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Acta Mathematica Sinica,English Series 2023年第11期39卷 2164-2180页

作者： xiang zhu Zhao Wen ZHENG Kun LI School of Mathematical Sciences Qufu Normal UniversityQufu 273165P.R.China College of Mathematics and Systems Science Guangdong Polytechnic Normal UniversityGuangzhou 510665P.R.China

In this paper,we consider the following quadratic pencil of Schr?dinger operators L(λ)generated in L~2(R~+)by the equation−y″+[p(x)+2λq(x)]y=λ^(2)y,x∈R^(+)=[0,+∞)with the boundary condition y′(0)/y(0)=β_(1)λ+β0-α_(1)λ+α0,where p(x)and q(x)are complex valued functions andα_(0),α_(1),β_(0),β_(1)are complex numbers withα_(0)β_(1)-α_(1)β_(0)≠*** is proved that L(λ)has a finite number of eigenvalues and spectral singularities,and each of them is of a finite multiplicity,if the conditions p(x),q′(x)∈AC(R^(+)),limx→∞[|p(x)|+|q(x)|+|q′(x)|]=0 and sup 0≤x0.

关键词： Schrodinger operator Strum-Liouville problems finite spectrum eigenparameter dependence

The Real-Time Simulation of Doppler Spread in Wireless Mobile Environment by RF Circuits

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Chinese Journal of Electronics 2015年第4期24卷 837-843页

作者： LI Zhen zhu xiang JI Wenli ZHENG Guoxin Key Laboratory of Specialty Fiber Optics and Optical Access Networks Shanghai University Technical Center of Shanghai Shentong Metro Group Co .Ltd

The time-varying characteristic of wireless channel under the high-speed mobile environments in tunnels causes the Doppler spread to the transmitted signals,which affects the performance of wireless communication systems. The real-time Doppler effect simulation methodology directly based on Radio frequency(RF) circuits is proposed to simulate different Doppler spread effects in real environments. Mixers and a Digital-to-analog(DA)converter circuit are utilized to spread the spectrum of RF signals. A PC platform with the interface written in C#is configured to control the spectrum spread *** radio channel emulator with the proposed methodology can replace the expensive fading simulating instruments with only 25.1ns system delay. Such an emulator has been applied to test the Multi-carrier wireless information local loop(McW i LL) wireless vehicle communication system in the laboratory to meet the requirement of metro Communication based train control(CBTC) system.

关键词： Doppler spread Channel simulation Circuits Tunnel Metro system

Some remarks on Wente's inequality and the Lorentz-Sobolev space

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Applied Mathematics(A Journal of Chinese Universities) 2016年第3期31卷 355-361页

作者： zhu xiang-rong CHEN Jie-cheng Department of Mathematica Zhejiang Normal University

In this note we consider Wente＇s type inequality on the Lorentz-Sobolev space. If f∈L^p1,q1（Rn）,G∈L^p2,q2 （Rn） and div G ≡ 0 in the sense of distribution where 1/p1＋1/p2=1/q ＋1/q2=1,1〈p1,p2〈∞, it is known that G. f belongs to the Hardy space H1 and furthermore ‖G· f‖N1≤C‖ f‖Lp1,q1（R2）‖G‖Lp2,q2（R2）Reader can see [9] Section 4 Here we give a new proof of this result. Our proof depends on an estimate of a maximal operator on the Lorentz space which is of some independent interest. Finally, we use this inequality to get a generalisation of Bethuel＇s inequality.

