On a class of discontinuous vector-valued functions and the associated quasi-variational inequalities

We study in detail a class of discontinuous vector-valued functions defined on a closed convex subset of Rn, which was introduced by B. Ricceri [7] and which is very useful in the theory of variational inequalities. The results are used to give a new proof for the existence theorem due to P. Cubiotti [3]. The proof allows us to have a better understanding of quasi-variational inequalities associated with the abovementioned class of functions.     

逻辑系统'Luk中命题积分真度的若干等式与不等式

对' Lukasiewicz逻辑系统,利用序结构知识和赋值函数保并、交、补、蕴涵运算的性质研究了命题的积分真度,推出了若干关于积分真度的等式与不等式,修正完善了积分真度的交推理规则,给出了积分真度的等式与不等式的一些应用,使较复杂的积分真度计算得以简化,或进行较合理的估值.     

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.     

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.     

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:

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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

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