Related papers: On Higher-Dimensional Oscillation in Ergodic Theor…
Modifications of Einstein's theory of gravitation have been extensively considered in the past years, in connection to both cosmology and quantum gravity. Higher-curvature and higher-derivative gravity theories constitute the main examples…
We study higher-order theories of gravitation; in particular, we will focus our attention on the second-order theory, in which conformal symmetry can be implemented.
It is possible to construct representations of the Lorentz group using four-dimensional harmonic oscillators. This allows us to construct three-dimensional wave functions with the usual rotational symmetry for space-like coordinates and…
This survey is focused on the results related to topologies on the groups of transformations in ergodic theory, Borel, and Cantor dynamics. Various topological properties (density, connectedness, genericity) of these groups and their…
We consider the asymptotic behavior of the multidimensional Laplace-type integral with a perturbed phase function. Under suitable assumptions, we derive a higher-order asymptotic expansion with an error estimate, generalizing some previous…
Extends previous work on a quintic-solving algorithm to equations of the eighth-degree.
We derive recursively the perturbation series for the ground-state energy of the D-dimensional anharmonic oscillator and resum it using variational perturbation theory (VPT). From the exponentially fast converging approximants, we extract…
Szemer\'edi's Theorem states that a set of integers with positive upper density contains arbitrarily long arithmetic progressions. Bergelson and Leibman generalized this, showing that sets of integers with positive upper density contain…
We construct analytical and numerical vortex solutions for an extended Skyrme-Faddeev model in a $(3+1)$ dimensional Minkowski space-time. The extension is obtained by adding to the Lagrangian a quartic term, which is the square of the…
This article deals with a nonrelativistic quantum mechanical study of a dynamical system which generalizes the isotropic harmonic oscillator system in three dimensions. The problem of interbasis expansions of the wavefunctions is completely…
The development of the theory of three-dimensional harmonic mappings is considered. The new classes of mappings that generate three-dimensional harmonic functions are introduced. The physical interpretation of these mappings is applied to…
We discuss an elementary derivation of variational symmetries and corresponding integrals of motion for the Lagrangian systems depending on acceleration. Providing several examples, we make the manuscript accessible to a wide range of…
Rank one transformations serve as a source of examples in ergodic theory, showing variety of algebraic, asymptotic and spectral properties of dynamical systems. The properties of a rank one transformation are closely related to the weak…
We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…
A method for extracting time-varying oscillatory motions from time series records is applied to Lagrangian trajectories from a numerical model of eddies generated by an unstable equivalent barotropic jet on a beta plane. An oscillation in a…
In the present paper we prove Besocovich weighted ergodic theorem for positive contractions acting on Orlich-Kantorovich space. Our main tool is the use of methods of measurable bundles of Banach-Kantorovich lattices.
We provide a higher dimensional extension of the gravitational decoupling method. This extended method allows to obtain new analytic and well behaved solutions that could be associated to higher dimensional stellar distributions.…
We obtain the lower bounds for ergodic convergence rates, including spectral gaps and convergence rates in strong ergodicity for time-changed symmetric L\'{e}vy processes by using harmonic function and reversible measure. As direct…
In the framework of statistical mechanics the properties of macroscopic systems are deduced starting from the laws of their microscopic dynamics. One of the key assumptions in this procedure is the ergodic property, namely the equivalence…
We report on a recent progress in constructing off-shell ${\cal N}=2, 4D$ supersymmetric integer higher-spin theory in terms of unconstrained harmonic analytic gauge superfields and their cubic interaction with the matter hypermultiplets.…