Automated Reasoning and Presentation Support for Formalizing Mathematics in Mizar

This paper presents a combination of several automated reasoning and proof presentation tools with the Mizar system for formalization of mathematics. The combination forms an online service called MizAR, similar to the SystemOnTPTP service for first-order automated reasoning. The main differences to SystemOnTPTP are the use of the Mizar language that is oriented towards human mathematicians (rather than the pure first-order logic used in SystemOnTPTP), and setting the service in the context of the large Mizar Mathematical Library of previous theorems,definitions, and proofs (rather than the isolated problems that are solved in SystemOnTPTP). These differences poses new challenges and new opportunities for automated reasoning and for proof presentation tools. This paper describes the overall structure of MizAR, and presents the automated reasoning systems and proof presentation tools that are combined to make MizAR a useful mathematical service.Comment: To appear in 10th International Conference on. Artificial Intelligence and Symbolic Computation AISC 201

Full sky harmonic analysis hints at large UHECR deflections

The full-sky multipole coefficients of the ultra-high energy cosmic ray (UHECR) flux have been measured for the first time by the Pierre Auger and Telescope Array collaborations using a joint data set with E > 10 EeV. We calculate these harmonic coefficients in the model where UHECR are protons and sources trace the local matter distribution, and compare our results with observations. We find that the expected power for low multipoles (dipole and quadrupole, in particular) is sytematically higher than in the data: the observed flux is too isotropic. We then investigate to which degree our predictions are influenced by UHECR deflections in the regular Galactic magnetic field (GMF). It turns out that the UHECR power spectrum coefficients $C_\ell$ are quite insensitive to the effects of the GMF, so it is unlikely that the discordance can be reconciled by tuning the GMF model. On the contrary, a sizeable fraction of uniformly distributed flux (representing for instance an admixture of heavy nuclei with considerably larger deflections) can bring simulations and observations to an accord.Comment: 8 pages, 4 figures and one table, JETPL style -- v2 as published in JETP

Quantum fluids in nanopores

We describe calculations of the properties of quantum fluids inside nanotubes of various sizes. Very small radius ($R$) pores confine the gases to a line, so that a one-dimensional (1D) approximation is applicable; the low temperature behavior of 1D $^4$He is discussed. Somewhat larger pores permit the particles to move off axis, resulting eventually in a transition to a cylindrical shell phase--a thin film near the tube wall; we explored this behavior for H$_2$. At even larger $R\sim 1$ nm, both the shell phase and an axial phase are present. Results showing strong binding of cylindrical liquids $^4$He and $^3$He are discussed.Comment: 8 pages, 4 figures, uses ws-ijmpb, graphicx, xspace; minor revisions from version published in Proc. 13th Intl. Conference on Recent Progress in Many-Body Theories (QMBT13), Buenos Aires, 200

Next--to--Leading Order QCD corrections for the B0B0ˉB^0 \bar{B^0}--mixing with an extended Higgs sector

We present a calculation of the B0-B0--mixing including Next--to--Leading Order (NLO) QCD corrections within the Two Higgs Doublet Model (2HDM). The QCD corrections at NLO are contained in the factor denoted by eta_2 which modifies the result obtained at the lowest order of perturbation theory. In the Standard Model case, we confirm the results for eta_2 obtained by Buras, Jamin and Weisz. The factor eta_2 is gauge and renormalization prescription invariant and it does not depend on the infrared behaviour of the theory, which constitutes an important test of the calculations. The NLO--calculations within the 2HDM enhance the LO--result up to 18%, which affects the correlation between M_H and V_{td}.Comment: 22 pages (LaTeX), 22 Postscript figures, version to appear in Nucl. Phys. B, corrected some typos and a sign in the program, which results in changes in Eqs. (71), (74) and (75). Due to these changes Eqs. (23) and (34) may be written in a more compact wa

Beam quality improvement of high-power semiconductor lasers using laterally inhomogeneous waveguides

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Appl. Phys. Lett. 113, 221107 (2018) and may be found at https://doi.org/10.1063/1.5054645.High-brightness vertical broad-area edge-emitting (HiBBEE) semiconductor lasers in the 1060 nm wavelength range with excellent beam quality in both lateral and vertical directions are presented. An approach to modify the thresholds of the transverse lateral modes of ridge-waveguide (RW) lasers is investigated. It has been experimentally shown that inhomogeneities in both sides of the ridges increase optical losses of the higher-order lateral modes as compared to the fundamental mode. The resulting enhancement in the contrast of the optical losses favors the emission of the fundamental mode and improves the beam quality. Reference RW HiBBEE lasers with a 15 μm wide conventional ridge and a 2.0 mm long cavity provide laterally multi-lateral mode emission which is typical for RW lasers with such wide and homogeneous ridges. On the other hand, RW HiBBEE lasers with triangular-shaped corrugations in both sides of 15 μm wide ridges provide single-lateral mode emission across a wide current range and improve the lateral M2 factor by more than a factor of 2 in the investigated current range. The corrugated RW HiBBEE lasers provide an almost 2 times higher brightness than the reference RW lasers

New limits on extragalactic magnetic fields from rotation measures

We take advantage of the wealth of rotation measures data contained in the NRAO VLA Sky Survey catalogue to derive new, statistically robust, upper limits on the strength of extragalactic magnetic fields. We simulate the extragalactic magnetic field contribution to the rotation measures for a given field strength and correlation length, by assuming that the electron density follows the distribution of Lyman-$\alpha$ clouds. Based on the observation that rotation measures from distant radio sources do not exhibit any trend with redshift, while the extragalactic contribution instead grows with distance, we constrain fields with Jeans' length coherence length to be below 1.7~nG at the $2\sigma$ level, and fields coherent across the entire observable Universe below 0.65~nG. These limits do not depend on the particular origin of these cosmological fields.Comment: 5 pages, 3 figures -- v2 to match PRL versio

Magnetic relaxation in metallic films: Single and multilayer structures

The intrinsic magnetic relaxations in metallic films will be discussed. It will be shown that the intrinsic damping mechanism in metals is caused by incoherent scattering of itinerant electron-hole pair excitations by phonons and magnons. Berger [L. Berger, Phys. Rev. B 54, 9353 (1996)] showed that the interaction between spin waves and itinerant electrons in multilayers can lead to interface Gilbert damping. Ferromagnetic resonance (FMR) studies were carried out using magnetic single and double layer films. The FMR linewidth of the Fe films in the double layer structures was found to always be larger than the FMR linewidth measured for the single Fe films having the same thickness. The increase in the FMR linewidth scaled inversely with the film thickness, and was found to be linearly dependent on the microwave frequency. These results are in agreement with Berger's predictions. (C) 2002 American Institute of Physics