On the Stability of a Linear Bioprocess Model With Recycle Loop

In this note, we treat a linear bioprocess model with recycle loop and analyze the spectrum of the closed-loop operator in order to discuss the exponential stability. It is shown that a$C_0$-semigroup generated by the closed-loop operator satisfies the spectrum determined growth assumption and that the recycle loop works effectively for the process through a numerical simulation.     

Generalized compensative weighted averaging aggregation operators

The compensative weighted averaging (CWA) operator is generalized to develop a class of powerful generalized compensative weighted averaging (GCWA) operators with a very fine range of compensatory effects. The conventional means are shown to be the special cases of the proposed GCWA operator. A few extensions are investigated by combining GCWA operator with ordered weighted averaging (OWA) and induced OWA (IOWA) operators. An exponential class of aggregation operators such as exponential CWA, exponential OWA and exponential IOWA operators are developed. The usefulness of GCWA operators is shown through several examples and a case-study.     

Delay-dependent exponential stability of stochastic delay differential system whose coefficients obey the polynomial growth condition

This article discusses the exponential stability of nonlinear stochastic delay differential systems (SDDSs) whose coefficients obey the polynomial growth condition. Delay-dependent criteria on almost sure exponential stability and pth moment exponential stability of such SDDSs have been established. By applying some novel techniques, our criteria work for many SDDSs including some cases in which the ?V operator has a complicated form, which seemingly prevents the existing results from being directly used. The range of order of moment exponential stability and the decay rate can be estimated through the coefficients of the system.     

An exponential membership function for fuzzy multiple objective linear programming

The operator “min” is one of the most frequently used aggregation operators in fuzzy decision. However, this operator is the softest operator and no allowance is made for any compensation. The “product” and other operators, some of them may be compensatory, are seldom used because of the nonlinearity of the resulting problem. In this paper, an exponential, instead of linear membership function is proposed. The advantages of using exponential membership are two fold. First, the resulting problems can be transformed to linear ones when the “product” and several other nonlinear aggregate operators are used. Secondly, exponential representation is more realistic than the linear ones usually used for some practical applications.     

基于IOWC-GOWA算子的区间组合预测模型

在连续区间数广义有序加权平均（C-GOWA）算子基础上,将IOWA算子和C-GOWA算子相结合,提出诱导有序加权连续区间广义有序加权平均（IOWC-GOWA）算子的概念。以指数支撑度作为相关性指标,构建新的组合预测模型。通过实例分析说明该模型能有效提高预测精度。     

Global exponential convergence of periodic neural networks with time-varying delays

In this paper, the global exponential convergence of a general class of periodic neural networks with time-varying delays is investigated. Based on the theory of mixed monotone operator, a testable algebraic criteria for ascertaining global exponential convergence is derived. Furthermore, the rate of exponential convergence and bound of the networks are also estimated. Finally, a numerical example is given to show the effectiveness of the obtained results.     

High-order time stepping Fourier spectral method for multi-dimensional space-fractional reaction–diffusion equations

This paper introduces a high-order time stepping scheme, that is based on using Fourier spectral in space and a fourth-order diagonal Padé approximation to the matrix exponential function for solving multi-dimensional space-fractional reaction–diffusion equations. The resulting time stepping scheme is developed based on an exponential time differencing approach such that it alleviates solving a large non-linear system at each time step while maintaining the stability of the scheme. The non-locality of the fractional operator in some other numerical schemes for these equations leads to full and dense matrices. This scheme is able to overcome such computational inefficiency due to the full diagonal representation of the fractional operator. It also attains spectral convergence for multiple spatial dimensions. The stability of the scheme is discussed through the investigation of the amplification symbol and plotting its stability regions, which provides an indication of the stability of the method. The convergence analysis is performed empirically to show that the scheme is fourth-order accurate in time, as expected. Numerical experiments on reaction–diffusion systems with application to pattern formation are discussed to show the effect of the fractional order in space-fractional reaction–diffusion equations and to validate the effectiveness of the scheme.     

