Some cubic birth and death processes and their related orthogonal polynomials

The orthogonal polynomials with recurrence relation (\la\_n+\mu\_n-z) F\_n(z)=\mu\_{n+1} F\_{n+1}(z)+\la\_{n-1} F\_{n-1}(z) with two kinds of cubic transition rates \la\_n and $\mu\_n,$ corresponding to indeterminate Stieltjes moment problems, are analyzed. We derive generating functions for these two classes of polynomials, which enable us to compute their Nevanlinna matrices. We discuss the asymptotics of the Nevanlinna matrices in the complex plane.Comment: latex2e, 17 page

String Branchings on Complex Tori and Algebraic Representations of Generalized Krichever-Novikov Algebras

The propagation differential for bosonic strings on a complex torus with three symmetric punctures is investigated. We study deformation aspects between two point and three point differentials as well as the behaviour of the corresponding Krichever-Novikov algebras. The structure constants are calculated and from this we derive a central extension of the Krichever-Novikov algebras by means of b-c systems. The defining cocycle for this central extension deforms to the well known Virasoro cocycle for certain kinds of degenerations of the torus. AMS subject classification (1991): 17B66, 17B90, 14H52, 30F30, 81T40Comment: 11 pages, amste

Difference-differential operators for basic adaptive discretizations and their central function systems

The concept of inherited orthogonality is motivated and an optimality statement for it is derived. Basic adaptive discretizations are introduced. Various properties of difference operators which are directly related to basic adaptive discretizations are looked at. A Lie-algebraic concept for obtaining basic adaptive discretizations is explored. Some of the underlying moment problems of basic difference equations are investigated in greater detail

Differential representations of dynamical oscillator symmetries in discrete Hilbert space

As a very important example for dynamical symmetries in the context of q-generalized quantum mechanics the algebra aa†−q−2a†a=1 is investigated. It represents the oscillator symmetry SUq(1,1) and is regarded as a commutation phenomenon of the q-Heisenberg algebra which provides a discrete spectrum of momentum and space, i.e., a discrete Hilbert space structure. Generalized q-Hermite functions and systems of creation and annihilation operators are derived. The classical limit q→1 is investigated. Finally the SUq(1,1) algebra is represented by the dynamical variables of the q-Heisenberg algebra

Oscillatory Difference Equations and Moment Problems

Abstract In this paper, we first consider some new oscillatory results with respect to the discrete Hermite polynomials of type I, respectively, type II and the Heim-Lorek polynomials. In the second part, we investigate the oscillatory and boundedness properties of the related orthogonality measures and the functions representing them. The polynomials considered so far in this article are closely related to the concept of the Wess-Ruffing discretization.</jats:p

Männerbildung - Erkundigungen zu einem offenen Feld: über die Inklusion von Männern in und durch Bildung

Die Autoren geben in diesem Beitrag einen Überblick über den aktuellen Stand der Männerbildung

Comparing algebraic and numerical solutions of classical diffusion process equations in computational financial mathematics

We revise the interrelations between the classical Black Scholes equation, the diffusion equation and Burgers equation. Some of the algebraic properties the diffusion equation shows are elaborated and qualitatively presented. The related numerical elementary recipes are briefly elucidated in context of the diffusion equation. The quality of the approximations to the exact solutions is compared throughout the visualizations. The article mainly is based on the pedagogical style of the presentations to the Novacella Easter School 2000 on Financial Mathematics

Repeatable Oblivious Shuffling of Large Outsourced Data Blocks

As data outsourcing becomes popular, oblivious algorithms have raised extensive attentions since their control flow and data access pattern appear to be independent of the input data they compute on and thus are especially suitable for secure processing in outsourced environments. In this work, we focus on oblivious shuffling algorithms that aim to shuffle encrypted data blocks outsourced to the cloud server without disclosing the permutation of blocks to the server. Existing oblivious shuffling algorithms suffer from issues of heavy communication and client computation costs when blocks have a large size because all outsourced blocks must be downloaded to the client for shuffling or peeling off extra encryption layers. To help eliminate this void, we introduce the ``repeatable oblivious shuffling\u27\u27 notation that restricts the communication and client computation costs to be independent of the block size. We present an efficient construction of repeatable oblivious shuffling using additively homomorphic encryption schemes. The comprehensive evaluation of our construction shows its effective usability in practice for shuffling large-sized blocks