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Asymptotic Behaviour of the Phase in Non-Smooth Obstacle Scattering

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Acta Mathematica Sinica,English Series 1997年第1期13卷 81-89页

作者： Chen Hua (Institute of Mathematics,Wuhan University,Wuhan 430072,China) Institute of Mathematics Wuhan University Wuhan China

In this paper,we study the asymptotic behaviour of the scattering phase s（λ）of the Dirichlet Laplacian associated with obstacle,where Ω is a bounded open subset of IRn（n≥2） with non-smooth boundaryΩ and connected complement Ωe=IRn\.We can prove that if Ω satisfies a certain geometrical condition,then where φ（λ）=[（4π）n/2Γ(1+（n/2）]-1|Ω|nλn/2,dn>0 depending only on n,and |·|j（j=n-1,n）is a j-dimensional Lebesgue measure.

关键词： Scattering phase Counting function Dirichlet Laplacian Obstacle Exterior boundary problem Tessellation of domains

Irregular but Nonfractal Drums and n-Dimensional Weyl Conjecture

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Acta Mathematica Sinica,English Series 1995年第2期11卷 168-178页

作者： Chen Hua Department of Mathematics Wuhan University Wuhan, 430072 China Department of Mathematics Wuhan University Wuhan People's Republic of China

In this paper, we study the asymptotics of the spectrum of the Dirichlet （or Neumann） Laplacian in a bounded open set ΩRn（n≥1） with irregular but nonfractal boundary Ω. We give a partial resolution of the Weyl conjecture, i.e. for the counting function Ni（λ）（i=0: Dirichlet; i=i: Neumann）, we have got a precise estimate of the remainder term Ψi（λ）=φ（λ）-Ni（λ） for large λ, where φ（λ） is the Weyl term. This implies that for the irregular but nonfractal drum Ω, not only the volume |Ω|n is spectral invariant but also the area of boundary |Ω|n-1 might be spectral invariant as well.

关键词： Math Irregular but Nonfractal Drums and n-Dimensional Weyl Conjecture

Structure and Two-dimensional Correlation Infrared Spectroscopy Study of a New One-dimensional Chain Compound: (4,4’-Hbpy)_3[NaMo_8O_(26)](4,4’- bpy)_2(H_2O)_4 (bpy = Bipydine)

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Chinese Journal of Structural Chemistry 2005年第9期24卷 1033-1038页

作者：陈义平张汉辉柯大梅沈小敏黄长沧孙瑞卿 Department of Chemistry Fuzhou University Fuzhou Fujian 350002 China Department of Chemistry Fuzhou University Fuzhou Fujian 350002 China State Key Laboratory of Structural Chemistry Fuzhou Fujian 350002 China

A novel compound, （4,4＇-Hbpy）3[NaMo8O26]（4,4＇-bpy）2（H2O）4 1 （bpy=bipydine）, was synthesized by the hydrothermal method. Single-crystal X-ray diffraction shows that compound 1 belongs to the monoclinic system, space group C2/m with a=19.1921（5）, b=18.6931（6）, c=9.3821（3） A° β=104.8020（11）°, V=3254.22（17）A°^3 C50H51Mo8N10NaO30, Mr=2062.52, Z=2, F（000）=2016, μ=1.591 mm^-1 and Dc=2.105 g/cm^3. The final R=0.0283 and wR=0.0912 for 3118 observed reflections （I〉20（I））. Compound 1 contains the β-[Mo8O26]^4-anion, sodium ion, 4,4＇-bpy and lattice crystalline water molecules. The β-[MosO26] units link the sodium ion to form a chain structure. The infinitechains of [Na（Mo8O26）]^3- blocks are surrounded by protonized 4,4＇-bpy cations, 4,4＇-bpy and lattice crystalline water molecules. The 2D-IR correlation spectroscopy study indicates that the stretching vibrations of Mo=O occur more preferentially due to the thermal effect. The TGA analysis shows that compound 1 has high thermal stability.