关键词： Lorentz space Wente type inequality Hardy space

A Note on Certain Block Spaces on the Unit Sphere

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Acta Mathematica Sinica,English Series 2006年第6期22卷 1843-1846页

作者： Xiao Feng YE xiang Rong zhu Department of Mathematics (Xixi Campus) Zhejiang University Hangzhou 310028 P. R. China

In this note, we clarify a relation between block spaces and the Hardy space. We obtain Bq^0.v belong to H^1（S^n-1）＋L（ln＋L）^1＋v（s^n-1）,v〉-1,q〉1,Furthermore,if v≥ 0, q 〉 1. we verify that block spaces Rq... 详细信息

关键词： block spaces Hardy space

Expansion of spherical cavity of strain-softening materials with different elastic moduli of tension and compression

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2007年第9期8卷 1380-1387页

作者： LUO Zhan-you zhu xiang-rong GONG Xiao-nan Ningbo Institute of Technology. Zhejiang University Ningbo 315100 China Geotechnical Engineering Institute Zhejiang University of Science and Technology Hangzhou 310012 China Geotechnical Engineering Institute Zhejiang University Hangzhou 310027 China

An expansion theory of spherical cavities in strain-softening materials with different moduli of tension and com-pression was presented. For geomaterials,two controlling parameters were introduced to take into account the different moduli and strain-softening properties. By means of elastic theory with different moduli and stress-softening models,general solutions cal-culating Tresca and Mohr-Coulomb materials' stress and displacement fields of expansion of spherical cavity were derived. The effects caused by different elastic moduli in tensile and compression and strain-softening rates on stress and displacement fields and development of plastic zone of expansion of cavity were analyzed. The results show that the ultimate expansion pressure,stress and displacement fields and development of plastic zone vary with the different elastic moduli and strain-softening prop-erties. If classical elastic theory is adopted and strain-softening properties are neglected,rather large errors may be the result.

关键词： Expansion of spherical cavity Tresca material Mohr-Coulomb material Elastic theory with different moduli of tension and compression Stress-dropping softening model

Static load test and load transfer mechanism study of squeezed branch and plate pile in collapsible loess foundation

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2007年第7期8卷 1110-1117页

作者： GAO Xiao-juan WANG Jin-chang zhu xiang-rong College of Civil Engineering and Architecture Zhejiang University Hangzhou 310027 China Institute of Architecture Engineering Henan University of Science and Technology Luoyang 471003 China Ningbo Institute of Technology Zhejiang University Ningbo 315005 China

As a special geological phenomenon, the character of collapsible loess foundation is collapsible when penetrated by water. This character leads to the soil losing load bearing capacity largely and may lead to foundation failure. Pile is a popular foundation used in collapsible loess. The squeezed branch and plate pile is a new type of pile developed in recent years and has not be used in a project before. In this paper three squeezed branch and plate piles are tested in collapsible loess after immersion processing. The results may be used for reference in similar construction project, and to provide theoretical references for de- signing of the squeezed branch and plate piles in engineering practice.

关键词： Collapsible loess foundation Squeezed branch and plate pile Immersion processing Full-scale static load test

Pyrolysis of rice husk and sawdust for liquid fuel

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Journal of Environmental Sciences 2006年第2期18卷 392-396页

作者： zhu Xi-feng ZHENG Ji-lu GUO Qing-xiang zhu Qing-shi Biomass Clean Energy Laboratory University of Science and Technology of China Hefei-230026 China

The paper is focused on studying how to convert rice husk and sawdust into liquid fuel. Rice husk, sawdust and their mixture were pyrolyzed at the temperature between 420℃ and 540℃, and the main product of liquid fuel was obtained. The experimental result showed that the yield of liquid fuel heavily depended on the kind of feedstock and pyrolysis temperature. In the experiments, the maximum liquid yields for rice husk, sawdust and their mixture were 56% at 465 ℃, 61% at 490℃ and 60% at 475℃ respectively. Analysis with GC-MS and other apparatus indicated that the liquid fuel is a complicated organic compound with low caloric value and can be directly used as fuel oil without any up-grading. As a crude oil, the liquid fuel can be refined to be vehicle oil.

关键词： solid organic waste rice husk sawdust pyrolysis liquid fuel

Average Fidelity of Teleportation in Quantum Noise Channel

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Communications in Theoretical Physics 2006年第5期45卷 802-806页

作者： HAO xiang ZHANG Rong zhu Shi-Qun School of Physical Science and Technology Suzhou University Suzhou 215006 China

The effects of amplitude damping in quantum noise channels on average fidelity of quantum teleportation are analyzed in Bloeh sphere representation for every stage of teleportation. When the quantum channels are varied from maximally entangled states to non-maximally entangled states, it is found that the effects of noise channels on the fidelity are nearly equivalent to each other for strong quantum noise. The degree of damage on the fidelity of non-maximally entangled channels is smaller than that of maximally entangled channels. The average fidelity of values larger than 2/3 may be one representation indirectly showing how much the unavoidable quantum noise is.