Multiple precision computation of some zeros of bessel functions by rigorous explicit formulae

In order to perform the rigorous computation of the zeros of Bessel functions, we exploit classical approximants going back to Euler and recently generalized in the light of the Trefftz-Fichera orthogonal invariants method. Working in multiple precision (up to 140 significant figures in decimal system), we compute explicit approximants obtaining more than 100 exact figures for the first positive zero. By inversion of this zero as a function of the order, we evaluate the first eigenvalue of the exponential potential Schrödinger operator with the same accuracy.     

On Characterizations of Exponential Stability of Nonlinear Discrete Dynamical Systems on Bounded Regions

In this paper, we discuss the quantitative characterization problems of the exponential stability and trajectory convergence property of nonlinear discrete dynamical systems on a bounded set of the state space. Through introducing two new concepts-the Lip constant of a nonlinear operator and strongly equivalent metrics of a norm-we show that the nonlinear discrete dynamical systems are exponentially stable on the bounded set if and only if the corresponding nonlinear operator is contractive under some strongly equivalent metrics, or if and only if the Lip constant of the nonlinear operator is less than one. In the latter case, we further show that the infimum of the exponential bounds of trajectories of the system equals exactly to the Lip constant. Based on the obtained results, we clearly explain how trajectory convergence properties of the systems are determined quantitatively by the Lip constant and strongly equivalent metrics. The obtained results not only are of importance in understanding the essence of exponential stability and trajectory convergence properties of nonlinear discrete dynamical systems on bounded sets of the state space but also provide some new, useful criteria of testing exponential stability and estimating convergence speed of trajectories of the systems.     

The effect of small delays in the feedback loop on the stability of neutral systems

It is well-known that exponential stabilization of a neutral system with unstable difference operator is only possible by allowing for control laws containing derivative feedback. We show that closed-loop stability of a neutral system with unstable open-loop difference operator obtained by applying a derivative feedback scheme is extremely sensitive to arbitrarily small time delays in the feedback loop.     

基于IIR指数平滑滤波与非线性Laplacian算子的边缘检测方法

本文提出了一种基于ＩＩＲ指数平滑滤波与非线性Ｌａｐｌａｃｉａｎ算子的边缘检测方法，具有以下特点；采用最佳指数平滑滤波器增强抗噪声能力，且可实现无限大窗口的快速递归运算；利用非线性Ｌａｐｌａｃｉａｎ算子只沿边缘增强边缘，充分利用了边缘的局部方向信息；引入边缘强度信息，在二阶零交叉处理根据边缘强度定位边缘；运算量独立于滤波器窗口尺寸，具有较高的计算效率，通过与ＬＯＧ算子的对比实验和在立体视觉中的应用表     

Local stabilization of the Burgers–Fisher equation via boundary control

Locally exponential stabilization for the Burgers–Fisher system is addressed by boundary control in this paper. For the nonlinear partial differential equation, a linear boundary feedback control law is applied to control the Burgers–Fisher system. Locally exponential stabilization of the closed loop system is established based on the relationship between operator theories and relations of different norms. Finally, the theory is validated through numerical simulations.     

Efficient exponential compact higher order difference scheme for convection dominated problems

Present work is the development of a finite difference scheme based on Richardson extrapolation technique. It gives an exponential compact higher order scheme (ECHOS) for two-dimensional linear convection-diffusion equations (CDE). It uses a compact nine point stencil, over which the governing equations are discretized for both fine and coarse grids. The resulting algebraic systems are solved using a line iterative approach with alternate direction implicit (ADI) procedure. Combining the solutions over fine and coarse grids, initially a sixth order solution over coarse grid points is obtained. The resultant solution is then extended to finer grid by interpolation derived from the difference operator. The convergence of the iterative procedure is guaranteed as the coefficient matrix of the developed scheme satisfies the conditions required to be monotone. The higher order accuracy and better rate of convergence of the developed algorithm have been demonstrated by solving numerous model problems.     

