ABSTRACT: Knop and Sahi introduced a family of non-homogeneous and nonsymmetric polynomials, Gα(x; q, t), indexed by compositions. An explicit formula for the bivariate Knop-Sahi polynomials reveals a connection between these polynomials and q-special functions. In particular, relations among the q-ultraspherical polynomials of Askey and Ismail, the two variable symmetric and non-symmetric Macd...

We begin by defining tensor products of vector spaces over a field and then we investigate some basic properties of these tensors, in particular the existence of bases and duality. After this, we investigate special kinds of tensors, namely, symmetric tensors and skew-symmetric tensors. Tensor products of modules over a commutative ring with identity will be discussed very briefly. They show up...

The alternating direction method of multipliers (ADMM) is an application of the Douglas-Rachford splitting method; and the symmetric version of ADMM which updates the Lagrange multiplier twice at each iteration is an application of the Peaceman-Rachford splitting method. Sometimes the symmetric ADMM works empirically; but theoretically its convergence is not guaranteed. It was recently found th...

We investigate complex PT-symmetric potentials, associated with quasi-exactly solvable non-hermitian models involving polynomials and a class of rational functions. We also look for special solutions of intertwining relations of SUSY Quantum Mechanics providing a partnership between a real and a complex PT-symmetric potential of the kind mentioned above. We investigate conditions sufficient to ...

The dynamic output feedback decentralized H∞ control and the reliability of the designed system (the maximal number of control-channel outages when the performance is still acceptable) is studied for symmetric composite systems. It is shown that the decentralized H∞ control problem can be simplified to a simultaneous H∞ control problem for two modified subsystems. A design method based on the s...

Schützenberger’s theorem for the ordinary RSK correspondence naturally extends to Chen et. al’s correspondence for matchings and partitions. Thus the counting of bilaterally symmetric k-noncrossing partitions naturally arises as an analogue for involutions. In obtaining the analogous result for 3-noncrossing partitions, we use a different technique to develop a MAPLE package for 2-dimensional v...

A general method is given in order to guarantee at least one nontrivial solution, as well as infinitely many radially symmetric solutions, for an abstract class of hemivariational inequalities. This abstract class contains some special cases studied by many authors. We remark that, differently from the classical literature, in the proofs we use the Cerami compactness condition and the principle...

Research has focused on increasing the treatment integrity of school-based interventions by utilizing performance feedback. The purpose of this study was to extend this literature by increasing special education teachers' treatment integrity for implementing antecedent and consequence procedures in an ongoing behavior support plan. A multiple baseline across teacher-student dyads (for two class...

Abstract Symmetric operators have benefited in different fields not only mathematics but also other sciences. They appeared the studies of boundary value problems and spectral theory. In this note, we present a new symmetric differential operator associated with special class meromorphically multivalent functions punctured unit disk. This study explores some its geometric properties. We conside...

We construct a kernel density estimator on symmetric spaces of non-compact type and establish an upper bound for its convergence rate, analogous to the minimax rate classical estimators Euclidean space. Symmetric include hyperboloids constant curvature −1 positive definite matrices. This paper obtains simplified formula in special case when space is normal distributions, 2-dimensional hyperbolo...