Behavioural equivalences of labelled transition systems are characterized in terms of homomorphic transformations. This permits relying on algebraic techniques for proving systems properties and reduces equivalence checking of two systems to studying the relationships among the elements of their structures. Di6erent algebraic characterizations of bisimulation-based equivalences in terms of part...

Application of algebraic multigrid method and approximate sparse inverses are applied as preconditioners for large algebraic systems arising in approximation of diffusion-reaction problems in 3-dimensional complex domains. Here we report the results of numerical experiments when using highly graded and locally refined meshes for problems with non-homogeneous and anisotropic coefficients that ha...

For us, G-bundles are taken in the fppf topology (or, equivalently, the étale topology). Remember that BunG depends on the choice of X, even though the notation suppresses this! Last time, Francois proved that BunGLn is an algebraic stack: • It satisfies descent in the fppf (equivalently, étale) topology; i.e., it’s a stack; • Its diagonal morphism is representable by an algebraic space (implyi...

In this paper (part three of the trilogy) we use low degree G 1 and G 2 continuous regular algebraic spline curves deened within parallelograms, to interpolate an ordered set of data points in the plane. We explicitly characterize curve families whose members have the required interpolating properties and possess a minimal number of innection points. The regular algebraic spline curves consider...

Let p : E−→B be a principal bundle with fibre and structure group the torus T ∼ = (C *) n over a topological space B. Let X be a nonsingular projective T-toric variety. One has the X-bundle π : E(X)−→B where E(X) = E × T X, π([e, x]) = p(e). This is a Zariski locally trivial fibre bundle in case p : E−→B is algebraic. The purpose of this note is to describe (i) the singular cohomology ring of E...

For an algebraic, normal-crossings degeneration over a local eld the local monodromy operator and its powers naturally de ne Galois equivariant classes in the `-adic (middle dimensional) cohomology groups of some precise strata of the special ber of a normal-crossings model associated to the ber product degeneration. The paper addresses the question whether these classes are algebraic. It is sh...

Let p : E−→B be a principal bundle with fibre and structure group the torus T ∼ = (C *) n over a topological space B. Let X be a nonsingular projective T-toric variety. One has the X-bundle π : E(X)−→B where E(X) = E × T X, π([e, x]) = p(e). This is a Zariski locally trivial fibre bundle in case p : E−→B is algebraic. The purpose of this note is to describe (i) the singular cohomology ring of E...

In this paper (part three of the trilogy) we use low degree G and G continuous regular algebraic spline curves de ned within parallelograms, to interpolate an ordered set of data points in the plane. We explicitly characterize curve families whose members have the required interpolating properties and possess a minimal number of in ection points. The regular algebraic spline curves considered h...

Suppose we have an equation with integer coefficients, e.g. y = x + x and we want to understand its solutions over a finite field. If we consider the solutions over C, the set of solutions is a complex manifold and can be studied using the powerful tools of complex analysis and algebraic topology. However, since the set of solutions over a finite field is also finite, and any obvious topology m...

In this paper, some of the results of Blok and Pigozzi on the local deductiondetachment theorems (LDDT) in Abstract Algebraic Logic, which followed pioneering work of Czelakowski on the same topic, are abstracted to cover logics formalized as π-institutions. The relationship between the LDDT and the property of various classes of I-matrices having locally definable principal I-filters is invest...