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| 1 | Homotopic mapping solving method for gain fluency of a laser pulse amplifier显示文摘The model for gain fluency of a laser pulse amplifier is studied. Using the homotopic mapping method, firstly, the system of the original model is packed up standardization; secondly, introducing a homotopic mapping, taking the property of the mapping, inducing a contrived parameter, the solving of a nonlinear problem translates into the solving of a linear problem. Then the approximate expressions of the solution for the corresponding model are obtained. And the precision for the approximate solution is compared. It illuminates that the obtained approximate solution using the homotopic mapping method possesses higher approximate degree. At one time, the expansion of solution through the homotopic mapping method can be kept in the analytic operation. Thus it also enables us through differential and integral operations to obtain other physics behavior for the gain fluency of laser pulse amplifier. | MO JiaQi1,2 1 Anhui Normal University, Wuhu 241000, China 2 Division of Computational Science, E-Institutes of Shanghai Universities, at SJTU, Shanghai 200240, China | 2009 | Science China(Physics,Mechanics & Astronomy)2009，52，7： | 124 |
| 2 | 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 |
| 3 | Nonlinear singular vectors and nonlinear singular values显示文摘A novel concept of nonlinear singular vector and nonlinear singular value is introduced, which is a natural generalization of the classical linear singular vector and linear singular value to the nonlinear category. The optimization problem related to the determination of nonlinear singular vectors and singular values is formulated. The general idea of this approach is demonstrated by a simple two-dimensional quasigeostrophic model in the atmospheric and oceanic sciences. The advantage and its applications of the new method to the predictability, ensemble forecast and finite-time nonlinear instability are discussed. This paper makes a necessary preparation for further theoretical and numerical investigations. | 穆穆 | 2000 | Science China Earth Sciences2000，43，4： | 37 |
| 4 | THE NONLINEAR SINGULARLY PERTURBED PROBLEMS FOR REACTION DIFFUSION EQUATIONS WITH TIME DELAY显示文摘A class of nonlinear for singularly perturbed problems for reaction diffusion equations with time delays are considered. Under suitable conditions, using theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems are studied. | 莫嘉琪 冯茂春 | 2001 | Acta Mathematica Scientia2001，21，2： | 31 |
| 5 | Optimal Control of Nonlinear Inverted Pendulum System Using PID Controller and LQR: Performance Analysis Without and With Disturbance Input显示文摘Linear quadratic regulator(LQR) and proportional-integral-derivative(PID) control methods, which are generally used for control of linear dynamical systems, are used in this paper to control the nonlinear dynamical system. LQR is one of the optimal control techniques, which takes into account the states of the dynamical system and control input to make the optimal control decisions.The nonlinear system states are fed to LQR which is designed using a linear state-space model. This is simple as well as robust. The inverted pendulum, a highly nonlinear unstable system, is used as a benchmark for implementing the control methods. Here the control objective is to control the system such that the cart reaches a desired position and the inverted pendulum stabilizes in the upright position. In this paper, the modeling and simulation for optimal control design of nonlinear inverted pendulum-cart dynamic system using PID controller and LQR have been presented for both cases of without and with disturbance input. The Matlab-Simulink models have been developed for simulation and performance analysis of the control schemes. The simulation results justify the comparative advantage of LQR control method. | Lal Bahadur Prasad Barjeev Tyagi Hari Om Gupta | 2014 | International Journal of Automation and computing2014，11，6： | 32 |
| 6 | AN AGGREGATE FUNCTION METHOD FOR NONLINEAR PROGRAMMING显示文摘This paper presents a new method, called the 'aggregate function' method, for solvingnonlinear programming problems. At first, we use the 'maximum' constraint in place of theoriginal constraint set to convert a multi-constrained optimization problem to a non-smoothbut singly constrained problem; we then employ the surrogate constraint concept and themaximum entropy principle to derive a smooth function, by which the non-smooth maximumconstraint is approximated and the original problem is converted to a smooth and singly con-strained problem; furthermore, we develop a multiplier penalty algorithm. The presentalgorithm has merits of stable and fast convergence and ease of computer implementation,and is particularly suitable to solving a nonlinear programming problem with a large num-ber of constraints. | 李兴斯 | 1991 | Science China Mathematics1991，34，12： | 30 |
