For m < n, any real analytic m-submanifold of complex n-space with a non-degenerate CR singularity is shown to be locally equivalent, under a formal holomorphic coordinate change, to a xed real algebraic variety de ned by linear and quadratic polynomials. The situation is analogous to Whitney's stability theorem for cross-cap singularities of smooth maps. The formal coordinate change is obtaine...

In this paper we consider the pair di usion process in more than two spatial dimensions. In this case we are able to prove just a local existence result, since it is not possible to deduce global a priori estimates for the equations as it can be done in the two dimensional case. The model includes a nonlinear system of reaction{ drift{di usion equations, a nonlinear ordinary di erential equatio...

We prove a type of converse of the Banach contraction mapping theorem for metric spaces: if X is a T 1 topological space and f : X ! X is a function with unique xed point a such that f n (x) converges to a for each x 2 X , then there exists a distance function d on X such that f is a contraction on the complete ultrametric space (X; d) with contractivity factor 1 2. We explore properties of the...

We consider a numerical method to verify the existence and uniqueness of the solutions of nonlinear hyperbolic problems with guaranteed error bounds. Using a C 1 nite element solution and an inequality constituting a bound on the norm of the inverse operator of the linearized operator, we numerically construct a set of functions which satisfy the hypothesis of Banach's xed point theorem for a c...

This paper describes a formalization of a class of xed-point problems on graphs and its applications. This class captures several wellknown graph theoretical problems such as those of shortest path type and for data ow analysis. An abstract solution algorithm of the xedpoint problem is formalized and its correctness is proved using a theorem proving system. Moreover, the validity of the A* algo...

The automatic conversion of oating point software implementations of algorithms to a equivalent xed point implementation which can be eeciently implemented in an FCCM remains an obstacle in the rapid systems prototyping design ow. Floating point to xed point conversion is tedious, error prone and requires a good knowledge of xed point computer arithmetic. This paper describes a software system ...

Domain-theoretic categories are axiomatised by means of categorical non-order-theoretic requirements on a cartesian closed category equipped with a commutative monad. An enrichment theorem showing that every axiomatic domain-theoretic category can be endowed with an intensional notion of approximation, the path relation, with respect to which the category Cpo-enriches is proved. Our analysis su...

Topological manifolds form an important class of topological spaces with applications throughout mathematics. However, the development of this scienti c area, even at the initial stage, requires non-trivial Brouwer's theorems: the xed point theorem, the topological invariance of degree, and the topological invariance of dimension, where each of them is provided for n-dimensional case. We presen...


 a variant of fixed point theorem is proved in the setting of s-metric spaces