8,693 research outputs found
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
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
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
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 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 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
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