Related papers: Monstrous Moonshine over Z?
We briefly review some recent advances in the study of the shadows of rotating black holes in alternative theories. The size and the shape of the shadow depend on the mass and the angular momentum, and they can also depend on other…
With increasingly accurate data on RR Lyrae stars we find that the Blazhko effect may be a rule rather than an exception. However, we still do not know what is the cause of this mysterious amplitude and phase modulation. In my talk, I…
We discuss two realizations of the colored Jones polynomials of a knot, one from an unnoticed work of the second author in 1994 on quantum R-matrices at roots of unity obtained from solutions of the pentagon identity, and another one from…
This article is part of an ongoing investigation of the two-dimensional Jacobian conjecture. In the first paper of this series, we proved the generalized Magnus' formula. In this paper, inspired by cluster algebras, we introduce a sequence…
Since various structural components of planetary nebulae manifest themselves differently, a combination of optical, infrared, submm, and radio techniques is needed to derive a complete picture of planetary nebulae. The effects of projection…
We survey recent developments on the Restriction conjecture.
Hochster's Monomial Conjecture and Canonical Element Conjecture date back some thirty resp. twenty years. They concern all noetherian commutative local rings, and were proved by their originator right away in equal characteristic. Thanks to…
We develop techniques to deal with monotonicity of sequences z_{n+1}/z_n and \sqrt[n]{z_n}. A series of conjectures of Zhi-Wei Sun and of Amdeberhan et al. are verified in certain unified approaches.
In the 1960s and 1970s a series of observations and theoretical developments highlighted the presence of several anomalies which could, in principle, be explained by postulating one of the following two working hypotheses: (i) the existence…
Recent cosmological and astrophysical observations point out that the Universe is in accelerating expansion and filled up with non-luminous matter. In order to explain the observed large scale structures and this accelerating behavior one…
Common envelope events have been associated with the formation of a planetary nebulae since its proposition more than forty five years ago. However, until recently there have been doubts as to whether a common envelope while the donor is…
There has been a new infusion of ideas in the study of the mechanism and early character of core--collapse supernovae. However, despite recent conceptual and computational progress, fundamental questions remain. Some are summarize herein.
An extension of the theory of General Relativity is proposed, based on pseudo-complex space-time coordinates. The new theory corresponds to the introduction of two, in general different, metrics which are connected through specific…
In our current cosmological model, the main constituents of the Universe are dark matter and dark energy, whose nature is unknown, and for which there is no place in the standard model of particle physics. How to include dark matter and…
Most cosmic rays are thought to be accelerated by the shocks of supernova explosions of very massive stars. Here we review one quantitative proposal, which predicted the spectral slopes, bend and cutoff about the cosmic ray spectrum across…
The recent detections of gravitational waves from binary systems of black holes are in remarkable agreement with the predictions of General Relativity. In this pedagogical mini-review, I will go through the physics of the different phases…
Based on Jensen formulae and the second kind of Chebyshev polynomials, another proof is presented for an extension of a curious binomial identity due to Z. W. Sun and K. J. Wu.
To a knot in 3-space, one can associate a sequence of Laurent polynomials, whose $n$th term is the $n$th colored Jones polynomial. The Volume Conjecture for small angles states that the value of the $n$-th colored Jones polynomial at…
The Chelyabinsk meteor sailed over skies in a streak of light that was momentarily brighter than the Sun. The Chelyabinsk superbolide is a complex and multi-aspect phenomenon. The Appendix to the book examines the role of cosmic collisions…
A review on recent astronomical observations indicating to unexpectedly abundant population of the contemporary and $ z \sim 10 $ universe by massive black holes in all mass ranges are is presented. It is argued that these black holes are…