Howson's Property for Semidirect Products of Semilattices by Groups

An inverse semigroup S is a Howson inverse semigroup if the intersection of finitely generated inverse subsemigroups of S is finitely generated. Given a locally finite action θ of a group G on a semilattice E, it is proved that E*_θG is a Howson inverse semigroup if and only if G is a Howson group. It is also shown that this equivalence fails for arbitrary actions.     

Classroom notes: A geometric method for the derivation of a special case of an F-distribution

The concept of stereographic projection from a circle to one of its tangent lines is applied in obtaining an F-distribution with degrees of freedom 1 and 3. The derivation brings out clearly the relationship between circular and non-circular distributions.     

A topological lower bound for the circular chromatic number of Schrijver graphs

In this paper, we prove that the Kneser graphs defined on a ground set of n elements, where n is even, have their circular chromatic numbers equal to their chromatic numbers. © 2005 Wiley Periodicals, Inc. J Graph Theory 49: 257–261, 2005     

A new nonlocal model for the restoration of textured images

In this paper, we focus on the mathematical and numerical study of a new nonlocal reaction-diffusion system for image denoising. This model is motivated by involving the decomposition approach of $H^{-1}$ norm suggested by Meyer [25] which is more appropriate to represent the oscillatory patterns and small details in the textured image. Based on Schaeffer''s fixed point theorem, we prove the existence and uniqueness of solution of the proposed model. To illustrate the efficiency and effectiveness of our model, we test the denoising experimental results as well we compare with some existing models in the literature.     

Homoclinic Solutions for A Class of Second Order Neutral Functional Differential Systems

By means of an extension of Mawhin's continuation theorem and some analysis methods, the existence of a set with 2kT-periodic solutions for a class of second order neutral functional differential systems is studied, and then the homoclinic solutions are obtained as the limit points of a certain subsequence of the above set.     

A verified method for bounding clusters of zeros of analytic functions

In this paper, we propose a verified method for bounding clusters of zeros of analytic functions. Our method gives a disk that contains a cluster of m   zeros of an analytic function f(z)$f(z)$. Complex circular arithmetic is used to perform a validated computation of n  -degree Taylor polynomial p(z)$p(z)$ of f(z)$f(z)$. Some well known formulae for bounding zeros of a polynomial are used to compute a disk containing a cluster of zeros of p(z)$p(z)$. A validated computation of an upper bound for Taylor remainder series of f(z)$f(z)$ and a lower bound of p(z)$p(z)$ on a circle are performed. Based on these results, Rouché's theorem is used to verify that the disk contains the cluster of zeros of f(z)$f(z)$. This method is efficient in computation of the initial disk of a method for finding validated polynomial factor of an analytic function. Numerical examples are presented to illustrate the efficiency of the proposed method.     

A regularity result for a minimum problem in orlicz-sobolev spaces with applications in the study of the dirichlet problem for the operator of hencky-nadai theory

The existence and uniqueness of the solution to the problem of minimum for functionals generated by N- functions are obtained in Orlicz-Sobolev spaces. Applications for some functionals dealing with Hencky theory are given.     

Optimal prediction of the ultimate maximum of Brownian motion

At time 0 start to observe a Brownian path. Based upon the information, which is continuously updated through the observation of the path, a stopping time is determined such that the path is as close as possible to its unknown ultimate maximum over a finite time interval. The closeness is measured by a q-mean or by a probability distance. This can be formulated as an optimal stopping problem. The method of proof relies upon a representation of a conditional expectation of the gain process and the principle of smooth fit (at a single point).     

A smoothing Newton's method for the construction of a damped vibrating system from noisy test eigendata

In this paper we consider an inverse problem for a damped vibration system from the noisy measured eigendata, where the mass, damping, and stiffness matrices are all symmetric positive‐definite matrices with the mass matrix being diagonal and the damping and stiffness matrices being tridiagonal. To take into consideration the noise in the data, the problem is formulated as a convex optimization problem involving quadratic constraints on the unknown mass, damping, and stiffness parameters. Then we propose a smoothing Newton‐type algorithm for the optimization problem, which improves a pre‐existing estimate of a solution to the inverse problem. We show that the proposed method converges both globally and quadratically. Numerical examples are also given to demonstrate the efficiency of our method. Copyright © 2008 John Wiley & Sons, Ltd.     

Cochran's statistical theorem for outer inverses of matrices and matrix quadratic forms

We extend the matrix version of Cochran's statistical theorem to outer inverses of a matrix. As applications, we investigate the Wishartness and independence of matrix quadratic forms for Kronecker product covariance structures.