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On three Differential Equations Associated with Chebyshev Polynomials of Degrees 3,4 and 6

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Acta Mathematica Sinica,English Series 2017年第1期33卷 21-36页

作者： Li chien SHEN Department of Mathematics University of Florida Gainesville FL 32611-8105

We shall study the differential equation y^l2=tn（y）-（1-2μ2）;where μ2 is a constant, tn（x） are the Chebyshev polynomials with n = 3,4,6. the solutions of the differential equations will be expressed explicitly in terms of the Weierstrass elliptic function which can be used to construct theories of elliptic functions based on 2F1 （1/4, 3/4; 1; z）, 2F1 （l/3, 2/3; 1; z）, 2F1 （1/6, 5/6; 1; z） and provide a unified approach to a set of identities of Rmanujan involving these hypergeometric functions.

关键词： Chebyshev polynomials Eisenstein series Jacobi theta functions Weierstrass ellipticfunction

On Schwarzian triangle Functions, Automorphic Forms and a Generalization of Ramanujan’s triple Differential Equations

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Acta Mathematica Sinica,English Series 2018年第11期34卷 1648-1662页

作者： Li chien SHEN Department of Mathematics University of Florida

Let G be the group of the fractional linear transformations generated by t（τ）=τ ＋ λ, S（τ）=（τ cos π/n ＋ sin π/n）/（-τ sin π/n ＋ cos π/n）;where λ=2（cos π/m ＋ cos π/n）/sin π/n;m, n is a pair of integers with either n ≥ 2, m ≥ 3 or n ≥ 3, m ≥ 2; τ lies in the upper half plane H.A fundamental set of functions f0, fi and f∞ automorphic with respect to G will be constructed from the conformal mapping of the fundamental domain of G. We derive an analogue of Ramanujan＇s triple differential equations associated with the group G and establish the connection of f0, fi and f∞ with a family of hypergeometric functions.

关键词： Hypergeometric function Schwarzian triangle function Jacobi theta functions Ramanu-jan's triple differential equations

Linear Gyro-Kinetic Response Function for Zonal Flows

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Plasma Science and technology 2011年第2期13卷 157-161页

作者： t.WAtARI y.HAMADA National Institute for Fusion Science

A linear response function for zonal flows is obtained by solving the gyro-kinetic equation. this is an extension of a previous work which adopted the method of ＂integrating along particle orbit＂ to solve the drift kinetic equation. the formula derived in this paper is used to calculate the dispersion relation of geodesic acoustic mode, which is then compared with that of the gyro-kinetic analytic formula.

关键词： zonal flow geodesic acoustic mode integrating along particle orbits

A Mixed-control Mechanism Model of Proeutectoid Ferrite Growth under Non-equilibrium Interface Condition in Fe-C Alloys

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Journal of Materials Science & technology 2004年第5期20卷 561-566页

作者： RuihengWU XueyuRUAN HongbingZHANG t.y.Hsu DepartmentofPlasticitytechnology ShanghaiJiaoTongUniversityShanghai200030China Departmentof.MaterialsEngineering ShanghaiInstituteofTechnologyShanghai200233China SchoolofMaterialsScieuceaudEugineering ShanghaiJiaoTougUuiversityShanghai200030China

By combining the α/γ interface migration and the carbon diffusion at the interface in Fe-C alloys, a mathematical model is constructed to describe the mixed-control mechanism for proeutectoid ferrite formation from austenite. In this model, the α/γ interface is treated as non-equilibrium interface, i.e., the carbon concentration of austenite at γ/α interface is obtained through theoretical calculation, instead of that assumed as the local equilibrium concentration. For isothermal precipitation of ferrite in Fe-C alloys, the calculated results show that the rate of interface migration decreases monotonically during the whole process, while the rate of carbon diffusion from γ/α interface into austenite increases to a peak value and then decreases. the process of ferrite growth may be considered as composed of three stages: the period of rapid growth, slow growth and finishing stage. the results also show that the carbon concentration of austenite at γ/α interface could not reach the thermodynamic equilibrium value even at the last stage of ferrite growth.

关键词： Proeutectoid ferrite precipitation Non-equilibrium interface Phase transformation kinetics Mixed-control mechanism

An Experi mental Study on Wave-Induced Dynamic Stresses in Seabed

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China Ocean Engineering 2006年第1期20卷 27-44页

作者： S.C.Chang L.K.chien J .G.Lin y.F.Chiu Department of Harbor and River Engineering National Taiwan Ocean University Taiwan China Harbor and Marine technology Center Taiwan China

A series of hydraulic model tests with horizontal movable seabed under regular wave actions have been carried out to investigate the dynamic interactions between water waves and seabed soil. Seabed dynamic stresses from experiments are, tound to differ from theoretical resuhs. the response of p0 in permeable seabed has a small decay and phase shift to the nonlinear wave actions, and the dynamic stresses, σs/p0, σh/p0 and u/p0, contain different phase shift characteristics. Such phenomena will strongly affect the dynamic stress path in seabed. If the phase shifts of σs. and σh are neglected, the stress path will become a straight line; otherwise, it will become an elliptical curve. In phase shift cases, the long axis of the p - q diagram will be shortened when the depth increases, and the short axis will become longer when the phase shift increases. For the p＇ - q＇ diagram, the larger the phase lag of u, the longer the short axis. Relative results offer useful information for the analysis of seabed stability.

