Related papers: On the half line: K. Ramachandra

This paper traces the seminal roles that physicists and mathematicians have played in the conceptual development of the biological sciences in the past, and especially in the 19th and 20th centuries.

Phillip L. Geissler made important contributions to the statistical mechanics of biological polymers, heterogeneous materials, and chemical dynamics in aqueous environments. He devised analytical and computational methods that revealed the…

Recent analyses of Brahmagupta's discourse on the cyclic quadrilateral, and of Baudh\=ayana's approximate quadrature of the circle, have shown that it is useful to submit mathematical texts to a form of literary analysis. Several passages…

This paper, which is dedicated to Alan Turing on the 50th anniversary of his death, gives an overview and discusses the philosophical implications of incompleteness, uncomputability and randomness.

Professor Sir Karl Popper (1902-1994) was one of the most influential philosophers of science of the twentieth century. However, in his most famous work he displays misunderstandings of science and mathematics at a basic level.

The diagonal representation and optical equivalence theorem are the E. C. G. Sudarshan's mid 20th century adventures in non-classical optics. It basically deals with a quantum mechanical description of photons to explain the quantum…

We give new nested radical equations of similar kind to Ramanujan's questions to the Indian Mathematical Society 100 years ago. While many have since considered these from the perspectives of the Notebooks of Ramanujan and from the theory…

C.V. Raman (1888 - 1970) was a creative scientist, enthusiastic teacher and a science celebrity in India. In all these roles, he communicated science effectively. In this essay, I ask how and why did he communicate science. I take a few…

In this note, by employing a nice property of semicircular distributions, we derive some identities for the Narayana polynomial and its derivatives.

This expository paper features a few highlights of Richard Stanley's extensive work in Ehrhart theory, the study of integer-point enumeration in rational polyhedra. We include results from the recent literature building on Stanley's work,…

This paper offers a glimpse of the major contributions made by Arabs to mathematics in middle ages history period. Its purpose is to stimulate interest in an object based on mutual respect and understanding. We give a short list of the most…

The analytical aspects of the "Trait\'e des \'equations" of Sharaf al-D\^in al-T\^us\^i (2nd half of the XIIth century) have been underlined by R. Rashed (1974, 1986). In the present paper, we consider again some of those aspects, when…

In this article, we are interested in the life and scientific work of the Belgian mathematician Paul Mansion. The year 2019 marks the centenary of his passing. We bring some new insights into Paul Mansion's work thanks to his scientific…

The results summarized here are intended as rigorous mathematical statements on various physical models coming from condensed matter physics, statistical mechanics (classical and quantum), quantum field theory and cold atoms physics. The…

In this paper we obtain some essential generalizations of certain Ramachandra's inequality, i. e. we obtain new lower estimates for the energies of some complicated signals generated by the Riemann zeta-function on the critical line.

In the first part of this short work (in the form of a comment) we add the plots of two more values of the Li-Keiper coefficients lambda5 and lambda6, computed as in our recent work where the first four values were in particular given. This…

This paper gives a short review of the history of statistical physics starting from D. Bernoulli's kinetic theory of gases in the 18th century until the recent new developments in nonequilibrium kinetic theory in the last decades of this…

The history of the development of the concept of complex numbers from the 16th to 19th centuries. The origin and refinement of the geometric and physical meaning of complex numbers, the emergence of vectoral analysis.

We suggest a continued fraction origin to Ramanujan's approximation to {(a-b)/(a+b)}^2 in terms of the arc length of an ellipse with semiaxes a and b. Moreover, we discuss the asymptotic accuracy of the approximation.

Mathematical aspects of contemporary classical and quantum gauge theory are sketched.