Generalization of the fractional Poisson distribution

A generalization of the Poisson distribution based on the generalized Mittag-Leffler function $E_{alpha, beta}(lambda)$ is proposed and the raw moments are calculated algebraically in terms of Bell polynomials. It is demonstrated, that the proposed distribution function contains the standard fractional Poisson distribution as a subset. A possible interpretation of the additional parameter $beta$ is suggested.

A fractal approach to the dark silicon problem: a comparison of 3D computer architectures -- standard slices versus fractal Menger sponge geometry

The dark silicon problem, which limits the power-growth of future computer generations, is interpreted as a heat energy transport problem when increasing the energy emitting surface area within a given volume. A comparison of two 3D-configuration models, namely a standard slicing and a fractal surface generation within the Menger sponge geometry is presented. It is shown, that for iteration orders $n>3$ the fractal model shows increasingly better thermal behavior. As a consequence cooling problems may be minimized by using a fractal architecture. Therefore the Menger sponge geometry is a good example for fractal architectures applicable not only in computer science, but also e.g. in chemistry when building chemical reactors, optimizing catalytic processes or in sensor construction technology building highly effective sensors for toxic gases or water analysis.

Towards a geometric interpretation of generalized fractional integrals - Erdelyi-Kober type integrals on $R^N$ as an example

A family of generalized Erdelyi-Kober type fractional integrals is interpreted geometrically as a distortion of the rotationally invariant integral kernel of the Riesz fractional integral in terms of generalized Cassini ovaloids on $R^N$. Based on this geometric view, several extensions are discussed.

Uniqueness of the fractional derivative definition

For the Riesz fractional derivative besides the well known integral representation two new differential representations are presented, which emphasize the local aspects of a fractional derivative. The consequences for a valid solution of the fractional Schroedinger equation are discussed.

Curvature interaction in collective space

For the Riemannian space, built from the collective coordinates used within nuclear models, an additional interaction with the metric is investigated, using the collective equivalent to Einsteins curvature scalar. The coupling strength is determined using a fit with the AME2003 ground state masses. An extended finite-range droplet model including curvature is introduced, which generates significant improvements for light nuclei and nuclei in the trans-fermium region.