Spectral gaps for periodic Schr\"odinger operators with strong magnetic fields

We consider Schr\"odinger operators $H^h = (ih d+{\bf A})^* (ih d+{\bf A})$ with the periodic magnetic field ${\bf B}=d{\bf A}$ on covering spaces of compact manifolds. Under some assumptions on $\bf B$, we prove that there are arbitrarily large number of gaps in the spectrum of these operators in the semiclassical limit of strong magnetic field $h\to 0$.Comment: 14 pages, LaTeX2e, xypic, no figure

Lifshitz fermionic theories with z=2 anisotropic scaling

We construct fermionic Lagrangians with anisotropic scaling z=2, the natural counterpart of the usual z=2 Lifshitz field theories for scalar fields. We analyze the issue of chiral symmetry, construct the Noether axial currents and discuss the chiral anomaly giving explicit results for two-dimensional case. We also exploit the connection between detailed balance and the dynamics of Lifshitz theories to find different z=2 fermionic Lagrangians and construct their supersymmetric extensions.Comment: Typos corrected, comment adde

The order of curvature operators on loop groups

For loop groups (free and based), we compute the exact order of the curvature operator of the Levi-Civita connection depending on a Sobolev space parameter. This extends results of Freed and Maeda-Rosenberg-Torres.Comment: to appear in Letters in Mathematical Physic

Non-catalytic bromination of benzene: a combined computational and experimental study

The non-catalytic bromination of benzene is shown experimentally to require high 5-14M concentrations of bromine in order to proceed at ambient temperatures to form predominantly bromobenzene, along with detectable (The non-catalytic bromination of benzene is shown experimentally to require high 5-14M concentrations of bromine in order to proceed at ambient temperatures to form predominantly bromobenzene, along with detectable (The non-catalytic bromination of benzene is shown experimentally to require high 5-14M concentrations of bromine in order to proceed at ambient temperatures to form predominantly bromobenzene, along with detectable

Numerical model of ultrasonic multi-channel data transfer for servicing subsea production complex

Various researchers focused on different problems, and we can conclude that a single effective communication design with a specific algorithm that could be used in all types of underwater channels was not found. The design of the transmission is highly dependent on the conditions of the canal, as various schemes are used in shallow and deep water, and various algorithms in turbulent and calm waters. The type of channel alignment also depends on parameters such as channel estimation and coding. The ever-growing demand for bandwidth, efficiency, spatial diversity and the performance of underwater acoustic communications has opened the door to using Multiple Input Multiple Output (MIMO) technology. In this paper, we propose a method of ultrasonic data transmission under water based on the MIMO technology (Many emitters, many receivers, or MIMO - Multilpe Input - Multiple Output). This approach will allow for multi-channel data transmission in water and significantly increase the speed of information transfer