Related papers: Matrix equations and trilinear commutation relatio…
The purpose of this paper is to investigate the well-posedness of several linear and nonlinear equations with a parabolic forward-backward structure, and to highlight the similarities and differences between them. The epitomal linear…
The notion of quantum matrix pairs is defined. These are pairs of matrices with non-commuting entries, which have the same pattern of internal relations, q-commute with each other under matrix multiplication, and are such that products of…
This article introduces a framework for measuring the uncertain behaviour of a changing system in terms of the solution of a class of fractional stochastic differential equations (fsDEs). This is accomplished via operational matrices based…
We investigate partial symmetry of solutions to semi-linear and quasi-linear elliptic problems with convex nonlinearities, in domains that are either axially symmetric or radially symmetric.
Field equations for n-frames h_a{}^\mu that are possible in the theory of absolute parallelism (AP) are considered. The methods of compatibility (or formal integrability) theory enable us to find the non-Lagrangian equation having unusual…
The electrostatic, spherically symmetric solutions of the general class of non-linear abelian gauge models, minimally coupled to gravity, are classified and discussed in terms of the ADM mass and the electromagnetic energy of the associated…
The properties of the phi^4 scalar field theory on a fuzzy sphere are studied numerically. The fuzzy sphere is a discretization of the sphere through matrices in which the symmetries of the space are preserved. This model presents three…
A dynamical fuzzy space might be described in terms of a dynamical three-index variable C_{ab}^c, which determines the algebraic relations f_a f_b =C_{ab}^c f_c of the functions f_a on a fuzzy space. A fuzzy analogue of the general…
Commutation formulae with respect to a non-symmetric affine connection are obtained in this paper. The components of commutation formulae in this paper are covariant derivatives of tensors with respect to symmetric and non-symmetric affine…
The general conditions under which the quadratic, uniform and monotonic convergence in the quasilinearization method of solving nonlinear ordinary differential equations could be proved are formulated and elaborated. The generalization of…
A dynamical fuzzy space might be described by a three-index variable C_{ab}^c, which determines the algebraic relations f_a f_b =C_{ab}^c f_c among the functions f_a on the fuzzy space. A fuzzy analogue of the general coordinate…
We propose an alternative approach that avoids the nonlinear equations for the Fourier coefficients that appear in the method of harmonic balance. We apply it to two simple illustrative examples.
Matrix models play an important role in studies of quantum gravity, being candidates for a formulation of M-theory, but are notoriously difficult to solve. In this work, we present a fresh approach by introducing a novel exact model…
In this article, we introduce a moving-frame approach to the geophysical equation of two-dimensional uniformly stratified rotational fluid in oceans and find a family of exact solutions containing ten arbitrary parameter functions.
The motion of a charged particle moving on a flat surface is studied through the constants of motion associated to the system, given the magnetic gauge. The usual Landau' solution and the non separable solution for the Landau's gauge are…
We study dynamics of a membrane and its matrix regularisation. We present the matrix regularisation for a membrane propagating in a curved space-time geometry in the presence of an arbitrary 3-form field. In the matrix regularisation, we…
Convenient parameterizations of matrices in terms of vectors transform (certain classes of) matrix equations into covariant (hence rotation-invariant) vector equations. Certain recently introduced such parameterizations are tersely…
The moving coframe method is applied to solve the local equivalence problem for the class of linear parabolic equations in two independent variables under an action of the pseudo-group of contact transformations. The structure equations and…
The problem of finding a canonical form of complex matrices up to conjugacy with the set of canonical matrices being a union of affine planes in the matrix space is considered. A solution of the problem is given producing a new canonical…
We describe a categorical approach to finite noncommutative geometries. Objects in the category are spectral triples, rather than unitary equivalence classes as in other approaches. This enables to treat fluctuations of the metric and…