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REDUCTIONS OF ADJOINT REPRESENTATIONS TO LAX REPRESENTATIONS FOR CONSTRAINED FLOWS

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Chinese Annals of mathematics,Series B 1996年第2期17卷 187-198页

作者： ZEng YUNBO department of Applied mathematics, tsinghua university, beij.ng 100084, china. TSIng hua UNIV DEPT APPL MATHBEIJING 100084PEOPLES R CHINA

Within framework of zero-curvature representation theory, the Lax representations for x- andtn-constrained flows of soliton hierarchy are obtained from reductions of adjoint representationsof the auxiliary linear problems. This method is applied to the third order spectral problem bytaking modified Boussinesq hierarchy as an illustrative example.

关键词： Constrained flow Lax representation Adjoint representation Soliton hierarchy

GRAPH-DIRECTED STRUCTURES OFSELF-SIMILAR SETS WITH OVERLAPSGRAPH-DIRECTED STRUCTURES OFSELF-SIMILAR SETS WITH OVERLAPSS

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Chinese Annals of mathematics,Series B 2000年第4期21卷 403-412页

作者： huasu RAOHUI departmentofmathematics TsinghuaUniversityBeijing100084China. departmentofmathematics WuhanUniversityWuhan430072China.

Some kinds of the self-similar sets with overlapping structures are studied by introducing the graph-directed constructions satisfying the open set condition that coincide with these sets. In this way, the dimensions ... 详细信息

关键词： Self-similar sets Graph-directed sets Overlapping Label Pisot number

RECOGNITION AND CLASSIFICATION FOR O(n)-EQUIVARIANT BIFURCATIONS WITH O(n)-CODIMENSION LESS THAN 5

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Chinese Annals of mathematics,Series B 1998年第4期19卷 391-400页

作者： WAng XIAOFEng (department of Applied mathematics, tsinghua university, beij.ng 100084, china.)TAng YUN (department of Applied mathematics, tsinghua university, beij.ng 100084, china.)WAng DUO (School of Mathematical Science, Peking universityl Beliing 10 Tsing hua Univ Dept Appl Math Beijing 100084 Peoples R China Peking Univ Sch Math Sci Beijing 100080 Peoples R China

Bifurcation problems equivariant under the standard action of the orthogonal group O(n) up to O(n)-codimension 4 are classified into 19 classes. For each class the normal form and one universal unfolding are calculate... 详细信息

关键词： O(n)-equivariant bifurcation Normal form Universal unfolding Recognition problem

Design methodology of a mini-missile considering flight performance and guidance precision

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Journal of Systems Engineering and Electronics 2024年第1期35卷 195-210页

作者： ZHAng Licong GOng Chunlin su hua ANDREA Da Ronch Shaanxi Aerospace Flight Vehicle Design Key Laboratory School of AstronauticsNorthwestern Polytechnical UniversityXi’an 710072China Faculty of Engineering and Physical Sciences University of SouthamptonSouthampton SO171BJUnited Kingdom

The design of mini-missiles(MMs)presents several novel *** stringent mission requirement to reach a target with a certain precision imposes a high guidance *** miniaturization of the size of MMs makes the design of the guidance,navigation,and control(GNC)have a larger-thanbefore impact on the main-body design(shape,motor,and layout design)and its design objective,i.e.,flight *** a trade-off between flight performance and guidance precision,all the relevant interactions have to be accounted for in the design of the main body and the GNC ***,a multi-objective and multidisciplinary design optimization(MDO)is *** pertinent to motor,aerodynamics,layout,trajectory,flight dynamics,control,and guidance are included in the proposed MDO *** optimization problem seeks to maximize the range and minimize the guidance *** problem is solved by using the nondominated sorting genetic algorithm *** optimum design that balances a longer range with a smaller guidance error is ***,lessons learned about the design of the MM and insights into the trade-off between flight performance and guidance precision are given by comparing the optimum design to a design provided by the traditional approach.