| 7 | High-Order Models of Nonlinear and Dispersive Wave in Water of Varying Depth with Arbitrary Sloping Bottom显示文摘High-order models with a dissipative term for nonlinear and dispersive wave in water of va-rying depth with an arbitrary sloping bottom are presented in this article.First,the formal derivations toany high order of μ(=h/λ,depth to deep-water wave length ratio)and ε(=α/h,wave amplitude todepth ratio)for velocity potential,particle velocity vector,pressure and the Boussinesq-type equations forsurface elevation η and horizontal velocity vector U at any given level in water are given.Then,the exactexplicit expressions to the fourth order of μ are derived.Finally,the linear solutions of η,U,C(phase ce-lerity)and C_g(group velocity)for a constant water depth are obtained.Compared with the Airy theory,excellent results can be found even for a water depth as large as the wave legnth.The present high-ordermodels are applicable to nonlinear regular and irregular waves in water of any varying depth(from shal-low to deep)and bottom slope(from mild to steep). | Hong Guangwen Professor, Coastal and Ocean Engineering Research Institute, Hohai University, Nanjing 210024, P. R. China. | 1997 | China Ocean Engineering1997，12，3： | 26 |
| 8 | Nonlinear balance constraints in 3DVAR data assimilation显示文摘In many applications of 3DVAR, the balance constraints can be considered via two main approaches: weak constraint method which adds penalty terms to the cost function; and proper defi- nition of the background error covariance matrix with non-zero cross-correlation sub-matrices. The weak constraint approach requires determining the weighting matrices of the penalty terms. The background error covariance approach does not require determining those additional weighting ma- trices. However, it is only applicable to those linear or linearized balance constraints. A novel ap- proach is proposed based on the background error covariance approach by generalizing the so-called Derber-Bouttier formulation. An assimilation experiment of estimating temperature and salinity from the sea surface dynamic height observation is given to illustrate the proposed treatments of nonlinear balance constraints. | ZHU Jiang YAN Changxiang | 2006 | Science China Earth Sciences2006，49，3： | 24 |
| 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 | ZnO varistors with high voltage gradient and low leakage current by doping rare-earth oxide显示文摘The surge arrester of 1000 kV gas-insulated substation (GIS) needs ZnO varistor with high voltage gradient to effectively improve the potential distribution along ZnO varistor column inside the metal-oxide surge arresters. In this paper, the elec-trical and structural parameters of ZnO varistors are changed by doping with some rare-earth oxides, and the mechanism which leads these changes is discussed. When rare-earth oxide additives are added into ZnO varistors, the growing speed is slowed down due to the stabilization of the new spinel phases formed in the grain-boundary by rare-earth oxide additives, then the size of ZnO grains is smaller, and the voltage gradient of varistor increases obviously. By adding suitable amount of oxides of metal Co and Mn, the leakage current can be effectively decreased and the nonlinearity coefficient increased. The novel ZnO varistor samples sintered with the optimal additives have a voltage gradient of 492 V/mm, and the nonlinearity coefficient of 76, but their leakage currents are only 1 μA. | HE JinLiang HU Jun LIN YuanHua | 2008 | Science China(Technological Sciences)2008，51，6： | 21 |
| 11 | Stability analysis of solutions to nonlinear stiff Volterra functional differential equations in Banach spaces显示文摘A series of stability, contractivity and asymptotic stability results of the solutions to nonlinear stiff Volterra functional differential equations (VFDEs) in Banach spaces is obtained, which provides the unified theoretical foundation for the stability analysis of solutions to nonlinear stiff problems in ordinary differential equations(ODEs), delay differential equations(DDEs), integro-differential equations(IDEs) and VFDEs of other type which appear in practice. | LI Shoufu | 2005 | Science China Mathematics2005，48，3： | 20 |
| 12 | THE PRECURSOR OF INSTABILITY FOR NONLINEAR SYSTEMS AND ITS APPLICATION TO EARTHQUAKE PREDICTION显示文摘By analysing the instability process of various nonlinear systems, we conclude that their instability precursors are the continual heightening of the response rate or response ratio.Applying this theory to earthquake prediction, we adopt the periodical change of the stress in crust caused by the tide-generating force as the loading and unloading. If we can measure the ratio of the response (such as crust deformation, gravity and seismicity) during the loading period to that during the unloading period, this parameter must contain some characteristic information about the seismogenic process.With nine earthquakes (M≥7) data that occurred in Chinese mainland during 1970-1988, we take the sum of square root o?energy of small earthquakes, which is called the released strain by Benioff, as the response to the tidal loading and unloading. We find that the response ratios of seven earthquakes increase obviously before the main earthquakes. | 尹祥础 尹灿 | 1991 | Science China Chemistry1991，34，8： | 19 |
| 13 | Nonlinear boundary value problem for biregular functions in Clifford analysis显示文摘The biregular function in Clifford analysis is discussed. Plemelj’s formula is obtained andnonlinear boundary value problem: is considered. Applying the methodof integral equations and Schauder fixed-point theorem, the existence of solution for the above problem is proved. | 黄沙 | 1996 | Science China Mathematics1996，39，11： | 19 |
