Approximation of Entropy Numbers

The purpose of this article is to develop a technique to estimate certain bounds for entropy numbers of diagonal operator on spaces of p-summable sequences for finite p greater than 1. The approximation method we develop in this direction works for a very general class of operators between Banach spaces, in particular reflexive spaces. As a consequence of this technique we also obtain that the entropy number of a bounded linear operator T between two separable Hilbert spaces is equal to the entropy number of the adjoint of T. This gives a complete answer to the question posed by B. Carl [4] in the setting of separable Hilbert spaces.Comment: 10 page

Gravity and Large Extra Dimensions

The idea that quantum gravity can be realized at the TeV scale is extremely attractive to theorists and experimentalists alike. This proposal leads to extra spacial dimensions large compared to the electroweak scale. Here we give a very systematic view of the foundations of the theories with large extra dimensions and their physical consequences.Comment: 26 pages, 3 diagram

Thoracic myelopathy due to ossified hypertrophied ligamentum flavum

Calcification of ligamentum flavum is a rare disease that was found to occur almost exclusively in Japanese population. However the disease is now being increasingly recognized as a cause of thoracic myeloradiculopathy in Indian Population. We report a case of thoracic myelopathy at multiple levels due to ossified and hypertrophied ligamentum flavum

The dynamics and control of large flexible space structures. Part B: Development of continuum model and computer simulation

The equations of motion of an arbitrary flexible body in orbit were derived. The model includes the effects of gravity with all its higher harmonics. As a specific example, the motion of a long, slender, uniform beam in circular orbit was modelled. The example considers both the inplane and three dimensional motion of the beam in orbit. In the case of planar motion with only flexible vibrations, the pitch motion is not influenced by the elastic motion of the beam. For large values of the square of the ratio of the structural modal frequency to the orbital angular rate the elastic motion was decoupled from the pitch motion. However, for small values of the ratio and small amplitude pitch motion, the elastic motion was governed by a Hill's 3 term equation. Numerical simulation of the equation indicates the possibilities of instability for very low values of the square of the ratio of the modal frequency to the orbit angular rate. Also numerical simulations of the first order nonlinear equations of motion for a long flexible beam in orbit were performed. The effect of varying the initial conditions and the number of modes was demonstrated

The dynamics and control of large flexible space structures. Volume 3, part B: The modelling, dynamics, and stability of large Earth pointing orbiting structures

The dynamics and stability of large orbiting flexible beams, and platforms and dish type structures oriented along the local horizontal are treated both analytically and numerically. It is assumed that such structures could be gravitationally stabilized by attaching a rigid light-weight dumbbell at the center of mass by a spring loaded hinge which also could provide viscous damping. For the beam, the small amplitude inplane pitch motion, dumbbell librational motion, and the anti-symmetric elastic modes are all coupled. The three dimensional equations of motion for a circular flat plate and shallow spherical shell in orbit with a two-degree-of freedom gimballed dumbbell are also developed and show that only those elastic modes described by a single nodal diameter line are influenced by the dumbbell motion. Stability criteria are developed for all the examples and a sensitivity study of the system response characteristics to the key system parameters is carried out

Supernovae as Probes of Extra Dimensions

Since the dawn of the new millennium, there has been a revived interest in the concept of extra dimensions.In this scenario all the standard model matter and gauge fields are confined to the 4 dimensions and only gravity can escape to higher dimensions of the universe.This idea can be tested using table-top experiments, collider experiments, astrophysical or cosmological observations. The main astrophysical constraints come from the cooling rate of supernovae, neutron stars, red giants and the sun. In this article, we consider the energy loss mechanism of SN1987A and study the constraints it places on the number and size of extra dimensions and the higher dimensional Planck scale.Comment: 5 pages, no figures, new references are adde