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Extremal eigenvalues of measure differential equations with fixed variation

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Science china Mathematics 2010年第10期53卷 2573-2588页

作者： ZHANG MeiRong 1,2.1 department of Mathematical Sciences,tsinghua {2.,beijing 1.0084,china 2.Zhou Pei-Yuan Center for Applied Mathematics,tsinghua {2.,beijing 1.0084,china 1. department of Mathematical Sciences Tsinghua University Beijing 100084 China2. Zhou Pei-Yuan Center for Applied Mathematics Tsinghua University Beijing 100084 China

In this paper we will study eigenvalues of measure differential equations which are motivated by physical problems when physical quantities are not absolutely *** taking Neumann eigenvalues of measure differential equations as an example,we will show how the extremal problems can be completely solved by exploiting the continuity results of eigenvalues in weak* topology of measures and the Lagrange multiplier rule for nonsmooth *** results can give another explanation for extremal eigenvalues of SturmLiouville operators with integrable potentials.

关键词： measure differential equation eigenvalue extremal value weak* topology Frechét derivative sub-differential

Electroluminescent properties of three ternary europium complexes with different phenanthroline derivatives

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Science china chemistry 2004年第4期47卷 326-334页

作者： BIAN Zuqiang1,2. GAO Deqing1, GUAN Min1, XIN Hao1, LI Fuyou1, HUANG Chunhui1, WANG Kezhi2.& JIN Linpei2.1. State Key Laboratory of Rare Earth Materials chemistry and Applications, Peking university, {2. 100871, china 2. department of chemistry, {2. Normal university, {2. 100875, china 1. State Key Laboratory of Rare Earth Materials chemistry and Applications Peking University 100871 Beijing China 2. department of chemistry Beijing Normal University 100875 Beijing China

Three ternary Eu(III) complexes with general formula of Eu(DBM)3LN (DBM = dibenzoylmethanate, and LN (N = 1-3 ) stand for three different 1,10-phenanthroline derivatives) have been synthesized for vacuum deposition films-based electroluminescent devices. The complex Eu(DBM)3L3 (L3 = 2.phenyl-3-[3-(carbazol-9-yl)propyl]imidazo[4,5-f]1,10-phenan-throline) was designed with an effort to combine the electron-transporting phenanthroline platform and the hole-transporting carbazole group into one molecule expecting to improve both electron and hole transporting properties simultaneously. The results show that the variation of the neutral ligands in Eu(III) mixed ligand complexes is a simple and effective approach to the improvement in the thermal stability, PL and EL properties of materials. A double-layer device with the configuration of ITO/TPD (50 nm)/Eu(DBM)3L3 (50 nm)/Mg0.9Ag0.1 (2.0 nm)/Ag (100 nm) exhibited Eu(III)-based pure red emission with a maximum brightness of 561 cd/m2.at 16 V, and an onset driving voltage of 8 V. A device with the configuration of ITO/TPD (50 nm)/[Eu(DBM)3L3 (5 nm):BCP (5 nm)]4/BCP (2. nm)/AIQ (10 nm) Mg0.9Ag0.9 (110 nm)/Ag (100 nm) gave high efficient and pure red light emission with a luminance of 1419 cd/m2. Keywords dibenzoylmethane - electroluminescence - lanthanide - N ligands

关键词： dibenzoylmethane electroluminescence lanthanide N ligands

Solving the input data in error correc-tion of optical fabrication by finite Fourier coefficient algorithm

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Science china(Technological Sciences) 2006年第1期49卷 50-60页

作者： CHENG Haobo1,2. SUN Guozheng3 & FENG Zhijing2.1. department of Optical Engineering, beijing Institute of Technology, beijing 100081, china 2. department of Precision Instruments and Mechanology, tsinghua university, beijing 1.0084, china 3. china North Industries Group Corporation, beijing 100089, china 1. department of Optical Engineering Beijing Institute of Technology Beijing 100081 China 2. department of Precision Instruments and Mechanology Tsinghua University Beijing 100084 China 3. china North Industries Group Corporation Beijing 100089 China

A free-form lens (FFL) is a special surface that is difficult to be fabricated. FFL are usually fabricated by computer-controlled optical surfacing (CCOS) technique. During CCOS, the material removal amount is determined by the unit removal function (URF) convoluting with the input data――the dwell time. When the removal amount and the URF are known, how to solve the input data involves the special algorithm――deconvolution. Usually, the input data are solved by virtue of low pass filter or iterative methods. However, an approximation solution would destroy the machining stability nec-essary to perform precisely CCOS. In this paper, to solve the input data, a new method that is based on the finite Fourier coefficient is put forward. It can give a continuous and accurate solution for fabricating choice. Several parameters are simulated, which influ-ence the process of CCOS, and evaluating on the effect of the method is also carried out. Experimental results verify that this method is suitable for guiding the manufacturing of high precision FFL.

关键词： optical fabrication, computer controlled optical surfacing, free-form lens, finite Fourier coefficient, error correction.

