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In this article, we discuss the basic theme of approximating functions by polynomial functions. Although it is exemplified by the classical theorem of Weierstrass, the theme goes much further. Even on the face of it, the advantage of polynomial approximations can be seen from the fact that unlike general continuous functions, it is possible to numerically feed polynomial interpolations of such functions...
Non-coding DNA, once thought of as ‘junk’, represents a very large portion of an organism’s genome. However, recent research has brought to lightmany functional elements present within non-coding DNA sequences and unravelled a fascinating array of functions performed by these elements. These findings have highlighted the nature of the evolutionary forces that led to the accumulation and retention...
In this article we introduce the reader to some pretty results concerning a circle and regions within it defined by various line segments. We have framed the results in terms of a pizza, so we could well call this an introduction to Pizza Geometry! The novel aspect is the variety of approaches used to prove these results.
Ya B Zeldovich was a pre-eminent Soviet physicist whose seminal contributions spanned many fields ranging from physical chemistry to nuclear and particle physics, and finally astrophysics and cosmology. This article attempts to convey some of the zest with which he did science and the important role he played in fostering and mentoring a whole generation of talented Soviet scientists.
“Anyone can invent human beings inside out or worlds like dumbbells or a gravitation that repels. The thing that makes such imaginations interesting is their translation into commonplace terms and a rigid exclusion of other marvels from the story.” (H. G. Wells, The Time Machine and other Stories)
V Raman is Emeritus Professor of Physics and Humanities at the Rochester Institute of Technology, Rochester, New York 14623, USA. He is available for giving Skype lectures in Indian universities.
Using the unsteady Bernoulli equation, we find solutions for the oscillatory motion of an incompressible and non-viscous liquid in a U-shaped tank. Alternative expressions for height-vs-time relation and the period are obtained through a transformation formula of the elliptic integral of the second kind. From the viewpoint of the mechanical energy conservation, the motion of the free surface can be...
The invention of logarithms saved much time and effort in astronomical and mathematical calculations. Until the advent of electronic calculating machines, they remained the most effective tool for scientists.
Soon after the discovery of the cosmic background radiation, Zeldovich and Sunyaev proposed that hot gas in galaxy clusters should cast a faint shadow because of the interaction between energetic electrons and the radiation photons. Sunayev-Zeldovich effect is now routinely observed, and it has become an important tool for studying the history of the universe.
Damodar Dharmananda Kosambi (1907–1966) was an eminent mathematician, scientist, innovative Marxist, a maverick scholar, and historian of contemporary India. Combining both versatility and a certain sense of virtuosity Kosambi made seminal contributions to a wide variety of disciplines spread across from pure and applied mathematics to archaeology and Indology. In the course of these writings he provided...
One of the activities that geneticists pursue is the generation of genetic maps of organisms that chart the locations of the different genes on the chromosomes. Damodar Dharmanada Kosambi was not a geneticist by training and profession, but amathematician. Yet, in 1944, Kosambi wrote a classic paper about mapping function in genetics in the journal Annals of Eugenics. His lone paper in genetics was...
In 1943 Kosambi published a paper titled ‘Statistics in function space’ in the Journal of the Indian Mathematical Society. This paper was the first to propose the technique of statistical analysis often called proper orthogonal decomposition today. This article describes the contents of that paper and Kosambi’s approach to the subject. It was only in 1967 that it began to be appreciated that the method...
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