Generalized exponential functions for system analysis and synthesis

Generalized exponential functions are defined and developed for the analysis and aynthesis of dynamical systems. Approximation of conventional response transforms in the 8-domain is implemented by utilizing non-integer-order complex operator 8v. The analysis technique is applied to a non-inductive long cable and to network systems. In addition, for the synthesis, ?aguorre-?eo functions in the 8-domain are extended into the non-integer-order 8v-domain in terms of generalized exponential functions. The application is demonstrated by an example     

Almost periodic cellular neural networks with neutral-type proportional delays

This paper presents a new result on the existence, uniqueness and generalised exponential stability of almost periodic solutions for cellular neural networks with neutral-type proportional delays and D operator. Based on some novel differential inequality techniques, a testable condition is derived to ensure that all the state trajectories of the system converge to an almost periodic solution with a positive exponential convergence rate. The effectiveness of the obtained result is illustrated by a numerical example.     

A Modified TOPSIS Method for Obtaining the Associated Weights of the OWA‐Type Operators

The ordered weighted averaging (OWA) operator proposed by Yager and its some extensions have been extensively utilized to perform the mean‐type aggregation of individual preference relations in group decision making. An important issue in the theory of the OWA‐type operators is the determination of the associated weights. In the present paper, the technique for order preference by similarity to ideal solution is modified to propose a new method for generating the associated weights under the environment of a group of additive reciprocal matrices. First, a consistent additive reciprocal matrix is obtained from each additive reciprocal matrix. It is further used to generate an ideal additive reciprocal matrix by using the arithmetic averaging operator. Then, a similarity degree between every additive reciprocal matrix and the ideal one is defined. Based on the similarity degree, the associated weights are determined by making use of an exponential function and they show that more importance is given to that with more similarity degree. Finally, a numerical example is carried out to illustrate the given method.     

On the output feedback stabilization for distributed semilinear systems

The output stabilization for a class of distributed semilinear system is obtained with stabilizing controls that depend on the output operator. Then, we give sufficient conditions for exponential, strong and weak stabilization. The obtained results are illustrated by examples and simulations.     

Robustness of stability of time-varying index-1 DAEs

We study exponential stability and its robustness for time-varying linear index-1 differential-algebraic equations. The effect of perturbations on the leading coefficient matrix is investigated. An appropriate class of allowable perturbations is introduced. Robustness of exponential stability with respect to a certain class of perturbations is proved in terms of the Bohl exponent and perturbation operator. Finally, a stability radius involving these perturbations is introduced and investigated. In particular, a lower bound for the stability radius is derived. The results are presented by means of illustrative examples.     

Delta 算子不确定系统的滑模变结构控制

研究算子系统滑模变结构控制的综合问题.首先,利用线性矩阵不等式方法给出了切换面存在的充分条件,分析了算子变结构控制系统的到达条件,将连续系统和离散系统统一到算子系统.基于指数趋近律,给出滑模变结构控制一般方法.其次,给出一类算子不确定系统的滑模控制器设计,分析了准滑动模态的渐近稳定性,使得系统具有良好的动态性能.最后,用一个仿真实例说明在采样周期取值非常小的前提下,该方法设计的滑模变结构控制仍具有可行性和有效性.     

An Orness Measure for Quasi-Arithmetic Means

In this paper, an orness measure to reflect the or-like degree of the quasi-arithmetic mean operator is proposed. With the generating function representation method, some properties of a quasi-arithmetic mean, associated with its orness measure, are analyzed. Then, the paper focuses on two kinds of parameterized quasi-arithmetic means with exponential function and power function generators respectively. Some properties of them are examined and compared. As the aggregation value for any set always monotonically increases with the orness level, the orness level can be used as a control parameter to represent the decision maker's preference. A generic method to get the quasi-arithmetic mean operator which makes the aggregation result consistent with its orness level is also examined. Finally, the properties of the quasi-arithmetic mean and that of the exponential and power function generators are extended to the weighted quasi-arithmetic mean by considering the importance of the aggregated elements