Markov or a maximum entropy random field model for a prior distribution may be viewed as a minimizer of a variational problem. Using notions from robust statistics, a variational filter referred to as a Huber gradient descent flow is proposed. It is a result of optimizing a Huber functional subject to some noise constraints and takes a hybrid form of a total variation diffusion for large gradie...

the stability of learning rate in neural network identifiers and controllers is one of the challenging issues which attracts great interest from researchers of neural networks. this paper suggests adaptive gradient descent algorithm with stable learning laws for modified dynamic neural network (mdnn) and studies the stability of this algorithm. also, stable learning algorithm for parameters of ...

The aim of this study is to analyze the resonant attractor-repeller points during the atmospheric descent of a spacecraft with small asymmetry. The mathematical simulation of spacecraft rotational motion uses an approximate non-linear system of equations obtained by the method of integral manifolds. Application of the averaging method and the Lyapunov method makes it possible to obtain realizat...

Using the Deift-Zhou steepest descent method, we derive locally uniform asymptotic formulas for the Meixner polynomials. So far as we know, the asymptotic behavior in a neighborhood of the origin has not been studied before. To fill this gap, we should impose a Cauchy integral, which is the uniformly bounded solution to a scalar Riemann-Hilbert problem, and which converges exponentially fast (a...

Using the steepest descent method of Deift-Zhou, we derive locally uniform asymptotic formulas for the Meixner polynomials. These include an asymptotic formula in a neighborhood of the origin, a result which as far as we are aware has not yet been obtained previously. This particular formula involves a Cauchy integral, which is the uniformly bounded solution to a scalar Riemann-Hilbert problem,...

In this paper we study the asymptotic behavior of a family of polynomials which are orthogonal with respect to an exponential weight on certain contours of the complex plane. The zeros of these polynomials are the nodes for complex Gaussian quadrature of an oscillatory integral on the real axis with a high order stationary point, and their limit distribution is also analyzed. We show that the z...

In this article we discuss teachers’ perceptions and experiences of a collaborative case study to adapt literacy approach originally designed for an Aotearoa New Zealand English-medium context. The was adapted meet the needs learners in school offering differing levels bilingual education. Our collaboration included facilitating researcher, supported by two researchers at University (of Ngāi Ta...

In this paper a new method for finding the solution of Fredholm integral equation based on hybrid neural networks have presented. The proposed neural net can get a real input vector and calculates its corresponding output vector. Next a learning algorithm based on the gradient descent method has been defined for adjusting the connection weights. Eventually, we have showed this method in compari...