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Multiplicity and Uniqueness of Positive Solutions for Nonhomogeneous Semilinear Elliptic Equation with Critical Exponent

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Acta Mathematicae Applicatae Sinica 2016年第1期32卷 81-94页

作者： Na ba Yan-yan WANG Lie ZHENG School of Science Hubei University of Technology Department of Mathematics Zhoukou Normal University

In this paper,we consider the following problem {-Δu（x）＋u（x）=λ（u^p（x）＋h（x））,x∈R^N,u（x）∈h^1（R^N）,u（x）〉0,x∈R^N,（＊）where λ 〉 0 is a parameter,p =（N＋2）/（N—2）.We will prove that there exists a positive constant 0 〈 A＊〈＋00such that（＊） has a minimal positive solution for λ∈（0,λ＊）,no solution for λ 〉 λ＊,a unique solution for λ = λ＊.Furthermore,（＊） possesses at least two positive solutions when λ∈（0,λ＊） and 3 ≤ N ≤ *** N ≥ 6,under some monotonicity conditions of h we show that there exists a constant 0 〈λ＊＊〈 λ＊ such that problem（＊）possesses a unique solution for λ∈（0,λ＊＊）.

关键词： nonhomogeneous semilinear elliptic problems multiplicity uniqueness

2.5D scattering of incident plane SH waves by a canyon in layered half-space

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Earthquake Science 2010年第1期23卷 25-33页

作者： Zhenning ba Jianwen Liang Department of Civil Engineering Tianjin University Tianjin 300072 China

This paper presents 2.5D scattering of incident plane SH waves by a canyon in layered half-space by the indirect boundary element method (IBEM). The free field response is carried out to give the displacements and stresses on the line which forms boundary of the canyon. The fictitious uniform moving loads are applied to the same line to calculate the Green's functions for the displacements and stresses. The amplitudes of the loads are determined by the boundary conditions. The displacements due to the free field and from the fictitious uniform moving loads have to be added to obtain the whole motion. The numerical results are carried out for the cases of a canyon in homogenous and in one layer over bedrock. The results show that the 2.5D wave scattering problem is essentially different from the 2D case, and there exist distinct differences between the wave amplification by a canyon in layered half-space and that in homogeneous half-space. The reasons for the distinct difference are explored, and the effects of the thickness and stiffness of the layer on the amplification are discussed.

关键词： canyon layered half-space plane SH wave amplification 2.5D scattering

Intracellular organelle networks： Understanding their organization and communication through systems-level modeling and analysis

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Frontiers in Biology 2017年第1期12卷 7-18页

作者： Qinle ba Ge Yang Department of Biomedical Engineering Carnegie Mellon University Pittsburgh PA 15213 USA Department of Computational Biology Carnegie Mellon University Pittsburgh PA 15213 USA

baCKGROUND： Membrane-bound intracellular organelles are biochemically distinct compartments used by eukaryotic cells for serving specialized physiological functions and organizing their internal environment. Recent studies revealed surprisingly extensive communication between these organelles and highlighted the network nature of their organization and communication. Since organization and communication of the organelles are carried out at the systems level through their networks, systems-level studies are essential for understanding the underlying mechanisms. METHODS： We reviewed recent studies that used systems-level quantitative modeling and analysis to understand organization and communication of intracellular organelle networks. RESULTS： We first review modeling and analysis studies on how fusion/fission and degradation/biogenesis, two essential and closely related classes of activities of individual organelles, collectively mediate the dynamic organization of their networks. We then turn to another important aspect of the dynamic organization of the organelle networks, namely how organelles are physically connected within their networks, a property referred to as the topology of the networks in mathematics, and summarize some of their distinct properties. Lastly, we briefly review modeling and analysis studies that aim to understand communication between different organelle networks, focusing on cellular calcium homeostasis as an example. We conclude with a brief discussion of future directions for research in this area. CONCLUSIONS： Together, the reviewed studies provide critical insights into how diverse activities of individual organelles collectively mediate the organization and communication of their networks. They demonstrate the essential role of systems- level modeling and analysis in understanding complex behavior of such networks.

