59,001 research outputs found

### Checking the transverse Ward-Takahashi relation at one loop order in 4-dimensions

Some time ago Takahashi derived so called {\it transverse} relations relating
Green's functions of different orders to complement the well-known
Ward-Green-Takahashi identities of gauge theories by considering wedge rather
than inner products. These transverse relations have the potential to determine
the full fermion-boson vertex in terms of the renormalization functions of the
fermion propagator. He & Yu have given an indicative proof at one-loop level in
4-dimensions. However, their construct involves the 4th rank Levi-Civita tensor
defined only unambiguously in 4-dimensions exactly where the loop integrals
diverge. Consequently, here we explicitly check the proposed transverse
Ward-Takahashi relation holds at one loop order in $d$-dimensions, with
$d=4+\epsilon$.Comment: 20 pages, 3 figures This version corrects and clarifies the previous
result. This version has been submitted for publicatio

### Effects of turbulent dust grain motion to interstellar chemistry

Theoretical studies have revealed that dust grains are usually moving fast
through the turbulent interstellar gas, which could have significant effects
upon interstellar chemistry by modifying grain accretion. This effect is
investigated in this work on the basis of numerical gas-grain chemical
modeling. Major features of the grain motion effect in the typical environment
of dark clouds (DC) can be summarised as follows: 1) decrease of gas-phase
(both neutral and ionic) abundances and increase of surface abundances by up to
2-3 orders of magnitude; 2) shifts of the existing chemical jumps to earlier
evolution ages for gas-phase species and to later ages for surface species by
factors of about ten; 3) a few exceptional cases in which some species turn out
to be insensitive to this effect and some other species can show opposite
behaviors too. These effects usually begin to emerge from a typical DC model
age of about 10^5 yr. The grain motion in a typical cold neutral medium (CNM)
can help overcome the Coulomb repulsive barrier to enable effective accretion
of cations onto positively charged grains. As a result, the grain motion
greatly enhances the abundances of some gas-phase and surface species by
factors up to 2-6 or more orders of magnitude in the CNM model. The grain
motion effect in a typical molecular cloud (MC) is intermediate between that of
the DC and CNM models, but with weaker strength. The grain motion is found to
be important to consider in chemical simulations of typical interstellar
medium.Comment: 20 pages, 10 figures and 2 table

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### Filtering for networked stochastic time-delay systems with sector nonlinearity

Copyright [2009] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This paper is concerned with the filtering problem for a class of discrete-time stochastic nonlinear networked control systems with network-induced incomplete measurements. The incomplete measurements include both the multiple random communication delays and random packet losses, which are modeled by a unified stochastic expression in terms of a set of indicator functions that is dependent on certain stochastic variable. The nonlinear functions are assumed to satisfy the sector nonlinearities. The purpose of the addressed filtering problem is to design a linear filter such that the filtering-error dynamics is exponentially mean-square stable. By using the linear-matrix-inequality (LMI) method and delay-dependent technique, sufficient conditions are derived which are dependent on the occurrence probability of both the random communication delays and missing measurement. The filter gain is then characterized by the solution to a set of LMIs. A simulation example is exploited to demonstrate the effectiveness of the proposed design procedures

### Convergence of Adaptive Finite Element Approximations for Nonlinear Eigenvalue Problems

In this paper, we study an adaptive finite element method for a class of a
nonlinear eigenvalue problems that may be of nonconvex energy functional and
consider its applications to quantum chemistry. We prove the convergence of
adaptive finite element approximations and present several numerical examples
of micro-structure of matter calculations that support our theory.Comment: 24 pages, 12 figure

### Bipartite graph partitioning and data clustering

Many data types arising from data mining applications can be modeled as
bipartite graphs, examples include terms and documents in a text corpus,
customers and purchasing items in market basket analysis and reviewers and
movies in a movie recommender system. In this paper, we propose a new data
clustering method based on partitioning the underlying bipartite graph. The
partition is constructed by minimizing a normalized sum of edge weights between
unmatched pairs of vertices of the bipartite graph. We show that an approximate
solution to the minimization problem can be obtained by computing a partial
singular value decomposition (SVD) of the associated edge weight matrix of the
bipartite graph. We point out the connection of our clustering algorithm to
correspondence analysis used in multivariate analysis. We also briefly discuss
the issue of assigning data objects to multiple clusters. In the experimental
results, we apply our clustering algorithm to the problem of document
clustering to illustrate its effectiveness and efficiency.Comment: Proceedings of ACM CIKM 2001, the Tenth International Conference on
Information and Knowledge Management, 200

### New Parametrization of Neutrino Mixing Matrix

Global fits to neutrino oscillation data are compatible with tri-bimaximal
mixing pattern, which predicts $\theta_{23} = \frac{\pi}{4}, \theta_{12} =
\sin^{-1} (\frac{1}{\sqrt{3}})$ and $\theta_{13} = 0$. We propose here to
parametrize the tri-bimaximal mixing matrix $V_{TBM}$ by its hermitian
generator $H_{TBM}$ using the exponential map. Then we use the exponential map
to express the deviations from tri-bimaximal pattern by deriving the hermitian
matrices $H_{z=0}$ and $H_1$. These deviations might come from the symmetry
breaking of the neutrino and charged lepton sectors.Comment: 10 pages, no figures, correted minor typo

### The Tensor Current Divergence Equation in U(1) Gauge Theories is Free of Anomalies

The possible anomaly of the tensor current divergence equation in U(1) gauge
theories is calculated by means of perturbative method. It is found that the
tensor current divergence equation is free of anomalies.Comment: Revtex4, 7 pages, 2 figure

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