关键词： octamolybdate sodium ion two-dimensional infrared (2D-IR) correlation spectroscopy

EXACT SOLITRAY WAVE SOLUTIONS ANDSINGULAR SOLUTIONS TO THETWO-DIMENSIONAL NONLINEARDISSIPATIVE-DISPERSIVE SYSTEM

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Acta Mathematica Scientia 2002年第2期22卷 249-253页

作者：李志斌陈天华 Department of Computer Science East China Normal University Shanghai 200062 China

An algorithm for constructing exact solitary wave solutions and singular solutions for a class of nonlinear dissipative-dispersive system is presented. With the aid of symbolic manipulation system Maple, some explicit... 详细信息

关键词： Nonlinear system exact solutions symbolic manipulation

A Fractal Lattice Ising Model with Pair and Triplet Interactions

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Chinese Physics Letters 1992年第10期9卷 537-540页

作者： QIN Yong CCAST(World laboratory)Beijing 100080 and Departrnent of Physics Beijing Normal UniversityBeijing100875

The equivalence of the Ising model on a fractal lattice having two-and three-site couplings with the Ising model having only two-site interaction in a non-zero magnetic field on the same lattice is derived by a partial tracing which effectively decimates triplet *** is shown that the system is in ordered phase and no phase transition exists at any finite *** trivial transition occurs at T=∞.In particular,we find that the pure triplet interaction Ising model is equivalent to one with pure nearest-neighbor pair interaction on the lattice,and the two systems have the same critical *** is in contrast with that of triangular lattice and Sierpinski gasket fractal.

关键词： temperature interaction Ising

Studying DDTs in agricultural soils of selected rural communities of Armenia

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Acta Geochimica 2020年第4期39卷 487-496页

作者： G.Tepanosyan L.Sahakyan O.Belyaeva M.Beglaryan D.Pipoyan A.Hovhannisyan A.Saghatelyan The Center for Ecological-Noosphere Studies of the National Academy of Sciences RA Abovian-68 Street0025 YerevanRepublic of Armenia

To study organochlorine pesticides and organophosphorus pesticides contents and assess pesticideinduced health risk in Armenia,the contents of pesticides were determined in 252 soil samples taken from relatively large plots of agricultural land in 25 rural *** results showed that only∑DDT contents were detected in 39 out of 252 soil *** identified contents of∑DDT mainly consisted of pp’-DDE,suggesting historical use.6 out of 12 rural communities are characterized by the presence of former pesticide storehouses *** excesses versus Maximum Acceptable Concentration were observed in 26 out of 39 samples and ranges from 1.03 to 464.9 *** health risk assessment showed that non-carcinogenic risk is below the allowable level(HQ<1).However,the carcinogenic risk is above the allowable level of<10^-4 in all cases when∑DDT is *** all studied rural communities,the presence of observed∑DDT and associated risk to the local population was detected mainly in the majority of sampling sites in Jrashen(Ararat region),Aramus(Kotayq region)and Khanjyan(Armavir region).Therefore,special attention should be given to the riskiest rural communities and risk reduction measures are needed to reduce or eliminate observed carcinogenic health effect.

关键词： Organochlorine pesticides ∑DDT Soil Pollution Health risk assessment

Dielectric Behavior of Middle Phase Microemulsion

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Chinese Chemical Letters 2000年第8期11卷 739-742页

作者： Lei, JP Li, Y Zhao, KS S China Normal Univ Dept Chem Guangzhou 510631 Peoples R China

Dielectric measurements were performed on middle phase microemulsions composed of sodium dodecylsulfate(SDS), cetyltrimethylammonium bromide(CTAB), n-butanol, n-heptane and brine. Distinct and unique dielectric behavior, with characteristic frequency dependence regularity on the salinity of the microemulsions, was observed in the low-frequency range from 10-10(3)Hz. It can be considered to be an interfacial polarization mechanism.

