c © W W L Chen, 1984, 2013. This chapter originates from material used by the author at Imperial College London between 1981 and 1990. It is available free to all individuals, on the understanding that it is not to be used for financial gain, and may be downloaded and/or photocopied, with or without permission from the author. However, this document may not be kept on any information storage an...

The algebraic approach originally concentrated on the use of equational logic as the basic formalism for specification. This use was successful in many senses. In particular, the good behaviour of equational logic with respect to a number of semantic constructs has helped to facilitate the study of new specification concepts and constructs. At the same time, the categorical techniques used for ...

We discuss the existence results for a fuzzy initial value problem of linear differential-algebraic equations and provide an explicit representation for the solution. A few illustrative examples are given. © 2014 Elsevier B.V. All rights reserved.

We give sufficient cohomological criteria for the classes of given varieties over a field k to be algebraically independent in the Grothendieck ring of varieties over k and construct some examples.

The graph copy function when restricted to the set of trees or of rooted trees is called the tree copy function or the rooted tree copy function, respectively. We show that both the set of tree copy functions and the set of rooted tree copy functions are strongly linearly independent. We also show that the set of all tree copy functions are algebraically independent but the set of all rooted tr...

In this article we propose a method of performing arithmetic operations on variables with unknown distribution. The approach to the evaluation results of arithmetic operations can select probability intervals of the algebraic equations and their systems solutions, of differential equations and their systems in case of histogram evaluation of the empirical density distributions of random paramet...

—This document presents an introduction of two commonly used power system differential algebraic equations for studying electromechanical oscillation and transient stability. Two types of generator models are used to formulate the power system model, respectively: the second-order classical model and the fourth-order generator model. An example is provided on the IEEE 9-bus system.

We show that the classical kernel and domain functions associated to an n-connected domain in the plane are all given by rational combinations of three or fewer holomorphic functions of one complex variable. We characterize those domains for which the classical functions are given by rational combinations of only two or fewer functions of one complex variable. Such domains turn out to have the ...