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| 1 | A CLASS OF NONLOCAL SINGULARLY PERTURBED PROBLEMS FOR NONLINEAR HYPERBOLIC DIFFERENTIAL EQUATION显示文摘The nonlocal singularly perturbed problems for the hyperbolic differential equation are considered. Under suitable conditions, using the fixed point theorem, the asymptotic behavior of solution for the initial boundary value problems is studied. | 莫嘉琪 | 2001 | Acta Mathematicae Applicatae Sinica2001，17，4： | 41 |
| 2 | Mathematical Models for Combined Refraction-Diffraction of Waves on Non-Uniform Current and Depth显示文摘Two mathematical models for combined refraction-diffraction of regular and irregular waves on non-uniform current in water of slowly varying topography are presented in this paper. Model I is derived by wave theory and variational principle separately. It has two kinds of expressions including the dissipation term. Model n is based on the energy conservation equation with energy flux through the wave crest lines in orthogonal curvilinear coordinates and the wave kinematic conservation equation. The analysis and comparison and special cases of these two models are also given. | Hong Guangwen Professor, Research Institute of Coastal and Ocean Engineering, Hohai University, 1 Xikang Road, Nanjing 210024 | 1996 | China Ocean Engineering1996，11，4： | 35 |
| 3 | Oscillation of Solutions of Nonlinear Partial Differential Equations of Neutral Type | Yu Yuanhong Liu Bin Liu Zhengrong Institute of Applied Mathematics, Academia Sinica, Beijing 100080, China Department of Mathematics, Hubei Normal College, Huangshi 435002. China Department of Mathematics, Yunnan University. Kunming 650091. China Institute of Applied Mathematics of Yunnan Province, Kunming 650091, China | 1997 | Acta Mathematica Sinica,English Series1997，13，4： | 39 |
| 4 | The Constrained Solutions of Two Matrix Equations | An Ping LIAO Zhong Zhi BAI Department of Mathematics. Hunan University. Changshu, 410082. P. R. China Department of Mathematics and Information Science, Changsha University, Changsha 410003. P. R. China Academy of Mathematics and System. Sciences. Chinese Academy of Sciences. Beijing 100080. P. R. China State Key Laboratory of Scientific/Engineering Computing. Chinese Academy of Sciences. Institute of Computational Mathematics and Scientific/Engineering Computing. Academy of Mathematics and System Sciences. Chinese Academy of Sciences. P. O. Box 2719. Beijing 100080. P. R. China | 2002 | Acta Mathematica Sinica,English Series2002，18，4： | 40 |
| 5 | Carbon and nitrogen storage in an age-sequence of Pinus densiflora stands in Korea显示文摘The carbon(C) and nitrogen(N) storage capabilities of Pinus densiflora in six different stand ages(10,27,30,32,44,and 71 years old) were investigated in Korea.Thirty sample trees were destructively harvested and 12 were excavated.Samples from the above and belowground tree components,coarse woody debris(CWD),forest floor,and mineral soil(0-30 cm) were collected.Tree biomass was highest in the 71-year-old stand(202.8 t ha-1) and lowest in the 10-year-old stand(18.4 t ha-1).C and N storage in the mineral soil was higher in the 71-year-old stand than in the other stands,mainly due to higher soil C and N concentrations.Consequently,the total ecosystem C and N storage(tree+forest floor+CWD+soil) was positively correlated with stand age:increasing from a minimum in the 10 year old stand(18.8 t C ha-1 and 1.3 t N ha-1) to a maximum in the 71-year-old stand(201.4 t C ha-1 and 8.5 t N ha-1).The total ecosystem C storage showed a similar sigmoidal pattern to that of tree C storage as a function of the age-sequence,while N storage in the CWD,forest floor and mineral soil showed no significant temporal trends.Our results provide important insights that will increase our understanding of C and N storage in P.densiflora stands and our ability to predict changes according to stand age in the region. | NOH Nam-Jin SON Yowhan LEE Sue-Kyoung SEO Kyung-Won HEO Su-Jin1 YI Myong-Jong PARK Pil-Sun KIM Rae-Hyun SON Yeong-Mo LEE Kyeong-Hak | 2010 | Science China(Life Sciences)2010，53，7： | 24 |
| 6 | On the Hyper-Order of Solutions of Some Second-Order Linear Differential Equations | CHEN Zong Xuan Department of Mathematics. Jiangxi Normal University. Nanchang 330027. P. R. China | 2002 | Acta Mathematica Sinica,English Series2002，18，1： | 24 |
| 7 | Some characteristics and evolution of the internal soliton in the northern South China Sea显示文摘Based on the observational data of an internal soliton in the northern South China Sea (SCS) on June 14, 1998, the possible source of the internal soliton is analyzed, and some of its characteristic parameters such as phase speed, wave length, etc. are computed. Based on the analyses of the vertical modes of the internal wave, the characteristics of the wave-induced current during the propagation of the internal soliton are studied. A regularized long wave (RLW) equation numerical model considering effects of multi-fac-tors is employed, and the observed environmental parame-ters are used as the initial conditions to simulate the propa-gation and evolution of the internal soliton in the continental shelf of the northern SCS. | Cai, SQ Gan, ZJ Long, XM | 2002 | Chinese Science Bulletin2002，47，1： | 23 |
