Theoretical planetary mass spectra - a predition for COROT

The satellite COROT will search for close-in exo-planets around a few thousand stars using the transit search method. The COROT mission holds the promise of detecting numerous exo-planets. Together with radial velocity follow-up observations, the masses of the detected planets will be known. We have devised a method for predicting the expected planetary populations and compared it to the already known exo-planets. Our method works by looking at all hydrostatic envelope solutions of giant gas planets that could possibly exist in arbitrary planetary nebulae and comparing the relative abundance of different masses. We have completed the first such survey of hydrostatic equilibria in an orbital range covering periods of 1 to 50 days. Statistical analysis of the calculated envelopes suggests division into three classes of giant planets that are distinguished by orbital separation. We term them classes G (close-in), H, and J (large separation). Each class has distinct properties such as a typical mass range. Furthermore, the division between class H and J appears to mark important changes in the formation: For close-in planets (classes G and H) the concept of a critical core-mass is meaningless while it is important for class J. This result needs confirmation by future dynamical analysis.Comment: 6 pages, 3 figures, MNRAS letter, accepted 2007 February

Social Entrepreneurship That Truly Benefits the Poor: An Integrative Justice Approach

The phenomenal growth of social entrepreneurship over thelast decade has ably demonstrated how technology, innovation, and anentrepreneurial spirit can afford better solutions to the vexing social andenvironmental problems of our time than can traditional aid and charitybasedefforts. In most cases, but not always, the poor and disadvantagedhave benefited from the growth of social entrepreneurship. In order toensure that social entrepreneurship does indeed benefit the poor, it isimperative that there be normative guidelines for fair and just engagementwith impoverished populations. A model that has been presented in themarketing and public policy literature is the integrative justice model (IJM)for impoverished populations. While the IJM was developed primarily in thecontext of multinational corporations (MNCs) operating in emerging markets,its applicability extends beyond MNCs. This article attempts to apply theIJM principles in the context of social entrepreneurship in order to providesocial entrepreneurial organizations (SEOs) with a normative frameworkaimed at ensuring that the poor truly benefit from their activities. Basedon this framework, the article suggests certain areas to which SEOs oughtto be particularly attentive in their practice. The article also makes somesuggestions for further research

Hamilton-Jacobi Approach for Power-Law Potentials

The classical and relativistic Hamilton-Jacobi approach is applied to the one-dimensional homogeneous potential, $V(q)=\alpha q^n$, where $\alpha$ and $n$ are continuously varying parameters. In the non-relativistic case, the exact analytical solution is determined in terms of $\alpha$, $n$ and the total energy $E$. It is also shown that the non-linear equation of motion can be linearized by constructing a hypergeometric differential equation for the inverse problem $t(q)$. A variable transformation reducing the general problem to that one of a particle subjected to a linear force is also established. For any value of $n$, it leads to a simple harmonic oscillator if $E>0$, an "anti-oscillator" if $E<0$, or a free particle if E=0. However, such a reduction is not possible in the relativistic case. For a bounded relativistic motion, the first order correction to the period is determined for any value of $n$. For $n >> 1$, it is found that the correction is just twice that one deduced for the simple harmonic oscillator ($n=2$), and does not depend on the specific value of $n$.Comment: 12 pages, Late

Relativistic quantum motion of spin-0 particles under the influence of non-inertial effects in the cosmic string space-time

We study solutions for the Klein-Gordon equation with vector and scalar potentials of the Coulomb types under the influence of non-inertial effects in the space-time of topological defects. We also investigate a quantum particle described by the Klein-Gordon oscillator in the background space-time generated by a string. An important result obtained is that the non-inertial effects restrict the physical region of the space-time where the particle can be placed. In addition, we show that these potentials can form bound states for the relativistic wave equation equation in this kind of background.Comment: arXiv admin note: text overlap with arXiv:1608.0669