关键词： average fidelity teleportation quantum noise channel Bloch sphere

Three-dimensional hydrodynamic and water quality model for TMDL development of Lake Fuxian,China

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Journal of Environmental Sciences 2012年第8期24卷 1355-1363页

作者： Lei Zhao Xiaoling Zhang Yong Liu Bin He xiang zhu Rui Zou Yuanguan zhu Research Center for Eco-Environmental Sciences Chinese Academy of SciencesBeijing 100085China College of Environmental Science and Engineering Key Laboratory of Water and Sediment Sciences(MOE)Peking UniversityBeijing 100871China Tetra Tech Inc.10306 Eaton PlaceSte 340FairfaxVA 22030USA Institute for Environmental Sciences Kunming 650034China

Lake Fuxian is the largest deep freshwater lake in China. Although its average water quality meets Class I of the China National Water Quality Standard （CNWQS）, i.e., GB3838-2002, monitoring data indicate that the water quality approaches the Class II threshold in some areas. Thus it is urgent to reduce the watershed load through the total maximum daily load （TMDL） program. A three-dimensional hydrodynamic and water quality model was developed for Lake Fuxian, simulating flow circulation and pollutant fate and transport. The model development process consists of several steps, including grid generation, initial and boundary condition configurations, and model calibration processes. The model accurately reproduced the observed water surface elevation, spatiotemporal variations in temperature, and total nitrogen （TN）, total phosphorus （TP）, and chemical oxygen demand （COD） concentrations, suggesting a reasonable numerical representation of the prototype system for further TMDL analyses. The TMDL was calculated using two interpretations of the water quality standards for Class I of the CNWQS based on the maximum instantaneous surface and annual average surface water concentrations. Analysis of the first scenario indicated that the TN, TP and COD loads should be reduced by 66%, 68% and 57%, respectively. Water quality was the highest priority; however, local economic development and cost feasibility for load reduction can pose significant issues. In the second interpretation, the model results showed that, under the existing conditions, the average water quality meets the Class I standard and therefore load reduction is unnecessary. Future studies are needed to conduct risk and cost assessments for realistic decision-making.

关键词： hydrodynamic and water quality model Lake Fuxian water quality prediction total maximum daily load

Defects and interface states related photocatalytic properties in reduced and subsequently nitridized Fe_3O_4/TiO_2

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Journal of Materials Science & Technology 2018年第6期34卷 931-941页

作者： Chang Liu xiang zhu Peng Wang Yisen Zhao Yongqing Ma Anhui Key Laboratory of Information Materials and Devices School of Physics and Materials Science Anhui University

The Fe3O4@TiO2 catalyst was reduced in a mixed H2/N2 atmosphere at temperatures of 400, 600, 800 and 1000 ℃ in order to produce the oxygen vacancies （Ov） and Ti^3＋; Simultaneously, Fe3O4 was reduced to Fe, a strongly magnetic material, beneficial for the magnetic separation after the photo-degradation. The optimal catalyst was obtained at the reducing temperature of 800℃, which possesses the good photocatalytic performance and recycled activities; Moreover, its saturation magnetization Ms is highest, reaching 23.8 emu g 1 which improves the magnetic separability. This optimal catalyst was subsequently treated in the NH3 atmosphere at temperatures of 500, 600 and 700 ℃, aiming to investigate the effects of N-doping in TiO2. The 600 ℃ treated catalyst exhibited the optimal photocatalytic performance. The factors that affect the photocatalytic performance are revealed and discussed in detail, including the ratio of Ov and N dopant in TiO2 as well as the interface states between TiO2 and the magnetic particles.

关键词： Photocatalyst Strong magnetic particles Magnetic separability Oxygen vacancy Nitrogen doping