Legal method and legal reflection: experiential learning in the law school

The two main themes of the conference centre around teaching experiences in legal education and theme and international and European perspectives in legal education.

[Review] M. Feistauer, J. Felcman, I. Straskbraba, Mathematical and Computational Methods for Compressible Flow, Oxford Science Publication, Oxford, ISBN 0198505884, 2004 (535pp.)

The growth of computer power allows the solution of complex problems related to compressible flow, which is an important class of problems in modern day CFD. Over the last 15 years or so, many review works on CFD have been published. This book concerns both mathematical and numerical methods for compressible flow. In particular, it provides a clear cut introduction as well as in depth treatment of modern numerical methods in CFD. This book is organised in two parts. The first part consists of Chapters 1 and 2, and is mainly devoted to theoretical discussions and results. Chapter 1 concerns fundamental physical concepts and theoretical results in gas dynamics. Chapter 2 describes the basic mathematical theory of compressible flow using the inviscid Euler equations and the viscous Navier–Stokes equations. Existence and uniqueness results are also included. The second part consists of modern numerical methods for the Euler and Navier–Stokes equations. Chapter 3 is devoted entirely to the finite volume method for the numerical solution of the Euler equations and covers fundamental concepts such as order of numerical schemes, stability and high-order schemes. The finite volume method is illustrated for 1-D as well as multidimensional Euler equations. Chapter 4 covers the theory of the finite element method and its application to compressible flow. A section is devoted to the combined finite volume–finite element method, and its background theory is also included. Throughout the book numerous examples have been included to demonstrate the numerical methods. The book provides a good insight into the numerical schemes, theoretical analysis, and validation of test problems. It is a very useful reference for applied mathematicians, numerical analysts, and practice engineers. It is also an important reference for postgraduate researchers in the field of scientific computing and CFD.

Parallel algorithms of the Purcell method for direct solution of linear systems

In this paper, we first demonstrate that the classical Purcell's vector method when combined with row pivoting yields a consistently small growth factor in comparison to the well-known Gauss elimination method, the Gauss–Jordan method and the Gauss–Huard method with partial pivoting. We then present six parallel algorithms of the Purcell method that may be used for direct solution of linear systems. The algorithms differ in ways of pivoting and load balancing. We recommend algorithms V and VI for their reliability and algorithms III and IV for good load balance if local pivoting is acceptable. Some numerical results are presented.

The completeness and soundness of temporal theories

Generally speaking, the term temporal logic refers to any system of rules and symbolism for representing and reasoning about propositions qualified in terms of time. In computer science, particularly in the domain of Artificial Intelligence, there are mainly two known approaches to the representation of temporal information: modal logic approaches including tense logic and hybrid temporal logic, and predicate logic approaches including temporal arguement method and reified temporal logic. On one hand, while tense logic, hybrid temporal logic and temporal argument method enjoy formal theoretical foundations, their expressiveness has been criticised as not power enough for representing general temporal knowledge; on the other hand, although reified temporal logic provides greater expressive power, most of the current systems following the temporal reification lack of complete and sound axiomatic theories. With there observations in mind, a new reified temporal logic with clear syntax and semantics in terms of a sound and complete axiomatic formalism is introduced in this paper, which retains all the expressive power of temporal reification.