1.

L~P SOLUTION OF GENERAL MEANFIELD BSDES WITH CONTINUOUS COEFFICIENTS





《数学物理学报(B辑英文版)》,2020年第4期


In this paper we consider one dimensional meanfield backward stochastic differential equations (BSDEs) under weak assumptions on the coefficient.Unlike[3],the generator of our meanfield BSDEs depends not only on the solution (Y,Z) but also on the law P_(Y )of Y.The first part of the paper is devoted to the existence and uniqueness of solutions in L~p,1p≤2,where the monotonicity conditions are satisfied.Next,we show that if the generator f is uniformly continuous in (μ,y,z),uniformly with respect to (t,ω),and if the terminal valueξbelongs to L~p(?,F,P) with 1p≤2,the meanfield BSDE has a unique L~psolution.

2.

Representation theorems for generators of BSDEs in L p spaces





Li Song Feng Hu Zengjing Chen《应用数学学报(英文版)》,2012年第28卷第2期


In this paper,we prove that the generator g of a class of backward stochastic differential equations (BSDEs) can be represented by the solutions of the corresponding BSDEs at point (t,y,z),when the terminal data is in L p spaces,for 1 < p ≤ 2.

3.

A note on Jensen’s inequality for BSDEs





Sheng Jun Fan《数学学报(英文版)》,2009年第25卷第10期


Under the Lipschitz assumption and square integrable assumption on g, Jiang proved that Jensen＇s inequality for BSDEs with generator g holds in general if and only if g is independent of y, g is super homogenous in z and g（t, 0） = 0, a.s., a.e.. In this paper, based on Jiang＇s results, under the same assumptions as Jiang＇s, we investigate the necessary and sufficient condition on g under which Jensen＇s inequality for BSDEs with generator g holds for some specific convex functions, which generalizes some known results on Jensen＇s inequality for BSDEs.

4.

INVARIANT REPRESENTATION FOR STOCHASTIC DIFFERENTIAL OPERATOR BY BSDES WITH UNIFORMLY CONTINUOUS COEFFICIENTS AND ITS APPLICATIONS





贾广岩 张娜《数学物理学报(B辑英文版)》,2013年第5期


In this paper, we prove that a kind of second order stochastic differential operator can be represented by the limit of solutions of BSDEs with uniformly continuous coe?cients. This result is a genera...

5.

Ktheory of Continuous Deformations of C＊algebras





Takahiro SUDO《数学学报(英文版)》,2007年第23卷第7期


We study Ktheory of continuous deformations of C＊algebras to obtain that their Ktheory is the same as that of the fiber at zero. We also consider continuous or discontinuous deformations of Cuntz and Toeplitz algebras.

6.

Asymmetric Wshaped and Mshaped soliton pulse generated from a weak modulation in an exponential dispersion decreasing fiber





《中国物理 B》,2017年第12期


We study localized waves on continuous wave background in an exponential dispersion decreasing fiber with two orthogonal polarization states. We demonstrate that asymmetric Wshaped and Mshaped soliton pulse can be generated from a weak modulation on continuous wave background. The numerical simulation results indicate that the generated asymmetric soliton pulses are robust against small noise or perturbation. In particular, the asymmetric degree of the asymmetric soliton pulse can be effectively controlled by changing the relative frequency of the two components. This character can be used to generate other nonlinear localized waves, such as dark–antidark and antidark–dark soliton pulse pair, symmetric Wshaped and Mshaped soliton pulse. Furthermore, we find that the asymmetric soliton pulse possesses an asymmetric discontinuous spectrum.

7.

Moment inequality and Hölder inequality for BSDEs





Shengjun Fan《应用数学学报(英文版)》,2009年第25卷第1期


Under the Lipschitz and square integrable assumptions on the generator g of BSDEs, this paper proves that if g is positively homogeneous in （y, z） and is decreasing in y, then the Moment inequality for BSDEs with generator g holds in general, and if g is positively homogeneous and subadditive in （y, z）, then the HSlder inequality and Minkowski inequality for BSDEs with generator g hold in general.

8.

Four Types of Percolation Transitions in the Cluster Aggregation Network Model





韩文臣 杨俊忠《中国物理快报》,2018年第1期


We study the percolation transition in a onespecies cluster aggregation network model, in which the parameter α describes the suppression on the cluster sizes. It is found that the model can exhibit four types of percolation transitions, two continuous percolation transitions and two discontinuous ones. Continuous and discontinuous percolation transitions can be distinguished from each other by the largest single jump. Two types of continuous percolation transitions show different behaviors in the time gap. Two types of discontinuous percolation transitions are different in the time evolution of the cluster size distribution. Moreover, we also find that the time gap may also be a measure to distinguish different discontinuous percolations in this model.

