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Effect of Interchain Coupling on Quantum Lattice Fluctuation and Fluctuation Induced Interchain order.Transition in Trans-polyacetylene

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Chinese Physics Letters 1997年第9期14卷 694-697页

作者：曾上游饶雪松吴长勤孙鑫 Department of Physics Fudan UniversityShanghai 200433

Based on the modified Su-Schrieffer-Heeger Harniltonian and by adding the interchain hopping term,we consider the effect of interchain coupling on quantum lattice fluctuation in trans-polyacetylene.It has been found that the interchain coupling does not always weaken quantum lattice fluctuation.After overcoming a barrier of 1 eV or so,the quantum lattice fluctuation can induce a transition of interchain order.The physical meaning of these features is discussed.

关键词： order. quantum lattice

Medium-range order.clusters in metal melts

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Science China(Technological Sciences) 2002年第2期45卷 113-119页

作者：边秀房潘学民秦绪波蒋民华 Key Laboratory of Liquid Structure and Heredity of Materials Ministry of EducationShandong UniversityJinan 250061China

Structures of molten metals Cu and Al,alloys Cu-Al,Al-Ni,Al-Fe and,Al-Si were investigated by using high temperature X-ray diffractometer.It has been found that there are not only short-range order.structures (SRO) but also medium range order.structures (MRO) in Cu-Al,Al-Ni,Al-Fe alloy melts.There are only short-range order.structures in the pure metals Cu and Al and Al-Si alloy melts at different temperatures.It has also been found that the presence and the disappearance of the MRO structures in molten metals are a function of temperature.Moreover,the pre-peak in the structure factor is an indication of MRO in molten metals.There is a pre-peak in each structure factor S(Q) of Al-Fe alloy melt containing 14 wt% Fe,16 wt% Fe and 19 wt% Fe at 1550℃,showing that there are the medium range order.structures in these alloy melts.For Al-35wt%Ni alloy,the pre-peak exists in S(Q) when the temperature is lower than 1300℃,and it is weakened drastically when the temperature surpasses 1300℃.The pre-peak occurs at values of scattering vector Q=18.5 nm-1 in the structural factor of Cu-12 wt %Al alloy melts at 1250℃.The height of the pre-peak in the melt decreases with increasing temperature.These results show that there exist not only the SRO structure but also MRO structure in the Al-TM melts,and the MRO is correspondent to the tendency of formation of chemical compound.The formation mechanism of the MRO is also studied in this work.Based on the measured results of Cu-Al alloy,a model of the MRO is presented.

关键词： liquid structure,structure factor,medium range order.

Uniform Convergence of Higher order.Quasi Hermite-Fejer Interpolation

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Chinese Science Bulletin 1994年第6期39卷 441-448页

作者：王子玉田继善 Department of Mathematics Henan University Kaifeng 475001 PRC

Let Xn={xkn=cosθkn: θkn=（kπ）/（n+1）, 1≤k≤n}be the node system which consists ofroots of Un （x） =（sin（n+1）θ）/（sinθ）（x=cosθ θ∈[0,π]）, the second kind Chebyshevpolynomical. All the symbols below have the same meaning as Ref. [1]if notspecifically defined. We shall consider a kind of new interpolating problem in thisnote. For any non-negative integer q and f∈C[-1, 1], it is well known that thepolynomial Qnq（f）∈ПN （N=2（q+1）（n+1） -1） satisfying the following conditions isuniquely determined:Qnq(f, xkn) =f(xkn), 1≤k≤n; Qnq（f,±1）=f（±1）,Qnqj(f,xkn)=cjkn, 1≤k≤n,1≤j≤2q+1,Qnqj（f,1）=djn, Qnqj（f,-1）=gjn, 1≤j≤q,where cjkn,djn, gjnare any given real numbers. Qnq（f）is called the higher order.uasi Hermite-Fejer interpolation of f.We

关键词： second kind Chebyshev nodes higher order quasi Hermite-Fejer interpolation uniform convergence approximation order.

MINIMAL-order.DYNAMIC DECOUPLING OF NONLINEAR SYSTEMS

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Science China Mathematics 1990年第5期33卷 617-624页

作者：夏小华高为炳 The Seventh Research Division Beijing University of Aeronoutics and Astronautics Beijing 100083 PRC

The minimal-order.dynamic decoupling problem of affine nonlinear control systems has been dealt with. An analytic algorithm is proposed, and, based upon it, a necessary and sufficient condition for the dynamic decoupling problem is given. Then, the structure of the decoupling compensator is characterized. The characterization and the properties of the algorithm make it possible to prove that for dynamic decouplable affine nonlinear control systems, the dynamic decoupling compensator obtained with the algorithm is a minimal-order.one.

关键词： nonlinear system dynamic state feedback decoupling minimal order.

