This paper presents adaptive algorithms for eigenvalue problems associated with non-selfadjoint partial differential operators. The basis for the developed algorithms is a homotopy method which departs from a wellunderstood selfadjoint problem. Apart from the adaptive grid refinement, the progress of the homotopy as well as the solution of the iterative method are adapted to balance the contrib...

We study several properties of a homotopy solution mapping, based on Zhang and Zhang's homotopy formulation, for continuous nonlinear complementarity problems with such non-monotone maps as quasi-monotone, E 0-, and exceptional regular functions. For these classes of complementarity problems, we establish several suucient conditions to assure the nonemptyness and boundedness of the homotopy sol...

Shape theory is an extension of homotopy theory which uses the idea of homotopy in its conception. By comparison, the theory of n-shape, which heretofore only has been defined for metrizable compacta, has as its basic notion that of n-homotopy instead of homotopy. We shall demonstrate that the theory of n-shape extends to the class of all Hausdorff compacta.

The relative homotopy theory of modules, including the (module) homotopy exact sequence, was developed by Peter Hilton (1965). Our thrust is to produce an alternative proof of the existence of the injective homotopy exact sequence with no reference to elements of sets, so that one can define the necessary homotopy concepts in arbitrary abelian categories with enough injectives and projectives, ...

We study some properties of A-homotopy groups: geometric interpretations of connectivity, excision results, and a re-interpretation of quotients by free actions of connected solvable groups in terms of covering spaces in the sense of A-homotopy theory. These concepts and results are well-suited to the study of certain quotients via geometric invariant theory. As a case study in the geometry of ...

Many dynamic systems and industrial control processes can be represented by a multirate sampled-data uncertain system, which consists of a continuous-time uncertain subsystem and a multirate discrete-time uncertain subsystem. The uncertainties in these systems arise from unmodeled dynamics, parameter uariations, sensor noises, actuator constraints, etc. As is the common practice the sampled-dat...

in this paper, we conduct a comparative study between the homotopy perturbation method (hpm) and adomian’s decomposition method (adm) for analytic treatment of nonlinear volterra integral equations, and we show that the hpm with a specific convex homotopy is equivalent to the adm for these type of equations.

Spaces of maps into classifying spaces for equivariant crossed complexes, II: The general topological group case. Abstract The results of a previous paper [3] on the equivariant homotopy theory of crossed complexes are generalised from the case of a discrete group to general topological groups. The principal new ingredient necessary for this is an analysis of homotopy coherence theory for cross...