Related papers: Comment on Dimensionless Units in the SI
The theory of modular forms and spherical harmonic analysis are applied to establish new best bounds towards the counting and equidistribution of rational points on spheres and other higher dimensional ellipsoids, in what may be viewed as a…
We study the density of the invariant measure of the Hurwitz complex continued fraction from a computational perspective. It is known that this density is piece-wise real-analytic and so we provide a method for calculating the Taylor…
It is proposed a possible new approach of quantum measurements (QMS), disconnected of the traditional interpretation of uncertainty relations and independent of any appeal to the strange idea of collapse (reduction) of wave functions. The…
This paper assesses the Everettian approach to the measurement problem, especially the version of that approach advocated by Simon Saunders and David Wallace. I emphasise conceptual, indeed metaphysical, aspects rather than technical ones;…
We study uncertainty relations for pairs of conjugate variables like number and angle, of which one takes integer values and the other takes values on the unit circle. The translation symmetry of the problem in either variable implies that…
Quantum coherence is a critical resource for many operational tasks. Understanding how to quantify and manipulate it also promises to have applications for a diverse set of problems in theoretical physics. For certain applications, however,…
Following the B. Hiley belief that unresolved problems of conventional quantum mechanics could be the result of a wrong mathematical structure, an alternative basic structure is suggested. Critical part of the structure is modification of…
We consider the problem of identifying the units of measurement in a data column that contains both numeric values and unit symbols in each row, e.g., "5.2 l", "7 pints". In this case we seek to identify the dimension of the column (e.g.…
To what extent are all astrophysical, dark, compact objects both black holes (BHs) and described by the Kerr geometry? We embark on the exercise of defying the universality of this remarkable idea, often called the "Kerr hypothesis". After…
We introduce an invariant linked to some foundational questions in geometric measure theory and provide bounds on this invariant by decomposing an arbitrary cycle into uniformly rectifiable pieces. Our invariant measures the difficulty of…
This paper studies and proposes a technique of function point counting for items classified as non-measurable. The main objective is to expand the conventional technique of counting to ensure that this comprises consistently the tasks…
In a seminal paper [8] it was shown that Heisenberg-limited measurements could be achieved without using entangled states by coupling the quantum resources to a common environment that could be measured, at least, in part. The authors also…
There exist measuring devices where an analog input is converted into a digital output. Such converters can have a nonlinear internal dynamics. We show how measurements with such converting devices can be understood using concepts from…
In the paper, only Static Spherically Symmetric space-times in four dimensions are considered within modified gravity models. The non-singular static metrics, including black holes not admitting a de Sitter core in the center and…
In this paper we present a new object counting method that is intended for counting similarly sized and mostly round objects. Unlike many other algorithms of the same purpose, the proposed method does not rely on identifying every object,…
It has been proposed that measurement in quantum mechanics results from spontaneous breaking of a symmetry of the measuring apparatus and could be a unitary process that preserves coherence. Viewed in this manner, it is argued,…
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…
A survey of recent results concerning cardinal invariants of measure and category. Submitted as a chapter of the upcoming Handbook of Set Theory.
This work deals with fitting of ellipses to noisy measurements. The literature knows many different approaches for this. The main representatives are presented and discussed in this paper. Furthermore, the case is considered when outliers…
In this study, we obtain new classes of linear codes over Hurwitz integers equipped with a new metric. We refer to the metric as Hurwitz metric. The codes with respect to Hurwitz metric use in coded modu- lation schemes based on quadrature…