This paper gives three noncompact variants of Lefschetz–Nielsen fixed-point theory parallel to developments that have occurred in surgery theory. Thus, we study when a proper map can be properly homotoped, or boundedly homotoped, or even homotoped in a C bounded fashion to a fixedpoint free map. As an example, the universal cover of a compact aspherical manifold always has a fixed-point free se...

The Split-Field Finite-Difference Time-Domain (SFFDTD) formulation is extended to periodic structures with Kerr-type nonlinearity. The optical Kerr effect is introduced by an iterative fixedpoint procedure for solving the nonlinear system of equations. Using the method, formation of solitons inside homogenous nonlinear media is numerically observed. Furthermore, the performance of the approach ...

We present two examples of nice normal spaces X having the property that for some fixedpoint free homeomorphism on X its tech-Stone extension has a fixed point. One of the spaces presented here is locally countable, locally compact, separable, normal, countably paracompact and weakly zero-dimensional. The other one is hereditarily normal and strongly zero-dimensional. Our construction of this e...

where h ∈ L1(0,T ;X) and f : [0,T ]×X →X. This is obtained if one takes F(u)(t)= h(t)−∫ t 0 a(t−s)f (s,u(s))ds in (1.1). Such problems are important from the viewpoint of applications since they cover nonlocal generalizations of integrodifferential equations arising in the mathematical modeling of heat conduction in materials with memory. Byszewski [6, 7] initiated the work concerning abstract ...

We present a compositional method which allows to overapproximate the set of attractors and under-approximate the set of basins of attraction of a Boolean network (BN). This merely consists in replacing a global fixed-point computation by a composition of local fixedpoint computations. Once these approximations have been computed, it becomes much more tractable to generate the exact sets of att...

Fixed-point simulation results are used for the performance measure of inverting matrices by Cholesky decomposition. The fixed-point Cholesky decomposition algorithm is implemented using a fixed-point reconfigurable processing element. The reconfigurable processing element provides all mathematical operations required by Cholesky decomposition. The fixed-point word length analysis is based on s...

We introduce methods which seem to be a new and promising tool in hierarchical fixedpoint problems. The goal of this note is to analyze the convergence properties of these new types of approximating methods for fixed-point problems. The limit attained by these curves is the solution of the general variational inequality, 0 ∈ (I −Q)x∞ +NFixP(x∞), where NFixP denotes the normal cone to the set of...

In this paper, we devote to investigation of the existence of positive solutions for the boundary value problem of nonlinear fractional differential equations { D0+u(t)+ f (t,u(t)) = 0, 0 < t < 1, u(0) = u′(0) = · · ·u(n−2)(0) = D0+u(1), where D0+ , D β 0+ are the standard Riemann-Liouville fractional derivative, n− 1 < α n , n−2 β n−1 , n 3 . By means of constructing an exact cone of the Banac...

Translation planes of order q and kernel containing KGGFðqÞ admitting fixedpoint-free collineation groups GK , each of whose point orbits is the set of nonzero vectors of a 2-dimensional K-subspace, are shown to permit spread-retraction and produce either Baer subgeometry or mixed partitions of a corresponding projective space. When the same translation plane or spread produces a number of part...

ion-Carrying Code ? Elvira Albert, Puri Arenas, Germán Puebla, and Manuel Hermenegildo 1 Complutense University of Madrid, {elvira,puri}@sip.ucm.es 2 Technical University of Madrid, {german,herme}@fi.upm.es 3 University of New Mexico, [email protected] Abstract. Abstraction-Carrying Code (ACC) has recently been proposed as a framework for mobile code safety in which the code supplier provides a pro...