9.

具有一般终端时刻和非一致线性增长生成元的倒向随机微分方程的$L^p$解





鹿高杰 江龙 李德鹏 范胜君《数学研究及应用》,2016年第36卷第1期


In this paper, we establish the existence of the minimal L~p(p 1) solution of backward stochastic differential equations(BSDEs) where the time horizon may be finite or infinite and the generators have a nonuniformly linear growth with respect to t. The main idea is to construct a sequence of solutions {(Y~n, Z~n)} which is a Cauchy sequence in S~p× M~p space, and finally we prove {(Y~n, Z~n)} converges to the L~p(p 1) solution of BSDEs.

10.

A Converse Comparison Theorem for gExpectations





LongJiang《应用数学学报(英文版)》,2004年第20卷第4期


With the help of a limit property of solutions of backward stochastic differential equations(BSDEs),this paper establishes a converse comparison theorem for deterministic generators g of BSDEs under the assumption g(t, y, 0) ≡0.

11.

Multidimensional BSDEs with weak monotonicity and general growth generators





Sheng Jun Fan Long Jiang《数学学报(英文版)》,2013年第29卷第10期


This paper aims at solving a multidimensional backward stochastic differential equation （BSDE） whose generator g satisfies a weak monotonicity condition and a general growth condition in y. We first establish an existence and uniqueness result of solutions for this kind of BSDEs by using systematically the technique of the priori estimation, the convolution approach, the iteration, the truncation and the Bihari inequality. Then, we overview some assumptions related closely to the monotonieity condition in the literature and compare them in an effective way, which yields that our existence and uniqueness result really and truly unifies the Mao condition in y and the monotonieity condition with the general growth condition in y, and it generalizes some known results. Finally, we prove a stability theorem and a comparison theorem for this kind of BSDEs, which also improves some known results.

12.

ON DISCONTINUOUS PERIODIC SOLUTION AND DISCONTINUOUS SOLITARY WAVE OF TWODIMENSION SHALLOW WATER EQUATION





黄思训《应用数学和力学(英文版)》,1987年第9期


In this papepr we discues discomunucus peridic solution and discontinuous solitarywave of the shallow water model of geophysical fiuid dynamics.When we consider theproperties of vajeciory necr non一epuiulmium nom point.i.e.singular we fund that if weintraduce the concept of gendralized solution smoothing continuous solution),then the system will produce discontinueus periodle solution and the condition ofdiscontinuous periodic solution can be obtahed When the system is dagenerated.we findthat the discontinucus solitary wave is existent in the system. In this paper we consider aserdes of problems and obtain analyvic expression of discontinuous solution.This result iscompared with squall lime in the anmosphere, and both of them have many thing in common.

13.

Theory and Applications of Discontinuous State Feedback Generating Chaos for Linear Systems





张晓丹 王震 赵品栋《中国物理快报》,2008年第25卷第2期


We investigate a kind of chaos generating technique on a type of ndimensional linear differential systems by adding feedback control items under a discontinuous state. This method is checked with some examples of numeric simulation. A constructive theorem is proposed for generalized synchronization related to the above chaotic system.

14.

Reflected and Doubly Reflected BSDEs for Levy Processes： Solutions and Comparison 被引次数：1





Qing Zhou《应用数学学报(英文版)》,2010年第26卷第2期


In this paper we study reflected and doubly reflected backward stochastic differential equations （BSDEs, for short） driven by Teugels martingales associated with L~vy process satisfying some moment condi tions and by an independent Brownian motion. For BSDEs with one reflecting barrier, we obtain a comparison theorem using the TanakaMeyer formula. For BSDEs with two reflecting barriers, we first prove the existence and uniqueness of the solutions under the Mokobodski＇s condition by using the Snell envelope theory and then we obtain a comparison result.

15.

Uniform invariance principle of discontinuous systems with parameter variation





Jumei Wei Rui Ma Xiaowu Mu《应用数学学报(英文版)》,2013年第29卷第4期


An extension of the invariance principle for a class of discontinuous righthand sides systems with parameter variation in the Filippov sense is proposed. This extension allows the derivative of an auxiliary function V, also called a Lyapunovlike function, along the solutions of the discontinuous system to be positive on some sets. The uniform estimates of attractors and basin of attractions with respect to parameters are also obtained. To this end, we use locally Lipschitz continuous and regular Lyapunov functions, as well as Filippov theory. The obtained results settled in the general context of differential inclusions, and through a uniform version of the LaSalle invariance principle. An illustrative example shows the potential of the theoretical results in providing information on the asymptotic behavior of discontinuous systems.

