Optimal Control of Nonlinear Fractional-Order Systems with Multiple Time-Varying Delays

Journal of Optimization Theory and Applications - This paper considers an optimal control problem governed by nonlinear fractional-order systems with multiple time-varying delays and subject to...     

Output feedback regulation of large-scale feedforward systems with discrete and distributed delays

Nonlinear Dynamics - This paper proposes an output feedback control strategy to achieve the global regulation of a class of large-scale feedforward nonlinear systems with discrete and distributed...     

Oscillation-preserving Legendre-Galerkin methods for second kind integral equations with highly oscillatory kernels

Numerical Algorithms - The original solutions of highly oscillatory integral equations usually have rapid oscillation, which means that conventional numerical approaches used to solve these...     

次线性期望下的一般中心极限定理

受Peng-中心极限定理的启发,本文主要应用G-正态分布的概念,放宽Peng-中心极限定理的条件,在次线性期望下得到形式更为一般的中心极限定理.首先,将均值条件E[X_n]=ε[X_n]=0放宽为|E[X_n]|+|ε[X_n]|=O(1/n);其次,应用随机变量截断的方法,放宽随机变量的2阶矩与2+δ阶矩条件;最后,将该定理的Peng-独立性条件进行放宽,得到卷积独立随机变量的中心极限定理.     

Quasi-periodic solutions for beam equations with the nonlinear terms depending on the space variable

ABSTRACT

This article is devoted to the study of a beam equation with an x-dependent nonlinear term. We construct an analytic and symplectic transformation which changes the Hamiltonian to its Birkhoff normal form. However, the infinitely many coefficients of the Hamiltonian generating this transformation have small denominators. We prove that these denominators do not vanish for all indices and the transformation is canonical. Applying the normal form to a KAM theorem, it is proved that the equation admits quasi-periodic solutions with prescribed frequencies for any fixed potential constant.     

Quadratic properties of least-squares solutions of linear matrix equations with statistical applications

Assume that a quadratic matrix-valued function \(\psi (X) = Q - X^{\prime }PX\) is given and let \(\mathcal{S} = \left\{ X\in {\mathbb R}^{n \times m} \, | \, \mathrm{trace}[\,(AX - B)^{\prime }(AX - B)\,] = \min \right\} \) be the set of all least-squares solutions of the linear matrix equation \(AX = B\). In this paper, we first establish explicit formulas for calculating the maximum and minimum ranks and inertias of \(\psi (X)\) subject to \(X \in {\mathcal S}\), and then derive from the formulas the analytic solutions of the two optimization problems \(\psi (X) =\max \) and \(\psi (X)= \min \) subject to \(X \in \mathcal{S}\) in the Löwner partial ordering. As applications, we present a variety of results on equalities and inequalities of the ordinary least squares estimators of unknown parameter vectors in general linear models.     

Estimation of potential gains from bank mergers: A novel two-stage cost efficiency DEA model

This paper develops a novel two-stage cost efficiency model to estimate and decompose the potential gains from Mergers and Acquisitions (M&As). In this model, a hypothetical DMU is defined as a combination of two or more candidate DMUs. The hypothetical DMU would surpass the traditional Production Possibility Set (PPS). In order to solve the problem, a Merger Production Possibility Set (PPS_M) is constructed. The model minimizes the total cost of the hypothetical DMU while maintaining its outputs at the current level, and estimates the overall merger efficiency by comparing its minimal total cost with its actual cost. Moreover, the overall merger efficiency could be decomposed into technical efficiency, harmony efficiency, and scale efficiency. We show that the model can be extended to a two-stage structure and these efficiencies can be decomposed to both sub-systems. To show the usefulness of the proposed approach, we applied it to a real dataset of top 20 most competitive Chinese City Commercial Banks (CCBs). We concluded that (1) there exist considerably potential gains for the proposed merged banks. (2) It is also shown that the main impact on potential merger gains are from technical and harmony efficiency. (3) As an interesting result we found that the scale effect works against the merger, indicating that it is not favorable for a full-scale merger.