Trace formulae for curvature of Jet Bundles over planar domain

For a domain \Omega in \mathbb{C} and an operator T in \mathcal{B}_n(\Omega), Cowen and Douglas construct a Hermitian holomorphic vector bundle E_T over \Omega corresponding to T. The Hermitian holomorphic vector bundle E_T is obtained as a pull-back of the tautological bundle S(n,\mathcal{H}) defined over \mathcal{G}r(n,\mathcal{H}) by a nondegenerate holomorphic map z\mapsto {\rm{ker}}(T-z) for z\in\Omega. To find the answer to the converse, Cowen and Douglas studied the jet bundle in their foundational paper. The computations in this paper for the curvature of the jet bundle are somewhat difficult to comprehend. They have given a set of invariants to determine if two rank n Hermitian holomorphic vector bundle are equivalent. These invariants are complicated and not easy to compute. It is natural to expect that the equivalence of Hermitian holomorphic jet bundles should be easier to characterize. In fact, in the case of the Hermitian holomorphic jet bundle \mathcal{J}_k(\mathcal{L}_f), we have shown that the curvature of the line bundle \mathcal{L}_f completely determines the class of \mathcal{J}_k(\mathcal{L}_f). In case of rank n Hermitian Holomorphic vector bundle E_f, We have calculated the curvature of jet bundle \mathcal{J}_k(E_f) and also have generalized the trace formula for jet bundle \mathcal{J}_k(E_f).Comment: 14 page

Single Photons from Relativistic Heavy Ion Collisions and Quark-Hadron Phase Transition

The present status of theoretical expectations of studies of single photons from relativistic heavy ion collisions is discussed. It is argued that the upper limit of single photon radiation from S+Au collisions at CERN SPS obtained by the WA80 collaboration perhaps rules out any reasonable description of the collision process which does not involve a phase transition to quark gluon plasma. Predictions for single photons from the quark-matter likely to be created in collision of two lead nuclei at RHIC and LHC energies are given with a proper accounting of chemical equilibration and transverse expansion. Finally, it is pointed out that, contrary to the popular belief of a quadrilateral dependence of electromagnetic radiations ($N_\gamma$) from such collisions on the number of charged particles ($N_{ch})$, we may only have $N_\gamma \propto N_{ch}^{1.2}$.Comment: Invited Talk given at Third International Conference on Physics and Astrophysics of Quark Gluon Plasma, Jaipur, India, March 199

A critical review of fundamental principles of Ayurveda

The fundamental principle holds a strong ground in Ayurveda. Every medical stream has its own science in which its matter is developed, evolved and explained. From creation of living to issues of health, disease and its treatment these fundamental principles are the root. These can be enumerated as Tridosha, Panchamahabhuta, Prakriti, Ojas, Dhatu, Mala, Agni, Manas, Atma etc. They are most unique and original approach to the material creation and it has all scope to incorporate the modern development in the elemental physics. The aim of Ayurveda is to maintain the proper equilibrium of dosa, dhatus, and mala constituent in order to preserve health in a healthy person and cure a disease in a diseased person.The presence of cognition as well as the absence of cognition is an indication of the mind. In the presence of senses with senses object and soul the man does not perceive a thing in the absence of mind that is to say that senses are unable to grasp the object in the absence of Manas. The term Ojas has been used in Ayurveda for the factor which prevents decay and degeneratioif the body and provides strength and support against a disease. Concept of Agni which incorporates all activities and factors responsible for digestion and metabolism in the living organism as known today, knowledge to these fundamental principles is a key to health and diseases .Maintenances of health depend on good and sound knowledge of these. Detail will be given in full paper. Keywords: Ayurveda, health, dosa, Agni, min