem. Both Markov chains having recurrent states only and Maxkov chains including also tran- sient states are treated. Under certain weak irreducibility and smoothness conditions of the generators, the desired asymptotic expansions axe constructed. Then error bounds are obtained.

关键词： Markov chain backward equation two-time scale asymptotic expansion

ON BOUNDEDNESS PROPERTY OF SINGUlAR INTEGRAl OPERATORS ASSOCIATED TO A SCHRODINGER OPERATOR IN A GENERAlIZED MORREY SPACE AND APPlICATIONS

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Acta Mathematica Scientia 2020年第5期40卷 1171-1184页

作者： Xuan Truong lE Thanh Nhan nguyen Ngoc Trong nguyen Division of Computational Mathematics and Engineering Institute for Computational ScienceTon Due Thang UniversityHo Chi Minh CityVietnam Faculty of Mathematics and Statistics Ton Due Thang UniversityHo Chi Minh CityVietnam Department of Mathematics Ho Chi Minh City University of EducationHo Chi Minh CityVietnam Department of Primary Education Ho Chi Minh City University of EducationHo Chi Minh CityVietnam

In this paper,we provide the boundedness property of the Riesz transforms associated to the Schrodinger operator■=-Δ+V in a new weighted Morrey space which is the generalized version of many previous Morrey type *** additional potential V considered in this paper is a non-negative function satisfying the suitable reverse Holder's *** results are new and general in many cases of *** an application of the boundedness property of these singular integral operators,we obtain some regularity results of solutions to Schrodinger equations in the new Morrey space.

关键词： weighted Morrey spaces Schodinger operator riesz transforms Regularity estima tes

Fully Completed Spherical Fuzzy Approach-Based Z Numbers(PHIModel)for Enhanced Group Expert Consensus

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Computers, Materials & Continua 2024年第7期80卷 1655-1675页

作者： Phi-Hung nguyen Research Center of Applied Sciences Faculty of BusinessFPT UniversityHanoi100000Vietnam

This study aims to establish an expert consensus and enhance the efficacy of decision-making processes by integrating Spherical Fuzzy Sets(SFSs)and Z-Numbers(SFZs).A novel group expert consensus technique,the PHImodel,is developed to address the inherent limitations of both SFSs and the traditional Delphi technique,particularly in uncertain,complex *** such contexts,the accuracy of expert knowledge and the confidence in their judgments are pivotal *** study provides the fundamental operational principles and aggregation operators associated with SFSs and Z-numbers,encompassing weighted geometric and arithmetic operators alongside fully developed operators tailored for SFZs ***,a case study and comparative analysis are conducted to illustrate the practicality and effectiveness of the proposed operators and *** the PHI model with SFZs numbers represents a significant advancement in decision-making frameworks reliant on expert ***,this combination serves as a comprehensive tool for decision-makers,enabling them to achieve heightened levels of consensus while concurrently assessing the reliability of expert *** case study results demonstrate the PHI model’s utility in resolving complex decision-making scenarios,showcasing its ability to improve consensus-building processes and enhance decision ***,the comparative analysis highlights the superiority of the integrated approach over traditional methodologies,underscoring its potential to revolutionize decision-making practices in uncertain environments.

关键词： Spherical fuzzy sets Delphi method Z-numbers expert consensus PHI model uncertainty

A novel finite element formulation for static bending analysis of functionally graded porous sandwich plates

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Frontiers of Structural and Civil Engineering 2022年第12期16卷 1599-1620页

作者： Van Chinh nguyen Trung Thanh TRAN Trung nguyen-THOI Quoc-Hoa PHAM Faculty of Mechanical Engineering Le Quy Don Technical UniversityHanoiVietnam laboratory for Applied and Industrial Mathematics Institute for Computational Science and Artificial IntelligenceVan Lang UniversityHo Chi Minh CityVietnam Faculty of Mechanical-Electrical and Computer Engineering Van Lang UniversityHo Chi Minh CityVietnam Faculty of Engineering and Technology Nguyen Tat Thanh UniversityHo Chi Minh CityVietnam

