1,948 research outputs found
An explicit height bound for the classical modular polynomial
For a prime m, let Phi_m be the classical modular polynomial, and let
h(Phi_m) denote its logarithmic height. By specializing a theorem of Cohen, we
prove that h(Phi_m) <= 6 m log m + 16 m + 14 sqrt m log m. As a corollary, we
find that h(Phi_m) <= 6 m log m + 18 m also holds. A table of h(Phi_m) values
is provided for m <= 3607.Comment: Minor correction to the constants in Theorem 1 and Corollary 9. To
appear in the Ramanujan Journal. 17 pages
Polyelectrolyte Adsorption
The problem of charged polymer chains (polyelectrolytes) as they adsorb on a
planar surface is addressed theoretically. We review the basic mechanisms and
theory underlying polyelectrolyte adsorption on a single surface in two
situations: adsorption of a single charged chain, and adsorption from a bulk
solution in solvent conditions. The behavior of flexible and
semi-rigid chains is discussed separately and is expressed as function of the
polymer and surface charges, ionic strength of the solution and polymer bulk
concentration. We mainly review mean-field results and briefly comment about
fluctuation effects. The phenomenon of polyelectrolyte adsorption on a planar
surface as presented here is of relevance to the stabilization of colloidal
suspensions. In this respect we also mention calculations of the inter-plate
force between two planar surfaces in presence of polyelectrolyte. Finally, we
comment on the problem of charge overcompensation and its implication to
multi-layers formation of alternating positive and negative polyelectrolytes on
planar surfaces and colloidal particles.Comment: 11 pages, 4 PS figures (Latex/RevTex), submitted to C.R. Acad. Sci
(Paris
On the power counting of loop diagrams in general relativity
A class of loop diagrams in general relativity appears to have a behavior
which would upset the utility of the energy expansion for quantum effects. We
show through the study of specific diagrams that cancellations occur which
restore the expected behaviour of the energy expansion. By considering the
power counting in a physical gauge we show that the apparent bad behavior is a
gauge artifact, and that the quantum loops enter with a well behaved energy
expansion.Comment: 29 pages, uses axodraw and epsfig.tex, one small .eps file is
included. The full PostScript version is also available as
http://het.phast.umass.edu/students/kakukk/powercount_hepth.p
A note on the index bundle over the moduli space of monopoles
Donaldson has shown that the moduli space of monopoles is diffeomorphic
to the space \Rat_k of based rational maps from the two-sphere to itself. We
use this diffeomorphism to give an explicit description of the bundle on
\Rat_k obtained by pushing out the index bundle from . This gives an
alternative and more explicit proof of some earlier results of Cohen and Jones.Comment: 9 page
On the String Consensus Problem and the Manhattan Sequence Consensus Problem
In the Manhattan Sequence Consensus problem (MSC problem) we are given
integer sequences, each of length , and we are to find an integer sequence
of length (called a consensus sequence), such that the maximum
Manhattan distance of from each of the input sequences is minimized. For
binary sequences Manhattan distance coincides with Hamming distance, hence in
this case the string consensus problem (also called string center problem or
closest string problem) is a special case of MSC. Our main result is a
practically efficient -time algorithm solving MSC for sequences.
Practicality of our algorithms has been verified experimentally. It improves
upon the quadratic algorithm by Amir et al.\ (SPIRE 2012) for string consensus
problem for binary strings. Similarly as in Amir's algorithm we use a
column-based framework. We replace the implied general integer linear
programming by its easy special cases, due to combinatorial properties of the
MSC for . We also show that for a general parameter any instance
can be reduced in linear time to a kernel of size , so the problem is
fixed-parameter tractable. Nevertheless, for this is still too large
for any naive solution to be feasible in practice.Comment: accepted to SPIRE 201
Delocalization of the axial charge in the chiral limit
The nucleon's axial vector charge, g_A, becomes delocalized in the chiral
limit. When m_\pi = 0, and SU(2)_L x SU(2)_R is exact, 1/3 of the nucleon's
axial charge is to be found at infinite distance from the nucleon. For finite
m_\pi this result is approached smoothly as m_\pi -> 0. We illustrate this
effect by considering the lepton-proton spin-spin interaction arising from Z^0
exchange as a function of m_\pi. Delocalization may have implications for
lattice calculations of g_A and in nuclei.Comment: Revised content: Further explanation of the limit m_pi -> 0 and an
example of a physical process (spin-spin interaction in a hydrogenic atom
mediated by Z^0 exchange) which can, in principle, measure the delocalization
of g_A. Ten pages using RevTeX; email correspondence to R.L. Jaffe
<[email protected]
In vitro and in vivo ocular biocompatibility of electrospun poly(ɛ-caprolactone) nanofibers.
Biocompatibility is a requirement for the development of nanofibers for ophthalmic applications. In this study, nanofibers were elaborated using poly(ε-caprolactone) via electrospinning. The ocular biocompatibility of this material was investigated. MIO-M1 and ARPE-19 cell cultures were incubated with nanofibers and cellular responses were monitored by viability and morphology. The in vitro biocompatibility revealed that the nanofibers were not cytotoxic to the ocular cells. These cells exposed to the nanofibers proliferated and formed an organized monolayer. ARPE-19 and MIO-M1 cells were capable of expressing GFAP, respectively, demonstrating their functionality. Nanofibers were inserted into the vitreous cavity of the rat's eye for 10days and the in vivo biocompatibility was investigated using Optical Coherence Tomography (OCT), histology and measuring the expression of pro-inflammatory genes (IL-1β, TNF-α, VEGF and iNOS) (real-time PCR). The OCT and the histological analyzes exhibited the preserved architecture of the tissues of the eye. The biomaterial did not elicit an inflammatory reaction and pro-inflammatory cytokines were not expressed by the retinal cells, and the other posterior tissues of the eye. Results from the biocompatibility studies indicated that the nanofibers exhibited a high degree of cellular biocompatibility and short-term intraocular tolerance, indicating that they might be applied as drug carrier for ophthalmic use
Role of Scalar Meson Resonances in $K_{L}^{0} \rightarrow \pi^{0} \gamma \gamma Decay
Corrections to decay induced by
scalar meson exchange are studied within chiral perturbation theory. In spite
of bad knowledge of scalar-mesons parameters, the calculated branching ratio
can be changed by a few percent.Comment: 18 pages of text, 2 figures (available upon request); preprint
IJS-TP-16-94 , TUM-T31-63-94
Parity Doubling Among the Baryons
We study the evidence for and possible origins of parity doubling among the
baryons. First we explore the experimental evidence, finding a significant
signal for parity doubling in the non-strange baryons, but little evidence
among strange baryons. Next we discuss potential explanations for this
phenomenon. Possibilities include suppression of the violation of the flavor
singlet axial symmetry () of QCD, which is broken by the triangle
anomaly and by quark masses. A conventional Wigner-Weyl realization of the
chiral symmetry would also result in parity
doubling. However this requires the suppression of families of \emph{chirally
invariant} operators by some other dynamical mechanism. In this scenario the
parity doubled states should decouple from pions. We discuss other explanations
including connections to chiral invariant short distance physics motivated by
large arguments as suggested by Shifman and others, and intrinsic
deformation of relatively rigid highly excited hadrons, leading to parity
doubling on the leading Regge trajectory. Finally we review the spectroscopic
consequences of chiral symmetry using a formalism introduced by Weinberg, and
use it to describe two baryons of opposite parity.Comment: 32 pages, 8 figures; v2 revised and expanded; submitted to Phys. Re
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