Opuscula Mathematica
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ISSN 1232-9274
e-ISSN: 2300-6919
Issue Date
2022
Volume
Vol. 42
Number
No. 3
Description
Journal Volume
Opuscula Mathematica
Vol. 42 (2022)
Projects
Pages
Articles
Monodromy invariant Hermitian forms for second order Fuchsian differential equations with four singularities
(Wydawnictwa AGH, 2022) Adachi, Shunya
We study the monodromy invariant Hermitian forms for second order Fuchsian differential equations with four singularities. The moduli space of our monodromy representations can be realized by certain affine cubic surface. In this paper we characterize the irreducible monodromies having the non-degenerate invariant Hermitian forms in terms of that cubic surface. The explicit forms of invariant Hermitian forms are also given. Our result may bring a new insight into the study of the Painlevé differential equations.
New aspects for the oscillation of first-order difference equations with deviating arguments
(Wydawnictwa AGH, 2022) Attia, Emad R.; El-Matary, Bassant M.
We study the oscillation of first-order linear difference equations with non-monotone deviating arguments. Iterative oscillation criteria are obtained which essentially improve, extend, and simplify some known conditions. These results will be applied to some numerical examples.
Growth of solutions of a class of linear fractional differential equations with polynomial coefficients
(Wydawnictwa AGH, 2022) Hamouda, Saada; Mahmoudi, Sofiane
This paper is devoted to the study of the growth of solutions of certain class of linear fractional differential equations with polynomial coefficients involving the Caputo fractional derivatives by using the generalized Wiman-Valiron theorem in the fractional calculus.
On Ambarzumian type theorems for tree domains
(Wydawnictwa AGH, 2022) Pivovarčik, Vâčeslav
It is known that the spectrum of the spectral Sturm-Liouville problem on an equilateral tree with (generalized) Neumann's conditions at all vertices uniquely determines the potentials on the edges in the unperturbed case, i.e. case of the zero potentials on the edges (Ambarzumian's theorem). This case is exceptional, and in general case (when the Dirichlet conditions are imposed at some of the pendant vertices) even two spectra of spectral problems do not determine uniquely the potentials on the edges. We consider the spectral Sturm-Liouville problem on an equilateral tree rooted at its pendant vertex with (generalized) Neumann conditions at all vertices except of the root and the Dirichlet condition at the root. In this case Ambarzumian's theorem can't be applied. We show that if the spectrum of this problem is unperturbed, the spectrum of the Neumann-Dirichlet problem on the root edge is also unperturbed and the spectra of the problems on the complimentary subtrees with (generalized) Neumann conditions at all vertices except the subtrees' roots and the Dirichlet condition at the subtrees' roots are unperturbed then the potential on each edge of the tree is 0 almost everywhere.
Distance irregularity strength of graphs with pendant vertices
(Wydawnictwa AGH, 2022) Susanto, Faisal; Wijaya, Kristiana; Slamin; Semaničová-Feňovčíková, Andrea
A vertex $k$-labeling $\phi:V(G)\rightarrow\{1,2,\dots,k\}$ on a simple graph $G$ is said to be a distance irregular vertex $k$-labeling of $G$ if the weights of all vertices of $G$ are pairwise distinct, where the weight of a vertex is the sum of labels of all vertices adjacent to that vertex in $G$. The least integer k for which G has a distance irregular vertex k-labeling is called the distance irregularity strength of $G$ and denoted by $\mathrm{dis}(G)$. In this paper, we introduce a new lower bound of distance irregularity strength of graphs and provide its sharpness for some graphs with pendant vertices. Moreover, some properties on distance irregularity strength for trees are also discussed in this paper.