On Linear Differential Equations Involving a Para-Grassmann Variable

As a first step towards a theory of differential equations involving para-Grassmann variables the linear equations with constant coefficients are discussed and solutions for equations of low order are given explicitly. A connection to n-generalized Fibonacci numbers is established. Several other classes of differential equations (systems of first order, equations with variable coefficients, nonlinear equations) are also considered and the analogies or differences to the usual (''bosonic'') differential equations discussed

Motzkin numbers of higher rank: Generating function and explicit expression

The generating function and an explicit expression is derived for the (colored) Motzkin numbers of higher rank introduced recently. Considering the special case of rank one yields the corresponding results for the conventional colored Motzkin numbers for which in addition a recursion relation is given

The vertex PI index and Szeged index of bridge graphs

AbstractRecently the vertex Padmakar–Ivan (PIv) index of a graph G was introduced as the sum over all edges e=uv of G of the number of vertices which are not equidistant to the vertices u and v. In this paper the vertex PI index and Szeged index of bridge graphs are determined. Using these formulas, the vertex PI indices and Szeged indices of several graphs are computed

A generalization of boson normal ordering

In this paper we define generalizations of boson normal ordering. These are based on the number of contractions whose vertices are next to each other in the linear representation of the boson operator function. Our main motivation is to shed further light onto the combinatorics arising from algebraic and Fock space properties of boson operators.Comment: 10 pages, 1 (LaTeX) figur

Wick's theorem for q-deformed boson operators

In this paper combinatorial aspects of normal ordering arbitrary words in the creation and annihilation operators of the q-deformed boson are discussed. In particular, it is shown how by introducing appropriate q-weights for the associated ``Feynman diagrams'' the normally ordered form of a general expression in the creation and annihilation operators can be written as a sum over all q-weighted Feynman diagrams, representing Wick's theorem in the present context.Comment: 9 page

November 28, 1968

https://scholarlycommons.obu.edu/arbn_65-69/1091/thumbnail.jp

Generalized Heisenberg algebras and k-generalized Fibonacci numbers

It is shown how some of the recent results of de Souza et al. [1] can be generalized to describe Hamiltonians whose eigenvalues are given as k-generalized Fibonacci numbers. Here k is an arbitrary integer and the cases considered by de Souza et al. corespond to k=2.Comment: 8 page

PaaSword: A Data Privacy and Context-aware Security Framework for Developing Secure Cloud Applications - Technical and Scientific Contributions

Most industries worldwide have entered a period of reaping the benefits and opportunities cloud offers. At the same time, many efforts are made to address engineering challenges for the secure development of cloud systems and software.With the majority of software engineering projects today relying on the cloud, the task to structure end-to-end secure-by-design cloud systems becomes challenging but at the same time mandatory. The PaaSword project has been commissioned to address security and data privacy in a holistic way by proposing a context-aware security-by-design framework to support software developers in constructing secure applications for the cloud. This chapter presents an overview of the PaaSword project results, including the scientific achievements as well as the description of the technical solution. The benefits offered by the framework are validated through two pilot implementations and conclusions are drawn based on the future research challenges which are discussed in a research agenda