MULTISTEP DISCRETIZATION OF INDEX 3 DAES

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Journal of Computational Mathematics 2000年第3期18卷 325-336页

作者： Yang Cao Qing-yang Li (department of Mathematics, tsinghua university,{2., china) 清华大学北京 100084

Studies the different types of multistep discretization of index 3 differential-algebraic equations in Hessenberg form. Existense, uniqueness and influence of perturbations; Local convergence of multistep discretizati... 详细信息

关键词： multistep methods Adams method BDF DAEs Index 3

Development of SOM combustion model for Reynolds-averaged and large-eddy simulation of turbulent combustion and its validation by DNS

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Science china(Technological Sciences) 2008年第8期51卷 1073-1086页

作者： ZHOU LiXing department of Engineering Mechanics, tsinghua university,{2., china department of Engineering Mechanics Tsinghua University Beijing 100084 China

The derivation and closure methods of the second-order moment (SOM) combus- tion model are proposed. The application of this model to Reynolds averaged (RANS) and large-eddy simulation (LES) of turbulent swirling diffusion combustion, jet diffusion combustion, and bluff-body stabilized premixed combustion is sum- marized. It is indicated that the SOM model is much better than the eddy-beak-up (EBU) and presumed PDF models widely used in commercial software and engi- neering. The SOM modeling results are close to those obtained using the most accurate but much more complex PDF equation model. Moreover, it can save much more computation time than the PDF equation model. Finally, the SOM model is validated by the direct numerical simulation (DNS) of turbulent reacting channel flows.

关键词： turbulent combustion second-order moment model Reynolds averaged simulation large-eddy simulation

DIMENSIONS OF SELF-AFFINE SETS WITH OVERLAPS

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Chinese Annals of Mathematics,Series B 2003年第3期24卷 275-284页

作者： HUA Su department of Mathematics, tsinghua university,{2., china. Tsing Hua Univ Dept Math Beijing 100084 Peoples R China

The authora develop an algorithm to show that a class of self-affine sets with overlaps can be viewed as sofic affine-invariant sets without overlaps,thus by using the results of [11] and [10],the hausdorff and minkow... 详细信息

关键词： self-affine set overlap hausdorff dimension minkowski dimension

Generalized gradient projection neural networks for nonsmooth optimization problems

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Science china(Information Sciences) 2010年第5期53卷 990-1005页

作者： LI GuoCheng 1 , SONG ShiJi 2.? & WU Cheng 2.1 department of Mathematics, beijing Information Science and Technology {2., beijing 100192. china 2.department of Automation, tsinghua university, beijing 1.0084, china 1. department of Mathematics Beijing Information Science and Technology University Beijing 100192 China2. Department of Automation Tsinghua University Beijing 100084 China

Generalized gradient projection neural network models are proposed to solve nonsmooth convex and nonconvex nonlinear programming problems over a closed convex subset of R n . By using Clarke’s generalized gradient, the neural network modeled by a differential inclusion is developed, and its dynamical behavior and optimization capabilities both for convex and nonconvex problems are rigorously analyzed in the framework of nonsmooth analysis and the differential inclusion theory. First for nonconvex optimization problems, the quasi convergence results similar to those achieved by previous work are proved. For convex optimization problems, the global convergence results are proved, i.e. any trajectory of the neural network converges to an asymptotically stable equilibrium point, which is an optimal solution of the primal problem whenever it exists. This result remains valid even if the initial condition is chosen outside the feasible set. In addition, an asymptotic control result involving a Tykhonov like regularization shows that any trajectory of the revised neural network can be forced to converge toward a particular optimal solution of the primal problem. Finally, two simulation optimization algorithms for solving the optimization and control problems are designed respectively, and three typical simulation experiments are illustrated to present the accuracy and efficiency of theoretical convergence results of this paper.

关键词： nonsmooth optimization problem generalized gradient projection networks differential inclu sions convergence

Preparation of MWNTs/Al_2._3 composites and their mechanical and electrical properties

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Science china(Technological Sciences) 2005年第6期48卷 622-631页

作者： FAN Jinpeng1,2. ZHAO Daqing1,2. XU Zening1,2.& WU Minsheng1,2.1. department of Mechanical Engineering, tsinghua university,{2., china 2. Key Laboratory for Advanced Manufacturing by Materials Processing Technology, tsinghua university,{2., china 1. department of Mechanical Engineering Tsinghua University 100084 Beijing China 2. Key Laboratory for Advanced Manufacturing by Materials Processing Technology Tsinghua University 100084 Beijing China

The mechanical and electrical properties of MWNTs/Al2.3 composite prepared fabricated by hot pressing are investigated. The relation between properties and microstructure of composites is also discussed. With 4wt% MWNTs as reinforcement, the fracture toughness of composite obtained reaches 5.55 MPa·m1/2. which is 80% higher than that of pure Al2.3 obtained in the same conditions. The main toughening mechanism is CNTs’ pinning alumina grain boundaries, and the pullout of CNTs takes effect also. Through adding 2.t% MWNTs and altering the mix method, the fracture toughness of the composite obtained is 3.97 MPa·m1/2. Furthermore, the electrical resistivity is as low as 8.4×10?3 ?·m, decreasing by 14 orders of magnitude compared with pure alumina ceramics. The function of CNTs in composite is related to the distribution state of CNTs in composite, and the distribution state of CNTs in matrix is dependent on preparation procedures.

关键词： MWNTs, alumina, composite, fracture toughness, electrical properties.

EXACT NONREFLECTING BOUNDARY CONDITIONS FOR AN ACOUSTIC PROBLEM IN THREE DIMENSIONS

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Journal of Computational Mathematics 2003年第1期21卷 15-24页

作者： Houde Han Chunxiong Zheng (department of Mathematical Sciences, tsinghua university,{2., china) department of Mathematical Sciences Tsinghua University 北京 100084

In this paper, nonreflecting artificial boundary conditions are considered for an acoustic problem in three dimensions. With the technique of Fourier decomposition under the orthogonal basis of spherical harmonics, three kinds of equivalent exact artificial boundary conditions are obtained on a spherical artificial boundary. A numerical test is presented to show the performance of the method.

关键词： Exterior problem Nonreflecting artificial boundary condition Acoustic equa-tion Three-dimensions.