关键词： middle phase microemulsions dielectric spectroscopy relaxation time

Preparation of cross-linked magnetic chitosan with quaternary ammonium and its application for Cr(Ⅵ) and P(Ⅴ) removal

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Journal of Environmental Sciences 2014年第12期26卷 2379-2386页

作者： Wei Yao Pinhua Rao Irene M.C.Lo Wenqi Zhang Wenrui Zheng School of Chemistry and Chemical Engineering Shanghai University of Engineering Science Department of Civil and Environmental Engineering The Hong Kong University of Science and Technology

Pollutants that exist in anionic species are issues of concern in water treatment. Compared to cationic pollutants, the removal of anionic pollutants by adsorption is more difficult because most adsorbents carry predominantly negative charges in neutral and alkaline environments. In this study, a cross-linked chitosan derivative with quaternary ammonium and magnetic properties（QM-chitosan） was prepared and employed to remove chromium（VI） and phosphorus（V）（Cr（VI） and P（V）） from aqueous environments. The QM-chitosan was characterized by Fourier transform infrared spectrometry（FT-IR）,thermogravimetric analysis（TGA）, energy dispersive X-ray（SEM-EDX） and zeta *** experiments show that QM-chitosan can effectively remove Cr（VI） and P（V）, and the main mechanism was believed to be electrostatic interaction. A pseudosecond-order model was fitted to describe the kinetic processes of Cr（VI） and P（V） removal. The adsorption isotherms of both Cr（VI） and P（V） on the QM-chitosan were well fitted by the Langmuir isotherm equation. The saturated adsorption capacity of P（V）（2.783 mmol/g） was found to be higher than that of Cr（VI）（2.323 mmol/g）, resulting from the size of the H2PO-4ions being smaller than that of the HCr O-4ions. However, the theoretical calculation and experimental results showed that QM-chitosan had a stronger affinity for Cr（VI） than P（V）. The adsorption–desorption of the QM-chitosan was evaluated, and high regeneration rates were demonstrated.

关键词： Magnetic chitosan Quaternary ammonium Cr(VI) P(V) Adsorption

Synthesis and Crystal Structure of a Novel Polymeric Complex [WS_4Cu_4(Py)_4(μ-CN)_2]_∞

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Chinese Journal of Structural Chemistry 2004年第3期23卷 292-295页

作者：焦昌梅乔善宝徐庆峰郎建平 School of Chemistry and Chemical Engineering Suzhou University Suzhou 215006 China Department of Chemistry Yancheng Normal College Yancheng 224002 China School of Chemistry and Chemical Engineering Suzhou University Suzhou 215006 China State Key Laboratory of Structural Chemistry Fujian Institute of Research on the Structure of Matter The Chinese Academy of Sciences Fuzhou Fujian 350002 China

The reaction of [Et4N]2WS4 with 4 equiv of CuCN in pyridine produced a new polymeric complex [WS4Cu4(Py)4(m-CN)2]∞ 1, whose crystal structure has been characterized by single-crystal X-ray analysis. 1 (C22H20Cu4N6S4W, Mr = 934.71) crystallizes in monoclinic, space group P21/m with a = 8.994(2), b = 16.038(3), c = 12.026(3) ? b = 90.85(1)? V = 1734.6(6) ?, Z = 2, Dc = 1.789 g/cm3, F(000) = 896, m(MoKa) = 59.8 cm-1 and T = 193 K. The structure was refined to R = 0.064 and Rw = 0.080 for 2209 observed reflections (I > 3.0s(I)). The X-ray analysis shows that the tetrahedral WS4 core is coordinated by four Cu atoms, forming a saddle-like WS4Cu4 unit. These repeating units are further interconnected by four Cum-CNCu bridges to generate a one-dimensional ladder-shaped structure. The W…Cu bond distances are 2.726(2) and 2.723(2) ? respectively.

关键词： synthesis crystal structure tungsten complex copper complex