Related papers: First integrals in the Brans-Dicke cosmology
The one-dimensional system of equations of isentropic gas dynamics is considered. First-order invariants of characteristics of this system are classified. Second-order invariants of characteristics are classified for polytropic processes.…
This work deals with cosmological models driven by real scalar field, described by standard dynamics in generic spherical, flat, and hyperbolic geometries. We introduce a first-order formalism, which shows how to relate the potential that…
This contribution is the first in a series of three: it reports on the construction of (a fine sheaf of) diffeomorphism invariant Colombeau algebras on open sets of Eucildean space, which completes earlier approaches. Part II and III will…
In this paper, to begin with, we review six different analytical methods which are widely used to derive symmetries, integrating factors, multipliers, Darboux polynomials and integrals of second order nonlinear ordinary differential…
New index transforms are investigated, which contain as the kernel products of the Bessel and modified Bessel functions. Mapping properties and invertibility in Lebesgue spaces are studied for these operators. Relationships with the…
Recently, the research community has been exploring fractional calculus to address problems related to cosmology; in this approach, the gravitational action integral is altered, leading to a modified Friedmann equation, then the resulting…
This work discuss the construction of braneworld solutions in modified gravity with Lagrange multipliers. We examine the general aspects of the model and present a first order formalism that help us to find analytic solutions of the…
The structure and properties of possible $q$-Minkowski spaces is discussed, and the corresponding non-commutative differential calculi are developed in detail and compared with already existing proposals. This is done by stressing its…
The presence of light scalars can have profound effects on early universe cosmology, influencing its thermal history as well as paradigms like inflation and baryogenesis. Effective supergravity provides a framework to make quantifiable,…
Identification of first and second turnaround radii in groups of galaxies provide interesting scaling relations and may constrain cosmological parameters.
For redundant second-class constraints the Dirac brackets cannot be defined and new brackets must be introduced. We prove here that the Jacobi identity for the new brackets must hold on the surface of the second-class constraints. In order…
n this paper we formulate necessary conditions for the integrability in the Jacobi sense of Newton equations $\ddot \vq=-\vF(\vq)$, where $\vq\in\C^n$ and all components of $\vF$ are polynomial and homogeneous of the same degree $l$. These…
In unimodular-like theories, the constants of nature are demoted from pre-given parameters to phase space variables. Their canonical duals provide physical time variables. We investigate how this interacts with an alternative approach to…
It is shown that a Dirac bracket algebra is isomorphic to the original Poisson bracket algebra of first class functions subject to first class constraints. The isomorphic image of the Dirac bracket algebra in the star-product commutator…
First principles should predetermine physical geometry and dynamics both together. In the "algebrodynamics" they follow solely from the properties of the biquaternion algebra $\B$ and the analysis over $\B$. We briefly present the…
A version of the Dirac equation is derived from first principles using a combination of quaternions and multivariate 4-vectors. The nilpotent form of the operators used allows us to derive explicit expressions for the wavefunctions of free…
As the third stage of the project multi-indexed orthogonal polynomials, we present, in the framework of 'discrete quantum mechanics' with pure imaginary shifts in one dimension, the multi-indexed Wilson and Askey-Wilson polynomials. They…
We complete the description of group gradings on finite-dimensional incidence algebras. Moreover, we classify the finite-dimensional graded algebras that can be realized as incidence algebras endowed with a group grading.
An important invariant of a polynomial $f$ is its Jacobian algebra defined by its partial derivatives. Let $f$ be invariant with respect to the action of a finite group of diagonal symmetries $G$. We axiomatically define an orbifold…
A generalized algebra of quantum observables, depending on extra dimensional constants, is considered. Some limiting forms of the algebra are investigated and their possible applications to the descriptions of interactions of fundamental…