Anisotropic spheres with uniform energy density in general relativity

An ansatz is developed to obtain interior solutions of the Einstein field equations for anisotropic spheres. This procedure necessitates a choice for the energy-density and the radial pressure. A class of solutions for a uniform energy-density source is presented. These anisotropic spheres match smoothly to the Schwarzschild exterior and are well-behaved in the interior of the sphere.     

On the qth power algorithm

Leonard and Pellikaan developed the qth power algorithm to compute module bases for the integral closure of the polynomial ring in a class of function fields. In this paper, their algorithm is adapted to efficiently obtain an -basis for a class of Riemann–Roch spaces without having to compute the entire integral closure. This reformulation allows one to determine the complexity of the algorithm. Further, we obtain a simple characterization of the integral closure.     

Quenching of aromatic ketone phosphorescence by sterically hindered alkenes

The deactivation of the excited states of triplet ketones by sterically hindered alkenes results in lower rate constants (usually due to increased activation energies) than by relatively unhindered alkenes.     

A Tolman-like Compact Model with Conformal Geometry

In this investigation, we study a model of a charged anisotropic compact star by assuming a relationship between the metric functions arising from a conformal symmetry. This mechanism leads to a first-order differential equation containing pressure anisotropy and the electric field. Particular forms of the electric field intensity, combined with the Tolman VII metric, are used to solve the Einstein–Maxwell field equations. New classes of exact solutions generated are expressed in terms of elementary functions. For specific parameter values based on the physical requirements, it is shown that the model satisfies the causality, stability and energy conditions. Numerical values generated for masses, radii, central densities, surface redshifts and compactness factors are consistent with compact objects such as PSR J1614-2230 and SMC X-1.     

A coherence-based approach for the pattern recognition of time series

A pattern recognition approach based on the frequency domain measure of squared coherence is a useful approach to identify linearly related groupings of time series over different periods of time. It is considered in an application to identify similar patterns of the yearly rates of change in the Gross Domestic Product (GDP) of twenty two highly developed countries in an econophysics context. The approach is also tested in simulation studies using linearly related time series, and it is shown to have a very good success rate of correct pattern matching.     

Regular models with quadratic equation of state

We provide new exact solutions to the Einstein–Maxwell system of equations which are physically reasonable. The spacetime is static and spherically symmetric with a charged matter distribution. We utilise an equation of state which is quadratic relating the radial pressure to the energy density. Earlier models, with linear and quadratic equations of state, are shown to be contained in our general class of solutions. The new solutions to the Einstein–Maxwell are found in terms of elementary functions. A physical analysis of the matter and electromagnetic variables indicates that the model is well behaved and regular. In particular there is no singularity in the proper charge density at the stellar centre unlike earlier anisotropic models in the presence of the electromagnetic field.     

A wavelet based investigation of long memory in stock returns

Using a wavelet-based maximum likelihood fractional integration estimator, we test long memory (return predictability) in the returns at the market, industry and firm level. In an analysis of emerging market daily returns over the full sample period, we find that long-memory is not present and in approximately twenty percent of 175 stocks there is evidence of long memory. The absence of long memory in the market returns may be a consequence of contemporaneous aggregation of stock returns. However, when the analysis is carried out with rolling windows evidence of long memory is observed in certain time frames. These results are largely consistent with that of detrended fluctuation analysis. A test of firm-level information in explaining stock return predictability using a logistic regression model reveal that returns of large firms are more likely to possess long memory feature than in the returns of small firms. There is no evidence to suggest that turnover, earnings per share, book-to-market ratio, systematic risk and abnormal return with respect to the market model is associated with return predictability. However, degree of long-range dependence appears to be associated positively with earnings per share, systematic risk and abnormal return and negatively with book-to-market ratio.     

Generalized Euclidean stars with equation of state

This article has a dual purpose: i) to provide a flavor of the scientific highlights of the landmark conference, GR3, held in July 1962 at Jablonna, near Warsaw; and, ii) to present a bird’s eye view of the tremendous advances that have occurred over the half century that separates GR3 and GR20, which was again held in Warsaw in July 2013.     

Conformal symmetries in static spherically symmetric spacetimes

We obtain the conformal symmetry vector in static, spherically symmetric spacetimes, in terms of functions subject to a number of integrability conditions that also place restrictions on the metric. Some conformal symmetries found previously are regained as special cases.