Related papers: Generalized Elitzur's Theorem and Dimensional Redu…

In this paper, we discuss possible qualitative approaches to the problem of KPZ universality. Throughout the paper, our point of view is based on the geometrical and dynamical properties of minimisers and shocks forming interlacing…

Using special quasigraded Lie algebras we obtain new hierarchies of integrable nonlinear vector equations admitting zero-curvature representations. Among them the most interesting is extension of the generalized Landau-Lifshitz hierarchy…

This paper is concerned with the design and analysis of symmetric low-regularity integrators for the semilinear Klein-Gordon equation. We first propose a general symmetrization procedure that allows for the systematic construction of…

First, we briefly review the Coset Space Dimensional Reduction scheme and the results of the best model so far. Then, we present the introduction of fuzzy coset spaces used as extra dimensions and perform a dimensional reduction. In turn,…

The ultraconfined light of plasmonic modes put their effective wavelength close to the mean free path of electrons inside the metal electron gas. The Drude model, which can not take the repulsive interactions of electrons into account, then…

I connect an old result of mine on a Lie algebra generalization of the Amitsur-Levitski theorem with equations for sheets in a reductive Lie algebra and with recent results of Kostant-Wallach on the variety of singular elements in a…

We obtain a generalized law of the iterated logarithm for a class of dependent processes with superdiffusive behaviour. Our results apply in particular to the Lorentz gas with infinite horizon.

The elasticity difference tensor, used in [1] to describe elasticity properties of a continuous medium filling a space-time, is here analysed from the point of view of the space-time connection. Principal directions associated with this…

This article deals with nonrelativistic study of a D-dimensional superintegrable system, which generalizes the ordinary isotropic oscillator system. The coefficients for the expansion between the hyperspherical and Cartesian bases…

Quantum versions of the hydrogen atom and the harmonic oscillator are studied on non Euclidean spaces of dimension N. 2N-1 integrals, of arbitrary order, are constructed via a multi-dimensional version of the factorization method, thus…

Extended geometry provides a unified framework for double geometry, exceptional geometry, etc., i.e., for the geometrisations of the string theory and M-theory dualities. In this talk, we will explain the structure of gauge transformations…

The paper contains an application of the generalized lattice model to multicomponent systems with internal degrees of freedom. The short-range inter-atomic repulsions and smooth long-range parts of the inter-atomic potentials are considered…

We prove bilinear inequalities for differential operators in $\mathbb{R}^2$. Such type inequalities turned out to be useful for anisotropic embedding theorems for overdetermined systems and the limiting order summation exponent. However,…

We describe a recursive algorithm that decomposes an algebraic set into locally closed equidimensional sets, i.e. sets which each have irreducible components of the same dimension. At the core of this algorithm, we combine ideas from the…

Enhancing and essentially generalizing previous results on a class of (1+1)-dimensional nonlinear wave and elliptic equations, we apply several new techniques to classify admissible point transformations within this class up to the…

An orthogonal approach to the fuzzification of both multisets and hybrid sets is presented. In particular, we introduce L-multi-fuzzy and L-fuzzy hybrid sets, which are general enough and in spirit with the basic concepts of fuzzy set…

We consider a generalization of the notion of a natural mechanical system to the case of additional forces of gyroscopic type. Such forces appear, for example, as a result of global reduction of a natural system with symmetry. We study…

In this text, we are concerned with ring epimorphisms, and more specifically universal localisations, from path algebras to matrix algebras. We are mainly focused on constructing ring epimorphisms and universal localisations by extending…

We consider general semilinear, multispeed Klein-Gordon systems in space dimension two with some non-degeneracy conditions. We prove that with small initial data such solutions are always global and scatter to a linear solution. This result…

Appealing to classical methods of order reduction, we reduce the Lifshitz system to a second order differential equation. We demonstrate its equivalence to well known gauge-invariant results. For a radiation dominated universe we express…