Related papers: Dimensionless Units in the SI
A solution to the part and whole problem is presented in this paper by using a complex mathematical representation that permits to define the Holon concept as a Basic Unit System that remains itself in spite of complex operations such as…
We discuss the role of fundamental constants and measurement data for the Planck, Avogadro and Boltzmann constants and the elementary electric charge in connection with the planned transition to new definitions of four base SI units (the…
The problem of existence of symmetric informationally-complete positive operator-valued measures (SICs for short) in every dimension is known as Zauner's conjecture and remains open to this day. Most of the known SIC examples are…
Defined by Lord Kelvin as the science of measurement it is described a fundamental fact of physics. The so called `natural' units represent the unique system of units conveniently used in the realm of High Energy Physics. The system of…
Symmetry is conventionally described in a contrariety manner that the system is either completely symmetric or completely asymmetric. Using group theoretical approach to overcome this dichotomous problem, we introduce the degree of symmetry…
We present a possible construction of coherent states on the unit circle as configuration space. In our approach the phase space is the product Z x S^1. Because of the duality of canonical coordinates and momenta, i.e. the angular variable…
Given an infinite iterated function system (IFS) $\mathcal{F}$, we define its dimension spectrum $D(\mathcal{F})$ to be the set of real numbers which can be realised as the dimension of some subsystem of $\mathcal{F}$. In the case where…
We consider a recent proposal [1] to redefine the kilogram in terms of natural constants. In our opinion, the main objective of the redefinition should be to build such a version of the SI system in which the electric measurements are…
This paper examines the potential role of unit consistency as a system design principle. Unit-consistent generalized matrix inverses and unit-invariant matrix decompositions are derived in support of this principle. Applications of the…
The asynchronous systems are the non-deterministic models of the asynchronous circuits from the digital electrical engineering. In the autonomous version, such a system is a set of functions x:R{\to}{0,1}^{n} called states (R is the time…
By using fundamental units c, h, G as conversion factors one can easily transform the dimensions of all observables. In particular one can make them all ``geometrical'', or dimensionless. However this has no impact on the fact that there…
The critical behaviour of three-dimensional disordered systems is investigated by analysing the spectral fluctuations of the energy spectrum. Our results suggest that the initial symmetries (orthogonal, unitary and symplectic) are broken by…
Considering coordinates as operators whose measured values are expectations between generalized coherent states based on the group SO(N,1) leads to coordinate noncommutativity together with full $N$ dimensional rotation invariance. Through…
Macroscopic behavior such as the lack of interference patterns has been attributed to "decoherence", a word with several possible definitions such as (1) the loss of off-diagonal density matrix elements, (2) the flow of information to the…
In scientific and engineering applications, physical quantities embodied as units of measurement (UoM) are frequently used. The loss of the Mars climate orbiter, attributed to a confusion between the metric and imperial unit systems,…
Meta-conformal invariance is a novel class of dynamical symmetries, with dynamical exponent $z=1$, and distinct from the standard ortho-conformal invariance. The meta-conformal Ward identities can be directly read off from the Lie algebra…
A variety is said to be coherent if the finitely generated subalgebras of its finitely presented members are also finitely presented. In a recent paper by the authors it was shown that coherence forms a key ingredient of the uniform…
A solution to the part and whole problem is presented in this paper by using a complex mathematical representation that permits to define the Holon concept as a unit that remains itself in spite of complex operations such as integration and…
The purpose of this article is to address the issues of dimensional consistency that arise in the process of replacing the ordinary time derivative operator by a fractional derivative operator in order to write a fractional differential…
This article gives an overview of the new SI and a few details as to how its setting up was achieved. Those interested in the story of how the kilogram was fixed by tying it to the Planck constant can go straight to section five. Otherwise,…