Semiring unions of a ring and a half-body

We describe the structure of semirings which are unions of a ring and a half-body.     

Imaging mesoscopic nuclear spin noise with a diamond magnetometer

Magnetic resonance imaging can characterize and discriminate among tissues using their diverse physical and biochemical properties. Unfortunately, submicrometer screening of biological specimens is presently not possible, mainly due to lack of detection sensitivity. Here we analyze the use of a nitrogen-vacancy center in diamond as a magnetic sensor for nanoscale nuclear spin imaging and spectroscopy. We examine the ability of such a sensor to probe the fluctuations of the "classical" dipolar field due to a large number of neighboring nuclear spins in a densely protonated sample. We identify detection protocols that appropriately take into account the quantum character of the sensor and find a signal-to-noise ratio compatible with realistic experimental parameters. Through various example calculations we illustrate different kinds of image contrast. In particular, we show how to exploit the comparatively long nuclear spin correlation times to reconstruct a local, high-resolution sample spectrum.     

Relaxation of fermionic excitations in a strongly attractive Fermi gas in an optical lattice

We theoretically study the relaxation of high energy single particle excitations into molecules in a system of attractive fermions in an optical lattice, both in the superfluid and the normal phase. In a system characterized by an interaction scale U and a tunneling rate t, we show that the relaxation rate scales as ～Ctexp[-αU(2)/t(2)ln(U/t)] in the large U/t limit. We obtain explicit expressions for the temperature and density dependent exponent α, both in the low temperature superfluid phase and the high temperature phase with pairing but no coherence between the molecules. We find that the relaxation rate decreases both with temperature and deviation of the fermion density from half filling. We show that quasiparticle and phase degrees of freedom are effectively decoupled within experimental time scales allowing for observation of ordered states even at high total energy of the system.     

Synthesis and study of the photochromic behavior of 3-[6′-nitro-1,3,3-trimethylspiro(indolino-2,2′-[2H]-chromen-5-yl)]propenoic acid and its ethyl ester

A new photochromic probe containing a spacer with the reactive carboxyl terminal group at the C5 atom of the photochrome molecule was synthesized. The spectral and kinetic study of the behavior of the new photochromic probes in toluene and ethanol was performed.     

Electron states in the two-band Hubbard model: Paramagnetic phase

The electron energy spectrum of the copper-based oxides is calculated in the two-band Hubbard model. The conditions for the onset of a localized spin state are studied. The effect of doping is also studied.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, Akademii Nauk SSSR, Vol. 180, pp. 94–104, 1990.     

Filtration of components of processes of random evolution

The problem of estimation of a nonobservable component θ_t for a two-dimensional process (θ_t, ξ_t) of random evolution (θ _t,ξ_t);x_t, 0≤t≤T, is investigated on the basis of observations of ξ_s. s≤t, where x _t is a homogeneous Markov process with infinitesimal operator Q. Applications to stochastic models of a (B,S)-market of securities is described under conditions of incomplete market. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 12, pp. 1701–1705, December, 1998.     

On Stable Runge–Kutta Methods for Solving Hyperbolic Equations by the Discontinuous Galerkin Method

Differential Equations - We consider Runge–Kutta methods whose stability domain includes a disk of maximum diameter for given number of stages and order. These methods are used to solve...     

Multiplication Factor for Subcritical Multiplying System and the Efficiency of Source Neutrons

Physics of Atomic Nuclei - In this paper, the analysis of the relation between the multiplication factor of neutrons of the multiplying system measured in critical experiments and the system...