关键词： intracellular organelle organelle network organelle communication network analysis systems modeling

Insight into crystal growth and upconversion luminescence property of tetragonal ba_(3)Sc_(2)F_(12) nanocrystals

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Rare Metals 2021年第1期40卷 113-122页

作者： juan Xie Guang-Chao Zheng Yang-Ming Hu Farhat Nosheen Zhi-Cheng Zhang Er-Jun Liang School of Physics and Microelectronics Zhengzhou UniversityZhengzhou 450001China Division of Science and Technology Department of ChemistryUniversity of EducationLahore 54770Pakistan Tianjin Key Laboratory of Molecular Optoelectronic Sciences Department of ChemistrySchool of ScienceTianjin University and Collaborative Innovation Center of Chemical Science and EngineeringTianjin 300072China

Sc-based nanomaterials have attracted considerable attention due to their unique optical properties different from those of Ln/Y-based ***,studies on Sc-based nanomaterials are far from ***,nanoscale alkaline(Ca,Sr and ba)scandium fluorides were almost ignored for their stringent synthetic ***,we synthesize high-quality tetragonal phase ba_(3)Sc_(2)F_(12) nanocrystals with uniform morphology and good dispersibility by carefully tailoring the reaction conditions,such as the molar ratio of reactants,temperature and reaction ***,the upconversion(UC)luminescence property of ba_(3)Sc_(2)F_(12):Yb/Er(Ho)samples is investigated in *** doping concentrations of sensitizer(Yb^(3+))and activator(Er^(3+)and Ho^(3+))are optimized for the strongest UC luminescence,of which the corresponding energy transfer processes are also ***,tetragonal ba_(3)Sc_(2)F_(12) nanocrystals can gradually transform into hexagonal ba_(4)Yb_(3)F_(17) nanocrystals with the increase in Yb^(3+)doping *** work provides a novel type of Sc-based nanomaterials with strong red UC emissions which are promising in high-resolution 3-dimensional color displays,laser,bioimaging and biolabels.

关键词： ba_(3)Sc_(2)F_(12)nanocrystals Crystal growth Upconversion Sc-based nanomaterials

Numerical Simulation in Applied Geophysics. The Mesoscale and the Macroscale

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Numerical Simulation in Applied Geophysics. The Mesoscale an...

Mass-producible low-cost flexible electronic fabrics for azo dye wastewater treatment by electrocoagulation

2017中国地球科学联合学术年会

作者： juan Enrique Santos Jing ba Purdue University Hohai University

＜正＞Seismic wave propagation is a common technique used in hydrocarbon exploration geophysics,mining and reservoir characterization and *** variations in the fluid and solid matrix properties of a fluid-saturated poroelastic material（a Biot medium）,such as fine layering,fractures and cracks at the mesoscale（on the order of centimeters）are common in the earth’s ***

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Chinese Journal of Chemical Engineering 2023年第7期59卷 222-230页

作者： Chaoyi Yin Jingyuan Ma Jian Qiu Ruifang Liu Long ba State Key Laboratory of Bioelectronics School of Biological Science and Medical Engineering Southeast UniversityNanjing 210096China State Key Laboratory of Materials-Oriented Chemical Engineering National Engineering Research Center for Special Separation MembraneCollege of Chemical EngineeringNanjing Tech UniversityNanjing 210009China

Electrocoagulation is progressively becoming an ecologically friendly water treatment method owing to its lack of secondary pollution,high active ingredient concentration,high treatment effectiveness,simple equipment,and simplicity of automated control ***,electrocoagulation is offered as a method for treating wastewater containing azo dyes using a revolutionary flexible electronic fabric that can be mass-producible at a reasonable price.A computer-controlled machine embroiders 316L stainless steel fiber(316L SSF)onto an insulating fabric to manufacture a flexible electronic device of cathode and anode with a monopolar arrangement on the fabric *** methyl orange(MO)solution to simulate azo dye wastewater,the decolorization rate of 500 ml MO reached 99.25% under the conditions of 50 mg·L^(-1)initial mass concentration,120 min electrolysis time,15 mA·g^(-1)current density,1 cm electrode spacing,0.1 mol·L^(-1)NaCl,pH 7.6,200 r·min^(-1)rotational speed of the stirrer,and 22-25℃ room *** addition,it is feasible to embroider flexible electronic fabrics with varied sizes and numbers of electrodes based on the amount of treated sewage to increase the degradation rate,which has significant practical application value.

