Related papers: Looking through newly to the amazing irrationals
A speculative discussion on the role of various symmetries in physics.
A metric space is indivisible if for any partition of it into finitely many pieces one piece contains an isometric copy of the whole space. Continuing our investigation of indivisible metric spaces, we show that a countable ultrametric…
Certain new inequalities for the sums of factorials are presented.
Motivated by problems arising in the relative trace formula and arithmetic invariant theory we prove the existence of rational points on orbits arising from certain infinitesimal symmetric spaces. As an application, we prove analogous…
In this paper we study number fields which are Euclidean with respect to a function different from the absolute value of the norm. We also show that the Euclidean minimum with respect to weighted norms may be irrational and not isolated.
This paper gives a short introduction into the metric theory of spaces with dilations.
Cosmological models that invoke a multiverse - a collection of unobservable regions of space where conditions are very different from the region around us - are controversial, on the grounds that unobservable phenomena shouldn't play a…
The paper is based on the recently proposed 4-dimensional optical space theory and draws some of its consequences for gravitation. Starting with the discussion of central movement, the paper proceeds to establish the a metric compatible…
This paper studies the question on whether machines can be rational. It observes the existing reasons why humans are not rational which is due to imperfect and limited information, limited and inconsistent processing power through the brain…
Several examples are used to illustrate how we deal cavalierly with infinities and unphysical systems in physics. Upon examining these examples in the context of infinities from Cantor's theory of transfinite numbers, the only known…
The notion of an orthogonality space was recently rediscovered as an effective means to characterise the essential properties of quantum logic. The approach can be considered as minimalistic; solely the aspect of mutual exclusiveness is…
We discuss whether science is in the process of being transformed from a quest for causality to a quest for correlation in light of the recent development in artificial intelligence. We observe that while a blind trust in the most seductive…
Experimental evidence for and against the existence of pentaquarks has accumulated rapidly in the last three years. If they exist, they would be dramatic examples of hadronic states beyond our well-tested and successful particle models. The…
{Researchers recently introduced interpolative metric spaces and established fixed-point theorems in this setting. We demonstrate that these metrics are a special case of b-metrics. On the other hand, suprametrics and b-suprametrics have…
A critical analysis of the relativistic formulation of matter reveals some surprising inconsistencies and paradoxes. Corrections are discovered which lead to the long-sought-after equality of the gravitational and inertial masses, which are…
Remarks on mathematical proof and the practice of mathematics.
The setting of metric spaces is very natural for numerous questions concerning manifolds, norms, and fractal sets, and a few of the main ingredients are surveyed here.
The search for dark matter is a very wide and active field of research. Many potential hints of dark matter have appeared recently which led to a burst of theoretical activity and model building. I necessarily concentrate here only in some…
Mathematical diffraction theory is concerned with the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and mixed spectra…
Emergence is a pregnant property in various fields. It is the fact for a phenomenon to appear surprisingly and to be such that it seems at first sight that it is not possible to predict its apparition. That is the reason why it has often…