18,863 research outputs found
Arithmetic Properties of Overpartition Pairs
Bringmann and Lovejoy introduced a rank for overpartition pairs and
investigated its role in congruence properties of , the number of
overpartition pairs of n. In particular, they applied the theory of Klein forms
to show that there exist many Ramanujan-type congruences for the number
. In this paper, we shall derive two Ramanujan-type identities and
some explicit congruences for . Moreover, we find three ranks as
combinatorial interpretations of the fact that is divisible by
three for any n. We also construct infinite families of congruences for
modulo 3, 5, and 9.Comment: 19 page
Finite-volume two-pion energies and scattering in the quenched approximation
We investigate how L\"uscher's relation between the finite-volume energy of
two pions at rest and pion scattering lengths has to be modified in quenched
QCD. We find that this relation changes drastically, and in particular, that
``enhanced finite-volume corrections" of order and occur at
one loop ( is the linear size of the box), due to the special properties of
the in the quenched approximation. We define quenched pion scattering
lengths, and show that they are linearly divergent in the chiral limit. We
estimate the size of these various effects in some numerical examples, and find
that they can be substantial.Comment: 22 pages, uuencoded, compressed postscript fil
Recommended from our members
Inference of the Distribution of Selection Coefficients for New Nonsynonymous Mutations Using Large Samples.
The distribution of fitness effects (DFE) has considerable importance in population genetics. To date, estimates of the DFE come from studies using a small number of individuals. Thus, estimates of the proportion of moderately to strongly deleterious new mutations may be unreliable because such variants are unlikely to be segregating in the data. Additionally, the true functional form of the DFE is unknown, and estimates of the DFE differ significantly between studies. Here we present a flexible and computationally tractable method, called Fit∂a∂i, to estimate the DFE of new mutations using the site frequency spectrum from a large number of individuals. We apply our approach to the frequency spectrum of 1300 Europeans from the Exome Sequencing Project ESP6400 data set, 1298 Danes from the LuCamp data set, and 432 Europeans from the 1000 Genomes Project to estimate the DFE of deleterious nonsynonymous mutations. We infer significantly fewer (0.38-0.84 fold) strongly deleterious mutations with selection coefficient |s| > 0.01 and more (1.24-1.43 fold) weakly deleterious mutations with selection coefficient |s| < 0.001 compared to previous estimates. Furthermore, a DFE that is a mixture distribution of a point mass at neutrality plus a gamma distribution fits better than a gamma distribution in two of the three data sets. Our results suggest that nearly neutral forces play a larger role in human evolution than previously thought
Geodesics in the space of measure-preserving maps and plans
We study Brenier's variational models for incompressible Euler equations.
These models give rise to a relaxation of the Arnold distance in the space of
measure-preserving maps and, more generally, measure-preserving plans. We
analyze the properties of the relaxed distance, we show a close link between
the Lagrangian and the Eulerian model, and we derive necessary and sufficient
optimality conditions for minimizers. These conditions take into account a
modified Lagrangian induced by the pressure field. Moreover, adapting some
ideas of Shnirelman, we show that, even for non-deterministic final conditions,
generalized flows can be approximated in energy by flows associated to
measure-preserving maps
Finite Temperature QCD with Wilson Quarks: A Study with a Renormalization Group Improved Gauge Action
Finite temperature transition in lattice QCD with degenerate Wilson quarks is
investigated on an lattice, using a renormalization group improved
gauge action. We find the following for the case:
1) The transition is smooth for a wide range of the quark mass.
2) The chiral transition is continuous.
3) The chiral condensation well satisfies a scaling relation with the
critical exponents of the 3 dimensional spin model. For , we find
that the chiral transition is of first order.Comment: 4 pages (6 figures), Postscript file, Contribution to Lattice 95
proceeding
The Kaon B-parameter with the Wilson Quark Action using Chiral Ward Identities
We present a detailed description of the method and results of our
calculation of the kaon B parameter using the Wilson quark action in quenched
QCD at . The mixing problem of the four-quark
operators is solved non-perturbatively with full use of chiral Ward identities.
We find in the continuum limit, which agrees with
the value obtained with the Kogut-Susskind quark action.Comment: 10 pages, latex source-file, 10 figures as epsf-file, uses
espcrc2.sty. Talk given at International Workshop on Lattice QCD on Parallel
Computers, 10-15 Mar 1997, Tsukuba, Japa
Conformal or Walking? Monte Carlo renormalization group studies of SU(3) gauge models with fundamental fermions
Strongly coupled gauge systems with many fermions are important in many
phenomenological models. I use the 2-lattice matching Monte Carlo
renormalization group method to study the fixed point structure and critical
indexes of SU(3) gauge models with 8 and 12 flavors of fundamental fermions.
With an improved renormalization group block transformation I am able to
connect the perturbative and confining regimes of the N_f=8 flavor system, thus
verifying its QCD-like nature. With N_f=12 flavors the data favor the existence
of an infrared fixed point and conformal phase, though the results are also
consistent with very slow walking. I measure the anomalous mass dimension in
both systems at several gauge couplings and find that they are barely different
from the free field value.Comment: 26 pages, 11 figure
- …