On multivariate logarithmic polynomials and their properties

In the paper, the author introduces a new notion “multivariate logarithmic polynomial”, establishes two recurrence relations, an explicit formula, and an identity for multivariate logarithmic polynomials by virtue of the Faà di Bruno formula and two identities for the Bell polynomials of the second kind in terms of the Stirling numbers of the first and second kinds, and constructs some determinantal inequalities, some product inequalities, and logarithmic convexity for multivariate logarithmic polynomials by virtue of some properties of completely monotonic functions.     

分数阶线性退化微分系统有限时间镇定性问题

本文通过构造新的Lyapunov函数,利用线性矩阵不等式(LMI)和广义Gronwall不等式,研究了分数阶线性退化微分系统的有限时间镇定性问题.充分考虑退化和扰动对系统稳定性的影响,给出了在状态反馈控制器作用下,分数阶退化微分系统在有限时间内镇定的充分条件.并通过两个例子验证了定理条件的可行性.     

Double Hopf bifurcation and chaos in Liu system with delayed feedback

In this paper, we consider the stability of equilibria, Hopf and double Hopf bifurcation in Liu system with delay feedback. Firstly, we identify the critical values for stability switches and Hopf bifurcationusing the method of bifurcation analysis. When we choose appropriate feedback strength and delay, two symmetrical nontrivial equilibria of Liusystem can be controlled to be stable at the same time, and the stable bifurcating periodic solutions occur in the neighborhood of the two equilibria at the same time. Secondly, by applying the normal form method and center manifold theory,the normal form near the double Hopf bifurcation, as well as classifications of local dynamics are analyzed. Furthermore, we give the bifurcation diagram to illustrate numerically that a family of stable periodic solutions bifurcated from Hopf bifurcation occur in a large region of delay and the Liu system with delay can appear the phenomenon of ``chaos switchover''.     

A new sequential systems of linear equations algorithm of feasible descent for inequality constrained optimization

Based on a new efficient identification technique of active constraints introduced in this paper, a new sequential systems of linear equations （SSLE） algorithm generating feasible iterates is proposed for solving nonlinear optimization problems with inequality constraints. In this paper, we introduce a new technique for constructing the system of linear equations, which recurs to a perturbation for the gradients of the constraint functions. At each iteration of the new algorithm, a feasible descent direction is obtained by solving only one system of linear equations without doing convex combination. To ensure the global convergence and avoid the Maratos effect, the algorithm needs to solve two additional reduced systems of linear equations with the same coefficient matrix after finite iterations. The proposed algorithm is proved to be globally and superlinearly convergent under some mild conditions. What distinguishes this algorithm from the previous feasible SSLE algorithms is that an improving direction is obtained easily and the computation cost of generating a new iterate is reduced. Finally, a preliminary implementation has been tested.     

分数阶Liu混沌系统及其电路实验的研究与控制

基于波特图的频域近似方法,研究了分数阶Liu混沌系统,并设计了一种树形电路单元来实现分数阶Liu混沌系统,通过对2.7阶Liu混沌系统的电路仿真和实验,以及α=0.8—0.1(步长0.1)Liu混沌系统的电路仿真,验证了树形电路单元的有效性,证实分数阶Liu混沌系统中确实存在混沌现象,且存在混沌的最低阶数为0.3. 设计简单有效的线性反馈控制器,实现了分数阶Liu混沌系统的混沌控制. 关键词： 分数阶Liu系统 电路实验 混沌控制     

SEQUENTIAL SYSTEMS OF LINEAR EQUATIONS ALGORITHM FOR NONLINEAR OPTIMIZATION PROBLEMS-INEQUALITY CONSTRAINED PROBLEMS

AbstractIn this paper, a new superlinearly convergent algorithm of sequential systems of linear equations (SSLE) for nonlinear optimization problems with inequality constraints is proposed. Since the new algorithm only needs to solve several systems of linear equations having a same coefficient matrix per iteration, the computation amount of the algorithm is much less than that of the existing SQP algorithms per iteration. Moreover, for the SQP type algorithms, there exist so-called inconsistent problems, i.e., quadratic programming subproblems of the SQP algorithms may not have a solution at some iterations, but this phenomenon will not occur with the SSLE algorithms because the related systems of linear equations always have solutions. Some numerical results are reported.     

On the critical Fujita exponents for solutions of quasilinear parabolic inequalities

This work is devoted to the study of critical blow-up phenomena for wide classes of quasilinear parabolic equations and inequalities. The model example for this treatment is well known and comes from the theory of turbulent diffusion:

(∗)     

A new characterization of Anderson’s inequality in <Emphasis Type="Italic">C</Emphasis><Subscript>1</Subscript>-classes

Let ℋ be a separable infinite dimensional complex Hilbert space, and let ℒ(H) denote the algebra of all bounded linear operators on ℋ into itself. Let A = (A ₁, A ₂,..., A _n), B = (B ₁, B ₂,..., B _n) be n-tuples of operators in ℒ(H); we define the elementary operators Δ _A,B : ℒ(H) ↦ ℒ(H) by

On the Matrix Equations of Higher Degrees

１　ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄｎｏｔａｔｉｏｎｓＦｏｌｌｏｗｉｎｇＲｅｆｅｒｅｎｃｅ［１］ｗｅｕｓｅＭｎ（Ｆ）ｆｏｒｎ－ｂｙ－ｎｍａｔｒｉｃｅｓｗｉｔｈｅｎｔｒｉｅｓｆｒｏｍＦ,ｓｐｅｃｉａｌ－ｌｙＭｎｆｏｒＭｎ（Ｃ）,ＡｆｏｒｔｈｅＨｅｒｍｉｔｉａｎａｄｊｏｉｎｔｏｆＡ,ｉ．ｅ．（Ａ）Ｔ,ｗｈｅｒｅＡｉｓｔｈｅｅｎｔｒｙｗｉｓｅｃｏｎｊｕｇａｔｅｏｆＡ,ａｎｄＡＴ,ｔｈｅｔｒａｎｓｐｏｓｅｏｆＡ;ＡＢｆｏｒｔｈｅｄｉｒｅｃｔｓｕｍｏｆｍａｔｒｉｃｅｓＡａｎｄＢ．ＬｅｔＸ∈Ｍｎｂｅｔ…     

杨辉三角矩阵(英文)

杨辉三角矩阵的性质吸引许多研究者．本文进一步研究杨辉矩阵,获得一些颇为有趣的性质