Related papers: A clearer approach for defining unit systems
The four SI base units are proposed to be redefined in two stages: first, the kilogram, mole and ampere should be defined, and then the kelvin. To realize the redefinition of a base unit of the SI in terms of fundamental physical constant…
Flexible systems are linear systems of inclusions in which the elements of the coefficient matrix are external numbers in the sense of nonstandard analysis. External numbers represent real numbers with small, individual error terms. Using…
We offer a unified treatment of distinct measures of well-posedness for homogeneous conic systems. To that end, we introduce a distance to infeasibility based entirely on geometric considerations of the elements defining the conic system.…
We investigate perturbed Hamiltonian systems with two degrees of freedom by renormalization group method, which derives a reduced equation called renormalization group equation (RGE) by handling secular terms. We found that RGE is not…
The recent paper by Mohr and Phillips (arXiv:1409.2794) describes several problems relating to the treatment of angle measurement within SI, the unit hertz, and quantities that can be considered countable (rather than measureable). However,…
We examine implications of angles having their own dimension, in the same sense as do lengths, masses, {\it etc.} The conventional practice in scientific applications involving trigonometric or exponential functions of angles is to assume…
This paper mainly deals with switched linear systems defined by a pair of Hurwitz matrices that share a common but not strict quadratic Lyapunov function. Its aim is to give sufficient conditions for such a system to be GUAS.We show that…
We study point and higher symmetries for the hydrodynamic-type systems with two independent variables $t$ and $x$ with and without explicit dependence of the equations on $t,x$. We consider those systems which possess an…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
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…
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…
In this paper will be introduced large, probably complete family of complex base systems, which are 'proper' - for each point of the space there is a representation which is unique for all but some zero measure set. The condition defining…
In the context of the variational bi-complex, we re-explain that irreducible gauge systems define a particular example of a Lie algebroid. This is used to review some recent and not so recent results on gauge, global and asymptotic…
The advent of high-resolution electron and scanning probe microscopy imaging has opened the floodgates for acquiring atomically resolved images of bulk materials, 2D materials, and surfaces. This plethora of data contains an immense volume…
Physical systems with symmetries are described by functions containing kinematical and dynamical parts. We consider the case when kinematical symmetries are described by a noncompact semisimple real Lie group $G$. Then separation of…
We introduce a new, open-source computational general relativity framework for the Wolfram Language called Gravitas, which boasts a number of novel and distinctive features as compared to the many pre-existing computational and numerical…
The linearity inherent in quantum mechanics limits current quantum hardware from directly solving nonlinear systems governed by nonlinear differential equations. One can opt for linearization frameworks such as Carleman linearization, which…
We consider integrable systems that are connected with orthogonal separation of variables in complex Riemannian spaces of constant curvature. An isomorphism with the hyperbolic Gaudin magnet, previously pointed out by one of us, extends to…
In this Thesis we develop the geometric formulations for higher-order autonomous and non-autonomous dynamical systems, and second-order field theories. In all cases, the physical information of the system is given in terms of a Lagrangian…
A method is presented that reduces the number of terms of systems of linear equations (algebraic, ordinary and partial differential equations). As a byproduct these systems have a tendency to become partially decoupled and are more likely…