Browsing by Subject "symmetry"

Now showing 1 - 7 of 7

Access status: Open Access ,
Concavity of solutions of a 2n-th order problem with symmetry
(2013) Al Twaty, Abdulmalik; Eloe, Paul W.
In this article we apply an extension of a Leggett-Williams type fixed point theorem to a two-point boundary value problem for a $2n$-th order ordinary differential equation. The fixed point theorem employs concave and convex functionals defined on a cone in a Banach space. Inequalities that extend the notion of concavity to $2n$-th order differential inequalities are derived and employed to provide the necessary estimates. Symmetry is employed in the construction of the appropriate Banach space.
Access status: Open Access ,
On classical symmetries of ordinary differential equations related to stationary integrable partial differential equations
(Wydawnictwa AGH, 2021) Tsyfra, Ivan
We study the relationship between the solutions of stationary integrable partial and ordinary differential equations and coefficients of the second-order ordinary differential equations invariant with respect to one-parameter Lie group. The classical symmetry method is applied. We prove that if the coefficients of ordinary differential equation satisfy the stationary integrable partial differential equation with two independent variables then the ordinary differential equation is integrable by quadratures. If special solutions of integrable partial differential equations are chosen then the coefficients satisfy the stationary KdV equations. It was shown that the Ermakov equation belong to a class of these equations. In the framework of the approach we obtained the similar results for generalized Riccati equations. By using operator of invariant differentiation we describe a class of higher order ordinary differential equations for which the group-theoretical method enables us to reduce the order of ordinary differential equation.
Access status: Open Access ,
On triangular (Dn)-actions on cyclic p-gonal Riemann surfaces
(2016) Tyszkowska, Ewa
A compact Riemann surface $X$ of genus $g\gt 1$ which has a conformal automorphism $\rho$ of prime order $p$ such that the orbit space $X/ \langle \rho \rangle$ is the Riemann sphere is called cyclic $p$-gonal. Exceptional points in the moduli space $\mathcal{M}_g$ of compact Riemann surfaces of genus $g$ are unique surface classes whose full group of conformal automorphisms acts with a triangular signature. We study symmetries of exceptional points in the cyclic $p$-gonal locus in $\mathcal{M}_g$ for which $\text{Aut}(X)/ \langle \rho \rangle$ is a dihedral group $D_n$.
Access status: Restricted ,
Struktura algebraiczna zbioru generatorów wieloparametrowych grup Liego
(Data obrony: 2010-07-05) Pajda, Anna
Wydział Matematyki Stosowanej
Access status: Restricted ,
Symetrie fulleroidów
(Data obrony: 2013-10-24) Szczerbowska, Joanna
Wydział Matematyki Stosowanej
Access status: Restricted ,
Zastosowanie teorii grup do całkowania quasi-liniowego równania różniczkowego drugiego rzędu
(Data obrony: 2010-07-05) Merchut, Paulina
Wydział Matematyki Stosowanej
Access status: Restricted ,
Zastosowanie teorii grup do całkowania zredukowanego równania dyfuzji
(Data obrony: 2011-07-04) Gardian, Rafał
Wydział Matematyki Stosowanej