Related papers: Samgamagr\=ama M\=adhava: An Updated Biography
In this article, a subclass of univalent harmonic mapping is introduced by restricting its analytic part to lie in the class $\mathcal{S}^{\delta}[\alpha]$, $0\leq \alpha < 1$, $-\infty < \delta < \infty$ which has been introduced and…
MSc thesis of the author offering an introduction to the operator algebraic approach to noncommutative geometry, with a treatment of some more advanced elements such as the noncommutative geometry of quantum groups, fuzzy physics, and…
Astronomical data generally consists of 2 or more high-resolution axes, e.g., X,Y position on the sky or wavelength and position-along-one-axis (long-slit spectrometer). Analyzing these multi-dimension observations requires combining 3D…
After describing Bhabha's early life at Bombay, now Mumbai, we discuss his research career at Cambridge, where he made many distinguished contributions to positron physics, cosmic rays and the meson theory. These include theory of…
Two inequalities concerning the symmetry of the zeta-function and the Ramanujan $\tau$-function are improved through the use of some elementary considerations.
A series transformation idea inspired by a formula of R. W. Gosper and some asymptotic expansions for the central binomial coefficients leads us to new accurate approximations for the Gamma function.
Meghnad Saha occupies a special role in the history of Indian science, having been a pioneer in its organization already from the oppressive colonial period and having left important legacies to post-colonial India like the Saha Institute…
The Data Analysis programme of the Australian Consortium for Interferometric Gravitational Astronomy (ACIGA) was set up in 1998 by the first author to complement the then existing ACIGA programmes working on suspension systems, lasers and…
This is an expanded version of my review of Nina Engelhardt's book "Modernism, Fiction and Mathematics", Edinburgh University Press 2018. A considerably shortened version will appear in the Notices of the AMS.
Manifold-valued functional data analysis (FDA) recently becomes an active area of research motivated by the raising availability of trajectories or longitudinal data observed on non-linear manifolds. The challenges of analyzing such data…
Telegraphic notes on the historical bibliography of the Gamma function and Eulerian integrals. Correction to some classical references. Some topics of the interest of the author. We provide some extensive (but not exhaustive) bibliography.…
From al-Sufi's tenth-century observation of the Andromeda Galaxy as a "little cloud" to contemporary space missions, Islamic astronomy represents a millennium-spanning tradition of innovation and knowledge. This study traces its trajectory…
We survey some recent applications of machine learning to problems in geometry and theoretical physics. Pure mathematical data has been compiled over the last few decades by the community and experiments in supervised, semi-supervised and…
State $g^{\hat{n}}\hat{a}^{\dag m}\left\vert \alpha \right\rangle $ and state $\hat{a}^{\dag m}g^{\hat{n}}\left\vert \alpha \right\rangle $ are same to state $\hat{a}^{\dag m}\left\vert g\alpha \right\rangle $, which is called as…
We compute the accuracy with which Omega and Lambda can be measured by combining future SN Ia and CMB experiments, deriving a handy expression for the SN Ia Fisher information matrix. The two data sets are found to be highly complementary:…
In 2018, McInnes et al. introduced a dimensionality reduction algorithm called UMAP, which enjoys wide popularity among data scientists. Their work introduces a finite variant of a functor called the metric realization, based on an…
This is the introduction I wrote for the multi-authored book "From Riemann to differential geometry and relativity", edited by L. Ji, A. Papadopoulos and S. Yamada (Berlin, Springer verlag, 2017). The book consists of twenty chapters,…
Computation models and specification methods seem to be worlds apart. The project on abstract state machines (in short ASMs, also known as evolving algebras) started as an attempt to bridge the gap by improving on Turing's thesis. We sought…
We describe the results of a search for time variability of the fine structure constant, alpha, using absorption systems in the spectra of distant quasars. Three large optical datasets and two 21cm/mm absorption systems provide four…
An approach to build Probabilistic Arithmetic in which initial values of all correlated random variables are known, but with varying degrees of accuracy. As a result of the proposed Probabilistic Arithmetic operations, variable values,…