HARISH  CHANDRA

CONTRIBUTION TO MATHEMATICS:

                The word mathematics is like a dangerous monster for some people. Many of the students who consider mathematics as their enemy would have thought that the subject mathematics should never have existed. But in this world of billions of population, there are many who not only love mathematics but take it up as their career.

Harish Chandra was one among such people in the olden times who was a well-known mathematician. Not only did he like the subject mathematics, but also made significant contributions to the world of mathematics which is undoubtedly praiseworthy. Harish Chandra was born on 11th of October, 1923 in Kanpur. He belonged to an upper middle class family which was a benefit to the educational career of Harish Chandra.

    Harish Chandra researched on “Semi Simple Lie Groups”. This was indeed his best research. He explained about the lie algebra where the ideal of the number were 0 and itself. Other achievements of Harish Chandra include Weyl’s character formula analogue, Plancherel measure for semi simple groups, philosophy of cusp forms, etc. he also worked at Neumann Professor in 1968 at the Institute of Advanced Study.

               Harish Chandra was a great mathematician of the twentieth century. His achievements and contributions were praiseworthy. He was honoured with AMS Cole Prize in 1954 for his outstanding work ‘Representations of Semi Simple Lie algebras and groups’. He was the Fellow of the Royal Society. He was given the Ramanujan Medal in 1974 for his wonderful works in mathematics. Not only in India, but Harish Chandra’s achievements were honoured outside India as well. He was given an honorary degree in the Yale University. Harish Chandra Research Institute (HRI) was started by the Government of India in the honour of his contributions in the field of mathematics.

                       C.RADHAKRISHNA RAO

CONTRIBUTIONS TO STATISTICAL THEORY AND APPLICATIONS

                                       C. Radhakrishna Rao is among the world leaders in statistical science over the last six decades. His research, scholarship, and professional services have had a profound influence on theory and applications of statistics.

Technical terms such as, Cramer-Rao inequality, Rao-Blackwellization, Rao’s Score Test, Fisher-Rao and Rao Theorems on second order efficiency of an estimator, Rao
metric and distance, Analysis of Dispersion (MANOVA) and Canonical Variate analysis and G-inverse of matrices appear in all standard books on statistics. Cramer-Rao Bound and Rao-Blackwellization are the most frequently quoted key words in statistical and engineering literature. Special uses of Cramer-Rao Bound under the technical term, Quantum Cramer- Rao Bound have appeared in Quantum Physics. Rao-Blackwellization has found applications in adaptive sampling, particle filtering in high-dimensional state spaces, dynamic Bayesian networks etc. These results have led to contributions of strategic significance to signal detection, tracking of non-friendly planes and recognition of objects by shape.

Rao has made some significant contributions to combinatorial mathematics for use in design of experiments, the most important of which is Orthogonal arrays (OA).The basic paper on the subject appeared in Proc. Edinburgh Math. Soc. (the referee of the paper reported that it is a fresh and original piece of work). The Japanese Quality Control Expert, G.Taguchi made extensive use of OA’s (described by Forbes Magazine as “new mantra” for industries), in industrial experimentation.
Rao defined a generalized inverse (g-inverse) of a matrix (singular or rectangular) and demonstrated its usefulness in the study of linear models and singular multivariate normal distributions.

He is the author of 14 books and about 350 research papers. Three of his books have been translated into several European and Chinese and Japanese languages