| 14 | NONLINEAR STABILITY OF NATURAL RUNGE-KUTTA METHODS FOR NEUTRAL DELAY DIFFERENTIAL EQUATIONS显示文摘This paper first presents the stability analysis of theoretical solutions for a class of nonlinear neutral delay-differential equations (NDDEs). Then the numerical analogous results, of the natural Runge-Kutta (NRK) methods for the same class of nonlinear NDDEs, are given. In particular, it is shown that the (k, l)-algebraic stability of a RK method for ODEs implies the generalized asymptotic stability and the global stability of the induced NRK method. | Cheng-jian Zhang(Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, P. R. China) | 2002 | Journal of Computational Mathematics2002，20，6： | 18 |
| 15 | On filter-successive linearization methods for nonlinear semidefinite programming显示文摘In this paper we present a filter-successive linearization method with trust region for solutions of nonlinear semidefinite programming. Such a method is based on the concept of filter for nonlinear programming introduced by Fletcher and Leyffer in 2002. We describe the new algorithm and prove its global convergence under weaker assumptions. Some numerical results are reported and show that the new method is potentially effcient. | LI ChengJin SUN WenYu | 2009 | Science China Mathematics2009，52，11： | 18 |
| 16 | NONLINEAR STOCHASTIC DYNAMICS: A SURVEY OF RECENT DEVELOPMENTS显示文摘This paper provides an overview of significant advances in nonlinearstochastic dynamics during the past two decades, including random response, stochas-tic stability, stochastic bifurcation, first passage problem and nonlinear stochasticcontrol. Topics for future research are also suggested. | 朱位秋 蔡国强 | 2002 | Acta Mechanica Sinica2002，18，6： | 18 |
| 17 | STUDY ON MIXED MODEL OF NEURAL NETWORK FOR FARMLAND FLOOD/DROUGHT PREDICTION显示文摘The paper concerns a flood/drought prediction model involving the continuation of time seriesof a predictand and the physical factors influencing the change of predictand.Attempt is made toconstruct the model by the neural network scheme for the nonlinear mapping relation based onmulti-input and single output.The model is found of steadily higher predictive accuracy by testingthe output from one and multiple stepwise predictions against observations and comparing theresults to those from a traditional statistical model. | 金龙 罗莹 郭光 林振山 | 1997 | Acta meteorologica Sinica1997，11，3： | 18 |
| 18 | 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 |
| 19 | Shear wave velocity structure of the crust and upper mantle underneath the Tianshan orogenic belt显示文摘From April, 2003 to September, 2004, a passive broadband seismic array consisting of 60 stations was deployed over the Tianshan orogenic belt by State Key Laboratory of Earthquake Dynamics, Institute of Geology, China Earthquake Administration. Among them, 51 stations make up an about 500-km-long profile across the Tianshan Mountains from Kuytun to Kuqa. The receiver function profile and S-wave velocity structure of the crust and upper mantle down to 100 km deep are obtained by using the re-ceiver function method (Liu et al. 1996, 2000). The main results can be summarized as follows: (1) A clear mountain root does not exist beneath the Tianshan Mountains, and the crust-mantle boundaries underneath the stations mostly have transitional structures. This implies that the material differentia-tion between the crust and mantle is not yet accomplished and the orogenic process is still going on. (2) The crust beneath the Tianshan Mountains has laterally blocked structures in direction perpendicular to the mountain strike, and the crust-mantle boundary has a clear dislocation structure. Both of them correspond to each other. (3) The offsets of the Moho discontinuity are highly correlated to the tectonic borders on the surface and that corresponding to the frontal southern Tianshan fault reaches to 14 km. This manifests that large vertical divergent movement took place between different blocks. This sup-ports the discontinuous model of the Tianshan orogeny, and the Tarim block subduction is restricted only to the southern side of the South Tianshan. (4) Inside the upper and middle crust of the Tianshan Mountains exist several low-velocity bodies correlated with high seismicity located on the moun-tain-basin jointures on both sides of the mountain and between different blocks, and the low-velocity bodies on the mountain-basin jointures are inclined obviously to the mountain. This implies that the low-velocity bodies may be correlated closely to the thrust and subduction of the basins on both sides of the mountain, the splicing of adjacent blocks and the fast uplift of the Tianshan Mountains. | LI Yu LIU QiYuan CHEN JiuHui LI ShunCheng GUO Biao LAI YuanGen | 2007 | Science China Earth Sciences2007，50，3： | 16 |
| 20 | Nonlinear ergodic theorem for semitopological semigroups of non-Lipschitzian mappings in Banach spaces显示文摘LET G be a semitopological semigroup, i. e. G is a semigroup with a Hausdorff topology such that for each s∈G the mapping s|→s·t and s|→t·s from G to G are continuous. G is called right reversible if any two closed left ideals of G have non-void intersection. In this case, (G,≤) is a directed system when the binary relation '≤' on G is defined by a≤b if and only if Let E be the uniformly convex Banach space | LI Gang and MA Jipu1. Department of Mathematics, Yangzhou Normal College, Yangzhou 225002, China 2. Department of Mathematics, Nanjing University, Nanjing 210093, China | 1997 | Chinese Science Bulletin1997，42，1： | 16 |
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