Synchronizability of Networks with Strongly Delayed Links: A Universal Classification

We show that for large coupling delays the synchronizability of delay-coupled networks of identical units relates in a simple way to the spectral properties of the network topology. The master stability function used to determine stability of synchronous solutions has a universal structure in the limit of large delay: it is rotationally symmetric around the origin and increases monotonically with the radius in the complex plane. We give details of the proof of this structure and discuss the resulting universal classification of networks with respect to their synchronization properties. We illustrate this classification by means of several prototype network topologies.     

具有脉冲扰动的比率相关功能性反应捕食者-食饵扩散模型的持续生存和周期解

本文考虑一类具有脉冲扰动的比率相关的捕食者一食饵扩散模型,利用比较原理研究了这类系统的持续生存和灭绝性,通过将脉冲反应扩散方程转化为相应的算子方程,并证明了解在适当空间的紧性,得到了周期解的存在性、唯一性和全局稳定性.最后分析了脉冲效应对系统性态的影响.     

时变线性大系统在结构扰动下的平稳振荡

该文应用大系统的分解方法及一个推广的不等式,研究了一类时变大系统在结构扰动下的平稳振荡问题,得到了一些新结果．     

离散大系统在结构扰动下周期解的存在性

对于离散系统稳定性的研究,近年来受到人们的重视,但对于周期解的研究,在文献中还很少看到。本文首先讨论了离散系统解的有界性,并且得到了若一个具有周期系数的差分方程的解为最终有界的,则存在周期解的结果。然后利用李雅普诺夫函数方法研究了离散大系统在结构扰动之下周期解的存在性和离散大系统的平稳振荡。     

参数扰动对企业行为的影响

经营管理者们很难对众多关键变量之间的影响关系做出准确判断,从而无法实现有效决策.为此,提出一种估算影响程度的方法.运用系统动力学原理建立企业的数学模型,即带时滞的一阶微分方程组(包含常参数、变参数和状态变量).基于灵敏度理论估计常参数和变参数扰动对状态变量的影响程度,并给出其在企业经营过程中的应用,包括扰动解的外推和参数间重要性的比较.以东城食糖经营公司为例进行分析研究,验证所提方法的可行性.     

Remarks on Perturbations of the Equation

Perturbations of the equation are discussed. The structure of near-orthogonal matrices is shown, and implicationsfor certain control problems are pointed out. Examples are givenand the circumstances are noted in which the real part of aneigenvalue can be expected to change sign. This paper was written while the author was on a Leave of Absenceat the Department of Mathematics, University of Salford.     

Exponential Stability of Discrete-Time Delayed Hopfield Neural Networks with Stochastic Perturbations and Impulses

This paper derives some sufficient conditions for exponential stability in the mean square of stochastic discrete-time delayed Hopfield neural networks (DHNN) with impulse effects. The Lyapunov–Krasovskii stability theory, Halanay inequality, and linear matrix inequality (LMI) are employed to investigate the problem. It is shown that the impulses in certain regions might preserve the stability property of the DHNN when the impulses-free part converges to its equilibrium point. Moreover, the feasible interval of the jump operator is also derived.     

Perturbations on the subdiagonals of Toeplitz matrices

Let L be an Hermitian linear functional defined on the linear space of Laurent polynomials. It is very well known that the Gram matrix of the associated bilinear functional in the linear space of polynomials is a Toeplitz matrix. In this contribution we analyze some linear spectral transforms of L such that the corresponding Toeplitz matrix is the result of the addition of a constant in a subdiagonal of the initial Toeplitz matrix. We focus our attention in the analysis of the quasi-definite character of the perturbed linear functional as well as in the explicit expressions of the new monic orthogonal polynomial sequence in terms of the first one.     

基于复杂网络的并联式项目群结构脆弱性评估

运用复杂网络研究并联式项目群的结构脆弱性。将项目群中的任务用节点表示、任务之间的依赖关系用边表示,依据任务的工期确定点权、任务之间的依赖强度确定边权,则并联式项目群被抽象为一个有向加权网络。在分析并联式项目群网络拓扑特征的基础上,构建并联式项目群脆弱性评估模型,并对一个并联式项目群进行脆弱性评估。仿真结果表明该方法可以对并联式项目群脆弱性进行定量化评估、能够有效识别结构中的脆弱环节。本研究为保障项目群顺利实施、抵御风险提供了新的思路。     

Perturbations of the Haar wavelet

Let be given. For any we construct a function having the following properties: (a) has support in . (b) . (c) If denotes the Haar function and , then . (d) generates an affine Riesz basis whose frame bounds (which are given explicitly) converge to as .

