Related papers: Samgamagr\=ama M\=adhava: An Updated Biography
The expansion law proposed by Padmanabhan suggests that the evolution of the volume of the horizon is due to the difference between the degrees of freedom on the horizon and the degrees of freedom in the bulk enclosed by the horizon. In…
The review presents rigorous results of the theory of fundamental equations of evolution of many-particle systems with collisions and also considers their connection with nonlinear kinetic equations describing the collective behavior of…
The M\=anava \'Sulvas\=utra, while less sophisticated than the other \'sulvas\=utras, is seen to contain some mathematical ideas and constructions not found in the other \'sulvas\=utras. Here we discuss some of these constructions and…
In this paper, using altering distance functions we obtain a generalization of the results due to B.K. Das and S. Gupta as well as the results given by B. Samet and H. Yazid. Moreover, we study the so-called property P for the contraction…
In this essay we give an introduction to conformal symmetry, based on the example of the Yamabe operator and its use in conformal differential geometry, and in representation theory.
Mathematical proof is undoubtedly the cornerstone of mathematics. The emergence, in the last years, of computing and reasoning tools, in particular automated geometry theorem provers, has enriched our experience with mathematics immensely.…
Few among us would know that the first mention of the sine and the enumeration of the first sine table are to be credited to Aryabhata. The method to generate this relies on the sine difference formula which is derived using ingenious…
For a metric space $(A,d)$, and a set $\Sigma$ of equations, a quantity is introduced that measures how far continuous operations must deviate from satisfying $\Sigma$ on $(A,d)$. }
The Ca II H & K lines are strong chromospheric diagnostics that can be used to determine the temperature stratification and magnetic structure of the solar atmosphere. The Atacama Large Millimetre/Submillimetre Array (ALMA) offers…
We introduce \emph{Astronomy and Computing}, a new journal for the growing population of people working in the domain where astronomy overlaps with computer science and information technology. The journal aims to provide a new communication…
Compositionality is a basic structural feature of both biological and artificial neural networks. Learning compositional functions via gradient descent incurs well known problems like vanishing and exploding gradients, making careful…
AI emulators for forecasting have emerged as powerful tools that can outperform conventional numerical predictions. The next frontier is to build emulators for long climate simulations with skill across a range of spatiotemporal scales, a…
Holm (ASR, 2018) claims that Scafetta (ASR 57, 2121-2135, 2016) is "irreproducible" because I would have left "undocumented" the values of two parameters (a reduced-rank index p and a regularization term) that he claimed to be requested in…
This is a revised version of the notes from the week-long course I gave at the Centre de Recerca Matematica, Barcelona, in September of 2010. The aim is to give a working overview of recent methods and results in "Blaschkean integral…
The workshop `Astrophysical Dynamics 1999/2000' followed a homonymous advanced research course, and both activities were organized by me. In this opening paper of the proceedings book, I describe them and document their strong impact on the…
In the past few years, substantial progress has been made in the understanding of the algebra of kappa classes on the moduli spaces of curves. My goal here is to provide a short introduction to the new results. Along the way, I will discuss…
In the present document I review the current organizational structure of Astronomy, Astrophysics and Space Physics in Greece. I briefly present the institutions where professional astronomers are pursuing research, along with some notes of…
Using SCM higher mathematics course allows you to: more clearly understandable apply theoretical material; deprive students of routine calculations; provide multilevel learning process, and therefore enhances cognitive interest and most…
In the quest for precision cosmology, one must ensure that the cosmology is accurate as well. We discuss figures of merit for determining from observations whether the dark energy is a cosmological constant or dynamical, with special…
We improve constants in the Rademacher-Menchov inequality.