Stability and Asymptoticity of Volterra Difference Equations: A Progress Report

We survey some of the fundamental results on the stability and asymptoticity of linear Volterra difference equations. The method of Ζ-transform is heavily utilized in equations of convolution type. An example is given to show that uniform asymptotic stability does not necessarily imply exponential stabilty. It is shown that the two notions are equivalent if the kernel decays exponentially. For equations of nonconvolution type, Liapunov functions are used to find explicit criteria for stability. Moreover, the resolvent matrix is defined to produce a variation of constants formula. The study of asymptotic equivalence for difference equations with infinite delay is carried out in Section 6. Finally, we state some problems

Stability and Asymptoticity of Volterra Difference Equations: A Progress Report

We survey some of the fundamental results on the stability and asymptoticity of linear Volterra difference equations. The method of Ζ-transform is heavily utilized in equations of convolution type. An example is given to show that uniform asymptotic stability does not necessarily imply exponential stabilty. It is shown that the two notions are equivalent if the kernel decays exponentially. For equations of nonconvolution type, Liapunov functions are used to find explicit criteria for stability. Moreover, the resolvent matrix is defined to produce a variation of constants formula. The study of asymptotic equivalence for difference equations with infinite delay is carried out in Section 6. Finally, we state some problems

Nonautonomous Difference Equations: Open Problems and Conjectures

Autonomous difference equations of the form xn+1 = ƒ (xn) may model populations of species with nonoverlaping generations such as fish, orchard pests, etc. The drawback of such models is that they do not account for environmental fluctuations or seasonal changes. Hence we are led to nonautonomous difference equations of the form xn+1 = ƒ (xn), n ∈ Ζ+. Our main focus in this note will be on periodic difference equations in which the sequence ƒn is periodic. Most of the open problems and conjectures in this part are motivated by recent work by Elaydi and Sacker [3], Elaydi and Yakubu [4] [5], and Elaydi [2]. The second part of the paper discussed the connection between a nonautonomous difference equation and its limiting equation. We present here several conjectures and open problems pertaining to the properties of omega limited sets (see Kempf [7]) and the question of lifting properties from the limiting equation to the original equation. For the convenience of the reader we introduce in Section 4 some rudiments of the theory of skew-product dynamical systems [8]

Is the World Evolving Discretely?

Difference Equations can model effectively almost all physical and artificial phenomena. Even the highly celebrated differential system of Lorenz [6], which models a fluid: =’x yx σσ + yrxxzy −+−=

The Yarmouk tributary to the Jordan river II: Infrastructure impeding the transformation of equitable transboundary water arrangements

This article explores the ways in which key components of infrastructure built on the Yarmouk tributary to the Jordan River induce or impede the transformation of existing transboundary water arrangements. Focussing on the Jordanian-Israeli Adassiyeh Weir and on the Jordanian-Syrian Wehdeh Dam, the article interprets archival documents, official river-gauging data, and interviews through a frame that highlights depoliticisation by hydrocracies within the politics of international infrastructure. The weir is found to be operated in a manner that prioritises Jordan's commitment to Israel when flows are low, and to be designed to bound the volume that Jordan can make use of during low or very high flows. The dam appears oversized but regulates the flow to the downstream weir when its reservoir does not lie empty. The design and operation of the infrastructure is found to partially and selectively depoliticise contentious transboundary water issues in a manner that privileges the more powerful actors. Transformation of the arrangements is impeded as the distribution and use of the flows is not questioned by the water authorities or the international diplomatic community, and alternative arrangements are not considered

OPTIMAL CONTROL FOR DISTRIBUTED CONTROL SYSTEMS

In modern cities, factories and high technology operations are run using distributed control. Distributed control involves the use of computer networks. Computer networks consist of computers on both ends, sensors, actuators, and communication links. However, control over computer networks faces many problems such as the delay and loss of control message and the delay or loss of sensor data. This paper proposes a new method such that the control system can handle the network delays and at the same time find an optimal controller. The method uses the modified zero-order hold to account for the delays and uses the linear matrix inequality optimization method to find the controller. This method also takes advantage of the polynomial representation of systems and constraints and places norm constraints on the problem

A PROPOSED SCHEME FOR AN ARAB QUALITY ASSURANCE AGENCY IN THE FIELD OF COMPUTING & INFORMATION TECHNOLOGY

Over the past few years scientists, researchers and experts form the Arab world and distinguished experts from all over the world in the field of information technology have been meeting annually at the Arab International Conference on Information Technology. Some of those experts had been trained in the field of quality assurance in higher education. This group was trained to perform external reviews and evaluations at the subject level and program level. Evaluations also could take place at the module level

An Automated Irrigation System for Greenhouses

Gaza Strip is a small region with limited agriculture land and water resources. Greenhouse technology allows farmers to optimize the use of this land. In this paper a computer-based control and monitoring system is designed and tested to automate drip irrigation. The model greenhouse can be used as a prototype where several sensors are connected to an acquisition and control system using a PC and a data acquisition card. The designed system can be used as a stand-alone system by lay farmers with no technical background where they can command full control through a screen command. The system is set up to handle several crops by using a user screen to adjust certain parameters on the front panel. A web server enables users to remotely monitor and control the greenhouse through VI's from any place in the world with internet access. Moreover, the system periodically generates alarms and automatically sends emails to notify users of the conditions inside greenhouse

General Allee Effect in Two-Species Population Biology

The main objective of this work is to present a general framework for the notion of the strong Allee effect in population models, including competition, mutualistic, and predator–prey models. The study is restricted to the strong Allee effect caused by an inter-specific interaction. The main feature of the strong Allee effect is that the extinction equilibrium is an attractor. We show how a ‘phase space core’ of three or four equilibria is sufficient to describe the essential dynamics of the interaction between two species that are prone to the Allee effect. We will introduce the notion of semistability in planar systems. Finally, we show how the presence of semistable equilibria increases the number of possible Allee effect cores