Chern-Simons Theory, Colored-Oriented Braids and Link invariants

A method to obtain explicit and complete topological solution of SU(2) Chern-Simons theory on $S^3$ is developed. To this effect the necessary aspects of the theory of coloured-oriented braids and duality properties of conformal blocks for the correlators of $SU(2)_k$ Wess-Zumino conformal field theory are presented. A large class of representations of the generators of the groupoid of coloured-oriented braids are obtained. These provide a whole lot of new link invariants of which Jones polynomials are the simplest examples. These new invariants are explicitly calculated as illustrations for knots upto eight crossings and two-component multicoloured links upto seven crossings.Comment: 48 pages + 20 diagram

A micro-computer based system to compute magnetic variation

A mathematical model of magnetic variation in the continental United States (COT48) was implemented in the Ohio University LORAN C receiver. The model is based on a least squares fit of a polynomial function. The implementation on the microprocessor based LORAN C receiver is possible with the help of a math chip, Am9511 which performs 32 bit floating point mathematical operations. A Peripheral Interface Adapter (M6520) is used to communicate between the 6502 based micro-computer and the 9511 math chip. The implementation provides magnetic variation data to the pilot as a function of latitude and longitude. The model and the real time implementation in the receiver are described

Path discrepancies between great circle and rhumb line

A mathematical model for a comparative analysis of great circle vs. rhumb line navigation in the continental United States has been developed at the Avionics Engineering Center, Ohio University. A FORTRAN simulation of the model has been implemented on the IBM 370 computer. The simulation predicts pertinent navigation information for the two flight paths. The basis for the project, which is a part of an M.S. thesis, is to provide a data base for computing discrepancies between the two flight paths. This document briefly describes the model and discusses the implications of the results obtained

Primary Leiomyosarcoma of Ovary

Primary ovarian leiomyosarcomas is a rare neoplasm which comprises less than 3% of ovarian tumors. Their origin, etiology, histologic features, clinical behavior, and optimal treatment are still obscure. We report a case of leiomyosarcoma of ovary, diagnosed on histopathology in a 60 year old female and discuss the literature

Logarithmic correction to the Bekenstein-Hawking entropy of the BTZ black hole

We derive an exact expression for the partition function of the Euclidean BTZ black hole. Using this, we show that for a black hole with large horizon area, the correction to the Bekenstein-Hawking entropy is $-3/2 log(Area)$, in agreement with that for the Schwarzschild black hole obtained in the canonical gravity formalism and also in a Lorentzian computation of BTZ black hole entropy. We find that the right expression for the logarithmic correction in the context of the BTZ black hole comes from the modular invariance associated with the toral boundary of the black hole.Comment: LaTeX, 10 pages, typos corrected, clarifications adde

Summary of studies for a solar optical telescope in space: 1968-1976

The primary objective of this review is to tabulate the basic recommendations of several solar telescope studies. A primary matrix, listing some of the basic optical parameters, was compiled and forms the basis for a table. From this table it is apparent that a strong consensus exists on the configuration of the telescope and on its fundamental dimensionless parameters. Other tables presented in this document address the basic approach of each study to the telescope design as well as to the design of critical subsystems. These subsystem problems include the material, coating, configuration, mounting, launch locks, and thermal control of the primary mirror, the structure of the main telescope and the instrument bay, the mechanisms for radiation rejection, thermal control, and meteoroid shielding, and methods of maintaining image quality by proper alignment and by image motion compensation

Polymorphous low grade adenocarcinoma-an unusual presentation

Polymorphous low-grade adenocarcinoma (PLGA) is a neoplasm that occurs frequently in the mucosa of the soft and hard palates, in the buccal mucosa and in the upper lip and is very rare within the nasopharynx. We present a case of PLGA, which presented as a nasal polyp

Chirality of Knots 9429_{42} and 107110_{71} and Chern-Simons Theory

Upto ten crossing number, there are two knots, $9_{42}$ and $10_{71}$ whose chirality is not detected by any of the known polynomials, namely, Jones invariants and their two variable generalisations, HOMFLY and Kauffman invariants. We show that the generalised knot invariants, obtained through $SU(2)$ Chern-Simons topological field theory, which give the known polynomials as special cases, are indeed sensitive to the chirality of these knots.Comment: 15 pages + 7 diagrams (available on request