| 8 | Dynamic Modeling and Simulation of Multi-body Systems Using the Udwadia-Kalaba Theory显示文摘Laboratory experiments were conducted for falling U-chain,but explicit analytic form of the general equations of motion was not presented.Several modeling methods were developed for fish robots,however they just focused on the whole fish's locomotion which does little favor to understand the detailed swimming behavior of fish.Udwadia-Kalaba theory is used to model these two multi-body systems and obtain explicit analytic equations of motion.For falling U-chain,the mass matrix is non-singular.Second-order constraints are used to get the constraint force and equations of motion and the numerical simulation is conducted.Simulation results show that the chain tip falls faster than the freely falling body.For fish robot,two-joint Carangiform fish robot is focused on.Quasi-steady wing theory is used to approximately calculate fluid lift force acting on the caudal fin.Based on the obtained explicit analytic equations of motion(the mass matrix is singular),propulsive characteristics of each part of the fish robot are obtained.Through these two cases of U chain and fish robot,how to use Udwadia-Kalaba equation to obtain the dynamical model is shown and the modeling methodology for multi-body systems is presented.It is also shown that Udwadia-Kalaba theory is applicable to systems whether or not their mass matrices are singular.In the whole process of applying Udwadia-Kalaba equation,Lagrangian multipliers and quasi-coordinates are not used.Udwadia-Kalaba theory is creatively applied to dynamical modeling of falling U-chain and fish robot problems and explicit analytic equations of motion are obtained. | ZHAO Han ZHEN Shengchao CHEN Ye-Hwa | 2013 | Chinese Journal of Mechanical Engineering2013，26，5： | 22 |
| 9 | A Survey of Unbalanced Flow Diagnostics and Their Application显示文摘This paper presents an extensive survey of the most commonly used tools for diagnosing unbalanced flow in the atmosphere, namely the Lagrangian Rossby number, Psi vector, divergence equation, nonlinear balance equation, generalized omega-equation, and departure from fields obtained by potential vorticity (PV) inversion. The basic thoery, assumptions as well as implementation and limitations for each of the tools are all discussed. These tools are applied to high-resolution mesoscale model data to assess the role of unbalanced dynamics in the generation of a mesoscale gravity wave event over the East Coast of the United States. Comparison of these tools in this case study shows that these various methods agree to a large extent with each other though they differ in details. | Fuqing Zhang Steven E. Koch Christopher A. Davis and Michael L. Kaplan | 2000 | Advances in Atmospheric Sciences2000，17，2： | 22 |
| 10 | The New Form of Time-Dependent Mild Slope Equation for Random Waves显示文摘The mild-slope equation derived by Berkhoff (1972), has widely been used in the numerical calculation of refraction and diffraction of regular waves. However, it is well known that the random sea waves has a significant effect in the refraction and diffraction problems. In this paper, a new form of time-dependent mild slope equation for irregular waves was derived with Fade approximation and Kubo’s time series concept. The equation was simplified using WKB method, and simple and practical irregular mild slope equation was obtained. Results of numerical calculations are compared with those of laboratory experiments. | Zhang Yonggang , Li Yucheng Teng Bin Doctor Degree Candidate, The National Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116023Professor, The National,Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116023Associate Professor, The National Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116023 | 1995 | China Ocean Engineering1995，10，4： | 21 |
| 11 | 伪双曲型积分-微分方程的H^1-Galerkin混合元法误差估计显示文摘1引言考虑如下一类具有Lipschitz连续边界(?)Ω的凸有界区域Ω上的伪双曲型积分微分方程其中Ω(?)Rd,(d=1,2,3)J=(0,T],对于固定的T,0 | 刘洋 李宏 何斯日古楞 | 2010 | 高等学校计算数学学报2010，32，1： | 21 |
| 12 | A CLASS OF SINGULARLY PERTURBED GENERALIZED BOUNDARY VALUE PROBLEMS FOR QUASI-LINEAR ELLIPTIC EQUATION OF HIGHER ORDER显示文摘The singularly perturbed generalized boundary value problems for the quasi_linear elliptic equation of higher order are considered. Under suitable conditions,the existence, uniqueness and asymptotic behavior of the generalized solution for the Dirichlet problems are studied. | MO Jia-qi(莫嘉琪) OUYANG Cheng(欧阳成) | 2001 | Applied Mathematics and Mechanics(English Edition)2001，22，3： | 19 |
| 13 | Gear geometry of cycloid drives显示文摘According to differential geometry and gear geometry, the equation of meshing for small teeth difference planetary gearing and a universal equation of conjugated profile are established based on cylindrical pin tooth and given motion. The correct meshing condition, contact line, contact ratio, calculating method for pin tooth's maximum contact point are developed. Investigation on the theory of conjugated meshing is carried out when the tooth difference numbers between pin wheel and cycloidal gear are 1, 2, 3 and ?1, respectively. A general method called enveloping method to generate hypocycloid and epicycloid is put forward. The correct meshing condition for cycloid pin wheel gearing is provided, and the contact line and the contact ratio are also discussed. | CHEN BingKui FANG TingTing LI ChaoYang WANG ShuYan | 2008 | Science China(Technological Sciences)2008，51，5： | 18 |
