Characterization of stadium-like domains via boundary value problems for the infinity Laplacian

We give a complete characterization, as "stadium-like domains", of convex subsets $\Omega$ of $\mathbb{R}^n$ where a solution exists to Serrin-type overdetermined boundary value problems in which the operator is either the infinity Laplacian or its normalized version. In case of the not-normalized operator, our results extend those obtained in a previous work, where the problem was solved under some geometrical restrictions on $\Omega$. In case of the normalized operator, we also show that stadium-like domains are precisely the unique convex sets in $\mathbb{R}^n$ where the solution to a Dirichlet problem is of class $C^{1,1} (\Omega)$.Comment: 21 page

The Future Asymptotic Behaviour of a Non-Tilted Bianchi Type IV Viscous Model

The future asymptotic behaviour of a non-titled Bianchi Type IV viscous fluid model is analyzed. In particular, we consider the case of a viscous fluid without heat conduction, and constant expansion-normalized bulk and shear viscosity coefficients. We show using dynamical systems theory that the only future attracting equilibrium points are the flat Friedmann-LeMaitre (FL) solution, the open FL solution and the isotropic Milne universe solution. We also show the bifurcations exist with respect to an increasing expansion-normalized bulk viscosity coefficient. It is finally shown through an extensive numerical analysis, that the dynamical system isotropizes at late times

Ricci flow on surfaces with conical singularities

This paper studies the normalized Ricci flow on surfaces with conical singularities. It's proved that the normalized Ricci flow has a solution for a short time for initial metrics with conical singularities. Moreover, the solution makes good geometric sense. For some simple surfaces of this kind, for example, the tear drop and the football, it's shown that they admit Ricci soliton metric.Comment: There is no revision to the paper, just this comment. Recently I found a gap in the proof of Theorem 1.1. Please see Remark 1.2 of arXiv:1305.4355 for detail

Normalization of the wavefunction obtained from perturbation theory based on a matrix method

We present the derivation of the normalization constant for the perturbation matrix method recently proposed. The method is tested on the problem of a binary waveguide array for which an exact and an approximate solution are known. In our analysis, we show that to third order the normalized matrix method approximate solution gives results coinciding with the exact known solution

Improving aircraft maintenance, repair, and overhaul: A novel text mining approach

Aircraft Maintenance, Repair and Overhaul (MRO) feedback commonly includes an engineer’s complex text-based inspection report. Capturing and normalizing the content of these textual descriptions is vital to cost and quality benchmarking, and provides information to facilitate continuous improvement of MRO process and analytics. As data analysis and mining tools requires highly normalized data, raw textual data is inadequate. This paper offers a textual-mining solution to efficiently analyse bulk textual feedback data. Despite replacement of the same parts and/or sub-parts, the actual service cost for the same repair is often distinctly different from similar previously jobs. Regular expression algorithms were incorporated with an aircraft MRO glossary dictionary in order to help provide additional information concerning the reason for cost variation. Professional terms and conventions were included within the dictionary to avoid ambiguity and improve the outcome of the result. Testing results show that most descriptive inspection reports can be appropriately interpreted, allowing extraction of highly normalized data. This additional normalized data strongly supports data analysis and data mining, whilst also increasing the accuracy of future quotation costing. This solution has been effectively used by a large aircraft MRO agency with positive results