We study several related problems on polynomials with integer coefficients. This includes the integer Chebyshev problem, and the Schur problems on means of algebraic numbers. We also discuss interesting applications to the approximation by polynomials with integer coefficients, and to the growth of coefficients for polynomials with roots located in prescribed sets. The distribution of zeros for...

We give examples of infinitely renormalizable quadratic polynomials Fc : z 7→ z 2 + c with stationary combinatorics whose Julia sets have Hausdorff dimension arbitrary close to 1. The combinatorics of the renormalization involved is close to the Chebyshev one. The argument is based upon a new tool, a “Recursive Quadratic Estimate” for the Poincaré series of an infinitely renormalizable map. Sto...

We give examples of infinitely renormalizable quadratic polynomials Fc : z 7→ z + c with stationary combinatorics whose Julia sets have Hausdorff dimension arbitrary close to 1. The combinatorics of the renormalization involved is close to the Chebyshev one. The argument is based upon a new tool, a “Recursive Quadratic Estimate” for the Poincaré series of an infinitely renormalizable map. Stony...

In this paper, a numerical method for solving the Fredholm and Volterra integral equations is presented. The method is based upon the second Chebyshev wavelet approximation. The properties of the second Chebyshev wavelet are first presented and then operational matrix of integration of the second Chebyshev wavelets basis and product operation matrix of it are derived. The second Chebyshev wavel...

in this study, the problem of determining an optimal trajectory of a nonlinear injection into orbit problem with minimum time was investigated. the method was based on orthogonal polynomial approximation. this method consists of reducing the optimal control problem to a system of algebraic equations by expanding the state and control vector as chebyshev or legendre polynomials with undetermined...

Data clustering is one of the important data mining methods. It is a process of finding classes of a data set with most similarity in the same class and most dissimilarity between different classes. The well known hard clustering algorithm (K -means) and Fuzzy clustering algorithm (FCM) are mostly based on Euclidean distance measure. In this paper, a comparative study of these algorithms with d...

the purpose of this study is to present an approximate numerical method for solving high order linear fredholm-volterra integro-differential equations in terms of rational chebyshev functions under the mixed conditions. the method is based on the approximation by the truncated rational chebyshev series. finally, the effectiveness of the method is illustrated in several numerical examples. the p...

We consider the problem of estimating a vector z in the regression model b = Az+w, where w is an unknown but bounded noise. As in many regularization schemes, we assume that an upper bound on the norm of z is available. To estimate z we propose a relaxation of the Chebyshev center, which is the vector that minimizes the worst-case estimation error over all feasible vectors z. Relying on recent ...