What is the relativistic Volterra lattice?

We develop a systematic procedure of finding integrable ''relativistic'' (regular one-parameter) deformations for integrable lattice systems. Our procedure is based on the integrable time discretizations and consists of three steps. First, for a given system one finds a local discretization living in the same hierarchy. Second, one considers this discretization as a particular Cauchy problem for a certain 2-dimensional lattice equation, and then looks for another meaningful Cauchy problems, which can be, in turn, interpreted as new discrete time systems. Third, one has to identify integrable hierarchies to which these new discrete time systems belong. These novel hierarchies are called then ''relativistic'', the small time step $h$ playing the role of inverse speed of light. We apply this procedure to the Toda lattice (and recover the well-known relativistic Toda lattice), as well as to the Volterra lattice and a certain Bogoyavlensky lattice, for which the ''relativistic'' deformations were not known previously.Comment: 48 pp, LaTe

Integrable discretizations of the spin Ruijsenaars-Schneider models

Integrable discretizations are introduced for the rational and hyperbolic spin Ruijsenaars--Schneider models. These discrete dynamical systems are demonstrated to belong to the same integrable hierarchies as their continuous--time counterparts. Explicit solutions are obtained for arbitrary flows of the hierarchies, including the discrete time ones.Comment: LaTeX fil

Separation of variables and B\"acklund transformations for the symmetric Lagrange top

We construct the 1- and 2-point integrable maps (B\"acklund transformations) for the symmetric Lagrange top. We show that the Lagrange top has the same algebraic Poisson structure that belongs to the $sl(2)$ Gaudin magnet. The 2-point map leads to a real time-discretization of the continuous flow. Therefore, it provides an integrable numerical scheme for integrating the physical flow. We illustrate the construction by few pictures of the discrete flow calculated in MATLAB.Comment: 19 pages, 2 figures, Matlab progra

KATRIN Sensitivity to Sterile Neutrino Mass in the Shadow of Lightest Neutrino Mass

The presence of light sterile neutrinos would strongly modify the energy spectrum of the Tritium \beta-electrons. We perform an analysis of the KATRIN experiment's sensitivity by scanning almost all the allowed region of neutrino mass-squared difference and mixing angles of the 3+1 scenario. We consider the effect of the unknown absolute mass scale of active neutrinos on the sensitivity of KATRIN to the sterile neutrino mass. We show that after 3 years of data-taking, the KATRIN experiment can be sensitive to mixing angles as small as sin^2 (2\theta_s) ~ 10^-2. Particularly we show that for small mixing angles, sin^2 (2\theta_s) < 0.1, the KATRIN experiment can gives the strongest limit on active-sterile mass-squared difference.Comment: 4 pages, 2 figures, matches the published versio

Backlund transformations for the sl(2) Gaudin magnet

Elementary, one- and two-point, Backlund transformations are constructed for the generic case of the sl(2) Gaudin magnet. The spectrality property is used to construct these explicitly given, Poisson integrable maps which are time-discretizations of the continuous flows with any Hamiltonian from the spectral curve of the 2x2 Lax matrix

Open Innovation, ambiguity and technological convergence

Objectives. Current paper aims to provide a fresh conceptual framework on the relationship among open innovation, decision ambiguity, and technological convergence. We argue that there is a curvilinear relationship between open innovation and both technological convergence and ambiguity. Contained level of convergence and ambiguity foster open innovation, whilst an excess of them is an impediment to collaboration. Technological convergence further acts as a moderator for ambiguity, in light of the benefits of isomorphism. Methodology. We propose a conceptual framework for open innovation decisions after accurately reviewing the main literature antecedents. Findings. We suggest an inverse u-shaped relationship between open innovation and either ambiguity or technological convergence. Research limits. In future, the theoretical framework proposed by thus study has to be tested with robust and proper statistical techniques on large scale samples. Practical implications. The model offers a heuristic for open innovation decisions under ambiguity. Originality of the study. To the best of our knowledge, the relationship linking open innovation, technological convergence and ambiguity emerges as a literature gap. This study tackles this issue, proposing an interpretation for the analysis of alliances decision in innovation

ISS and TPD study of the adsorption and interaction of CO and H2 on polycrystalline Pt

The adsorption and interaction of CO and H2 on polycrystalline Pt has been studied using ion scattering spectroscopy (ISS) and temperature programmed desorption (TPD). The ISS results indicate that the initial CO adsorption on Pt takes place very rapidly and saturates the Pt surface with coverage close to a monolayer. ISS also shows that the CO molecules adsorb at an angular orientation from the surface normal and perhaps parallel to the surface. A TPD spectrum obtained after coadsorbing C-12 O-16 and C-13 O-18 on Pt shows no isotopic mixing, which is indicative of molecular CO adsorption. TPD spectra obtained after coadsorbing H2 and CO on polycrystalline Pt provides evidence for the formation of a CO-H surface species