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

Agile optical confocal microscopy instrument architectures for high flexibility imaging

Ideally, a no-moving parts fast and agile scanning confocal microscope system is required that can produce true real-time 3-D scans with precision and repeatability. In this paper, such agile optical confocal microsopy designs are proposed that enable high speed precise non-invasive 3-D imaging. These compact confocal microscopes can provide real-time pin-point focussed imaging to enable confocal slices in-vivo, thus greatly reducing motion artifacts. These microscopes can be modified into interferometric microscopes for phase contrast imaging. The proposed microscopes can also greatly improve confocal fluorescence imaging as needed for cancer detection. An ultracompact confocal probe tip connected to a single ultra-thin fiber is another design option allowing flexibility for usage in tight cavities

An analysis of the impact of soft skills on Malaysian technical institutions

Many people recognize the importance of technical skills as knowledge and proficiencies required in the accomplishment of professional jobs. However, the importance and applicability of soft skills are mostly ignored despite the fact that, it is a process how individual carry himself in an organization or professional environment for the progress of that individual and the organization he found himself. The paper explored into some journals from the previous the literatures, some soft skills were identified such as communication, lifelong learning, entrepreneurship, leadership, and teamwork, problem solving and critical among TVET institutions in Malaysia. Document analysis was conducted as a methodology for this study. The impacts of these soft skills on TVET related institutions like polytechnics, training centers and universities in Malaysia. It was indicated that, the result of the impact of soft skills on these institutions was generally moderate. The paper concluded that, technical skills alone could not bring about the organizational development there must be a compliment of soft skills for any organizational sustainability. Supplementary of soft and technical skills conceptual model was formulated. The paper was concluded by saying that, the competitive nature of the present situation, soft skills are essential because they have affected all aspect of human development. Some recommendations were suggested, teachers, lecturers and instructor must teach students soft skills for complete individual proficiencies and organizational sustainability

Demand estimation and merger simulations for drugs: Logits v. AIDS

We use ADHD drugs sales data from 2000-2003 and compare estimates of elasticities and merger simulations from three different demand models. Models include logit, random coefficients logit, and conditional AIDS demand model with multistage budgeting. The magnitude of cross-price elasticities is larger in the third model in comparison to the first two, and some of the cross-price elasticities are estimated to be negative. Hypothetical merger simulations show larger price effects for the multistage AIDS model in comparison to the discrete choice models

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

Selecting Miners within Blockchain-based Systems Using Evolutionary Algorithms for Energy Optimisation

In this paper, we represent the problem of selecting miners within a blockchain-based system as a subset selection problem. We formulate the problem of minimising blockchain energy consumption as an optimisation problem with two conflicting objectives: energy consumption and trust. The proposed model is compared across different algorithms to demonstrate its performance.Comment: To appear in 2021 Genetic and Evolutionary Computation Conference Companion (GECCO '21 Companion), July 10--14, 2021, Lille, Franc