Related papers: The theorem that was none - II. The profound 70s
Astronomy is in an era where all-sky surveys are mapping the Galaxy. The plethora of photometric, spectroscopic, asteroseismic and astrometric data allows us to characterise the comprising stars in detail. Here we quantify to what extent…
The seminal paper "J.T. Stafford, Module structure of Weyl algebras, J. London Math. Soc. (2) 18 (1978), no. 3, 429--442" was a major step forward in our understanding of Weyl algebras. Beginning with Serre's Theorem on free summands of…
We construct models of universe with a generalized equation of state $p=(\alpha \rho+k\rho^{1+1/n})c^2$ having a linear component and a polytropic component. In this paper, we consider negative indices $n<0$. In that case, the polytropic…
We have developed a two-dimensional orbit averaged Fokker-Planck model of stellar clusters which expands on spherically symmetric one-dimensional models to include rotation and ellipticity. Physical effects such as collisions, finite…
In this PhD Thesis we study the occurrence of powerful stellar outbursts in the late phases of evolution of stars like the Sun. This is one of the most controversial topics in the field, as the extraordinary variety of shapes revealed by…
We survey the complexity class $\exists \mathbb{R}$, which captures the complexity of deciding the existential theory of the reals. The class $\exists \mathbb{R}$ has roots in two different traditions, one based on the Blum-Shub-Smale model…
We discuss cosmological models for an eternal universe. Physical observables show no singularity from the infinite past to the infinite future. While the universe is evolving, there is no beginning and no end - the universe exists forever.…
We provide a brief chronological guide to the literature on non-Riemannian cosmological models. Developments in this field are traced back to the early seventies and are given in table form.
One of the most reliable means of studying the stellar interior is through the apsidal motion in double line eclipsing binary systems since these systems present errors in masses, radii, and effective temperatures of only a few per cent. On…
In the 80's H. Masur and W. Veech defined two numerical invariants of strata of abelian differentials: the volume and the Siegel-Veech constant. Based on numerical experiments, A. Eskin and A. Zorich proposed a series of conjectures for the…
Lorentzian manifolds with vanishing second covariant derivative of the Riemann tensor are studied. Their existence, classification and explicit local expression are considered. Related issues and open questions are briefly commented.
The behaviour of expanding cosmological models with collisionless matter and a positive cosmological constant is analysed. It is shown that under the assumption of plane or hyperbolic symmetry the area radius goes to infinity, the…
Context. It is common for massive stars to engage in binary interaction. In close binaries, the components can enter a contact phase, where both stars overflow their respective Roche lobes simultaneously. While there exist observational…
We very briefly discuss the role of no-go theorems in constructing models of new physics beyond the SM.
As suggested by the title, it has recently become clear that theorems of Nonstandard Analysis (NSA) give rise to theorems in computability theory (no longer involving NSA). Now, the aforementioned discipline divides into classical and…
A non-existence theorem of classical electrodynamics in odd-dimensional spacetimes is shown to be invalid. The source of the error is pointed out, and is then demonstrated during the derivation of the fields generated by a uniformly moving…
The time evolution of the universe is usually mathematically described under a continuous time and thus time reversible. Here, the consequences of studying the evolution of a homogenous isotropic universe by time continuous reversible…
In a series of four papers we determine structures whose existence is dual, in the sense of complementary, to the existence of stars or combs. Here, in the second paper of the series, we present duality theorems for combinations of stars…
This paper investigates the concept of Nothing from both philosophical and mathematical perspectives, distinguishing between absolute non-being (nihil) and relational negation as a principle of difference. It explores how mathematics…
The presence or absence of star clusters in galaxies, and the properties of star cluster populations compared to their host galaxy properties, are important observables for validating models of cluster formation, galaxy formation, and…