We survey some recent developments in the theory of orthogonal polynomials defined by differential equations. The key finding is that there exist orthogonal polynomials defined by 2nd order differential equations that fall outside the classical families of Jacobi, Laguerre, and Hermite polynomials. Unlike the classical families, these new examples, called exceptional orthogonal polynomials, fea...

In this paper we study a new probability associated with any given belief function b, i.e. the orthogonal projection π[b] of b onto the probability simplex P. We provide an interpretation of π[b] in terms of a redistribution process in which the mass of each focal element is equally distributed among its subsets, establishing an interesting analogy with the pignistic transformation. We prove th...

This paper presents an improved local ternary pattern (LTP) for automatic target recognition (ATR) in infrared imagery. Firstly, a robust LTP (RLTP) scheme is proposed to overcome the limitation of the original LTP for achieving the invariance with respect to the illumination transformation. Then, a soft concave-convex partition (SCCP) is introduced to add some flexibility to the original conca...

Up to orthogonal transformation, a solid closed convex cone K in the Euclidean space Rn+1 is the epigraph of a nonnegative sublinear function f : Rn → R. This work explores the link between the geometric properties of K and the analytic properties of f . Mathematics Subject Classification: 46B10, 46B20, 52A41.

The construction of boundary filters without DC leakage for two-channel paraunitary FIR filter banks is considered. The design procedure is based on orthogonal boundary filters which are optimal in a weighted mean square error sense in the Fourier domain and on Householder transformation of boundary filter matrices. Simulation results are presented for boundary filters based on minimum-phase Da...

A new update algorithm for space–time equalization of wireless time-division multiple access signals is presented. The method is based on a modified QR factorization that reduces the computational complexity of the traditional QR-decomposition based recursive least squares method and maintains numerical stability. Square roots operations are avoided due to the use of an approximately orthogonal...

In this paper the authors develop a new algorithm to solve the standard discrete-time algebraic Riccati equation by using a skewHamiltonian transformation and the square-root method. The algorithm is structure-preserving and efficient because the Hamiltonian structure is fully exploited and only orthogonal transformations are used. The efficiency and stability of the algorithm are analyzed. Num...

One more model of a q-harmonic oscillator based on the q-orthogonal polynomials of Al-Salam and Carlitz is discussed. The explicit form of q-creation and q-annihilation operators, q-coherent states and an analog of the Fourier transformation are established. A connection of the kernel of this transform with a family of self-dual biorthogonal rational functions is observed.

The bilinear equations of the N -component KP and BKP hierarchies and a corresponding extended Miwa transformation allow us to generate quadrilateral and circular lattices from conjugate and orthogonal nets, respectively. The main geometrical objects are expressed in terms of Baker functions. ∗Partially supported by CICYT: proyecto PB95–0401 1

We present a direct algorithm for computing an orthogonal similarity transformation which interchanges neighboring diagonal blocks in a matrix in real Schur form. The algorithm does not require the solution of the associated Sylvester equation. Numerical tests suggest the backward stability of the scheme.