| 14 | The Optimal Design of TMD for Offshore Structures显示文摘This paper presents the optimal design procedure of Tuned Mass Damper(TMD)for re-ducing vibration of an actual steel jacket offshore platform excited by random wave loading.In this study,a frequency domain is taken.The force on the structure is determined by use of the linearized Morisonequation for an input Power Spectral Density(PSD)of wave elevation.The sensitivity of optimum valuesof TMD to characteristic parameters of random wave spectrum is analyzed.An optimized TMD designfor the modeled platform is given based on design conditions and the findings of the study. | Sau Lon James HU Tomotsuka TAKAYAMA | 1999 | China Ocean Engineering1999，14，2： | 18 |
| 15 | A new method for judging the computational stability of the difference schemes of nonlinear evolution equations显示文摘For the non-conservative difference schemes of nonlinear evolution equations with aperiodic boundary conditions, taken one-dimensional nonlinear advection equation as an example, a new method for judging the computational stability is given. It is proved to be practical and effective through several numerical examples. The stability criteria obtained by this method are really the necessary conditions of computational stability. | LIN Wantao Jl Zhongzhen WANG Bin YANG Xiaozhong | 2000 | Chinese Science Bulletin2000，45，15： | 18 |
| 16 | A class of discounted models for singular diffusion control显示文摘A kind of discounted problems for singular diffusion control have been studied. The drift and diffusion coefficients of state process are nonlinear. The class of models has been basically extended from a corresponding one established by Karatzes et al. before. By applying some analysis methods different from earlier works, the sufficient and necessary conditions of the existence of optimal control have been obtained. If an optimal control exists, it is a 'transient reflection' of state process for two lines. | LIU Kunhui, QIN Mingda & LU Chuanlai1. College of Sciences, Northern Jiaotong University, Beijing 100044, China 2. Department of Mathematics and Mechanics, Beijing University of Science and Technology, Beijing 100083 .China 3. Department of Information Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China Correspondence should be addressed to Lu Chuanlai | 2000 | Chinese Science Bulletin2000，45，5： | 17 |
| 17 | A new almost periodic type of solutions of second order neutral delay differential equations with piecewise constant argument显示文摘A definition of pseudo almost periodic sequence is given and the existence of pseudo al-most periodic seguence to difference equation is studied. Based on these, the existence of pseudo almost periodic solutions to neutral delay differential equations with piecewise constant argument is inves-tigated. | 袁荣 | 2000 | Science China Mathematics2000，43，4： | 17 |
| 18 | On Mechanism of Heat-Conduction and Equation of Thermal Conductivity of Liquid显示文摘The recently presented equation for nonequilibrium state of gases is hereextended to liquid,and thus an equation of thermal conductivity for normal liquid is de-rived.The equation is applied to both polar and nonpolar liquids,with the average error of608 experlmental values being 1.75% based upon 110 compounds of 29 types of structures.This method is far better than all the other methods published. | 张克武 | 1993 | Science China Mathematics1993，36，3： | 16 |
| 19 | A perturbation-incremental scheme for studying Hopf bifurcation in delayed differential systems显示文摘A new method, called perturbation-incremental scheme (PIS), is presented to investigate the periodic solution derived from Hopf bifurcation due to time delay in a system of first-order delayed differential equations. The method is summarized as three steps, namely linear analysis at critical value, perturba- tion and increment for continuation. The PIS can bypass and avoid the tedious calculation of the center manifold reduction (CMR) and normal form. Meanwhile, the PIS not only inherits the advantages of the method of multiple scales (MMS) but also overcomes the disadvantages of the incremental harmonic balance (IHB) method. Three delayed systems are used as illustrative examples to demonstrate the validity of the present method. The periodic solution derived from the delay-induced Hopf bifurcation is obtained in a closed form by the PIS procedure. The validity of the results is shown by their consis- tency with the numerical simulation. Furthermore, an approximate solution can be calculated in any required accuracy. | CHUNG Kwok Wai | 2009 | Science China(Technological Sciences)2009，52，3： | 15 |
| 20 | Invariant sets and solutions to the generalized thin film equation显示文摘The invariant sets and the solutions of the 1+2-dimensional generalized thin film equation are discussed. It is shown that there exists a class of solutions to the equations, which are invariant with respect to the set E0 = {u : ux = vxF(u), uy = vyF(u)}, where v is a smooth function of variables x, y and F is a smooth function of u. This extends the results of Galaktionov (2001) and for the l+l-dimensional nonlinear evolution equations. | Chang-zheng QU & Chun-rong ZHU Center for Nonlinear Studies, Northwest University, Xi’an 710069, China Department of Mathematics, Northwest University, Xi’an 710069, China Department of Mathematics, Anhui Normal University, Wuhu 241000, China | 2007 | Science China Mathematics2007，50，6： | 15 |
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