Related papers: Irrational centers
This note provides a critical discussion of the \textit{Critical Cost-Efficiency Index} (CCEI) as used to assess deviations from utility-maximizing behavior. I argue that the CCEI is hard to interpret, and that it can disagree with other…
We refer to the classic definition of a singularity in Einstein's general relativity (based on geodesic incompletness) as well as to some other criteria to evaluate the nature of singularities in cosmology. We review what different…
To make precise the sense in which nature fails to respect classical physics, one requires a formal notion of classicality. Ideally, such a notion should be defined operationally, so that it can be subjected to a direct experimental test,…
We prove a central limit theorem for a sequence of random variables whose means are ambiguous and vary in an unstructured way. Their joint distribution is described by a set of measures. The limit is (not the normal distribution and is)…
This chapter deals with error and uncertainty in data. Treats their measuring methods and meaning. It shows that uncertainty is a natural property of many data sets. Uncertainty is fundamental for the survival os living species, Uncertainty…
In this paper, we investigate the existence of a point in the plane of a unit polygon, that is at rational distance from each vertex of the polygon. A negative answer is obtained in almost all cases.
I offer an analysis of the Principle of Sufficient Reason and its relevancy for the scientific endeavour. I submit that the world is not, and cannot be, rational - only some brained beings are. The Principle of Sufficient Reason is not a…
A solid observational characterization of cluster regions around the virial radius would allow us to improve considerably our understanding of the physics of galaxy clusters as a whole: sadly current and planned experiments will not allow…
A critical review is presented on the most recent attempt to generally explain the notion of "statistical symmetry". This particular explanation, however, is incomplete and misses one important and essential aspect. The aim of this short…
The article demonstrates that logic is not necessarily singleton and does not always have the standard interpretation of negation. Appropriate generalizations of logic are suggested. Positive logic and multivalued negation operations are…
A precise definition of a black hole has long been absent in causal set theory. I first show that the local finiteness of the theory cannot be interpreted as a complete discretization condition, and the theory still admits continua, which I…
We review possible measures of complexity which might in particular be applicable to situations where the complexity seems to arise spontaneously. We point out that not all of them correspond to the intuitive (or "naive") notion, and that…
We report on progress in the qualitative study of rational points on rationally connected varieties over number fields, also examining integral points, zero-cycles, and non-rationally connected varieties. One of the main objectives is to…
The notion of $p_g$-ideals for normal surface singularities has been proved to be very useful. On the other hand, the core of ideals has been proved to be very important concept and also very mysterious one. However, the computation of the…
We discuss the objectives of any endeavor in creating artificial intelligence, AI, and provide a possible alternative. Intelligence might be an unintended consequence of curiosity left to roam free, best exemplified by a frolicking infant.…
From Sturmian and Christoffel words we derive a strictly increasing function $\Delta:[0,\infty)\to\mathbb{R}$. This function is continuous at every irrational point, while at rational points, left-continuous but not right-continuous.…
This text is an introduction to the study of NIP (or dependent) theories. It is meant to serve two purposes. The first is to present various aspects of NIP theories and give the reader the background material needed to understand almost any…
An attempt is made in order to clarify the so called regular black holes issue. It is revisited that if one works within General Relativity minimally coupled with non linear source, mainly of electromagnetic origin, and within a static…
The purpose of this article is to motivate the study of invariant, and especially conformally invariant, differential pairings. Since a general theory is lacking, this work merely presents some interesting examples of these pairings,…
This paper is devoted to studying the asymptotic behaviour of solutions to generalized non-commensurate fractional systems. To this end, we first consider fractional systems with rational orders and introduce a criterion that is necessary…