A characterization of quadratic-multiplicative mappings

In the spirit of some earlier studies of Jean Dhombres, Roman Ger and Ludwig Reich we discuss the alienation problem for quadratic and multiplicative mappings

Anomalous particle-number fluctuations in a three-dimensional interacting Bose-Einstein condensate

The particle-number fluctuations originated from collective excitations are investigated for a three-dimensional, repulsively interacting Bose-Einstein condensate (BEC) confined in a harmonic trap. The contribution due to the quantum depletion of the condensate is calculated and the explicit expression of the coefficient in the formulas denoting the particle-number fluctuations is given. The results show that the particle-number fluctuations of the condensate follow the law $\sim N^{22/15}$ and the fluctuations vanish when temperature approaches to the BEC critical temperature.Comment: RevTex, 4 page

Classification of phase transitions of finite Bose-Einstein condensates in power law traps by Fisher zeros

We present a detailed description of a classification scheme for phase transitions in finite systems based on the distribution of Fisher zeros of the canonical partition function in the complex temperature plane. We apply this scheme to finite Bose-systems in power law traps within a semi-analytic approach with a continuous one-particle density of states $\Omega(E)\sim E^{d-1}$ for different values of $d$ and to a three dimensional harmonically confined ideal Bose-gas with discrete energy levels. Our results indicate that the order of the Bose-Einstein condensation phase transition sensitively depends on the confining potential.Comment: 7 pages, 9 eps-figures, For recent information on physics of small systems see "http://www.smallsystems.de

Ulam type stability problems for alternative homomorphisms

We introduce an alternative homomorphism with respect to binary operations and investigate the Ulam type stability problem for such a mapping. The obtained results apply to Ulam type stability problems for several important functional equations.ArticleJOURNAL OF INEQUALITIES AND APPLICATIONS. 2014:228 (2014)journal articl

Number Fluctuation and the Fundamental Theorem of Arithmetic

We consider N bosons occupying a discrete set of single-particle quantum states in an isolated trap. Usually, for a given excitation energy, there are many combinations of exciting different number of particles from the ground state, resulting in a fluctuation of the ground state population. As a counter example, we take the quantum spectrum to be logarithms of the prime number sequence, and using the fundamental theorem of arithmetic, find that the ground state fluctuation vanishes exactly for all excitations. The use of the standard canonical or grand canonical ensembles, on the other hand, gives substantial number fluctuation for the ground state. This difference between the microcanonical and canonical results cannot be accounted for within the framework of equilibrium statistical mechanics.Comment: 4 pages, 4 figures. To be submitted to Phys. Rev. Let

Ceramic Microbial Fuel Cells Stack: Power generation in standard and supercapacitive mode

© 2018 The Author(s). In this work, a microbial fuel cell (MFC) stack containing 28 ceramic MFCs was tested in both standard and supercapacitive modes. The MFCs consisted of carbon veil anodes wrapped around the ceramic separator and air-breathing cathodes based on activated carbon catalyst pressed on a stainless steel mesh. The anodes and cathodes were connected in parallel. The electrolytes utilized had different solution conductivities ranging from 2.0 mScm-1 to 40.1 mScm-1, simulating diverse wastewaters. Polarization curves of MFCs showed a general enhancement in performance with the increase of the electrolyte solution conductivity. The maximum stationary power density was 3.2 mW (3.2 Wm-3) at 2.0 mScm-1 that increased to 10.6 mW (10.6 Wm-3) at the highest solution conductivity (40.1 mScm-1). For the first time, MFCs stack with 1 L operating volume was also tested in supercapacitive mode, where full galvanostatic discharges are presented. Also in the latter case, performance once again improved with the increase in solution conductivity. Particularly, the increase in solution conductivity decreased dramatically the ohmic resistance and therefore the time for complete discharge was elongated, with a resultant increase in power. Maximum power achieved varied between 7.6 mW (7.6 Wm-3) at 2.0 mScm-1 and 27.4 mW (27.4 Wm-3) at 40.1 mScm-1

Remarks on the Cauchy functional equation and variations of it

This paper examines various aspects related to the Cauchy functional equation $f(x+y)=f(x)+f(y)$, a fundamental equation in the theory of functional equations. In particular, it considers its solvability and its stability relative to subsets of multi-dimensional Euclidean spaces and tori. Several new types of regularity conditions are introduced, such as a one in which a complex exponent of the unknown function is locally measurable. An initial value approach to analyzing this equation is considered too and it yields a few by-products, such as the existence of a non-constant real function having an uncountable set of periods which are linearly independent over the rationals. The analysis is extended to related equations such as the Jensen equation, the multiplicative Cauchy equation, and the Pexider equation. The paper also includes a rather comprehensive survey of the history of the Cauchy equation.Comment: To appear in Aequationes Mathematicae (important remark: the acknowledgments section in the official paper exists, but it appears before the appendix and not before the references as in the arXiv version); correction of a minor inaccuracy in Lemma 3.2 and the initial value proof of Theorem 2.1; a few small improvements in various sections; added thank