We study derivations and Fredholm modules on metric spaces with a Dirichlet form. In particular, on finitely ramified fractals, we show that there is a non-trivial Fredholm module if and only if the fractal is not a tree. This result relates Fredholm modules and topology, and refines and improves known results on p.c.f. fractals.

In this paper, Adomian method has been applied to approximate the solution of fuzzy volterra-fredholm integral equation. That, by using parametric form of fuzzy numbers, a fuzzy volterra-fredholm integral equation has been converted to a system of volterra-fredholm integral equation in crisp case. Finally, the method is explained with illustrative examples.

We provide an introduction to Fredholm theory and discuss using the Fredholm determinant to compute pure-point spectra.

We define a notion of topological degree for a class of maps (called orientable), defined between real Banach spaces, which are Fredholm of index zero. We introduce first a notion of orientation for any linear Fredholm operator of index zero between two real vector spaces. This notion (which does not require any topological structure) allows to define a concept of orientability for nonlinear Fr...

In this paper we propose a framework for supervised and semi-supervised learning based on reformulating the learning problem as a regularized Fredholm integral equation. Our approach fits naturally into the kernel framework and can be interpreted as constructing new data-dependent kernels, which we call Fredholm kernels. We proceed to discuss the “noise assumption” for semi-supervised learning ...

We develop a nonlinear Fredholm alternative theory involving k-ball and k-set perturbations of general homeomorphisms as well as of homeomorphisms that are nonlinear Fredholm maps of index zero. Various generalized first Fredholm theorems are given and finite solvability of general (odd) Fredholm maps of index zero is also studied. We apply these results to the unique and finite solvability of ...

NEW ALGORITHMS FOR NUMERICAL SOLUTION OF NONLINEAR INTEGRO-DIFFERENTIAL EQUATIONS OF THIRD ORDER USING HAAR WAVELETS M. Fayyaz a and M. Azram b * Department of Computer Science, CECOS University Peshawar, Pakistan. [email protected] b Faculty of Engineering, IIUM, Kuala Lumpur 50728, Malaysia. [email protected] ABSTRACT: This paper deals with the extension of earlier work [3] (designed for Fre...

It is shown that the inverse scattering problem for the three-dimensional SchrSdinger equation with a potential having no spherical symmetry can be solved using a Fredholm integral equation. The integral operator studied here is shown to be compact and self-adjoint with its spectrum in [-1, 1]. The relationship between solutions of this Fredholm equation and of a related RiemannHilbert problem ...

1.1 (Fredholm operators). Let X, Y be real Banach spaces and denote their dual spaces by X, Y . A bounded linear operator D : X → Y is called Fredholm if it has a closed image and if its kernel and cokernel (the quotient space Y/imD) are finite dimensional. Equivalently, there exists a bounded linear operator T : Y → X such that the operators TD− idX and DT − idY are compact. The Fredholm index...

1. Summary. In Part I, we develop a nonlinear Fredholm alternative theory involving k-ball and k-set perturbations of general homeomorphisms as well as of homeomorphisms that are nonlinear Fredholm maps of index zero. Various generalized first Fredholm theorems are given and finite solvability of general (odd) Fredholm maps of index zero is also studied. We apply these results to the unique and...