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.

Efficient algorithms for a class of partitioning problems

The problem of optimally partitioning the modules of chain- or tree-like tasks over chain-structured or host-satellite multiple computer systems is addressed. This important class of problems includes many signal processing and industrial control applications. Prior research has resulted in a succession of faster exact and approximate algorithms for these problems. Polynomial exact and approximate algorithms are described for this class that are better than any of the previously reported algorithms. The approach is based on a preprocessing step that condenses the given chain or tree structured task into a monotonic chain or tree. The partitioning of this monotonic take can then be carried out using fast search techniques

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

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

Parametric binary dissection

Binary dissection is widely used to partition non-uniform domains over parallel computers. This algorithm does not consider the perimeter, surface area, or aspect ratio of the regions being generated and can yield decompositions that have poor communication to computation ratio. Parametric Binary Dissection (PBD) is a new algorithm in which each cut is chosen to minimize load + lambda x(shape). In a 2 (or 3) dimensional problem, load is the amount of computation to be performed in a subregion and shape could refer to the perimeter (respectively surface) of that subregion. Shape is a measure of communication overhead and the parameter permits us to trade off load imbalance against communication overhead. When A is zero, the algorithm reduces to plain binary dissection. This algorithm can be used to partition graphs embedded in 2 or 3-d. Load is the number of nodes in a subregion, shape the number of edges that leave that subregion, and lambda the ratio of time to communicate over an edge to the time to compute at a node. An algorithm is presented that finds the depth d parametric dissection of an embedded graph with n vertices and e edges in O(max(n log n, de)) time, which is an improvement over the O(dn log n) time of plain binary dissection. Parallel versions of this algorithm are also presented; the best of these requires O((n/p) log(sup 3)p) time on a p processor hypercube, assuming graphs of bounded degree. How PBD is applied to 3-d unstructured meshes and yields partitions that are better than those obtained by plain dissection is described. Its application to the color image quantization problem is also discussed, in which samples in a high-resolution color space are mapped onto a lower resolution space in a way that minimizes the color error

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

Lie and Noether symmetries of geodesic equations and collineations

The Lie symmetries of the geodesic equations in a Riemannian space are computed in terms of the special projective group and its degenerates (affine vectors, homothetic vector and Killing vectors) of the metric. The Noether symmetries of the same equations are given in terms of the homothetic and the Killing vectors of the metric. It is shown that the geodesic equations in a Riemannian space admit three linear first integrals and two quadratic first integrals. We apply the results in the case of Einstein spaces, the Schwarzschild spacetime and the Friedman Robertson Walker spacetime. In each case the Lie and the Noether symmetries are computed explicitly together with the corresponding linear and quadratic first integrals.Comment: 19 page

Investigation of Parietal Polysaccharides from Retama raetam Roots

This study characterizes the cell wall hemicellulose and pectins polymers of Retama raetam. This species develops a particularly important root system and is adapted to arid areas. The cellulose, hemicelluloses and pectins were extracted. The cellulose remains the major component of the wall (27% for young roots and 80% for  adult roots), hemicelluloses (14.3% for young roots and 3.6%  for adult roots) and pectins (17.3% for young roots and 4.1% for adult roots). The monosaccharidic composition of water soluble extracts determined by gas liquid chromatography (GLC) and completed by infrared (FTIR) spectroscopy of hemicellulosic shows the presence of xylose as a major monosaccharide in the non-cellulose polysaccharides (47.8% for young roots and 59.5% for adult roots). These results indicate the presence of the homogalacturonans and rhamnogalacturonans in pectin. This study constitutes the preliminary data obtained in the biochemical analysis of the parietal compounds of the roots of a species which grows in an arid area in comparison with those of its aerial parts.Keywords: Retama raetam, Roots, Cell Wall, Investigation, Polysaccharides, Monosaccharidi

Ricci Collineations of the Bianchi Type II, VIII, and IX Space-times

Ricci and contracted Ricci collineations of the Bianchi type II, VIII, and IX space-times, associated with the vector fields of the form (i) one component of $\xi^a(x^b)$ is different from zero and (ii) two components of $\xi^a(x^b)$ are different from zero, for $a,b=1,2,3,4$, are presented. In subcase (i.b), which is $\xi^a= (0,\xi^2(x^a),0,0)$, some known solutions are found, and in subcase (i.d), which is $\xi^a =(0,0,0,\xi^4(x^a))$, choosing $S(t)=const.\times R(t)$, the Bianchi type II, VIII, and IX space-times is reduced to the Robertson-Walker metric.Comment: 12 Pages, LaTeX, 1 Table, no figure