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The Existence of Positive Solution for Singular Boundary Value Problems of First Order Differential Equation on Unbounded Domains

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Acta Mathematicae Applicatae Sinica 2009年第1期25卷 95-104页

作者： Xing-qiu zhang Jing-xian Sun Department of Mathematics Liaocheng University Liaocheng Shandong 252059 China Department of Mathematics Xuzhou Normal University Xuzhou Jiangsu 221116 China

By constructing a special cone and using cone compression and expansion fixed point theorem, this paper presents some existence results of positive solutions of singular boundary value problem on unbounded domains for a class of first order differential equation. As applications of the main results, two examples are given at the end of this paper.

关键词： Singular equation unbounded domain positive solution

Mixed eigenvalues of p-Laplacian

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Frontiers of Mathematics in China 2015年第2期10卷 249-274页

作者： Mu-fa CHEN Lingdi WANG Yuhui zhang School of Mathematical Sciences Beijing Normal University Beijing 100875 China School of Mathematics and Information Sciences Henan University Kaifeng 475004 China

The mixed principal eigenvalue of p-Laplacian （equivalently, the optimal constant of weighted Hardy inequality in Lp space） is studied in this paper. Several variational formulas for the eigenvalue are presented. As applications of the formulas, a criterion for the positivity of the eigenvalue is obtained. Furthermore, an approximating procedure and some explicit estimates are presented case by case. An example is included to illustrate the power of the results of the paper.

关键词： p-Laplacian Hardy inequality in Lp space mixed boundaries,explicit estimates eigenvalue approximating procedure

A Finite-Dimensional Completely Integrable System Associated with Boussinesq Hierarchy

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Communications in Theoretical Physics 2009年第12期52卷 1081-1086页

作者： CHEN Lan-Xin zhang Jun-xian China University of Mining and Technology Beijing 100083 China Shijiazhuang University Shijiazhuang 050035 China

In this paper, a new completely integrable system related to the complex spectral problem -φ xx＋（i/4）wpx＋（i/4）（wp）x＋（1/4）vφ=iλφxand the constrained flows of the Boussinesq equations axe generated. According to the viewpoint of Hamiltonian mechanics, the Euler-Lagrange equations and the Legendre transformations, a reasonable Jacobi-Ostrogradsky coordinate system is obtained. Moreover, by means of the constrained conditions between the potentiaJ u, v and the eigenfunction φ, the involutive representations of the solutions for the Boussinesq equation hieraxchy axe given.

关键词： eigenvalue problem constraint flow symplectic manifold completely integrability involutive representation

Mixed eigenvalues of discrete p-Laplacian

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Frontiers of Mathematics in China 2014年第6期9卷 1261-1292页

This paper deals with the principal eigenvalue of discrete p-Laplacian on the set of nonnegative integers. Alternatively, it is studying the optimal constant of a class of weighted Hardy inequalities. The main goal is the quantitative estimates of the eigenvalue. The paper begins with the case having reflecting boundary at origin and absorbing boundary at infinity. Several variational formulas are presented in different formulation： the difference form, the single summation form, and the double summation form. As their applications, some explicit lower and upper estimates, a criterion for positivity （which was known years ago）, as well as an approximating procedure for the eigenvalue are obtained. Similarly, the dual case having absorbing boundary at origin and reflecting boundary at presented at the end of Section 2 to infinity is also studied. Two examples are illustrate the value of the investigation.