关键词： wave-induced dynamic stresses movable seabed hydraulic model test stress path

Dynamic stiffness for thin-walled structures by power series

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2006年第8期7卷 1351-1357页

作者： ZHU Bin LEUNG A.y.t. Department of Civil Engineering Zhejiang University Hangzhou 310027 China Department of Building and Construction City University of Hong Kong Hong Kong China

the dynamic stiffness method is introduced to analyze thin-walled structures including thin-walled straight beams and spatial twisted helix beam. A dynamic stiffness matrix is formed by using frequency dependent shape functions which are exact solutions of the governing differential equations. With the obtained thin-walled beam dynamic stiffness matrices, the thin-walled frame dynamic stiffness matrix can also be formulated by satisfying the required displacements compatibility and forces equilib-rium, a method which is similar to the finite element method (FEM). then the thin-walled structure natural frequencies can be found by equating the determinant of the system dynamic stiffness matrix to zero. By this way, just one element and several elements can exactly predict many modes of a thin-walled beam and a spatial thin-walled frame, respectively. Several cases are studied and the results are compared with the existing solutions of other methods. the natural frequencies and buckling loads of these thin-walled structures are computed.

关键词： Dynamic stiffness method thin-wall structures Power series Buckling

CONStRUCtION OF QUANtUM FIELD tHEORy OF DISLOCAtIONS BASED ON tHE NON-RIEMANNIANPLAStICIty

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Acta Metallurgica Sinica(English Letters) 1998年第6期11卷 405-411页

作者： t.Hasebe y.Imaida Doshisha Univ Kyoto Japan

A new microscopic approach was proposed, which bridges the order gap between the dislocation theory and the crystalline plasticity based on the quantum field theory of dislocations. the Ginzburg-Landau equation was derived rigorously from the quantized Hamiltonian for a crystal body containing a large number of dislocations, which gives the reaction-diffusion (RD) type differential equations. the RD equation describes periodic patterning shown in PSBs, etc.. relationship between the proposed theory and the concepts appeared in the non-Riemannian plasticity was extensively discussed by introducing the gauge field of dislocations. (Edited author abstract) 15 Refs.

关键词： crystalline plasticity field theory Non-Riemannian plasticity,dislocation theory gauge field

Processing and Performance of Alumina Fiber Reinforced Alumina Composites

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Journal of Materials Science & technology 2003年第4期19卷 337-340页

作者： P.y.Leet t.Uchijima t.yano Research Laboratory for Nuclear Reactors Tokyo Institute of Technology2-12-1O-okayamaMeguro-kuTokyo152-8550JapanResearch Laboratory for Nuclear ReactorsTokyo Institute of Technology2-12-1O-okayamaMeguro-kuTokyo152-8550JapanResearch Laboratory for Nuclear ReactorsTokyo Institute of Technology2-12-1O-okayamaMeguro-kuTokyo152-8550Japan

Processing of alumina fiber-reinforced alumina matrix composites by hot-pressing was described. the mechanical properties of the composites fabricated by different sintering conditions including temperature and pressure have been investigated. the results indicated that the higher sintering temperature and pressure corresponded to the higher bulk density and higher maximum strength of the composite, whereas the pseudo-ductility of the composite was lower. the preliminary results of the composite with monazite-coated fibers showed that maximum strength could be improved up to 35% compared with the noncoated fiber composite in the same sintering condition. Moreover, the fracture behavior of the composite changed from completely brittle fracture to non-brittle fracture under the suitable sintering conditions. SEM observation of the fracture surface indicated that the coating worked as a protective barrier and avoided sintering of the fibers together even at high temperature and pressure during densification process.

关键词： Al2O3/Al2O3 composites Mechanical properties Hot-pressing Fiber reinforced composites

Recent advances in regulatory t cells induced by B cells

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Cellular & Molecular Immunology 2018年第5期15卷 539-541页

作者： chien-Hui chien Bor-Luen Chiang Graduate Institute of Clinical Medicine National Taiwan UniversityTaipei City 10048TaiwanChina Department of Medicinal Research National Taiwan University HospitalTaipei City 10002TaiwanChina

Naïve CD4+CD25−t cells activated in the presence of naïve splenic B cells may differentiate into CD4+CD25+Foxp3−regulatory t cells,which were named treg-of-B cells by our group(table 1).In addition,the oral delivery of antigenactivated naive Peyer’s patch B cells induced treg-of-B(P)cells with an increased suppressive function.3 Our recent article reported that peritoneal B-1a cells produced more IL-10;moreover,B-1a cells promoted the induction of treg-of-B1a cells in an IL-10-independent manner.1 In our studies,splenic B2-cell-induced treg-of-B cells,Peyer’s patch B-cell-induced treg-of-B(P)and peritoneal B-1a-cell-induced treg-of-B1a cells shared similar phenotypes and *** group subsequently reported that adoptive transfer these treg-of-B cells protected mice from several disease models,including allergic asthma,rheumatoid arthritis and inflammatory bowel ***,we summarize the suppression and induction mechanism of treg-of-B cells(Figure 1).

关键词： Foxp3 peritoneal patch