Related papers: Normalizers of planar systems with known first int…
In this paper, we prove some value distribution results which lead to some normality criteria for a family of analytic functions. These results improve some recent results.
We give explicit formulas as well as a quadratic time algorithm to solve (so called) generalized Vandermonde's systems of p linear equations and n variables. It allows in particular to find all (so called Lagrange's) interpolation polynoms…
A center of a differential system in the plane $\mathbb{R}^2$ is an equilibrium point $p$ having a neighborhood $U$ such that $U\setminus \{p\}$ is filled of periodic orbits. A center $p$ is global when $\mathbb{R}^2\setminus \{p\}$ is…
We introduce a simple method to estimate the system parameters in continuous dynamical systems from the time series. In this method, we construct a modified system by introducing some constants (controlling constants) into the given…
In this paper we developed an integrating factor matrix method to derive conditions for the existence of first integrals. We use this novel method to obtain first integrals, along with the conditions for their existence, for two and three…
Apparently, all partial differential equations that describe physical phenomena in space-time can be cast into a universal quasilinear, first-order form. In this paper, we do two things. First, we describe some broad features of systems of…
A Hamiltonian renormalization group is presented. Such a formulation is relevant for chiralic systems and more appropriate than the Lagrangian formalism. An application to 1D system is presented.
The aim of this paper is to derive on the basis of the Euler's formula several analytical relations which hold for certain classes of planar graphs and which can be useful in algorithmic graph theory.
Polynomial dynamical systems describing interacting particles in the plane are studied. A method replacing integration of a polynomial multi--particle dynamical system by finding polynomial solutions of a partial differential equations is…
In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…
Our main purpose is to give multiple examples for using the available implementations for computing the normalization of an affine ring, computing the minimial generators of the normalization as an algebra over the original ring and…
In this note we give an explicit parametrization of the modular curve associated to the normalizer of a non-split Cartan subgroup of level 9. We determine all integral points of this modular curve. As an application, we give an alternative…
The connection between symmetries and linearizations of discrete-time dynamical systems is being inverstigated. It is shown, that existence of semigroup structures related to the vector field and having linear representations enables…
We tackle the regularisation of a differential system related to generalised Krawtchouk polynomials. We show a straightforward connection between certain auxiliary quantities involving the recurrence coefficients of these polynomials and…
The principle of finding an integrating factor for a none exact differential equations is extended to a class of third order differential equations. If the third order equation is not exact, under certain conditions, an integrating factor…
We give an introduction into diffraction theory for aperiodic order. We focus on an approach via dynamical systems and the phenomenon of pure point diffraction. We review recent results and sketch proofs. We then present a new uniform…
In this study, a recursive solution technique in conjunction with generalized integrating factors is presented and applied to address first and second order linear differential equations. This approach demonstrates practical utility in…
The intrinsic nature of a problem usually suggests a first suitable method to deal with it. Unfortunately, the apparent ease of application of these initial approaches may make their possible flaws seem to be inherent to the problem and…
This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…
This primer is intended as an introduction to differential forms, a central object in modern mathematical physics, for scientists and engineers.