An extension of Fourier analysis for the n-torus in the magnetic field and its application to spectral analysis of the magnetic Laplacian

We solved the Schr{\"o}dinger equation for a particle in a uniform magnetic field in the n-dimensional torus. We obtained a complete set of solutions for a broad class of problems; the torus T^n = R^n / {\Lambda} is defined as a quotient of the Euclidean space R^n by an arbitrary n-dimensional lattice {\Lambda}. The lattice is not necessary either cubic or rectangular. The magnetic field is also arbitrary. However, we restrict ourselves within potential-free problems; the Schr{\"o}dinger operator is assumed to be the Laplace operator defined with the covariant derivative. We defined an algebra that characterizes the symmetry of the Laplacian and named it the magnetic algebra. We proved that the space of functions on which the Laplacian acts is an irreducible representation space of the magnetic algebra. In this sense the magnetic algebra completely characterizes the quantum mechanics in the magnetic torus. We developed a new method for Fourier analysis for the magnetic torus and used it to solve the eigenvalue problem of the Laplacian. All the eigenfunctions are given in explicit forms.Comment: 32 pages, LaTeX, minor corrections are mad

Expression and purification of functional human glycogen synthase-1:glycogenin-1 complex in insect cells

We report the successful expression and purification of functional human muscle glycogen synthase (GYS1) in complex with human glycogenin-1 (GN1). Stoichiometric GYS1:GN1 complex was produced by co-expression of GYS1 and GN1 using a bicistronic pFastBac™-Dual expression vector, followed by affinity purification and subsequent size-exclusion chromatography. Mass spectrometry analysis identified that GYS1 is phosphorylated at several well-characterised and uncharacterised Ser/Thr residues. Biochemical analysis, including activity ratio (in the absence relative to that in the presence of glucose-6-phosphate) measurement, covalently attached phosphate estimation as well as phosphatase treatment, revealed that recombinant GYS1 is substantially more heavily phosphorylated than would be observed in intact human or rodent muscle tissues. A large quantity of highly-pure stoichiometric GYS1:GN1 complex will be useful to study its structural and biochemical properties in the future, which would reveal mechanistic insights into its functional role in glycogen biosynthesis

A really simple approximation of smallest grammar

In this paper we present a really simple linear-time algorithm constructing a context-free grammar of size O(g log (N/g)) for the input string, where N is the size of the input string and g the size of the optimal grammar generating this string. The algorithm works for arbitrary size alphabets, but the running time is linear assuming that the alphabet Sigma of the input string can be identified with numbers from 1,ldots, N^c for some constant c. Algorithms with such an approximation guarantee and running time are known, however all of them were non-trivial and their analyses were involved. The here presented algorithm computes the LZ77 factorisation and transforms it in phases to a grammar. In each phase it maintains an LZ77-like factorisation of the word with at most l factors as well as additional O(l) letters, where l was the size of the original LZ77 factorisation. In one phase in a greedy way (by a left-to-right sweep and a help of the factorisation) we choose a set of pairs of consecutive letters to be replaced with new symbols, i.e. nonterminals of the constructed grammar. We choose at least 2/3 of the letters in the word and there are O(l) many different pairs among them. Hence there are O(log N) phases, each of them introduces O(l) nonterminals to a grammar. A more precise analysis yields a bound O(l log(N/l)). As l \leq g, this yields the desired bound O(g log(N/g)).Comment: Accepted for CPM 201

The Second Swift BAT Gamma-Ray Burst Catalog

We present the second Swift Burst Alert Telescope (BAT) catalog of gamma-ray bursts (GRBs), which contains 476 bursts detected by the BAT between 2004 December 19 and 2009 December 21. This catalog (hereafter the BAT2 catalog) presents burst trigger time, location, 90% error radius, duration, fluence, peak flux, time-averaged spectral parameters and time-resolved spectral parameters measured by the BAT. In the correlation study of various observed parameters extracted from the BAT prompt emission data, we distinguish among long-duration GRBs (L-GRBs), short-duration GRBs (S-GRBs), and short-duration GRBs with extended emission (S-GRBs with E.E.) to investigate differences in the prompt emission properties. The fraction of L-GRBs, S-GRBs and S-GRBs with E.E. in the catalog are 89%, 8% and 2% respectively. We compare the BAT prompt emission properties with the BATSE, BeppoSAX and HETE-2 GRB samples. We also correlate the observed prompt emission properties with the redshifts for the GRBs with known redshift. The BAT T90 and T50 durations peak at 70 s and 30 s, respectively. We confirm that the spectra of the BAT S-GRBs are generally harder than those of the L-GRBs. The time-averaged spectra of the BAT S-GRBs with E.E. are similar to those of the L-GRBs. Whereas, the spectra of the initial short spikes of the S-GRBs with E.E. are similar to those of the S-GRBs. We show that the BAT GRB samples are significantly softer than the BATSE bright GRBs, and that the time-averaged Epeak of the BAT GRBs peaks at 80 keV which is significantly lower energy than those of the BATSE sample which peak at 320 keV. The time-averaged spectral properties of the BAT GRB sample are similar to those of the HETE-2 GRB samples. By time-resolved spectral analysis, we find that only 10% of the BAT observed photon indices are outside the allowed region of the synchrotron shock model.Comment: 65 pages, 33 figures, 13 tables, Accepted in ApJS, Nine machine-readable tables are available at http://swift.gsfc.nasa.gov/docs/swift/results/bat2_catalog