ON OSCILLATION THEOREMS FOR HIGHER order.DIFFERENTIAL EQUATIONS

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数学研究 1994年第1期 56-59页

作者： Chen Zongxuan(Dept of Math,Jiangxi Normal Univ)Nanchang

ＯＮＯＳＣＩＬＬＡＴＩＯＮＴＨＥＯＲＥＭＳＦＯＲＨＩＧＨＥＲＯＲＤＥＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ￥ＣｈｅｎＺｏｎｇｘｕａｎ（ＤｅｐｔｏｆＭａｔｈ，ＪｉａｎｇｘｉＮｏｒｍａｌＵｎｉｖ）ＮａｎｃｈａｎｇＡ... 详细信息

ＯＮＯＳＣＩＬＬＡＴＩＯＮＴＨＥＯＲＥＭＳＦＯＲＨＩＧＨＥＲＯＲＤＥＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ￥ＣｈｅｎＺｏｎｇｘｕａｎ（ＤｅｐｔｏｆＭａｔｈ，ＪｉａｎｇｘｉＮｏｒｍａｌＵｎｉｖ）ＮａｎｃｈａｎｇＡｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐ...

关键词： Linear differential equation entire function zero-sequence order.

Effect of the repeated melting of mother ingot on the stability of icosahedral phase precipitated from Zr-Al-Ni-Cu-Ag glass

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Science China(Technological Sciences) 2003年第6期46卷 639-644页

作者：闫志杰李金富王鸿华何顺荣周尧和 State Key Lab of Metal Matrix Composites Shanghai Jiao Tong University Shanghai 200030 China Taiyuan Heavy Machinery Institute Taiyuan 030024 China

Differential scanning calorimetry (DSC) shows that repeated melting of mother ingot improves the stability of icosahedral phase (I-phase) precipitated from Zr65Al7.5Ni10Cu12.5Ag5 glass. The Kissinger analysis of crystallization implies that the effective activation energies for the pre-cipitation of I-phase and its decomposition considerably increases due to the repeated melting of mother ingot. Repeated melting of mother ingot refines ingot microstructure. Because of structure heredity, the size of the short-range order. (SROs) in the glassy alloy produced from the mother ingot with finer microstructure becomes smaller, which makes the rearrangement of atoms more difficult, and the I-phase more stable.

关键词： metallic glass, icosahedral phase, decomposition, short-range order.

The generalized solution of ill-posed boundary problem

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Science China Mathematics 2006年第7期49卷 902-911页

作者： CAO Weiping & MA Jipu Department of Mathematics and Physics, Huaihai Institute of Technology, Lianyungang 222005, China Y. Y. Tseng Functional Analysis Research Centre, Harbin Normal University, Harbin 150080, China Department of Mathematics and Physics Huaihai Institute of Technology Lianyungang China Y. Y. Tseng Functional Analysis Research Centre Harbin Normal University Harbin China

In this paper, we define a kind of new Sobolev spaces, the relative Sobolev spaces Wk0,p(Ω, Σ). Then an elliptic partial differential equation of the second order.with an ill-posed boundary is discussed. By utilizing the ideal of the generalized inverse of an operator, we introduce the generalized solution of the ill-posed boundary problem. Eventually, the connection between the generalized inverse and the generalized solution is studied. In this way, the non-instability of the minimal normal least square solution of the ill-posed boundary problem is avoided.

关键词： generalized inverse of operator, generalized solution, ill-posed boundary problem, elliptic partial differential equations of second order.

Molecular dynamics simulation of calcium fluoride——Crystalline, superionic, molten and quenched-amorphous phases

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Science China Chemistry 1995年第1期38卷 28-38页

作者：程兆年郏正明张静陈念贻 Shanghai Institute of Metallurgy and Laboratory of Computer Chemistry Chinese Academy of SciencesShanghai 200050 China

The results from the molecular dynamics simulations on crystalline, superionic, molten and quenched-amorphous states of calcium fluoride system are reported. The Ca++ and F- sublattices are studied by using the method of bond order.parameters. The result shows that both Ca++ and F- sublattices can be described with the bond-orientation normal distribution model. In the superionic phase the Ca++ cations keep their original stable fcc frame, but in the F- case random distortion generates from their original simple cubic (sc) structure. The simulation on the molten phase gives three radial distribution functions that are difficult to separate from the experimental X-ray diffraction data. The simulation of quenched-amorphous state shows that a dense random packing of equivalent spheres centered by Ca++ cations occurs in the system simulated. However, the system quenched is not stable enough because the Ca++ cation and F- anions around it do not form themselves into a certain configuration.

关键词： molecular dynamics simulation CaF2 superionic phase molten CaF2 CaF2 computer glass bond orientational order.

A result of complex oscillation for differential equations f''+(Q_1e^p+Q_2)f=0

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Chinese Science Bulletin 1996年第17期41卷 1418-1422页

作者：袁文俊 Institute of Mathematics Chinese Academy of Sciences Beijing 100080 Department of Mathematics Xinjiang Normal University Urumqi 830053 China

In this note, we solve a problem of complex oscillation for the differential equations f″+(Q1（z）eP（z）+Q2（z）)f=0,（1） where Q1（z）, Q2（z） are meromorphic, P（z） is entire. Under the entire coefficients the problem has been discussed by Bank et al., Yuan et al. We will use the standard notations of Nevanlinna’s theory, σ（f）, λ（f） and λ（f） denote the growth order. the exponent of convergence of zeros and distinct zeros of f（z）,

关键词： complex oscillation exponent of convergence growth order.