Related papers: The theorem that was none - II. The profound 70s
We argue that Godel's completeness theorem is equivalent to completability of consistent theories, and Godel's incompleteness theorem is equivalent to the fact that this completion is not constructive, in the sense that there are some…
We present a version of G\"odel's Second Incompleteness Theorem for recursively enumerable consistent extensions of a fixed axiomatizable theory, by incorporating some bi-theoretic version of the derivability conditions. We also argue that…
The time evolution of a class of completely integrable discrete Lotka-Volterra s ystem is shown not unique but have two different ways chosen randomly at every s tep of generation. This uncertainty is consistent with the existence of…
We present a new stellar evolution code and a set of results, demonstrating its capability at calculating full evolutionary tracks for a wide range of masses and metallicities. The code is fast and efficient, and is capable of following…
This paper continues the author's previous study \cite{Kura20}, showing that several weak principles inspired by non-normal modal logic suffice to derive various refined forms of the second incompleteness theorem. Among the main results of…
We provide here the documentation of the new version of the spectral evolution model PEGASE. PEGASE computes synthetic spectra of galaxies in the UV to near-IR range from 0 to 20 Gyr, for a given stellar IMF and evolutionary scenario (star…
In the present paper we discuss a selection of facts and questions related to observations and evolutionary calculations of massive single stars and massive stars in interacting binaries. We focus on the surface chemical abundances, the…
We propose an extremely simple mathematical model that is shown to be able to account for more than 99 per cent of all the variation in economic and demographic macrodynamics of the world for almost two millennia of its history. This…
About a quarter of massive binary stars undergo mass transfer while both stars burn hydrogen at their cores, first on the thermal and then on the nuclear timescale. The nuclear timescale mass transfer leads to observable counterparts: the…
The spectral theorem of the linear 2D Euler operator in Sobolev spaces is presented as a corollary of the spectral theorem in $\ell_2$ space in [Li,00]. Study on the (dashed) line model introduced in [Li,01] is continued. Specifically,…
In the 1950s and 1960s Tate proved some duality theorems in the Galois cohomology of finite modules and abelian varieties. As for most of Tate's work this has had a profound influence on mathematics with many applications and further…
Existence theorem is proven for the generating equations of the split involution constraint algebra. The structure of the general solution is established, and the characteristic arbitrariness in generating functions is described.
An attempt is made to explain the spiral structure of spiral galaxies through a possible rotation of the Universe. To this end, we write down a possible form of the metric, and we calculate the necessary quantities (Rik, Tik, ...) in order…
Most of the literature on change-point analysis by means of hypothesis testing considers hypotheses of the form H0 : \theta_1 = \theta_2 vs. H1 : \theta_1 != \theta_2, where \theta_1 and \theta_2 denote parameters of the process before and…
The purpose of this paper is to join two different threads of the recent literature on random fields on the sphere, namely the statistical analysis of higher order angular power spectra on one hand, and the construction of second-generation…
We present the Boltzmann moment equation approach for the dynamics of stars (BEADS-2D), which is a finite-difference Eulerian numerical code designed for the modelling of anisotropic and non-axisymmetric flat stellar disks. The BEADS-2D…
A hydrodynamic model for small acoustic oscillations in a cloud of stars is built, taking into account the self-consistent gravitational field in equilibrium with a non-zero second correlation moment. It is assumed that the momentum flux…
In this review I highlight the role played by spectrophotometric models in the study of galaxy evolution in distant clusters. I summarize the main achievements of the modeling of k+a spectra, the derivation of the star formation rate in…
In the first part I set out some unexplored historical material about the early development of cosmic topology. In the second part I briefly comment new developments in the field since the Lachieze-Rey & Luminet report (1995), both from a…
Pusey, Barrett, and Rudolph introduce a new no-go theorem for hidden-variables models of quantum theory. We make precise the class of models targeted and construct equivalent models that evade the theorem. The theorem requires assumptions…