Asymptotic behaviour of Verblunsky coefficients

Let , ζh≠ζk, h≠k and |ζj|=1, j=1,…,m, and consider the polynomials orthogonal with respect to , , where μ is a finite positive Borel measure on the unit circle with infinite points in its support, such that the reciprocal of its Szeg? function has an analytic extension beyond |z|<1. In this paper we deduce the asymptotic behaviour of their Verblunsky coefficients. By means of this result, an asymptotic representation for these polynomials inside the unit circle is also obtained.     

RECONDITIONED SPECTRAL PROJECTED GRADIENT METHOD ON CONVEX SETS

The spectral gradient method has proved to be effective for solving large-scale uncon-strained optimization problems.It has been recently extended and combined with theprojected gradient method for solving optimization problems on convex sets.This combi-nation includes the use of nonmonotone line search techniques to preserve the fast localconvergence.In this work we further extend the spectral choice of steplength to accept pre-conditioned directions when a good preconditioner is available.We present an algorithmthat combines the spectral projected gradient method with preconditioning strategies toincrease the local speed of convergence while keeping the global properties.We discussimplementation details for solving large-scale problems.     

One-dimensional center-based l 1-clustering method

Motivated by the method for solving center-based Least Squares—clustering problem (Kogan in Introduction to clustering large and high-dimensional data, Cambridge University Press, 2007; Teboulle in J Mach Learn Res 8:65–102, 2007) we construct a very efficient iterative process for solving a one-dimensional center-based l ₁—clustering problem, on the basis of which it is possible to determine the optimal partition. We analyze the basic properties and convergence of our iterative process, which converges to a stationary point of the corresponding objective function for each choice of the initial approximation. Given is also a corresponding algorithm, which in only few steps gives a stationary point and the corresponding partition. The method is illustrated and visualized on the example of looking for an optimal partition with two clusters, where we check all stationary points of the corresponding minimizing functional. Also, the method is tested on the basis of large numbers of data points and clusters and compared with the method for solving the center-based Least Squares—clustering problem described in Kogan (2007) and Teboulle (2007).     

2H(e,e(')p)n reaction at high recoil momenta

The 2H(e,e(')p)n cross section was measured in Hall A of the Thomas Jefferson National Accelerator Facility near the top of the quasielastic peak (x(Bj)=0.964) at a four-momentum transfer squared, Q(2)=0.665 (GeV/c) (2) (omega=0.368 GeV, W=2.057 GeV), and for recoil momenta up to 550 MeV/c. The measured cross section deviates by 1-2sigma from a state-of-the-art calculation at low recoil momenta. At high recoil momenta the cross section is well described by the same calculation; however, in this region, final-state interactions and interaction currents are predicted to be large, and alternative choices of nucleon-nucleon potential and nucleon current operator may result in significant spread in the calculations.     

Using AI methodologies in mathematical modeling of production systems

This research was supported in part by Sandia National Laboratories Grant No. 56-4617. Sandia is managed by AT&;T Technologies for the U.S. Department of Energy.     

Rearrangements of summable numerical series

In this paper we obtain the necessary and sufficient conditions on permutations of numerical series which transformed any B-summable series into an A-summable series, where A and B are matrices satisfying certain conditions.Translated from Matematicheskie Zametki, Vol. 13, No. 1, pp. 13–20, January, 1973.     

Approximate energy expression in the calculation of photoelectron transition energies

The possibilities of using approximate self-consistent field energy functionals to reduce computation required in calculating photoelectron transition energies is examined. Numerical results for the H₂O molecule indicate that this is possible without unacceptable deterioration in accuracy of results in favourable cases.