Szeg˝ o's procedure to connect orthogonal polynomials on the unit circle and orthogonal polynomials on [−1, 1] is generalized to nonsymmetric measures. It generates the so-called semi-orthogonal functions on the linear space of Laurent polynomials Λ, and leads to a new orthogonality structure in the module Λ × Λ. This structure can be interpreted in terms of a 2 × 2 matrix measure on [−1, 1], a...

Electric Dipole f -values have been obtained between the seven 3d J=4 even states, and all the 3d 4p J=3,4,5 odd states. Seventy two of these exceed 0.01 and are published here. The average agreement between the length and velocity gauges is 1.8%. Due to the small size of the f -values, non-orthogonality effects may be significant in shell jump cases, as we have here. Many of the odd levels are...

Sufficient conditions ensuring weak lower semi-continuity of the optimal value function are presented. To this end, refined inner semi-continuity properties of set-valued maps are introduced which meet the needs of the weak topology in Banach spaces. The results are applied to prove the existence of solutions in various worst-case robust optimal control problems governed by semilinear elliptic ...

Various concepts of orthogonality on the real line are reviewed that arise in connection with quadrature rules. Orthogonality relative to a positive measure and Gauss-type quadrature rules are classical. More recent types of orthogonality include orthogonality relative to a sign-variable measure, which arises in connection with Gauss-Kronrod quadrature, and power (or implicit) orthogonality enc...

The zeros of semi-orthogonal functions with respect to a probability measure µ supported on the unit circle can be applied to obtain Szeg˝ o quadrature formulas. The discrete measures generated by these formulas weakly converge to the orthogonality measure µ. In this paper we construct families of semi-orthogonal functions with interlacing zeros, and give a representation of the support of µ in...

In the forward link of WCDMA systems, the multipath propagation channel destroys the orthogonality of the spreading codes and therefore causes multi-user interference (MUI). In this paper, we propose new training-based and semi-blind space-time chip equalizer receivers for the forward link of WCDMA systems with a continuous code-multiplexed pilot. Both Least-Squares (LS) algorithms for block pr...

In this paper we introduce an algebraic theory of classical matrix orthogonal polynomials as a particular case of the semi-classical ones, defined by a distributional equation for the corresponding orthogonality functional. This leads to several properties that characterize the classical matrix families, among them, a structure relation and a second order differo-differential equation. In the p...

We consider the weak analogues of certain strong stochastic numerical schemes considered in [10], namely a Adams-Bashforth scheme and a semi-implicit leapfrog scheme. We show that the weak version of the Adams-Bashforth scheme converges weakly with order 2, and the weak version of the semi-implicit leapfrog scheme converges weakly with order 1. We also note that the weak schemes are computation...

In this paper, the concept of semi-compatibility and weak compatibility in Fuzzy metric space has been applied to prove a common fixed point theorem. We improve the result of Kumar and Pant [14] by dropping the condition of continuity of the mapping and using semi-compatibility and weak compatibility of the mappings in place of compatibility.