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

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