Related papers: Feuilletages en droites, \'{e}quations des eikonal…
The survey is devoted to the rationality question of finite linear groups. We concentrate on lower-dimensional cases, especially on the case of dimension four.
We study equivariant geometry and rationality of moduli spaces of points on the projective line, for twists associated with permutations of the points.
In this paper we introduce and investigate a new kind of functional (including ordinary and evolutionary partial) differential equations. The main goal of this paper is to explore our new philosophy by some examples on functional ODEs and…
In this paper, we discuss foliations by real curves. We investigate differential equations which are modifications of du/dx = v along leaves. Our focus is on having a solution operator so that u is continuous if v is continuous.
In [8], some exact splittings are proposed for inhomogeneous quadratic differential equations including, for example, transport equations, kinetic equations, and Schr{\"o}dinger type equations with a rotation term. In this work, these exact…
A gauge-invariant form of the nonlinear Hodge equations is studied.
In this note, we study polynomial and rational lemniscates as trajectories of related quadratic differentials. Many classic results can be then proved easily...
Based on the concept of manifold valued generalized functions we initiate a study of nonlinear ordinary differential equations with singular (in particular: distributional) right hand sides in a global setting. After establishing several…
Electric fields are commonly visualized with field line diagrams, which only unambiguously specify the field's direction. We consider two simple questions. First, can one deduce if an electric field is conservative, as required e.g. in…
Vector fields can arise in the cosmological context in different ways, and we discuss both abelian and nonabelian sector. In the abelian sector vector fields of the geometrical origin (from dimensional reduction and Einstein-Eddington…
In this paper, we study non-linear differential equations associated with Legendre polynomials and their applications. From our study of non- linear differential equations, we derive some new and explicit identities for Legendre…
This research is concerned with the nonhomogeneous linear complex differential equation $$ f^{(k)}+A_{k-1}f^{(k-1)}+\cdots+A_{1}f'+A_{0}f=A_{k} $$ in the complex plane. In the higher order case, the mutual relations between coefficients and…
The existence and analyticity of solutions to linear systems of moment differential equations with analytic coefficients is studied. The relation of solutions of such systems with respect to linear moment differential equations is…
In this paper, we investigate vector fields on polyhedral complexes and their associated trajectories. We study vector fields which are analogue of the gradient vector field of a function in the smooth case. Our goal is to define a nice…
We show that much of the theory of finite tight frames can be generalised to vector spaces over the quaternions. This includes the variational characterisation, group frames, and the characterisations of projective and unitary equivalence.…
The light-front dynamics is an efficient approach to study of field theory and of relativistic composite systems (nuclei at relativistic relative nucleon momenta, hadrons in the quark models). The explicitly covariant version of this…
We study solutions to conformally invariant equations with isolated singularties.
The classical fields with fractional derivatives are investigated by using the fractional Lagrangian formulation.The fractional Euler-Lagrange equations were obtained and two examples were studied.
In this note we study existence of positive radial solutions in annuli and exterior domains for a class of nonlinear equations driven by Pucci extremal operators subject to a H\'enon type weight. Our approach is based on the shooting method…
Different (not only by sign) affine connections are introduced for contravariant and covariant tensor fields over a differentiable manifold by means of a non-canonical contraction operator, defining the notion dual bases and commuting with…