关键词： mini-missiles(MMs) guidance navigation and control(GNC)system multi-objective optimization multidisciplinary design optimization(MDO) flight performance guidance precision

Strain Gradient Finite Element Formulation of Flexoelectricity in Ferroelectric Material Based on Phase-Field Method

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Acta Mechanica Solida Sinica 2024年第4期37卷 570-579页

作者： Shuai Wang Hengchang su Min Yi Li-hua Shao National Key Laboratory of Strength and Structural Integrity Institute of Solid MechanicsSchool of Aeronautic Science and EngineeringBeihang UniversityBeijing100191People’s Republic of China State Key Laboratory of Mechanics and Control for Aerospace Structures and Institute for Frontier Science and Key Laboratory for Intelligent Nano Materials and Devices of Ministry of Education and College of Aerospace Engineering Nanjing University of Aeronautics and AstronauticsNanjing210016People’s Republic of China

Flexoelectricity is a two-way coupling effect between the strain gradient and electric field that exists in all dielectrics,regardless of point group ***,the high-order derivatives of displacements involved in the strain gradient pose challenges in solving electromechanical coupling problems incorporating the flexoelectric *** this study,we formulate a phase-field model for ferroelectric materials considering the flexoelectric effect.A four-node quadrilateral element with 20 degrees of freedom is constructed without introducing high-order shape *** microstructure evolution of domains is described by an independent order parameter,namely the spontaneous polarization governed by the time-dependent Ginzburg–Landau *** model is developed based on a thermodynamic framework,in which a set of microforces is introduced to construct the constitutive relation and evolution *** the flexoelectric part of electric enthalpy,the strain gradient is determined by interpolating the mechanical strain at the node via the values of Gaussian integration points in the isoparametric *** model is shown to be capable of reproducing the classic analytical solution of dielectric materials incorporating the flexoelectric *** model is verified by duplicating some typical phenomena in flexoelectricity in cylindrical tubes and truncated pyramids.A comparison is made between the polarization distribution in dielectrics and *** model can reproduce the solution to the boundary value problem of the cylindrical flexoelectric tube,and demonstrate domain twisting at domain walls in ferroelectrics considering the flexoelectric effect.

关键词： Flexoelectricity Phase-field method Ferroelectrics Domain configuration

Optical system for extremely large spectroscopic survey telescope

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Science china.Physics,Mechanics & Astronomy) 2024年第7期67卷 158-174页

作者： Ding-qiang su hua Bai Xiangyan Yuan Xiangqun Cui Key Laboratory of the Ministry of Education School of Astronomy and Space ScienceNanjing UniversityNanjing 210023China Nanjing Institute of Astronomical Optics and Technology(NIAOT) Chinese Academy of SciencesNanjing 210042China university of Chinese Academy of Sciences Nanjing 211135China School of Astronomy and Space Science University of Chinese Academy of SciencesBeijing 101408China

This article presents research work on a spectroscopic survey *** idea is as follows:for such a telescope,a pure reflecting optical system is designed,which should have an aperture and a field of view(FOV)both as large as possible and excellent image quality,and then a strip lensm(lens-prism)atmospheric dispersion corrector(S-ADC)is added,only for correcting the atmospheric *** the fund limitation and the simplicity of scaling up,some 12-m telescopes are designed as ***,Korsch,and Meinel put forward the four-mirror Nasmyth systems I and II,which are used in this *** of 1.5°,2°,and 2.5°are *** all systems,the image qualities are *** the S-ADC relaxes the optical glass size restriction,this 12-m telescope with a FOV of 2.5°can be magnified in proportion to a 16-m *** etendue(from Frenchétendue)and focal surface will now be the largest in the *** such a telescope,a pure reflecting optical system can also be obtained.A subsequent coudésystem is designed with excellent image quality.

