A fundamental limitation exists in the achievable tracking performance of systems in which the plant has a single input and two outputs (SITO). For a SITO plant in a unity feedback configuration, we consider the optimal reference tracking controller in the £2 sense. The results are compared to the limiting cost of cheap control problems for SITO plants. AMS subject classification. 93C35.

Properties of the q-ultraspherical polynomials for q being a primitive root of unity are derived using a formalism of the soq(3) algebra. The orthogonality condition for these polynomials provides a new class of trigonometric identities representing discrete finite-dimensional analogs of q-beta integrals of Ramanujan. Mathematics Subject Classifications (1991). 17B37, 33D80

In spite of many efforts over the past 50 years, the irreducible representations of the Lie algebra of a simple algebraic group over a field of prime characteristic are poorly understood. Recent work on quantum groups at a root of unity has provided new impetus for the subject. This article surveys what has been done and what remains to be done.

We study properties of the Drazin index of regular elements in a ring with a unity 1. We give expressions for generalized inverses of 1−ba in terms of generalized inverses of 1−ab. In our development we prove that the Drazin index of 1 − ba is equal to the Drazin index of 1 − ab. 2000 Mathematics subject classification. primary 15A09; secondary 16U99.

A class of random discrete distributions P is introduced by means of a recursive splitting of unity. Assuming supercritical branching, we show that for partitions induced by sampling from such P a power growth of the number of blocks is typical. Some known and some new partition structures appear when P is induced by a Dirichlet splitting. AMS 2000 subject classifications: Primary 60G09, 60C05

Parataxis is the main grammatical feature of Chinese sentences while hypotaxis is the main grammatical feature of English. Similarly, Chinese classical paintings stress on the psychological harmony of subject-object unity and Western classical paintings on extrinsic form. It is found that the aesthetic thinking of classical painting is reflected in English and Chinese syntactic structure.

Watermark recovery is often based on cross-correlating images with pseudo-noise sequences, as access to un-watermarked originals is not required. Successful recovery of these watermarks is determined by the (periodic or aperiodic) sequence autoand cross-correlation properties. This paper presents several methods of extending the dimensionality of 1D sequences in order to utilise the advantages ...

The term probabilistic constrained programming means the same as chance constrained programming, i.e., optimization of a function subject to certain conditions where at least one is formulated so that a condition, involving random variables, should hold with a prescribed probability. The probability is usually not prescribed exactly but a lower bound is given instead which is in practice near u...

We define a notion of unitarizability for weight modules over a generalized Weyl algebra (of rank one, with commutative coeffiecient ring R), which is assumed to carry an involution of the form X∗ = Y , R∗ ⊆ R. We prove that a weight module V is unitarizable iff it is isomorphic to its finitistic dual V . Using the classification of weight modules by Drozd, Guzner and Ovsienko, we obtain necess...