Related papers: First integrals in the Brans-Dicke cosmology
The Einstein field equations for several cosmological models reduce to polynomial systems of ordinary differential equations. In this paper we shall concentrate our attention to the spatially homogeneous diagonal G_2 cosmologies. By using…
Using the Brans-Dicke theory of gravitation we put under investigation a hypothetical universe filled with a fermionic field (with a self interaction potential) and a matter constituent ruled by a barotropic equation of state. It is shown…
Three solutions of the Brans-Dicke theory with a self-interacting quartic potential and perfect fluid distribution are presented for a spatially flat geometry. The physical behavior is consistent with the recent cosmological scenario…
We show that Jacobi fields of a completely integrable Hamiltonian system of m degrees of freedom also make up a completely integrable system. They provide m additional first integrals which characterize a relative motion.
These notes focus on the minimization of convex functionals using first-order optimization methods, which are fundamental in many areas of applied mathematics and engineering. The primary goal of this document is to introduce and analyze…
Double coverings of the orthogonal groups of the real and complex spaces are considered. The relation between discrete transformations of these spaces and fundamental automorphisms of Clifford algebras is established, where an isomorphism…
This paper is devoted to the study of some connections between coadjoint orbits in infinite dimensional Lie algebras, isospectral deformations and linearization of dynamical systems. We explain how results from deformation theory,…
Some integral properties of Jack polynomials, hypergeometric functions and invariant polynomials are studied for real normed division algebras.
We continue the study of symmetries in the Lagrangian formalism of arbitrary order with the help of the so-called Anderson-Duchamp-Krupka equations. For the case of second-order equations and arbitrary vector fields we are able to establish…
Despite much recent theoretical and observational progress in our knowledge of the early universe, many fundamental questions remain only partially answered. Here, we review the latest achievements and persisting problems in the…
We discuss the cosmological implications of an extended Brans-Dicke theory presented recently, in which there is an energy exchange between the scalar field and ordinary matter, determined by the theory. A new mass scale is generated in the…
This survey is the continuation of a series of works aimed at applying tools from Singularity Theory to Differential Equations. More precisely, we utilize the powerfull Milnor's Fibration Theory to give geometric-topological classifications…
We study pseudo-Abelian integrals associated with polynomial deformations of slow-fast Darboux integrable systems. Under some assumptions we prove local boundedness of the number of their zeros.
We use precise asymptotic expansions for Jacobi functions $\phi^{(\alpha,\beta)}_\lambda$ parameters $\alpha$, $\beta$ satisfying $\alpha>1/2$, $\alpha>\beta>-1/2$, to generalizing classical H\"ormander-type multiplier theorem for the…
We consider Hilbert algebras with a supplementary Fr\'echet topology and get various extensions of the algebraic structure by using duality techniques. In particular we obtain optimal multiplier-type involutive algebras, which in…
We consider complex rational vector fields that admit a first integral whose logarithmic derivative lies in a finite extension of the rational function field $K$. In view of the Prelle-Singer theorem, these are the rational vector fields…
We pose a new algebraic formalism for studying differential calculus in vector bundles. This is achieved by studying various functors of differential calculus over arbitrary graded commutative algebras (DCGCA) and applying this language to…
The genus gen(D) of a finite-dimensional central division algebra D over a field F is defined as the collection of classes [D'] in the Brauer group Br(F), where D' is a central division F-algebra having the same maximal subfields as D. For…
Progress in early Universe cosmology, including strings, extra dimensions, inflation, phase transitions, and baryogenesis, is reviewed.
We define and study the properties of Darboux-type transformations between Sturm--Liouville problems with boundary conditions containing rational Herglotz--Nevanlinna functions of the eigenvalue parameter (including the Dirichlet boundary…