关键词： Discrete p-Laplacian mixed eigenvalue variational formula,explicit estimate positivity criterion approximating procedure

Microstructure and mechanical properties of TiN/AlN multilayers deposited by filtered vacuum arc deposition

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中国有色金属学会会刊：英文版 2004年第z1期14卷 234-237页

作者： zhang Xu zhang Hui-xing zhang Tong-he WU xian-ying Key Laboratory of Beam Technology and Material Modification of Ministry of Education Institute of Low Energy Nuclear Physics Beijing Normal UniversityBeijing Radiation Center Beijing 100875 China Key Laboratory of Beam Technology and Material Modification of Ministry of EducationInstitute of Low Energy Nuclear Physics Beijing Normal UniversityBeijing Radiation Center Beijing 100875 China Key Laboratory of Beam Technology and Material Modification of Ministry of EducationInstitute of Low Energy Nuclear Physics Beijing Normal UniversityBeijing Radiation Center Beijing 100875 China Key Laboratory of Beam Technology and Material Modification of Ministry of EducationInstitute of Low Energy Nuclear Physics Beijing Normal UniversityBeijing Radiation Center Beijing 100875 China

Nanometer TiN/AlN multilayers were prepared on silicon substrate by filtered vacuum arc *** structures of the nanometer TiN/AlN multilayer were studied by using X-ray diffraction. The 12 nm TiN/AlN multiplayer is composed of cubic TiN structure and hexagonal wurzite AlN structure, but the 2 nm period multilayer is composed of face centered cubic structure TiN and AlN with strong (200) texture. The surface roughness, hardness and elastic modulus of multilayer are dependent on the period of multilayer. The hardness of the TiN/AlN multilayers is higher than that suggested by a simple rule of mixture. The peaking hardness of nanometer TiN/AlN multilayers at period of 2 nm is about 42 GPa, much higher than that of 12 nm. The wear resistance of the nanometer TiN/AlN multilayers was also studied.

关键词： multilayer filtered arc nanometer wear

failure of hanging roofs in sublevel caving by shock collision and stress superposition

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Journal of Rock Mechanics and Geotechnical Engineering 2016年第6期8卷 886-895页

作者： Zong-xian zhang Department of Arctic Technology University Center in Svalbard

Hanging roofs or high hang-ups.a common problem in sublevel caving mining,usually result in a large ore loss and undermine mining *** paper analyzed the formation of a hanging roof and showed that increased confining pressure and reduced free surface were its main *** order to break down a hanging roof,a new method based on shock wave collision and stress superposition was *** this method,two blastholes containing multi-primer at different positions are simultaneously initiated at *** doing this,a new free surface and a swell room can be *** these holes are fired,a long delay time is given to the next blasthole so that the fragments from the first twohole blasting have enough time to fall *** new method was applied to three hanging roofs in one production area,and all of them were successfully broken *** inspection indicated that almost no damage was caused in the nearby drifts/tunnels due to the new *** addition,the far field vibrations were found to be smaller than the maximum vibrations induced by some other blasts.

关键词： Shock wave collision Hanging roof Sublevel caving Rock fracture Hang-up Underground mining

Pricing and Inventory Control Strategy for a Periodic-Review Energy Buy-Back System

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Journal of Systems Science & Complexity 2016年第4期29卷 1018-1033页

作者： zhang Jihong CHEN Hongqiao DING Xiaosong LI xian International Business School Beijing Foreign Studies University Institute of Applied Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences DECIDE Research Group Department of Computer and Systems Sciences Stockholm University

Along with the rapid development of economics and enhancement of industrialization, the power demand keeps rising and frequently creates mismatch between demand and supply in *** provides miscellaneous energy buy-back programs with great opportunities. Such programs, when activated, offer certain amount of financial compensations to participants for reducing their energy consumption during peak time. They aim at encouraging participants to shift their electricity usage from peak to non-peak time, and thereby release the demand pressure during peak time. This paper considers a periodic-review joint pricing and inventory decision model under an energy buy-back program over finite planning horizons, in which the compensation levels, setup cost and additive random demand function are incorporated. The objective is to maximize a manufacturer's expected total *** using Veinott's conditions, it is shown that the manufacturer's optimal decision is a state dependent(s, S, P) policy under a peak market condition, or partly an(s, S, A, P) policy under the normal market condition.

关键词： Additive demand function energy buy-back program joint pricing and inventory control Veinott's conditions.

