Related papers: Groups, drift and harmonic measures
This article focuses on the study of cut groups, i.e., the groups which have only trivial central units in their integral group ring. We provide state of art for cut groups. The results are compiled in a systematic manner and have also been…
We consider the bidimensional Stokes problem for incompressible fluids in stream function-vorticity. For this problem, the classical finite elements method of degree one converges only to order one-half for the L2 norm of the vorticity. We…
The paper proposes a novel hybrid method for solving equilibrium problems and fixed point problems. By constructing specially cutting-halfspaces, in this algorithm, only an optimization program is solved at each iteration without the…
For macroscopic quantum systems, we study what are measured when equilibrium fluctuations of macrovariables are measured in an ideal way that mimics classical ideal measurements as closely as possible. We find that the symmetrized time…
Harmonic frames of prime order are investigated. The primary focus is the enumeration of inequivalent harmonic frames, with the exact number given by a recursive formula. The key to this result is a one-to-one correspondence developed…
We investigate a measure of quantum coherence and its extension to quantify quantum macroscopicity. The coherence measure can also quantify the asymmetry of a quantum state with respect to a given group transformation. We then show that a…
The presence of symmetries in a Hamiltonian system usually implies the existence of conservation laws that are represented mathematically in terms of the dynamical preservation of the level sets of a momentum mapping. The symplectic or…
In this note we give some new results concerning the subgroup commutativity degree of a finite group $G$. These are obtained by considering the minimum of subgroup commutativity degrees of all sections of $G$.
We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and…
This note is an attempt to give an answer for the following old I.M. Gelfand's question: why some important problems of integral geometry (e.g., the Radon transform and others) are related to harmonic analysis on groups, but for other quite…
It is wellknown that the ordinary calculus is inadequate to handle fractal structures and processes and another suitable calculus needs to be developed for this purpose. Recently it was realized that fractional calculus with suitable…
In data streams, the data distribution of arriving observations at different time points may change - a phenomenon called concept drift. While detecting concept drift is a relatively mature area of study, solutions to the uncertainty…
In this paper, we initiate the harmonic analysis of Gaussian multiplicative chaos (GMC) on the circle, i.e. the study of its Fourier coefficients. In particular, we show that almost surely GMC is a so-called Rajchman measure which means…
The aim of this paper is to present a simple generalization of bosonic string theory in the framework of the theory of fractional variational problems. Specifically, we present a fractional extension of the Polyakov action, for which we…
A new framework for deriving equations of motion for constrained quantum systems is introduced, and a procedure for its implementation is outlined. In special cases the framework reduces to a quantum analogue of the Dirac theory of…
Quantifying coherence has received increasing attention, and considerable work has been directed towards finding coherence measures. While various coherence measures have been proposed in theory, an important issue following is how to…
The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the…
The purpose of the present paper is to present the main applications of a new method for the determination of the fractal structure of plane curves. It is focused on the inverse problem, that is, given a curve in the plane, find its fractal…
The so-called quantum measurement problems are solved from a new perspective. One of the main observations is that the basic entities of our world are {\it particles}, elementary or composite. It follows that each elementary process, hence…
A formula to calculate the quantum fluctuations of energy in small subsystems of a hot and relativistic gas is derived. We find an increase in fluctuations for subsystems of small sizes, but we agrees with the energy fluctuations in the…