Classification of Low Dimensional Lie Super-Bialgebras

A thorough analysis of Lie super-bialgebra structures on Lie super-algebras osp(1|2) and super-e(2) is presented. Combined technique of computer algebraic computations and a subsequent identification of equivalent structures is applied. In all the cases Poisson-Lie brackets on supergroups are found. Possibility of quantizing them in order to obtain quantum groups is discussed. It turns out to be straightforward for all but one structures for super-E(2) group.Comment: 15 pages, LaTe

Kappa-contraction from SUq(2)SU_q(2) to Eκ(2)E_{\kappa}(2)

We present contraction prescription of the quantum groups: from $SU_q(2)$ to $E_{\kappa}(2)$. Our strategy is different then one chosen in ref. [P. Zaugg, J. Phys. A {\bf 28} (1995) 2589]. We provide explicite prescription for contraction of $a, b, c$ and $d$ generators of $SL_q(2)$ and arrive at $^*$ Hopf algebra $E_{\kappa}(2)$.Comment: 3 pages, plain TEX, harvmac, to be published in the Proceedings of the 4-th Colloqium Quantum Groups and Integrable Systems, Prague, June 1995, Czech. J. Phys. {\bf 46} 265 (1996

Initial report from the ICFA Neutrino Panel

In July 2013 ICFA established the Neutrino Panel with the mandate "To promote international cooperation in the development of the accelerator-based neutrino-oscillation program and to promote international collaboration in the development a neutrino factory as a future intense source of neutrinos for particle physics experiments". This, the Panel's Initial Report, presents the conclusions drawn by the Panel from three regional "Town Meetings" that took place between November 2013 and February 2014. After a brief introduction and a short summary of the status of the knowledge of the oscillation parameters, the report summarises the approved programme and identifies opportunities for the development of the field. In its conclusions, the Panel recognises that to maximise the discovery potential of the accelerator-based neutrino-oscillation programme it will be essential to exploit the infrastructures that exist at CERN, FNAL and J-PARC and the expertise and resources that reside in laboratories and institutes around the world. Therefore, in its second year, the Panel will consult with the accelerator-based neutrino-oscillation community and its stakeholders to: develop a road-map for the future accelerator-based neutrino-oscillation programme that exploits the ambitions articulated at CERN, FNAL and J-PARC and includes the programme of measurement and test-beam exposure necessary to ensure the programme is able to realise its potential; develop a proposal for a coordinated "Neutrino RD" programme, the accelerator and detector R&D programme required to underpin the next generation of experiments; and to explore the opportunities for the international collaboration necessary to realise the Neutrino Factory.Comment: ICFA Neutrino Panel 2014(01

Quantum E(2) groups and Lie bialgebra structures

Lie bialgebra structures on $e(2)$ are classified. For two Lie bialgebra structures which are not coboundaries (i.e. which are not determined by a classical $r$-matrix) we solve the cocycle condition, find the Lie-Poisson brackets and obtain quantum group relations. There is one to one correspondence between Lie bialgebra structures on $e(2)$ and possible quantum deformations of $U(e(2))$ and $E(2)$.Comment: 8 pages, plain TEX, harvmac, to appear in J. Phys.

C5AC_5^A axial form factor from bubble chamber experiments

A careful reanalysis of both Argonne National Laboratory and Brookhaven National Laboratory data for weak single pion production is done. We consider deuteron nuclear effects and normalization (flux) uncertainties in both experiments. We demonstrate that these two sets of data are in good agreement. For the dipole parametrization of $C_5^A(Q^2)$, we obtain $C_5^A(0)=1.19\pm 0.08$, $M_A=0.94\pm 0.03$ GeV. As an application we present the discussion of the uncertainty of the neutral current 1$\pi^0$ production cross section, important for the T2K neutrino oscillation experiment.Comment: 16 pages, 8 figures, 2 table

Statistics of non-linear stochastic dynamical systems under L\'evy noises by a convolution quadrature approach

This paper describes a novel numerical approach to find the statistics of the non-stationary response of scalar non-linear systems excited by L\'evy white noises. The proposed numerical procedure relies on the introduction of an integral transform of Wiener-Hopf type into the equation governing the characteristic function. Once this equation is rewritten as partial integro-differential equation, it is then solved by applying the method of convolution quadrature originally proposed by Lubich, here extended to deal with this particular integral transform. The proposed approach is relevant for two reasons: 1) Statistics of systems with several different drift terms can be handled in an efficient way, independently from the kind of white noise; 2) The particular form of Wiener-Hopf integral transform and its numerical evaluation, both introduced in this study, are generalizations of fractional integro-differential operators of potential type and Gr\"unwald-Letnikov fractional derivatives, respectively.Comment: 20 pages, 5 figure

Information dynamics: Temporal behavior of uncertainty measures

We carry out a systematic study of uncertainty measures that are generic to dynamical processes of varied origins, provided they induce suitable continuous probability distributions. The major technical tool are the information theory methods and inequalities satisfied by Fisher and Shannon information measures. We focus on a compatibility of these inequalities with the prescribed (deterministic, random or quantum) temporal behavior of pertinent probability densities.Comment: Incorporates cond-mat/0604538, title, abstract changed, text modified, to appear in Cent. Eur. J. Phy