92 research outputs found
Proof of two conjectures of Z.-W. Sun on congruences for Franel numbers
For all nonnegative integers n, the Franel numbers are defined as We confirm two conjectures of Z.-W. Sun on
congruences for Franel numbers: \sum_{k=0}^{n-1}(3k+2)(-1)^k f_k &\equiv 0
\pmod{2n^2}, \sum_{k=0}^{p-1}(3k+2)(-1)^k f_k &\equiv 2p^2 (2^p-1)^2
\pmod{p^5}, where n is a positive integer and p>3 is a prime.Comment: 8 pages, minor changes, to appear in Integral Transforms Spec. Func
Asymptotic Expansions for the Conditional Sojourn Time Distribution in the -PS Queue
We consider the queue with processor sharing. We study the
conditional sojourn time distribution, conditioned on the customer's service
requirement, in various asymptotic limits. These include large time and/or
large service request, and heavy traffic, where the arrival rate is only
slightly less than the service rate. The asymptotic formulas relate to, and
extend, some results of Morrison \cite{MO} and Flatto \cite{FL}.Comment: 30 pages, 3 figures and 1 tabl
On arithmetic partitions of Z_n
Generalizing a classical problem in enumerative combinatorics, Mansour and
Sun counted the number of subsets of without certain separations. Chen,
Wang, and Zhang then studied the problem of partitioning into
arithmetical progressions of a given type under some technical conditions. In
this paper, we improve on their main theorems by applying a convolution formula
for cyclic multinomial coefficients due to Raney-Mohanty.Comment: 10 pages, 1 figure, European J. Combin. (2008),
doi:10.1016/j.ejc.2008.11.00
Mirror Symmetry and Other Miracles in Superstring Theory
The dominance of string theory in the research landscape of quantum gravity
physics (despite any direct experimental evidence) can, I think, be justified
in a variety of ways. Here I focus on an argument from mathematical fertility,
broadly similar to Hilary Putnam's 'no miracles argument' that, I argue, many
string theorists in fact espouse. String theory leads to many surprising,
useful, and well-confirmed mathematical 'predictions' - here I focus on mirror
symmetry. These predictions are made on the basis of general physical
principles entering into string theory. The success of the mathematical
predictions are then seen as evidence for framework that generated them. I
attempt to defend this argument, but there are nonetheless some serious
objections to be faced. These objections can only be evaded at a high
(philosophical) price.Comment: For submission to a Foundations of Physics special issue on "Forty
Years Of String Theory: Reflecting On the Foundations" (edited by G. `t
Hooft, E. Verlinde, D. Dieks and S. de Haro)
Generalized empty-interval method applied to a class of one-dimensional stochastic models
In this work we study, on a finite and periodic lattice, a class of
one-dimensional (bimolecular and single-species) reaction-diffusion models
which cannot be mapped onto free-fermion models.
We extend the conventional empty-interval method, also called
{\it interparticle distribution function} (IPDF) method, by introducing a
string function, which is simply related to relevant physical quantities.
As an illustration, we specifically consider a model which cannot be solved
directly by the conventional IPDF method and which can be viewed as a
generalization of the {\it voter} model and/or as an {\it epidemic} model. We
also consider the {\it reversible} diffusion-coagulation model with input of
particles and determine other reaction-diffusion models which can be mapped
onto the latter via suitable {\it similarity transformations}.
Finally we study the problem of the propagation of a wave-front from an
inhomogeneous initial configuration and note that the mean-field scenario
predicted by Fisher's equation is not valid for the one-dimensional
(microscopic) models under consideration.Comment: 19 pages, no figure. To appear in Physical Review E (November 2001
Methods for Optical Calibration of the BigBite Hadron Spectrometer
The techniques for optical calibration of Jefferson Lab's large-acceptance
magnetic hadron spectrometer, BigBite, have been examined. The most consistent
and stable results were obtained by using a method based on singular value
decomposition. In spite of the complexity of the optics, the particles'
positions and momenta at the target have been precisely reconstructed from the
coordinates measured in the detectors by means of a single back-tracing matrix.
The technique is applicable to any similar magnetic spectrometer and any
particle type. For 0.55 GeV/c protons, we have established the vertex
resolution of 1.2 cm, angular resolutions of 7 mrad and 16 mrad (in-plane and
out-of-plane, respectively), and a relative momentum resolution of 1.6%.Comment: 26 pages, 13 figure
Search for three-nucleon short-range correlations in light nuclei
We present new data probing short-range correlations (SRCs) in nuclei through the measurement of electron scattering off high-momentum nucleons in nuclei. The inclusive ^{4}He/^{3}He cross section ratio is observed to be both x and Q^{2} independent for 1.52, our data support the hypothesis that a previous claim of three-nucleon correlation dominance was an artifact caused by the limited resolution of the measurement. While 3N-SRCs appear to have an important contribution, our data show that isolating 3N-SRCs is significantly more complicated than for 2N-SRCs.United States. Department of Energy (Contract DE-AC05-06OR23177)United States. Department of Energy (Contract DE-AC02-06CH11357)United States. Department of Energy (Contract DE-FG02-96ER40950
Use of SMS texts for facilitating access to online alcohol interventions: a feasibility study
A41 Use of SMS texts for facilitating access to online alcohol interventions: a feasibility study
In: Addiction Science & Clinical Practice 2017, 12(Suppl 1): A4
Track D Social Science, Human Rights and Political Science
Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/138414/1/jia218442.pd
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