     

Perturbations of positive semigroups on AM-spaces

We consider positive perturbations of positive semigroups on AM-spaces and prove a result which is the dual counterpart of a famous perturbation result of Desch in AL-spaces. As an application we present unbounded perturbations of the shift semigroup.     

Classification of Structural Complexity for Mine Ventilation Networks

The mine ventilation system is most important and technical measure for ensuring safety production in mines. The structural complexity of a mine ventilation network can directly affect the safety and reliability of the underground mining system. Quantitatively justifying the degree of complexity can contribute to providing a deeper understanding of the essential characteristics of a network. However, so far, there is no such a model which is able to simply, practically, reasonably, and quantitatively determine or compare the structural complexity of different ventilation networks. In this article, by analyzing some typical parameters of a mine ventilation network, we conclude that there is a linear functional relationship among five key parameters (number of ventilation network branches, number of nodes, number of independent circuits, number of independent paths, and number of diagonal branches). Correlation analyses for the main parameters of ventilation networks are conducted based on SPSS. Based on these findings, a new evaluation model for the structural complexity of ventilation network (which is represented by C) has been proposed. By combining SPSS classification analyses results with the characteristics of mine ventilation networks, standards for the complexity classification of mine ventilation systems are put forward. Using the developed model, we carried out analyses and comparisons for the structural complexity of ventilation networks for typical mines. Case demonstrations show that the classification results correspond to the actual situations. © 2014 Wiley Periodicals, Inc. Complexity 21: 21–34, 2015     

Perturbations of positive semigroups on $$L_p$$-spaces

We give a characterization of a variation of constants type estimate relating two positive semigroups on (possibly different) \(L_p\)-spaces to one another in terms of corresponding estimates for the respective generators and of estimates for the respective resolvents. The results have applications to kernel estimates for semigroups induced by accretive and non-local forms on \(\sigma \)-finite measure spaces.     

The Evolution of Linearized Perturbations of Parallel Flows

The equations of an incompressible fluid are linearized for small perturbations of a basic parallel flow. The initial-value problem is then posed by use of Fourier transforms in space. Previous results are systematized in a general framework and used to solve a series of problems for prototypical examples of basic shear flow and of initial disturbance. The prototypes of shear flow are (a) plane Couette flow bounded by rigid parallel walls, (b) plane Couette flow bounded by rigid walls at constant pressure, (c) unbounded two-layer flow with linear velocity profile in each layer, (d) a piecewise linear profile of a boundary layer on a rigid wall. The prototypes of initial perturbation are the fundamental ones: (i) a point source of the field of the transverse velocity (represented by delta functions), (ii) an unbounded sinusoidal field of the transverse velocity, (iii) a point source of the lateral component of vorticity, (iv) a sinusoidal field of the lateral vorticity. Detailed solutions for an inviscid fluid are presented, but the problem for a viscous fluid is only broached.     

On Asymptotic Effects of Boundary Perturbations in Exponentially Shaped Josephson Junctions

A parabolic integro differential operator \(\mathcal{L}\) , suitable to describe many phenomena in various physical fields, is considered. By means of equivalence between \(\mathcal{L}\) and the third order equation describing the evolution inside an exponentially shaped Josephson junction (ESJJ), an asymptotic analysis for (ESJJ) is achieved, explicitly evaluating, boundary contributions related to the Dirichlet problem.     

Perturbations on bidegreed graphs minimizing the spectral radius

One common problem in spectral graph theory is to determine which graphs, under some prescribed constraints, maximize or minimize the spectral radius of the adjacency matrix. Here we consider minimizers in the set of bidegreed, or biregular, graphs with pendant vertices and given degree sequence. In this setting, we consider a particular graph perturbation whose effect is to decrease the spectral radius. Hence we restrict the structure of minimizers for k-cyclic degree sequences.     

The Sensitivity of a Spline Function to Perturbations of the Knots

In this paper we study the sensitivity of a spline function, represented in terms of B-splines, to perturbations of the knots. We do this by bounding the difference between a primary spline and a secondary spline with the same B-spline coefficients, but different knots. We give a number of bounds for this difference, both local bounds and global bounds in general L ^p-spaces. All the bounds are based on a simple identity for divided differences.     

Rotating Singular Perturbations of the Laplacian

We study a system of a quantum particle interacting with a singular time-dependent uniformly rotating potential in 2 and 3 dimensions: in particular we consider an interaction with support on a point (rotating point interaction) and on a set of codimension 1 (rotating blade). We prove the existence of the Hamiltonians of such systems as suitable self-adjoint operators and we give an explicit expression for the unitary dynamics. Moreover we analyze the asymptotic limit of large angular velocity and we prove strong convergence of the time-dependent propagator to some one-parameter unitary group as Communicated by Gian Michele GrafSubmitted 07/10/03, accepted 09/12/03