Artykuły (CN-OpMath)
Stały identyfikator URI dla tej kolekcji
Artykuły czasopisma Opuscula Mathematica
Przeglądanie
Ostatnie wpływy
- ArtykułOtwarty dostępReverse Lieb-Thirring inequality for the half-line matrix Schrödinger operator(Wydawnictwa AGH, 2024) Weder, RicardoWe prove a reverse Lieb-Thirring inequality with a sharp constant for the matrix Schrödinger equation on the half-line
- ArtykułOtwarty dostępOn expansive three-isometries(Wydawnictwa AGH, 2024) Suciu, LaurianThe sub-Brownian 3-isometries in Hilbert spaces are the natural counterparts of the 2-isometries, because all of them have Brownian-type extensions in the sense of J. Agler and M. Stankus. We show that all powers $T^n$ for $n\geq 2$ of every expansive 3-isometry $T$ are sub-Brownian, even if $T$ does not have such a property. This fact induces some useful relations between the corresponding covariance operators of $T$. We analyze two matrix representations of $T$ in order to get some conditions under which $T$ is sub-Brownian, or $T$ admits the Wold-type decomposition in the sense of S. Shimorin. We show that the restriction of $T$ to its range is sub-Brownian of McCullough's type, and that under some conditions on $\mathcal{N}(T^*)$, $T$ itself is sub-Brownian, and it admits the Wold-type decomposition.
- ArtykułOtwarty dostępSymmetric 2×2 matrix functions with order preserving property(Wydawnictwa AGH, 2024) Štoudková Růžičková, VieraIt is known that the discrete matrix Riccati equation has the order preserving property under some assumptions. In this paper we formulate and prove the converse statement for the case when the dimensions of the matrices are $2 \times 2$ and the order preserving property holds for all such symmetric matrices
- ArtykułOtwarty dostępPositive solutions of nonpositone sublinear elliptic problems(Wydawnictwa AGH, 2024) Godoy, TomasConsider the problem $-\Delta u=\lambda f(\cdot, u) $ in $\Omega$, $u=0$ on $\partial\Omega$, $u\gt 0$ in $\Omega$, where $\Omega$ is a bounded domain in $\mathbb{R}^{n}$ with $C^{2}$ boundary when $n\geq2$, $\lambda\gt 0$, and where $f\in C (\overline{\Omega}\times[0,\infty)) $ satisfies $\lim_{s\rightarrow\infty}s^{-p}f(\cdot, s) =\gamma$ for some $p\in(0,1)$ and some $\gamma\in C(\overline{\Omega}) $ such that $\gamma\neq 0$ a.e. in $\Omega$ and, for some positive constants $c$ and $c^{\prime}$, $\gamma^{-}\leq cd_{\Omega}^{\beta}$ for some $\beta\in (\frac{n-1}{n},\infty)$ and $(-\Delta)^{-1}\gamma\geq c^{\prime}d_{\Omega}$, where $d_{\Omega}(x):=dist ( x,\partial \Omega) $ and $\gamma^{-}:=-\min(0,\gamma)$. Under these assumptions we show that for $\lambda$ large enough, the above problem has a positive weak solution $u\in C^{1}(\overline{\Omega})$ such that, for some constant $c^{\prime\prime}\gt 0$, $u\geq c^{\prime\prime}d_{\Omega}$ in $\Omega$.
- ArtykułOtwarty dostępFacial graceful coloring of plane graphs(Wydawnictwa AGH, 2024) Czap, JúliusLet $G$ be a plane graph. Two edges of $G$ are facially adjacent if they are consecutive on the boundary walk of a face of $G$. A facial edge coloring of $G$ is an edge coloring such that any two facially adjacent edges receive different colors. A facial graceful $k$-coloring of $G$ is a proper vertex coloring $c:V(G)\rightarrow\{1,2,\dots,k\}$ such that the induced edge coloring $c^{\prime}:E(G)\rightarrow\{1,2,\dots,k-1\}$ defined by $c^{\prime(uv)}=|c(u)-c(v)|$ is a facial edge coloring. The minimum integer $k$ for which $G$ has a facial graceful $k$-coloring is denoted by $\chi_{fg}(G)$. In this paper we prove that $\chi_{fg}(G)\leq 14$ for every plane graph $G$ and $\chi_{fg}(H)\leq 9$ for every outerplane graph $H$. Moreover, we give exact bounds for cacti and trees.