Sigmoidal cosine series on the interval

We construct a set of functions, say, psi([r])(n) composed of a cosine function and a sigmoidal transformation gamma(r) of order r > 0. The present functions are orthonormal with respect to a proper weight function on the interval [-1, 1]. It is proven that if a function f is continuous and piecewise smooth on [-1, 1] then its series expansion based on psi([r])(n) converges uniformly to f so long as the order of the sigmoidal transformation employed is 0 < r

Bayesian training of mixture density networks

Mixture Density Networks (MDNs) are a well-established method for modelling the conditional probability density which is useful for complex multi-valued functions where regression methods (such as MLPs) fail. In this paper we extend earlier research of a regularisation method for a special case of MDNs to the general case using evidence based regularisation and we show how the Hessian of the MDN error function can be evaluated using R-propagation. The method is tested on two data sets and compared with early stopping.

Generalized Variational Inequalities for Upper Hemicontinuous and Demi Operators with Applications to Fixed Point Theorems in Hilbert Spaces

∗ The final version of this paper was sent to the editor when the author was supported by an ARC Small Grant of Dr. E. Tarafdar.

Uniform Convergence of the Newton Method for Aubin Continuous Maps

* This work was supported by National Science Foundation grant DMS 9404431.

Sufficient Conditions of Optimality for Control Pproblem Governed by Variational Inequalities

* This work was completed while the author was visiting the University of Limoges. Support from the laboratoire “Analyse non-linéaire et Optimisation” is gratefully acknowledged.

Acceleration of Convergence in Dontchev’s Iterative Method for Solving Variational Inclusions

2000 Mathematics Subject Classification: 47H04, 65K10.

Applications of the Fréchet subdifferential

2000 Mathematics Subject Classification: 46A30, 54C60, 90C26.

Time-Dependent Differential Inclusions and Viability

AMS subject classification: Primary 34A60, Secondary 49J52.

Application of the D-Fullness Technique for Breakdown Point Study of the Trimmed Likelihood Estimator to a Generalized Logistic Model

2000 Mathematics Subject Classification: 62J12, 62F35

Exponential approximation in the norms and semi-norms

The deviations of some entire functions of exponential type from real-valued functions and their derivatives are estimated. As approximation metrics we use the Lp-norms and power variations on R. Theorems presented here correspond to the Ganelius and Popov results concerning the one-sided trigonometric approximation of periodic functions (see [4, 5 and 8]). Some related facts were announced in [2, 3, 6 and 7].

An Iterative Procedure for Solving Nonsmooth Generalized Equation

2000 Mathematics Subject Classification: 47H04, 65K10.

Steffensen Methods for Solving Generalized Equations

2000 Mathematics Subject Classification: 65G99, 65K10, 47H04.

Density of Polynomials in the L^2 Space on the Real and the Imaginary Axes and in a Sobolev Space

2000 Mathematics Subject Classification: 41A10, 30E10, 41A65.

Selections, Paracompactness and Compactness

2000 Mathematics Subject Classification: 54C60, 54C65, 54D20, 54D30.

The Lindelöf number greater than continuum is u-invariant

2000 Mathematics Subject Classification: 54C35, 54D20, 54C60.