16.

A NEW DIRECT DISCONTINUOUS GALERKIN METHOD WITH SYMMETRIC STRUCTURE FOR NONLINEAR DIFFUSION EQUATIONS





Chad Vidden Jue Yan《计算数学(英文版)》,2013年第6期


In this paper we continue the study of discontinuous Galerkin finite element methods for nonlinear diffusion equations following the direct discontinuous Galerkin （DDG） meth ods for diffusion problems [17] and the direct discontinuous Galerkin （DDG） methods for diffusion with interface corrections [18]. We introduce a numerical flux for the test func tion, and obtain a new direct discontinuous Galerkin method with symmetric structure. Second order derivative jump terms are included in the numerical flux formula and explicit guidelines for choosing the numerical flux are given. The constructed scheme has a sym metric property and an optimal L2 （L2） error estimate is obtained. Numerical examples are carried out to demonstrate the optimal （k ＋ 1）th order of accuracy for the method with pk polynomial approximations for both linear and nonlinear problems, under onedimensional and twodimensional settings.

17.

FAST ALGORITHM FOR CALDERóNZYGMUND OPERATORS:CONVERGENCE SPEED AND ROUGH KERNEL





《数学物理学报(B辑英文版)》,2016年第2期


In this article, we consider a fast algorithm for first generation CaldernZygmund operators. First, we estimate the convergence speed of the relative approximation algorithm.Then, we establish the continuity on Besov spaces and TriebelLizorkin spaces for the operators with rough kernel.

18.

Characteristics of phase transitions via intervention in random networks





贾啸 洪劲松 杨宏春 杨春 史晓红 胡建全《中国物理 B》,2014年第7期


We present a percolation process in which the classical Erdo¨s–Re′nyi(ER) random evolutionary network is intervened by the product rule(PR) from some moment t0. The parameter t0is continuously tunable over the real interval [0, 1].This model becomes the random network under the Achlioptas process at t0= 0 and the ER network at t0= 1. For the percolation process at t0≤ 1, we introduce a relatively slowgrowing point, after which the largest cluster begins growing faster than that in the ER model. A weakly discontinuous transition is generated in the percolation process at t0≤ 0.5.We take the relatively slowgrowing point as the lower pseudotransition point and the maximum gap point of the order parameter as the upper pseudotransition point. The critical point can be approximately predicted by each fitting function of the two points about t0. This contributes to understanding the rapid mergence of the large clusters at the critical point.The numerical simulations indicate that the lower pseudotransition point and the upper pseudotransition point are equal in the thermodynamic limit. When t0> 0.5, the percolation processes generate a continuous transition. The scaling analyses of several quantities are presented, including the relatively slowgrowing point, the duration of the relatively slowgrowing process, as well as the relatively maximum strength between the percolation percolation at t0< 1 and the ER network about different t0. The presented mechanism can be viewed as a twostage percolation process that has many potential applications in the growth processes of real networks.

19.

Monotone projected gradient methods for largescale boxconstrained quadratic programming





ZHOU Bin GAO Li & DAI Yuhong School of Mathematical Sciences and LMAM Peking University Beijing 100871 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China《中国科学A辑(英文版)》,2006年第49卷第5期


Inspired by the success of the projected BarzilaiBorwein (PBB) method for largescale boxconstrained quadratic programming, we propose and analyze the monotone projected gradient methods in this paper. We show by experiments and analyses that for the new methods, it is generally a bad option to compute steplengths based on the negative gradients. Thus in our algorithms, some continuous or discontinuous projected gradients are used instead to compute the steplengths. Numerical experiments on a wide variety of test problems are presented, indicating that the new methods usually outperform the PBB method.

20.

Paths to Synchronization on Complex Networks with External Drive





邹莹莹 李海红《中国物理快报》,2014年第10期


We investigate the dynamics of the Kuramoto model on complex networks with part of the oscillators subjected to an external drive. It is found that the mutual synchronization is attracted to the drive when the frequency of the drive is close to the mean frequency of oscillators and, otherwise, mutual synchronization coexists with the driven synchronization. We also find that the synchronization between the mutual synchronization and the driven synchronization is dependent on the network topology when the coupling strength among oscillators is far away from the global synchronization in the absence of the drive. The transition is continuous on ErdoesRenyi networks while it is discontinuous on scale free networks.
