Given a positive Borel measure whose support is an infinite set of points in the real line the problem of the construction of an orthogonal polynomial sequence (OPS) with respect to that measure is known as direct problem. An inverse problem (IP) consists in finding the orthogonality measure when only some information is known about a given OPS (e.g., via a three-term recurrence relation, or vi...

To achieve interoperability, modern information systems and e-commerce applications use mappings to translate data from one representation to another. In dynamic environments like the Web, data sources may change not only their data but also their schemas, their semantics, and their query capabilities. Such changes must be reflected in the mappings. Mappings left inconsistent by a schema change...

An XML-to-relational mapping scheme consists of a procedure for shredding XML documents into relational databases, a procedure for publishing databases back as documents, and a set of constraints the databases must satisfy. In previous work, we discussed two notions of information preservation for mapping schemes: losslessness, which guarantees the complete reconstruction of a document from a d...

We develop a combinatorial model of the associated Hermite polynomials and their moments, and prove their orthogonality with a sign-reversing involution. We find combinatorial interpretations of the moments as complete matchings, connected complete matchings, oscillating tableaux, and rooted maps and show weight-preserving bijections between these objects. Several identities, linearization form...

A trellis coded 4-ary Pulse Amplitude Modulation (4-PAM) is presented, where the encoding algorith derived from Distance Preserving Mapping (DPM) algorithm. In this work, we modify DPM algorithm for 4-PAM and obtain a new construction mapping binary sequences to permutation sequences, are obtained by permuting symbols of constellation. The resulting codebook formed way termed mappings. We also ...

Many theoretical problems in quantum technology can be formulated and addressed as constrained optimization problems. The most common mechanical constraints such as, e.g., orthogonality of isometric unitary matrices, CPTP property channels, conditions on density seen quotient or embedded Riemannian manifolds. This allows to use techniques for solving quantum-mechanical In the present work, we i...

We propose discrete mappings of second order that have a discrete analogue of Lyapunov function. The mappings are extensions of the integrable Quispel-RobertsThompson (QRT) mapping, and a discrete Lyapunov function of the mappings is identical to an explicit conserved quantity of the QRT mapping. Moreover we can obtain a differential and an ultradiscrete limit of the mappings preserving the exi...