In [L1] the author introduced the canonical basis for the plus part of a quantized enveloping algebra of type A,D or E. (The same method applies for nonsimplylaced types, see [L3, 12.1].) Another approach to the canonical basis was later found in [Ka]. In [L1] we have also found that the set parametrizing the canonical basis has a natural piecewise linear structure that is, a collection of bije...

Let q ≥ 1 be an integer, S denote the unit sphere embedded in the Euclidean space Rq+1, and μq be its Lebesgue surface measure. We establish upper and lower bounds for sup f∈B p,ρ ∣∣∣∣ ∫ Sq fdμq − M ∑ k=1 wkf(xk) ∣∣∣∣ , xk ∈ S , wk ∈ R, k = 1, · · · ,M, where B p,ρ is the unit ball of a suitable Besov space on the sphere. The upper bounds are obtained for choices of xk and wk that admit exact q...

This paper is a continuation of our previous research on quadratic harnesses, that is, processes with linear regressions and quadratic conditional variances. Our main result is a construction of a Markov process from given orthogonal and martingale polynomials. The construction uses a two-parameter extension of the Al-Salam–Chihara polynomials and a relation between these polynomials for differ...

J. Morais has recently introduced certain complete orthogonal sets of monogenic polynomials over 3D prolate spheroids with remarkable properties. The underlying functions take on either values in the reduced and full quaternions (identified, respectively, with R3 and R4), and are generally assumed to be nullsolutions of the well known Riesz and Moisil-Théodoresco systems in R3. In continuation ...

Introduction Rational Chebyshev approximation to reciprocals of certain entire functions by reciprocals of polynomials on the positive real axis has recently attracted the attention of many mathematicians . By developing certain new methods of approach we successfully attacked ([3]-[6]) some of the related problems . This paper is a continuation of our earlier papers ([3]-[6] ) . The results of...

Three-dimensional (3D) limit analysis of stability of slopes is presented. Such analyses are not common because of the difficulties in constructing three-dimensional mechanisms of failure in frictional soils. While examples of 3D translational failure patterns are known, no admissible rotational mechanisms for frictional soils have been described in the literature. A class of admissible rotatio...

Previous studies demonstrated that brain signals encode information about specific features of simple auditory stimuli or of general aspects of natural auditory stimuli. How brain signals represent the time course of specific features in natural auditory stimuli is not well understood. In this study, we show in eight human subjects that signals recorded from the surface of the brain (electrocor...

In this paper, variety means a class of similar algebras—i.e., models of one firstorder language without relation symbols—which is defined by the satisfaction of some fixed sets of equations. A variety is locally finite if all of its finitely generated members are finite. Following J. Berman and P. Idziak [2], the G-spectrum, or generative complexity, of a locally finite variety C, is the funct...