Magnetic translation groups in an n-dimensional torus

A charged particle in a uniform magnetic field in a two-dimensional torus has a discrete noncommutative translation symmetry instead of a continuous commutative translation symmetry. We study topology and symmetry of a particle in a magnetic field in a torus of arbitrary dimensions. The magnetic translation group (MTG) is defined as a group of translations that leave the gauge field invariant. We show that the MTG on an n-dimensional torus is isomorphic to a central extension of a cyclic group Z_{nu_1} x ... x Z_{nu_{2l}} x T^m by U(1) with 2l+m=n. We construct and classify irreducible unitary representations of the MTG on a three-torus and apply the representation theory to three examples. We shortly describe a representation theory for a general n-torus. The MTG on an n-torus can be regarded as a generalization of the so-called noncommutative torus.Comment: 29 pages, LaTeX2e, title changed, re-organized, to be published in Journal of Mathematical Physic

Shape and blocking effects on odd-even mass differences and rotational motion of nuclei

Nuclear shapes and odd-nucleon blockings strongly influence the odd-even differences of nuclear masses. When such effects are taken into account, the determination of the pairing strength is modified resulting in larger pair gaps. The modified pairing strength leads to an improved self-consistent description of moments of inertia and backbending frequencies, with no additional parameters.Comment: 7 pages, 3 figures, subm to PR

Gas Dynamics in the LINER Galaxy NGC 5005: Episodic Fueling of a Nuclear Disk

We report high-resolution CO(1-0) observations in the central 6 kpc of the LINER galaxy NGC 5005 with the Owens Valley Radio Observatory millimeter array. Molecular gas is distributed in three components - a ring at a radius of about 3 kpc, a strong central condensation, and a stream to the northwest of the nucleus but inside the 3 kpc ring. The central condensation is a disk of about 1 kpc radius with a molecular gas mass of 2 x 10^9 M_sun. The stream between the 3 kpc ring and the nuclear disk lies on a straight dust lane seen in the optical. If this material moves in the plane of the galaxy, it has a velocity offset by up to ~ 150 km/s from galactic rotation. We suggest that an optically inconspicuous stellar bar lying within the 3 kpc ring can explain the observed gas dynamics. This bar is expected to connect the nuclear disk and the ring along the position angle of the northwest stream. A position-velocity cut in this direction reveals features which match the characteristic motions of gas in a barred potential. Our model indicates that gas in the northwest stream is on an x_1 orbit at the bar's leading edge; it is falling into the nucleus with a large noncircular velocity, and will eventually contribute about 2 x 10^8 M_sun to the nuclear disk. If most of this material merges with the disk on its first passage of pericenter, the gas accretion rate during the collision will be 50 M_sun/yr. We associate the nuclear disk with an inner 2:1 Lindblad resonance, and the 3 kpc ring with an inner 4:1 Lindblad resonance. The high rate of bar-driven inflow and the irregular appearance of the northwest stream suggest that a major fueling event is in progress in NGC 5005. Such episodic (rather than continuous) gas supply can regulate the triggering of starburst and accretion activity in galactic nuclei. (abridged)Comment: 26 pages, 12 figures, AASTeX, ApJ in press (Feb. 10, 2000). For full-resolution figures, see http://www.ovro.caltech.edu/mm/science/science.htm

GRB 110709A, 111117A and 120107A: Faint high-energy gamma-ray photon emission from Fermi/LAT observations and demographic implications

Launched on June 11, 2008, the LAT instrument onboard the $Fermi$ Gamma-ray Space Telescope has provided a rare opportunity to study high energy photon emission from gamma-ray bursts. Although the majority of such events (27) have been iden tified by the Fermi LAT Collaboration, four were uncovered by using more sensiti ve statistical techniques (Akerlof et al 2010, Akerlof et al 2011, Zheng et al 2 012). In this paper, we continue our earlier work by finding three more GRBs ass ociated with high energy photon emission, GRB 110709A, 111117A and 120107A. To s ystematize our matched filter approach, a pipeline has been developed to identif y these objects in near real time. GRB 120107A is the first product of this anal ysis procedure. Despite the reduced threshold for identification, the number of GRB events has not increased significantly. This relative dearth of events with low photon number prompted a study of the apparent photon number distribution. W e find an extremely good fit to a simple power-law with an exponent of -1.8 $\pm$ 0.3 for the differential distribution. As might be expected, there is a substa ntial correlation between the number of lower energy photons detected by the GBM and the number observed by the LAT. Thus, high energy photon emission is associ ated with some but not all of the brighter GBM events. Deeper studies of the pro perties of the small population of high energy emitting bursts may eventually yi eld a better understanding of these entire phenomena.Comment: accepted to Ap