Supersymmetric version of a hydrodynamic system in Riemann invariants and its solutions

In this paper, a supersymmetric extension of a system of hydrodynamic type equations involving Riemann invariants is formulated in terms of a superspace and superfield formalism. The symmetry properties of both the classical and supersymmetric versions of this hydrodynamical model are analyzed through the use of group-theoretical methods applied to partial differential equations involving both bosonic and fermionic variables. More specifically, we compute the Lie superalgebras of both models and perform classifications of their respective subalgebras. A systematic use of the subalgebra structures allow us to construct several classes of invariant solutions, including travelling waves, centered waves and solutions involving monomials, exponentials and radicals.Comment: 30 page

A central limit theorem for the zeroes of the zeta function

On the assumption of the Riemann hypothesis, we generalize a central limit theorem of Fujii regarding the number of zeroes of Riemann's zeta function that lie in a mesoscopic interval. The result mirrors results of Soshnikov and others in random matrix theory. In an appendix we put forward some general theorems regarding our knowledge of the zeta zeroes in the mesoscopic regime.Comment: 22 pages. Incorporates referees suggestions. Contains minor corrections to published versio

Physics in Riemann's mathematical papers

Riemann's mathematical papers contain many ideas that arise from physics, and some of them are motivated by problems from physics. In fact, it is not easy to separate Riemann's ideas in mathematics from those in physics. Furthermore, Riemann's philosophical ideas are often in the background of his work on science. The aim of this chapter is to give an overview of Riemann's mathematical results based on physical reasoning or motivated by physics. We also elaborate on the relation with philosophy. While we discuss some of Riemann's philosophical points of view, we review some ideas on the same subjects emitted by Riemann's predecessors, and in particular Greek philosophers, mainly the pre-socratics and Aristotle. The final version of this paper will appear in the book: From Riemann to differential geometry and relativity (L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017

Looking backward: From Euler to Riemann

We survey the main ideas in the early history of the subjects on which Riemann worked and that led to some of his most important discoveries. The subjects discussed include the theory of functions of a complex variable, elliptic and Abelian integrals, the hypergeometric series, the zeta function, topology, differential geometry, integration, and the notion of space. We shall see that among Riemann's predecessors in all these fields, one name occupies a prominent place, this is Leonhard Euler. The final version of this paper will appear in the book \emph{From Riemann to differential geometry and relativity} (L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017

Quantum Spin Chains and Riemann Zeta Function with Odd Arguments

Riemann zeta function is an important object of number theory. It was also used for description of disordered systems in statistical mechanics. We show that Riemann zeta function is also useful for the description of integrable model. We study XXX Heisenberg spin 1/2 anti-ferromagnet. We evaluate a probability of formation of a ferromagnetic string in the anti-ferromagnetic ground state in thermodynamics limit. We prove that for short strings the probability can be expressed in terms of Riemann zeta function with odd arguments.Comment: LaTeX, 7 page

Zeta function regularization in Casimir effect calculations and J.S. Dowker's contribution

A summary of relevant contributions, ordered in time, to the subject of operator zeta functions and their application to physical issues is provided. The description ends with the seminal contributions of Stephen Hawking and Stuart Dowker and collaborators, considered by many authors as the actual starting point of the introduction of zeta function regularization methods in theoretical physics, in particular, for quantum vacuum fluctuation and Casimir effect calculations. After recalling a number of the strengths of this powerful and elegant method, some of its limitations are discussed. Finally, recent results of the so called operator regularization procedure are presented.Comment: 16 pages, dedicated to J.S. Dowker, version to appear in International Journal of Modern Physics

The association between diurnal sleep patterns and emotions in infants and toddlers attending nursery

Background: Childcare programs often include mandatory naptime during the day. Loss of daytime sleep could lead to a moderate-to-large decrease in self-regulation, emotion processing, and learning in early childhood. Nevertheless, daytime sleep has been less accurately studied than nighttime sleep. This study aims to explore the relationship between diurnal sleep habits in nursery settings, nocturnal sleep quality, and post-nap emotional intensity in infants and toddlers. Methods: Data of 92 children (52 girls, 40 boys) aged 6 to 36 months were obtained. Sleep habits as well as positive and negative emotions were monitored by educators during nursery times through a sleep and emotion diary for two weeks. Results: Explorative analyses showed that diurnal sleep hours decreased across age groups (except for females aged 25–36 months) and that all age groups had a lower amount of nocturnal sleep than is recommended by the National Sleep Foundation. Partial correlation analysis showed significant correlation between daytime sleep onset latency and positive emotions. Mediation analyses showed that daytime napping is relevant for emotional functioning independently of nocturnal sleep quality. Conclusions: Daytime sleep in early childhood seems to be linked to the management of positive and negative emotions and could play a role in healthy development of emotional processes

Two-Fermion Production in Electron-Positron Collisions

This report summarizes the results of the two-fermion working group of the LEP2-MC workshop, held at CERN from 1999 to 2000. Recent developments in the theoretical calculations of the two fermion production process in the electron-positron collision at LEP2 center of the mass energies are reported. The Bhabha process and the production of muon, tau, neutrino and quark pairs is covered. On the basis of comparison of various calculations, theoretical uncertainties are estimated and compared with those needed for the final LEP2 data analysis. The subjects for the further studies are identified.Comment: 2-fermion working group report of the LEP2 Monte Carlo Workshop 1999/2000, 113 pages, 24 figures, 35 table

Fractional Dirac Bracket and Quantization for Constrained Systems

So far, it is not well known how to deal with dissipative systems. There are many paths of investigation in the literature and none of them present a systematic and general procedure to tackle the problem. On the other hand, it is well known that the fractional formalism is a powerful alternative when treating dissipative problems. In this paper we propose a detailed way of attacking the issue using fractional calculus to construct an extension of the Dirac brackets in order to carry out the quantization of nonconservative theories through the standard canonical way. We believe that using the extended Dirac bracket definition it will be possible to analyze more deeply gauge theories starting with second-class systems.Comment: Revtex 4.1. 9 pages, two-column. Final version to appear in Physical Review