关键词： Flexible electronic fabric 316L Stainless steel fiber Embroidery Electrocoagulation Wastewater treatment

Robust Designs Through Risk Sensitivity:An Overview

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Journal of Systems Science & Complexity 2021年第5期34卷 1634-1665页

作者： baSAR Tamer Coordinated Science Laboratory University of Illinois1308 West MainUrbanaIL 61801USA.

This is an overview paper on the relationship between risk-averse designs based on exponential loss functions with or without an additional unknown(adversarial)term and some classes of stochastic *** particular,the paper discusses the equivalences between risk-averse controller and filter designs and saddle-point solutions of some corresponding risk-neutral stochastic differential games with different information structures for the *** of the by-products of these analyses is that risk-averse controllers and filters(or estimators)for control and signal-measurement models are robust,through stochastic dissipation inequalities,to unmodeled perturbations in controlled system dynamics as well as signal and the measurement *** paper also discusses equivalences between risk-sensitive stochastic zero-sum differential games and some corresponding risk-neutral three-player stochastic zero-sum differential games,as well as robustness issues in stochastic nonzero-sum differential games with finite and infinite populations of players,with the latter belonging to the domain of mean-field games.

关键词： Mean-field games risk-sensitive control risk-sensitive filtering risk-sensitive games risk sensitivity robustness

Statistical theory for hydrogen bonding fluid system of A_aD_d type(II):Properties of hydrogen bonding networks

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Science China Chemistry 2007年第1期50卷 11-17页

作者： WANG HaiJun HONG XiaoZhong GU Fang ba XinWu College of Chemistry and Environment Science Hebei UniversityBaoding 071002China International Center for Materials Physics Chinese Academy of SciencesShenyang 110016China College of Physics Science and Technology Hebei UniversityBaoding 071002China

Making use of the invariant property of the equilibrium size distribution of the hydrogen bonding clus- ters formed in hydrogen bonding system of AaDd type,the analytical expressions of the free energy in pregel and postgel regimes are *** the gel free energy and the scaling behavior of the number of hydrogen bonds in gel phase near the critical point are investigated to give the corre- sponding scaling exponents and scaling ***,some properties of intermolecular and in- tramolecular hydrogen bonds in the system,sol and gel phases are *** a result,the explicit relationship between the number of intramolecular hydrogen bonds and hydrogen bonding degree is obtained.

关键词： hydrogen bonding network gel phase scaling law

A direct position determination method with combined TDOA and FDOA based on particle filter

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Chinese Journal of Aeronautics 2018年第1期31卷 161-168页

作者： Zhiyu LU Bin ba Jianhui WANG Wenchao LI Daming WANG China National Digital Switching System Engineering & Technological R&D Cente Zhengzhou 450000 China Jiuquan Satellite Launch Center Jiuquan 735000 China

The localization of a stationary transmitter using moving receivers is considered. The original Direct Position Determination （DPD） methods, with combined Time Difference of Arrival （TDOA） and Frequency Difference of Arrival （FDOA）, do not perform well under low Signal-to-Noise Ratio （SNR）, and worse still, the computation cost is difficult to accept when the computational capabilities are limited. To get better positioning performance, we present a new DPD algorithm that proves to be more computationally efficient and more precise for weak signals than the conventional approach. The algorithm partitions the signal received with the same receiver into multiple non-overlapping short-time signal segments, and then uses the TDOA, the FDOA and the coherency among the short-time signals to locate the target. The fast maximum likelihood estimation, one iterative method based on particle filter, is designed to solve the problem of high computation load. A secondary but important result is a derivation of closed-form expressions of the Cramer-Rao Lower Bound （CRLB）. The simulation results show that the algorithm proposed in this paper outperforms the traditional DPD algorithms with more accurate results and higher computational efficiency, and especially at low SNR, it is more close to the CRLB.

关键词： Direct position determination Cramer-Rao lower bound Frequency difference of arrival Time difference of arrival Particle filter