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Symmetry is one of the most general and useful concepts in physics. A theory or a system that has a symmetry is fundamentally constrained by it. The same constraints do not apply when the symmetry is broken. The quantitative determination…

Measures of irrationality are a numerical way of quantifying how far a given variety is from being rational (or rationally connected, uniruled, etc.). In the last two decades, there has been renewed interest in the study of these…

Porosity and dimension are two useful, but different, concepts that quantify the size of fractal sets and measures. An active area of research concerns understanding the relationship between these two concepts. In this article we will…

Many attempts have been made to characterise and solve the infamous measurement problem of quantum mechanics by advocating, implicitly or explicitly, different realist perspectives. As a result, we are still uncertain where this problem and…

The main aim of this paper is to present an overview of the need of a new way of coping the fundamental equations of physics, see the references. Our main aim is to build a new metrics in which both time and space are included, but in some…

Symmetries are a key concept to connect mathematical elegance with physical insight. We consider measurement assemblages in quantum mechanics and show how their symmetry can be described by means of the so-called discrete bundles. It turns…

This is a short survey paper, partly meant as a research announcement. Its purpose is to highlight some aspects of the interplay between quantales, inverse semigroups, and groupoids. Many of the results mentioned have not yet been presented…

We survay some nice result concerning the irrationals with a metric space point of view.Here is ofcourse nothing new may be or an expert in this field.

In 2019 the International System of units (SI) conceptually re-invented itself. This was necessary because quantum-electronic devices had become so precise that the old SI could no longer calibrate them. The new system defines values of…

In the framework of special relativity, all particles are point-like or string-like. This nature of particles has caused the divergence difficulties in quantum field, string and superstring theories. In the framework of special relativity,…

Gauge symmetries are often highlighted as a fundamental cornerstone of modern physics. But at the same time, it is commonly emphasized that gauge symmetries are not a fundamental feature of nature but merely redundancies in our description.…

We introduce the notion of angular values for deterministic linear difference equations and random linear cocycles. We measure the principal angles between subspaces of fixed dimension as they evolve under nonautonomous or random linear…

Comparing and recognizing metrics can be extraordinarily difficult because of the group of diffeomorphisms. Two metrics, that could even be the same, could look completely different in different coordinates. This is the gauge problem. The…

A careful look at an allegedly well-known century-old concept reveals interesting aspects in it that have generally avoided recognition in literature. There are four different kinds of physical observables known or proclaimed as…

Consider an orthogonal polyhedron, i.e., a polyhedron where (at least after a suitable rotation) all faces are perpendicular to a coordinate axis, and hence all edges are parallel to a coordinate axis. Clearly, any facial angle and any…

"Symmetry" was one of the most important methodological themes in 20th-century physics and is probably going to play no lesser role in physics of the 21st century. As used today, there are a variety of interpretations of this term, which…

We critically evaluate the treatment of the notion of measurement in the Consistent Histories approach to quantum mechanics. We find such a treatment unsatisfactory because it relies, often implicitly, on elements external to those provided…

We propose a generalization of the concept of symmetry as a continuous function of the reference center or line location. We suggest that this concept can be applied to many closed systems and exploring its time evolution. When the function…

The primary objective of the present paper is to develop the theory of quantization dimension of an invariant measure associated with an iterated function system consisting of finite number of contractive infinitesimal similitudes in a…

The concept of measurement is discussed. It is argued that counting process in mathematics is also measurement which requires a basic unit. The idea of scale is put forward. The basic unit itself, which are composed of the infinitesimal of…