Economically study regarding modernizing of the final working of the car radiators through implementation of an articulated robot in a flexible manufacturing cell

In this paper the authors purpose the conception and modelling of a possible application in a circular flexible manufacturing cell. This flexible cell is composed from five manufacturing points for realizing the final technological itinerary of a type of radiator. This flexible manufacturing cell is served by an industrial articulated robot, which possess in his cinematic chain three degrees of freedom, type RRT. In virtue of real values of the functional parameters which are input data in the analysis of the flexible manufacturing cell, had been dignify the cost of the flexible manufacturing cell, determining the value of the included industrial robot in the system and the value of the entire flexible cell where the robot realize the manipulating process of the radiators. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Iterative Methods for Pseudomonotone Variational Inequalities and Fixed-Point Problems

In this paper, we introduce an iterative scheme for finding a common element of the set of solution of a pseudomonotone, Lipschitz-continuous variational inequality problem and the set of common fixed points of an infinite family of nonexpansive mappings. The proposed iterative method combines two well-known schemes: extragradient and approximate proximal methods. We derive some necessary and sufficient conditions for strong convergence of the sequences generated by the proposed scheme.     

Couplings of Brownian Motions of Deterministic Distance in Model Spaces of Constant Curvature

We consider the model space \(\mathbb {M}^{n}_{K}\) of constant curvature K and dimension \(n\ge 1\) (Euclidean space for \(K=0\), sphere for \(K>0\) and hyperbolic space for \(K<0\)), and we show that given a function \(\rho :[0,\infty )\rightarrow [0, \infty )\) with \(\rho (0)=\mathrm {dist}(x,y)\) there exists a coadapted coupling (X(t), Y(t)) of Brownian motions on \(\mathbb {M}^{n}_{K}\) starting at (x, y) such that \(\rho (t)=\mathrm {dist}(X(t),Y(t))\) for every \(t\ge 0\) if and only if \(\rho \) is continuous and satisfies for almost every \(t\ge 0\) the differential inequality

$$\begin{aligned} -(n-1)\sqrt{K}\tan \left( \tfrac{\sqrt{K}\rho (t)}{2}\right) \le \rho '(t)\le -(n-1)\sqrt{K}\tan \left( \tfrac{\sqrt{K}\rho (t)}{2}\right) +\tfrac{2(n-1)\sqrt{K}}{\sin (\sqrt{K}\rho (t))}. \end{aligned}$$

In other words, we characterize all coadapted couplings of Brownian motions on the model space \(\mathbb {M}^{n}_{K}\) for which the distance between the processes is deterministic. In addition, the construction of the coupling is explicit for every choice of \(\rho \) satisfying the above hypotheses.

     

Compact Hankel Forms on Planar Domains

A Hankel form on a Hilbert function space is a bounded, symmetric, bilinear form [., .] satisfying [fx, y] = [x, fy] for a class of multipliers f. We prove analogs of Weyl–Horn and Ky Fan inequalities for compact Hankel forms, and apply them to estimate the related eigenvalues, both for Hardy–Smirnov and Bergman spaces norms associated to multiply connected planar domains. In the case of the unit disk, we investigate the asymptotic of some measures constructed by eigenfunctions of Hankel operators with certain Markov functions as symbols. Submitted: May 2, 2008. Accepted: June 28, 2008.     

Continuity of the first eigenvalue for a family of degenerate eigenvalue problems

For each \({\alpha\in[0,2)}\) we consider the eigenvalue problem \({-{\rm div}(|x|^\alpha \nabla u)=\lambda u}\) in a bounded domain \({\Omega\subset \mathbb{R}^N}\) (\({N\geq 2}\)) with smooth boundary and \({0\in \Omega}\) subject to the homogeneous Dirichlet boundary condition. Denote by \({\lambda_1(\alpha)}\) the first eigenvalue of this problem. Using \({\Gamma}\)-convergence arguments we prove the continuity of the function \({\lambda_1}\) with respect to \({\alpha}\) on the interval \({[0,2)}\).     

Irreducibility criteria for compositions of polynomials with integer coefficients

We provide irreducibility criteria for some classes of compositions of polynomials with integer coefficients of the form \(F\circ G\), with F being a quadratic irreducible polynomial and G a polynomial of arbitrary degree.     

New Rates of Convergence for the Iterates of Some Positive Linear Operators

In this paper, we give quantitative results for the convergence of the iterates of some positive linear operators which preserve the functions \(e_0\) and \(e_1\), respectively, \(e_0\) and \(e_2\). We obtain estimates in terms of moduli of smoothness and we improve some previous results. We give examples for the q-Bernstein, the q-Bernstein-Durrmeyer, the q-Stancu, the q-Meyer-Konig–Zeller, the King type of the q-Bernstein and the King type of the q-genuine-Bernstein-Durrmeyer operators. We observe that some q-operators (\(0<q<1\)) provide better convergence for the iterates than the corresponding classical operators (\(q=1\)).