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

On constrained uniform approximation

The problem of uniform approximants subject to Hermite interpolatory constraints is considered with an alternate approach. The uniqueness and the convergence aspects of this problem are also discussed. Our approach is based on work of P. Kirchberger (1903) and a generalization of Weierstrass approximation theorem

Benign Osteoblastoma Involving Maxilla: A Case Report and Review of the Literature

Background. Osteoblastoma is a rare benign tumor. This tumor is characterized by osteoid and bone formation with the presence of numerous osteoblasts. The lesion is more frequently seen in long bones and rarely involves maxilla and mandible. Due to its clinical and histological similarity with other bone tumors such as osteoid osteoma and fibro-osseous lesions, osteoblastoma presents a diagnostic dilemma. Case Report. Very few cases of osteoblastomas involving maxillofacial region have been reported in the literature. This case report involves osteoblastoma involving right maxilla in an 18-year-old male patient. Following detailed clinical examination, radiological interpretation, and histopathological diagnosis, surgical excision was performed. The patient was followed up for a period of 3 years and was disease free. Summary and Conclusion. Benign osteoblastoma involving jaw bones is a rare tumor. There is a close resemblance of this tumor with other lesions such as fibro-osseous lesions and odontogenic tumors and thus faces a diagnostic challenge. Surgical excision with a long-term follow-up gives good prognosis to this lesion—Benign Osteoblastoma

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

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

Photoexcitation and photoionization from the 2p53p[5/2]2,3 levels in neon

We present measurements of the excitation spectra from the 2p53p [5/2]3,2 levels in neon using two-step laser excitation and ionization in conjunction with an optogalvanic detection in dc and rf discharge cells. The 2p53p [5/2]3,2 intermediate levels have been approached via the collisionally populated 2p53s [3/2]2 metastable level. The Rydberg series 2p5(2P3/2)nd [7/2]4 (12 ⩽ n ⩽ 44), 2p5(2P3/2)ns [3/2]2 (13 ⩽ n ⩽ 35) and the parity forbidden transitions 2p5(2P3/2)np [5/2]3 (13 ⩽ n ⩽ 19) have been observed from the 2p53p [5/2]3 level, whereas the 2p5(2P3/2)nd [7/2]3 (12 ⩽ n ⩽ 44), 2p5(2P3/2)ns [3/2]2 (13 ⩽ n ⩽ 35), and 2p5(2P1/2)nd′ [5/2]3 (9 ⩽ n ⩽ 12) Rydberg series have been observed from the 2p53p[5/2]2 level in accordance with the ΔJ = ΔK = ± 1 selection rules. The photoionization cross sections from the 2p53p [5/2]3 intermediate level have been measured at eight ionizing laser wavelengths (399, 395, 390, 385, 380, 370, 364, and 355 nm) and that from the 2p53p [5/2]2 level at 401.8 nm. These measurements are in excellent agreement with the experimental values reported in the literature, while the experimental data lie much below the theoretically calculated photoionization cross sections curve

Positive impact of low-dose, high-energy radiation on bone in partial- and/or full-weightbearing mice

Astronauts traveling beyond low Earth orbit will be exposed to galactic cosmic radiation (GCR); understanding how high energy ionizing radiation modifies the bone response to mechanical unloading is important to assuring crew health. To investigate this, we exposed 4-mo-old female Balb/cBYJ mice to an acute space-relevant dose of 0.5 Gy 56Fe or sham (n = ~8/group); 4 days later, half of the mice were also subjected to a ground-based analog for 1/6 g (partial weightbearing) (G/6) for 21 days. Microcomputed tomography (µ-CT) of the distal femur reveals that 56Fe exposure resulted in 65-78% greater volume and improved microarchitecture of cancellous bone after 21 d compared to sham controls. Radiation also leads to significant increases in three measures of energy absorption at the mid-shaft femur and an increase in stiffness of the L4 vertebra. No significant effects of radiation on bone formation indices are detected; however, G/6 leads to reduced % mineralizing surface on the inner mid-tibial bone surface. In separate groups allowed 21 days of weightbearing recovery from G/6 and/or 56Fe exposure, radiation-exposed mice still exhibit greater bone mass and improved microarchitecture vs. sham control. However, femoral bone energy absorption values are no longer higher in the 56Fe-exposed WB mice vs. sham controls. We provide evidence for persistent positive impacts of high-LET radiation exposure preceding a period of full or partial weightbearing on bone mass and microarchitecture in the distal femur and, for full weightbearing mice only and more transiently, cortical bone energy absorption values

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