关键词： telescopes spectroscopic survey

To enhance the reproduction of Phanerochaete chrysosporium by adding natural lixiviums in liquid medium

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Journal of Environmental Sciences 2003年第6期15卷 808-814页

作者： LIN Gang, WEN Xiang-hua, QIAN Yi (department of Environmental Science and Engineering, tsinghua university, beij.ng 100084, china. department of Environmental Science and Engineering Tsinghua University Beijing 100084 Chin

Great promotion to the reproduction of white rot fungus Phanerochaete chrysosporium by adding natural lixiviums such as from wood, maize core and potato in liquid medium was found in this research. Incubated in the liquid medium contained 10 mg/L glucose as carbon source with natural lixiviums for three days, the production of mycelium pellet reaches more than 80 g/L, which is 5 times more than that of without natural lixiviums. Incubated in the liquid medium contained 5 mg/L glucose as carbon source with natural lixiviums for three days, the production of mycelium pellet can reach 69.5 g/L, while the production in the medium without natural lixiviums is very low. When the liquid medium contained 1—20 g/L glucose as carbon source, the production of mycelium pellet in 3 d can only reach 12.5 g/L to 14.5 g/L. The fungus in the medium with potato lixiviums are easily contaminated by other microorganisms and in the medium with maize core lixiviums are easily bulking, while in the medium with wood lixiviums are neither easily contaminated nor bulking. Medium with wood lixiviums can produce more pellet than other medium, endure contamination and keep better sedimentation capacity. So that, wood lixivium is better additive to the culture of white rot fungi in liquid medium. Addition of the mixture of wood, maize core and potato lixiviums is of advantage to the production of mycelium pellet. The difference of the production in the medium with different amount of wood lixiviums showed little in the first 3 d, while it expanded after 3 d. Wood lixiviums stimulate the growth of P. chrysosporium instead of supply organics which fungi need.

关键词： white rot fungi medium additive

Application and Comparison of Two SGS Models in Large Eddy Simulation of FreeTurbulent Jet Flow

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Communications in Nonlinear Science and Numerical Simulation 1999年第1期4卷 12-19页

作者： Hong YAN and Mingde su (department of Engineering Mechanics, tsinghua university, beij.ng 100084, china. department of Engineering Mechanics Tsinghua University Beijing 100084 China

Large eddy simulations of spatially evolved turbulent round jets were presented. The two SGS models called the standard Smagorinsky’s eddy viscosity model and the non-eddy viscosity stimulated small scale(SSS) model developed by Shah & Ferziger were applied. The Reynolds number of the flow was taken as 10000 based on the orifice diameter and the axial velocity in the orifice. The comparison between these two models showed that the standard Smagorinsky’s viscosity model with Smagorinsky’s constant of 0.1 underestimated the turbulent intensity, while the SSS model showed a better agreement with the experiment. Also the SSS model was used to investigate the development of vortex. The convective boundary condition at the outflow boundary was adopted to ensure less effect of noise on the upstream.

关键词： stimulated small scale model smagorinsky’s eddy viscosity model Round jet, Large eddy simulation

Dimensions of a class of high-dimensional homogeneous Moran sets and Moran classes

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Progress in Natural Science:Materials International 2002年第9期12卷 17-22页

作者： YAN Ping(department of Mathematical Sciences, tsinghua university, beij.ng 100084, china. Tsing hua Univ Dept Math Sci Beijing 100084 Peoples R China

A class of high-dimensional homogeneous Moran sets and Moran classes are introduced and some dimensional properties are studied. The Hausdorff dimension, modified lower box-counting dimension, lower and upper box-counting dimension, and packing dimension of high-dimensional homogeneous and partial homogeneous Cantor sets are determined. Moreover, a kind of fractal E is obtained, which is not regular but with the property Dimw(Ed) = dDimw(E), where w denotes any of the dimensions mentioned above.

关键词： Moran set Moran class homogeneous Cantor set partial homogeneous Cantor set dimension.