Equivalent power law potentials

It is shown that the radial Schroedinger equation for a power law potential and a particular angular momentum may be transformed using a change of variable into another Schroedinger equation for a different power law potential and a different angular momentum. It is shown that this leads to a mapping of the spectra of the two related power law potentials. It is shown that a similar correspondence between the classical orbits in the two related power law potentials exists. The well known correspondence of the Coulomb and oscillator spectra is a special case of a more general correspondence between power law potentials.Comment: 10 pages. Typographical mistakes in the earlier version are correcte

Adverse Selection and Private Health Insurance Coverage in India - A Rational Behaviour Model of Insurance Agents under Asymmetric Information

In the backdrop of the low level of health insurance coverage in India, this study examines the determinants of the scaling-up process of health insurance by analyzing the rational behaviour of an insurance agent facing a trade-off between selling health insurance and other forms of insurance subject to his limited time and efforts, and the implications of such behaviour on adverse selection and equity. The paper presents various pre-conditions affecting the rational behaviour of insurance agents and also discusses two new concepts insurance habit and asymmetric information on health insurance schemes. Further, the study examines various strategies followed by insurance agents for maximizing their net incomes. The theoretical proposition is empirically validated by applying a binary Probit model and the primary data collected by the author is used in this context. The study concludes that given the existing incentive systems in the Indian insurance market for promoting various forms of insurance, the low level of insurance awareness among the general public, coupled with the dominant role of insurance agents in the market results in a situation of : 1. Low level of health insurance coverage, 2. No adverse selection and 3. Inequity in health insurance coverage.Health Insurance, Insurance Agent, Asymmetric Information, Adverse Selection and Insurance Habit

Persistence based analysis of consensus protocols for dynamic graph networks

This article deals with the consensus problem involving agents with time-varying singularities in the dynamics or communication in undirected graph networks. Existing results provide control laws which guarantee asymptotic consensus. These results are based on the analysis of a system switching between piecewise constant and time-invariant dynamics. This work introduces a new analysis technique relying upon classical notions of persistence of excitation to study the convergence properties of the time-varying multi-agent dynamics. Since the individual edge weights pass through singularities and vary with time, the closed-loop dynamics consists of a non-autonomous linear system. Instead of simplifying to a piecewise continuous switched system as in literature, smooth variations in edge weights are allowed, albeit assuming an underlying persistence condition which characterizes sufficient inter-agent communication to reach consensus. The consensus task is converted to edge-agreement in order to study a stabilization problem to which classical persistence based results apply. The new technique allows precise computation of the rate of convergence to the consensus value.Comment: This article contains 7 pages and includes 4 figures. it is accepted in 13th European Control Conferenc