Critical points for least-squares problems involving certain analytic functions, with applications to sigmoidal nets

Critical Points for Least - Squares ProblemsInvolving

This paper deals with nonlinear least-squares problems involving the tting to data of parameterized analytic functions. For generic regression data, a general result establishes the countability, and under stronger assumptions niteness, of the set of functions giving rise to critical points of the quadratic loss function. In the special case of what are usually called \single-hidden layer neura...

Existence of three positive solutions for nonsmooth functional involving the p-biharmonic operator

This paper is concerned with the study of the existence of positive solutions for a Navier boundaryvalue problem involving the p-biharmonic operator; the right hand side of problem is a nonsmoothfunctional with variable parameters. The existence of at least three positive solutions is establishedby using nonsmooth version of a three critical points theorem for discontinuous functions. Our resul...

Some Properties of Certain Subclasses of Close-to-Convex and Quasi-convex Functions with Respect to 2k-Symmetric Conjugate Points

Fekete-Szeg"o problems for analytic functions in the space of logistic sigmoid functions based on quasi-subordination

In this paper, we define new subclasses ${S}^{*}_{q}(alpha,Phi),$ ${M}_{q}(alpha,Phi)$ and ${L}_{q}(alpha,Phi)$ of analytic functions in the space of logistic sigmoid functions based on quasi--subordination and determine the initial coefficient estimates $|a_2|$ and $|a_3|$ and also determine the relevant connection to the classical Fekete--Szeg"o inequalities. Further, we discuss the improved ...

On the method of finite spheres in applications: towards the use with ADINA and in a surgical simulator

In this paper we report some recent advances regarding applications using the method of finite spheres; a truly meshfree numerical technique developed for the solution of boundary value problems on geometrically complex domains. First, we present the development of a preprocessor for the generation of nodal points on twodimensional computational domains. Then, the development of a specialized v...