Matter Inheritance Symmetries of Spherically Symmetric Static Spacetimes

In this paper we discuss matter inheritance collineations by giving a complete classification of spherically symmetric static spacetimes by their matter inheritance symmetries. It is shown that when the energy-momentum tensor is degenerate, most of the cases yield infinite dimensional matter inheriting symmetries. It is worth mentioning here that two cases provide finite dimensional matter inheriting vectors even for the degenerate case. The non-degenerate case provides finite dimensional matter inheriting symmetries. We obtain different constraints on the energy-momentum tensor in each case. It is interesting to note that if the inheriting factor vanishes, matter inheriting collineations reduce to be matter collineations already available in the literature. This idea of matter inheritance collineations turn out to be the same as homotheties and conformal Killing vectors are for the metric tensor.Comment: 15 pages, accepted for publication in Int. J. of Mod. Phys.

Ricci Collineations for Non-Degenerate, Diagonal and Spherically Symmetric Ricci Tensors

The expression of the vector field generator of a Ricci Collineation for diagonal, spherically symmetric and non-degenerate Ricci tensors is obtained. The resulting expressions show that the time and radial first derivatives of the components of the Ricci tensor can be used to classify the collineation, leading to 64 families. Some examples illustrate how to obtain the collineation vector

Augmenting computer networks

Three methods of augmenting computer networks by adding at most one link per processor are discussed: (1) A tree of N nodes may be augmented such that the resulting graph has diameter no greater than 4log sub 2((N+2)/3)-2. Thi O(N(3)) algorithm can be applied to any spanning tree of a connected graph to reduce the diameter of that graph to O(log N); (2) Given a binary tree T and a chain C of N nodes each, C may be augmented to produce C so that T is a subgraph of C. This algorithm is O(N) and may be used to produce augmented chains or rings that have diameter no greater than 2log sub 2((N+2)/3) and are planar; (3) Any rectangular two-dimensional 4 (8) nearest neighbor array of size N = 2(k) may be augmented so that it can emulate a single step shuffle-exchange network of size N/2 in 3(t) time steps

Conformal Ricci collineations of static spherically symmetric spacetimes

Conformal Ricci collineations of static spherically symmetric spacetimes are studied. The general form of the vector fields generating conformal Ricci collineations is found when the Ricci tensor is non-degenerate, in which case the number of independent conformal Ricci collineations is \emph{fifteen}; the maximum number for 4-dimensional manifolds. In the degenerate case it is found that the static spherically symmetric spacetimes always have an infinite number of conformal Ricci collineations. Some examples are provided which admit non-trivial conformal Ricci collineations, and perfect fluid source of the matter

Fast orthogonal derivatives on the star

AbstractIn many numerical problems there is the need for obtaining derivatives in the X and Y directions of m variables at each point on an n×n plane. We consider the case where these derivatives are obtained using spectral methods (i.e. n fast Fourier transforms of length n are taken for each component, multiplied by the wave numbers and reverse transformed).On the CDC STAR-100 all data points corresponding to a plane must be stored in contiguous locations if advantage is to be taken of the powerful pipeline hardware of the machine. This means that derivatives in one direction are obtained very efficiently while derivatives in the orthogonal direction require either the substantial overhead of transposition or the use of scalar operations with no benefits of pipelining.An algorithm is described that overcomes this problem by taking derivatives of all components simultaneously. This is made possible by perfect shuffling of data to effect a pseudo-transposition that permits the FFT routine to take transforms of all m components on a plane at one time. Practical experience with this algorithm for m=5 and n=32 shows a 10% speedup for X-derivatives and a 32% speedup for Y-derivatives over the conventional algorithms (in which X and Y derivatives are taken one component at a time and Y derivatives require transposition of data).A theoretical analysis based on available STAR-100 vector instruction timing data predicts that this algorithm is superior to the conventional algorithm for M ≥ 2, n ≤ 128 (problem sizes of practical interest). We show how further improvement in running time may be obtained if derivatives of several components on more than one plane are required.This analysis is applicable to the new generation of STAR computers (the CDC Cyber 203s) since vector instruction timings are essentially unchanged in the new machines

[Accepted Manuscript] Galleria mellonella is low cost and suitable surrogate host for studying virulence of human pathogenic Vibrio cholerae.

Vibrio cholerae causes a severe diarrheal disease affecting millions of people worldwide, particularly in low income countries. V. cholerae successfully persist in aquatic environment and its pathogenic strains results in sever enteric disease in humans. This dual life style contributes towards its better survival and persistence inside host gut and in the environment. Alternative animal replacement models are of great value in studying host-pathogen interaction and for quick screening of various pathogenic strains. One such model is Galleria mellonella, a wax worm which has a complex innate immune system and here we investigate its suitability as a model for clinical human isolates of O1 El TOR, Ogawa serotype belonging to two genetically distinct subclades found in Pakistan (PSC-1 and PSC-2). We demonstrate that the PSC-2 strain D59 frequently isolated from inland areas, was more virulent than PSC-1 strain K7 mainly isolated from coastal areas (p=0.0001). In addition, we compared the relative biofilm capability of the representative strains as indicators of their survival and persistence in the environment and K7 showed enhanced biofilm forming capabilities (p=0.004). Finally we present the annotated genomes of the strains D59 and K7, and compared them with the reference strain N16961

Wave Equation on Spherically Symmetric Lorentzian Metrics

Wave equation on a general spherically symmetric spacetime metric is constructed. Noether symmetries of the equation in terms of explicit functions of θ and ϕ are derived subject to certain differential constraints. By restricting the metric to flat Friedman case the Noether symmetries of the wave equation are presented. Invertible transformations are constructed from a specific subalgebra of these Noether symmetries to convert the wave equation with variable coefficients to the one with constant coefficients

Weyl collineations that are not curvature collineations

Though the Weyl tensor is a linear combination of the curvature tensor, Ricci tensor and Ricci scalar, it does not have all and only the Lie symmetries of these tensors since it is possible, in principle, that "asymmetries cancel". Here we investigate if, when and how the symmetries can be different. It is found that we can obtain a metric with a finite dimensional Lie algebra of Weyl symmetries that properly contains the Lie algebra of curvature symmetries. There is no example found for the converse requirement. It is speculated that there may be a fundamental reason for this lack of "duality".Comment: 9 page

Youth Driven Engagement in the Homestay Program

Community-based tourism (CBT) is one of the tourist attracting ways involving local community which aims to develop and to enhance the era as well as to bring renewal to the local community. It includes the involvement of youth. CBT comes in various types and this study was conducted to find how CBT can create youth engagement in the homestay program. There were various factors that motivate youth to participate in homestay program. This study involved one case study of a qualitative study conducted in a district in Sabah, namely in Kundasang. In this study, Mersilou Homestay and Walai Tokou Homestay were chosen to be used as a place of study to review factors youth engagement in the homestay program. Data collection was through interviews in partial structures. Data were analyzed using NviVo 10 software and based on certain themes. The findings shown that there were several factors which drive engagement of youth in the homestay program in terms of interests, income, parental encouragement and comfort working in their own areas. In conclusion, the engagement of youth in the homestay program is based on the factors discovered in the study