This article aims to propose a finite element formulation based on Quasi-3D theory for the static bending analysis of functionally graded porous(FGP)sandwich *** FGP sandwich plates consist of three layers including the bottom skin of homogeneous metal,the top skin of fully ceramic and the FGP core layer with uneven porosity distribution.A quadrilateral(Q4)element with nine degrees of freedom(DOFs)per node is derived and employed in analyzing the static bending response of the plate under uniform and/or sinusoidally distributed *** accuracy of the present finite element formulation is verified by comparing the obtained numerical results with the published results in the ***,some numerical examples are performed to examine the effects of the parameters including power-law index k and porosity coefficient on the static bending response of rectangular FGP sandwich *** addition,a problem with a complicated l-shape model is conducted to illustrate the superiority of the proposed finite element method.

关键词： sandwich plates functionally graded porous static bending Quasi-3D theory Q4 element

Non-Negative Adaptive Mechanism-Based Sliding Mode Control for Parallel Manipulators with Uncertainties

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Computers, Materials & Continua 2023年第2期74卷 2771-2787页

作者： Van-Truong nguyen Department of Mechatronics Engineering Hanoi University of IndustryHanoi159999Vietnam

In this paper,a non-negative adaptive mechanism based on an adaptive nonsingular fast terminal sliding mode control strategy is proposed to have finite time and high-speed trajectory tracking for parallel manipulators with the existence of unknown bounded complex uncertainties and external *** proposed approach is a hybrid scheme of the online non-negative adaptive mechanism,tracking differentiator,and nonsingular fast terminal sliding mode control(NFTSMC).Based on the online non-negative adaptive mechanism,the proposed control can remove the assumption that the uncertainties and disturbances must be bounded for the NFTSMC *** proposed controller has several advantages such as simple structure,easy implementation,rapid response,chattering-free,high precision,robustness,singularity avoidance,and finite-time *** all control parameters are online updated via tracking differentiator and non-negative adaptive law,the tracking control performance at high-speed motions can be better in real-time requirement and disturbance rejection ***,simulation results validate the effectiveness of the proposed method.

关键词： Parallel manipulator uncertainties and disturbances nonsingular fast terminal sliding mode control non-negative adaptive mechanism tracking differentiator

NORMAl FAMIlY OF MEROMORPHIC FUNCTIONS SHARING HOlOMORPHIC FUNCTIONS AND THE CONVERSE OF THE BlOCH PRINCIPlE

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Acta Mathematica Scientia 2017年第3期37卷 623-656页

作者： nguyen Van THIN Department of Mathematics Thai Nguyen University of EducationLuong Ngoc Quyen StreetThai Nguyen cityThai NguyenViet Nam

In 1996, C. C. Yang and P. C. Hu [8] showed that： let f be a transcendental meromorphic function on the complex plane, and a ≠ 0 be a complex number; then assume that n 〉 2, n1,… , nk are nonnegative integers such that n1＋… ＋ nk ≥1; thus fn（f′）n1…（f（k））nk-a has infinitely zeros. The aim of this article is to study the value distribution of differential polynomial, which is an extension of the result of Yang and Hu for small function and all zeros of f having multiplicity at least k ≥2. Namely, we prove that fn（f′）n1…（f（k））nk-a（z） has infinitely zeros, where f is a transcendental meromorphic function on the complex plane whose all zeros have multiplicity at least k≥ 2, and a（z） 0 is a small function of f and n ≥ 2, n1,… ,nk are nonnegative integers satisfying n1＋ …＋ nk ≥1. Using it, we establish some normality criterias for a family of meromorphic functions under a condition where differential polynomials generated by the members of the family share a holomorphic function with zero points. The results of this article are supplement of some problems studied by d. Yunbo and G. Zongsheng [6], and extension of some problems studied X. Wu and Y. Xu [10]. The main result of this article also leads to a counterexample to the converse of Bloeh＇s principle.

关键词： Normal family Nevanlinna theory meromorphic function sharing function differential pOlynomial