1,250 research outputs found
Inequalities for means of chords, with application to isoperimetric problems
We consider a pair of isoperimetric problems arising in physics. The first
concerns a Schr\"odinger operator in with an attractive
interaction supported on a closed curve , formally given by
; we ask which curve of a given length
maximizes the ground state energy. In the second problem we have a loop-shaped
thread in , homogeneously charged but not conducting,
and we ask about the (renormalized) potential-energy minimizer. Both problems
reduce to purely geometric questions about inequalities for mean values of
chords of . We prove an isoperimetric theorem for -means of chords
of curves when , which implies in particular that the global extrema
for the physical problems are always attained when is a circle. The
article finishes with a discussion of the --means of chords when .Comment: LaTeX2e, 11 page
Extra quark-lepton generations and precision measurements
The existence of extra chiral generations with all fermions heavier than M_Z
is strongly disfavoured by the precision electroweak data. However the data are
fitted nicely even by a few extra generations, if one allows neutral leptons to
have masses close to 50 GeV. The data allow inclusion of one additional
generation of heavy fermions in SUSY extension of Standard Model if chargino
and neutralino have masses close to 60 GeV with \Delta m =~ 1 GeV.Comment: 14 pages, 5 figure
Action at a distance as a full-value solution of Maxwell equations: basis and application of separated potential's method
The inadequacy of Li\'{e}nard-Wiechert potentials is demonstrated as one of
the examples related to the inconsistency of the conventional classical
electrodynamics. The insufficiency of the Faraday-Maxwell concept to describe
the whole electromagnetic phenomena and the incompleteness of a set of
solutions of Maxwell equations are discussed and mathematically proved. Reasons
of the introduction of the so-called ``electrodynamics dualism concept"
(simultaneous coexistence of instantaneous Newton long-range and
Faraday-Maxwell short-range interactions) have been displayed. It is strictly
shown that the new concept presents itself as the direct consequence of the
complete set of Maxwell equations and makes it possible to consider classical
electrodynamics as a self-consistent and complete theory, devoid of inward
contradictions. In the framework of the new approach, all main concepts of
classical electrodynamics are reconsidered. In particular, a limited class of
motion is revealed when accelerated charges do not radiate electromagnetic
field.Comment: ReVTeX file, 24pp. Small corrections which do not have influence
results of the paper. Journal reference is adde
Process mapping of laser surface modification of AISI 316L stainless steel for biomedical applications
A 1.5-kW CO2 laser in pulsed mode at 3 kHz was used to investigate the effects of varied laser process parameters and resulting morphology of AISI 316L stainless steel. Irradiance and residence time were varied between 7.9 to 23.6 MW/cm2 and 50 to 167 µs respectively. A strong correlation between irradiance, residence time, depth of processing and roughness of processed steel was established. The high depth of altered microstructure and increased roughness were linked to higher levels of both irradiance and residence times. Energy fluence and surface temperature models were used to predict levels of melting occurring on the surface through the analysis of roughness and depth of the region processed. Microstructural images captured by the SEM revealed significant grain structure changes at higher irradiances, but due to increased residence times, limited to the laser in use, the hardness values were not improved
Real forms of the complex twisted N=2 supersymmetric Toda chain hierarchy in real N=1 and twisted N=2 superspaces
Three nonequivalent real forms of the complex twisted N=2 supersymmetric Toda
chain hierarchy (solv-int/9907021) in real N=1 superspace are presented. It is
demonstrated that they possess a global twisted N=2 supersymmetry. We discuss a
new superfield basis in which the supersymmetry transformations are local.
Furthermore, a representation of this hierarchy is given in terms of two
twisted chiral N=2 superfields. The relations to the s-Toda hierarchy by H.
Aratyn, E. Nissimov and S. Pacheva (solv-int/9801021) as well as to the
modified and derivative NLS hierarchies are established
Bloggers Behavior and Emergent Communities in Blog Space
Interactions between users in cyberspace may lead to phenomena different from
those observed in common social networks. Here we analyse large data sets about
users and Blogs which they write and comment, mapped onto a bipartite graph. In
such enlarged Blog space we trace user activity over time, which results in
robust temporal patterns of user--Blog behavior and the emergence of
communities. With the spectral methods applied to the projection on weighted
user network we detect clusters of users related to their common interests and
habits. Our results suggest that different mechanisms may play the role in the
case of very popular Blogs. Our analysis makes a suitable basis for theoretical
modeling of the evolution of cyber communities and for practical study of the
data, in particular for an efficient search of interesting Blog clusters and
further retrieval of their contents by text analysis
RNA Polymerase Pausing during Initial Transcription
In bacteria, RNA polymerase (RNAP) initiates transcription
by synthesizing short transcripts that are
either released or extended to allow RNAP to escape
from the promoter. The mechanism of initial transcription
is unclear due to the presence of transient
intermediates and molecular heterogeneity. Here,
we studied initial transcription on a lac promoter
using single-molecule fluorescence observations
of DNA scrunching on immobilized transcription
complexes. Our work revealed a long pause (‘‘initiation
pause,’’ �20 s) after synthesis of a 6-mer RNA;
such pauses can serve as regulatory checkpoints.
Region sigma 3.2, which contains a loop blocking
the RNA exit channel, was a major pausing determinant.
We also obtained evidence for RNA backtracking
during abortive initial transcription and for
additional pausing prior to escape. We summarized
our work in a model for initial transcription, in which
pausing is controlled by a complex set of determinants
that modulate the transition from a 6- to a
7-nt RNA
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