Nanoencapsulation of hexavalent chromium with nanoscale zero-valent iron:High resolution chemical mapping of the passivation layer

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Journal of Environmental Sciences 2018年第5期30卷 4-13页

作者： Xiao-yue Huang Lan Ling Wei-xian zhang State Key Laboratory for Pollution Control College of Environmental Science and EngineeringTongji UniversityShanghai 200092China Shanghai Institute of Pollution Control and Ecological Security Shanghai 200092China

Solid phase reactions of Cr（Ⅵ） with Fe（0） were investigated with spherical-aberration-corrected scanning transmission electron microscopy（Cs-STEM） integrated with X-ray energy-dispersive spectroscopy（XEDS）. Near-atomic resolution elemental mappings of Cr（Ⅵ）–Fe（0） reactions were acquired. Experimental results show that rate and extent of Cr（Ⅵ） encapsulation are strongly dependent on the initial concentration of Cr（Ⅵ） in solution. Low Cr loading in nZⅥ（〈1.0 wt%） promotes the electrochemical oxidation and continuous corrosion of n ZⅥ while high Cr loading（〉1.0 wt%） can quickly shut down the Cr uptake. With the progress of iron oxidation and dissolution, elements of Cr and O counter-diffuse into the nanoparticles and accumulate in the core region at low levels of Cr（Ⅵ）（e.g., 〈 10 mg/L）. Whereas the reacted n ZⅥ is quickly coated with a newly-formed layer of 2–4 nm in the presence of concentrated Cr（Ⅵ）（e.g., 〉 100 mg/L）. The passivation structure is stable over a wide range of pH unless pH is low enough to dissolve the passivation layer. X-ray photoelectron spectroscopy（XPS） depth profiling reconfirms that the composition of the newly-formed surface layer consists of Fe（Ⅲ）–Cr（Ⅲ）（oxy）hydroxides with Cr（Ⅵ） adsorbed on the outside surface. The insoluble and insulating Fe（Ⅲ）–Cr（Ⅲ）（oxy）hydroxide layer can completely cover the n ZⅥ surface above the critical Cr loading and shield the electron transfer. Thus, the fast passivation of nZⅥ in high Cr（Ⅵ） solution is detrimental to the performance of nZⅥ for Cr（Ⅵ） treatment and remediation.

关键词： Nanoscale zero-valent iron (nZVI) Hexavalent chromium Solid phase reaction Passivation Spherical-aberration-correctedscanning transmission electronmicroscopy (Cs-STEM)

Tensile force correction calculation method for prestressed construction of tension structures

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2008年第9期9卷 1201-1207页

作者： Xin ZHUO Guo-fa zhang Koichiro ISHIKAWA Dao-an LOU Department of Civtl Engmeermg Zhejiang University Hangzhou 310027 China Department of Architecture and Civil Engineering Fukui University Fukui 910-8507 Japan Zhejiang Zhancheng Construction Group Co. Ltd. Hangzhou 310005 China

factors such as errors during the fabrication or construction of structural components and errors of calculation as- sumption or calculation methods, are very likely to cause serious deviation of many strings’ actual prestressing forces from the designed values during tension structure construction or service period, and further to threaten the safety and reliability of the structure. Aiming at relatively large errors of the prestressing force of strings in a tension structure construction or service period, this paper proposes a new finite element method (FEM), the "tensile force correction calculation method". Based on the measured prestressing forces of the strings, this new method applies the structure from the zero prestressing force status approach to the measured prestressing force status for the first phase, and from the measured prestressing force status approach to the designed prestressing force status for the second phase. The construction tensile force correction value for each string can be obtained by multi-iteration with FEM. Using the results of calculation, the strings’ tensile force correction by group and in batch will be methodic, simple and accurate. This new calculation method can be applied to the prestressed correction construction simulation analysis for tension structures.

关键词： Tension structures Prestressed construction High precision