Search results for " Mathematica"

Order of products of elements in finite groups

2018

If G is a finite group, p is a prime, and x∈G, it is an interesting problem to place x in a convenient small (normal) subgroup of G, assuming some knowledge of the order of the products xy, for certain p‐elements y of G.

Analītiskā ģeometrija plaknē

1947

Combined Analysis of Neutrino and Antineutrino Oscillations at T2K.

2017

T2K reports its first results in the search for CP violation in neutrino oscillations using appearance and disappearance channels for neutrino- and antineutrino-mode beams. The data include all runs from January 2010 to May 2016 and comprise 7.482 ×10^(20) protons on target in neutrino mode, which yielded in the far detector 32 e-like and 135 μ-like events, and 7.471 × 10^(20) protons on target in antineutrino mode, which yielded 4 e-like and 66 μ-like events. Reactor measurements of sin(2)2θ(13) have been used as an additional constraint. The one-dimensional confidence interval at 90% for the phase δCP spans the range (−3.13, −0.39) for normal mass ordering. The CP conservation hypothesis …

Precise measurement of the neutrino mixing parameter θ23 from muon neutrino disappearance in an off-axis beam

2014

New data from the T2K neutrino oscillation experiment produce the most precise measurement of the neutrino mixing parameter theta_{23}. Using an off-axis neutrino beam with a peak energy of 0.6 GeV and a data set corresponding to 6.57 x 10^{20} protons on target, T2K has fit the energy-dependent nu_mu oscillation probability to determine oscillation parameters. Marginalizing over the values of other oscillation parameters yields sin^2 (theta_{23}) = 0.514 +0.055/-0.056 (0.511 +- 0.055), assuming normal (inverted) mass hierarchy. The best-fit mass-squared splitting for normal hierarchy is Delta m^2_{32} = (2.51 +- 0.10) x 10^{-3} eV^2/c^4 (inverted hierarchy: Delta m^2_{13} = (2.48 +- 0.10) …

Measurement of the inclusive $\nu_{\mu}$ charged current cross section on iron and hydrocarbon in the T2K on-axis neutrino beam

2014

We report a measurement of the $\nu_\mu$ inclusive charged current cross sections on iron and hydrocarbon in the T2K on-axis neutrino beam. The measured inclusive charged current cross sections on iron and hydrocarbon averaged over the T2K on-axis flux with a mean neutrino energy of 1.51 GeV are $(1.444\pm0.002(stat.)_{-0.157}^{+0.189}(syst.))\times 10^{-38}\mathrm{cm}^2/\mathrm{nucleon}$, and $(1.379\pm0.009(stat.)_{-0.147}^{+0.178}(syst.))\times 10^{-38}\mathrm{cm}^2/\mathrm{nucleon}$, respectively, and their cross section ratio is $1.047\pm0.007(stat.)\pm0.035(syst.)$. These results agree well with the predictions of the neutrino interaction model, and thus we checked the correct treatme…

The beam and detector of the NA62 experiment at CERN

2017

NA62 is a fixed-target experiment at the CERN SPS dedicated to measurements of rare kaon decays. Such measurements, like the branching fraction of the $K^{+} \rightarrow \pi^{+} \nu \bar\nu$ decay, have the potential to bring significant insights into new physics processes when comparison is made with precise theoretical predictions. For this purpose, innovative techniques have been developed, in particular, in the domain of low-mass tracking devices. Detector construction spanned several years from 2009 to 2014. The collaboration started detector commissioning in 2014 and will collect data until the end of 2018. The beam line and detector components are described together with their early …

Measurement of the c0 Baryon Lifetime

2018

We report a measurement of the lifetime of the $��_c^0$ baryon using proton-proton collision data at center-of-mass energies of 7 and 8~TeV, corresponding to an integrated luminosity of 3.0 fb$^{-1}$ collected by the LHCb experiment. The sample consists of about 1000 $��_b^-\to��_c^0��^-\bar��_�� X$ signal decays, where the $��_c^0$ baryon is detected in the $pK^-K^-��^+$ final state and $X$ represents possible additional undetected particles in the decay. The $��_c^0$ lifetime is measured to be $��_{��_c^0} = 268\pm24\pm10\pm2$ fs, where the uncertainties are statistical, systematic, and from the uncertainty in the $D^+$ lifetime, respectively. This value is nearly four times larger than, …

Solid-solid phase transition in hard ellipsoids

2009

We present a computer simulation study of the crystalline phases of hard ellipsoids of revolution. A previous study [P. Pfleiderer and T. Schilling, Phys. Rev. E 75, 020402 (2007)]. showed that for aspect ratios a/bor=3 the previously suggested stretched-fcc phase [D. Frenkel and B. Mulder, Mol. Phys. 55, 1171 (1985)] is unstable with respect to a simple monoclinic phase with two ellipsoids of different orientations per unit cell (SM2). In order to study the stability of these crystalline phases at different aspect ratios and as a function of density we have calculated their free energies by thermodynamic integration. The integration path was sampled by an expanded ensemble method in which …

Pattern-Recognition: a Foundational Approach

2015

This paper aims at giving a contribution to the ongoing attempt to turn the theory of pattern-recognition into a rigorous science. In this article we address two problems which lie at the foundations of pattern-recognition theory: (i) What is a pattern? and (ii) How do we come to know patterns? In so doing much attention will be paid to tracing a non-arbitrary connection between (i) and (ii), a connection which will be ultimately based on considerations relating to Darwin’s theory of evolution.

Object, Structure, and Form

2012

The main task of this paper is to develop the non-Platonist view of mathematics as a science of structures I have called, borrowing the label from Putnam, `realism with the human face'. According to this view, if by `object' we mean what exists independently of whether we are thinking about it or not, mathematics is a science of patterns (structures), where patterns are neither objects nor properties of objects, but aspects (or aspects of aspects, etc.) of concrete objects which dawn on us when we represent objects (or aspects of... within a given system (of representation). Mathematical patterns, therefore, are real, because they ultimately depend on concrete objects, but are neither objec…