The learning time of a simple neural network model is obtained through an analytic computation of the eigenvalue spectrum for the Hessian matrix, which describes the second order properties of the cost function in the space of coupling coefficients. The form of the eigenvalue distribution suggests new techniques for accelerating the learning process, and provides a theoretical justification for...

This paper considers the basic economic order quantity (EOQ) model when all parameters, such as the demand rate, the ordering cost, and the inventory holding cost, are uncertain, and furthermore, their probability information is also unknown. To address the uncertainty, we adopt a robustness-based approach. In this approach, each unknown parameter is described as a continuous value restricted t...

In this paper the Wilson nonconforming nite element is considered for solving a class of two-dimensional second-order elliptic boundary value problems. Superconvergence estimates and error expansions are obtained for both uniform and non-uniform rectangular meshes. A new lower bound of the error shows that the usual error estimates are optimal. Finally a discussion on the error behaviour in neg...

The paper studies the approximation error in stochastic particle methods for spatially inhomogeneous population balance equations. The model includes advection, coagulation and inception. Sufficient conditions for second order approximation with respect to the spatial discretization parameter (cell size) are provided. Examples are given, where only first order approximation is observed.

now a days, structures with planar geometry such as sheet metals, have attracted special consideration among advanced techno logia, and hence investing vibration behavior of sheet metal is of prim important . in particular regarding dynamical investigations, if the natural frequencies get ignored, the resonance phenomena can exert noun computing damages to the structure and systems. in this res...