We propose a simple framework of algebraic constructions for software specification, modular design and development. Algebraic constructions generalise (parameterised) modules by allowing on one hand a rather arbitrary collection of elements to form the parameter and on the other hand dependencies between the module elements to be spelled out explicitly. Algebraic constructions are specified in...

January 23, 2013 Frances Kirwan’s book Complex algebraic curves is an excellent introduction to complex algebraic curves (see [5]). Whenever possible I have included a page reference to the book, in the form [5]. Another beautiful book on this subject is Rick Miranda’s book Algebraic curves and Riemann surfaces (see [6]). To get a feeling what is higher-dimensional complex algebraic geometry, s...

A generalised Thurston-Bennequin invariant for a Q-singularity of a real algebraic variety is defined as a linking form on the homologies of the real link of the singularity. The main goal of this paper is to present a method to calculate the linking form in terms of the very good resolution graph of a real normal unibranch singularity of a real algebraic surface. For such singularities, the va...

In this work, we propose a robust and easily implemented algebraic multigrid method as a stand-alone solver or a preconditioner in Krylov subspace methods for solving either symmetric and positive definite or saddle point linear systems of equations arising from the finite element discretization of the vector Laplacian problem, linear elasticity problem in pure displacement and mixed displaceme...

Abslraet--We consider the design of a feedback control law for control systems described by a class of nonlinear differential-algebraic equations so that certain desired outputs track given reference inputs. The nonlinear differential-algebraic control system being considered is not in state variable form. Assumptions are introduced and a procedure is developed such that an equivalent state rea...

Over the years, the Circus family of notation has been used for specification, programming, and verification by refinement in many applications. Circus Time, a timed variant of Circus, plays a key role in dealing with timed behaviours. While most of the semantic developments of Circus Time have tended to focus on the denotational and operational sides, the work on its algebraic semantics is fru...

In this paper we consider the notions of the Hamming weight and the algebraic normal form. We solve an open problem devoted to checking divisibility of the weight by 2. We generalize the criterion for checking the evenness of the weight in two ways. Our main result states that for checking whether the Hamming weight of f is divisible by 2, k > 1, it is necessary and sufficient to know its algeb...