Abstract : In this paper, we prove a uniqueness theorem of non-constant meromorphic functions of hyper-order less than $1$ sharing two values CM and two partial shared values IM with their shifts. Our result in this paper improves and extends the corresponding results from Chen-Lin \cite{CL2016}, Charak-Korhonen-Kumar \cite{CKK2016}, Heittokangas-Korhonen-Laine-Rieppo-Zhang \cite{HKLRZ2009} and Li-Yi \cite{LY2016}. Some examples are provided to show that some assumptions of the main result of the paper are necessary.
Abstract : In this paper we study the theory of knotoids and braidoids and the theory of pseudo knotoids and pseudo braidoids on the torus $T$. In particular, we introduce the notion of {\it mixed knotoids} in $S^2$, that generalizes the notion of mixed links in $S^3$, and we present an isotopy theorem for mixed knotoids. We then generalize the Kauffman bracket polynomial, $$, for mixed knotoids and we present a state sum formula for $$. We also introduce the notion of {\it mixed pseudo knotoids}, that is, multi-knotoids on two components with some missing crossing information. More precisely, we present an isotopy theorem for mixed pseudo knotoids and we extend the Kauffman bracket polynomial for pseudo mixed knotoids. Finally, we introduce the theories of {\it mixed braidoids} and {\it mixed pseudo braidoids} as counterpart theories of mixed knotoids and mixed pseudo knotoids, respectively. With the use of the $L$-moves, that we also introduce here for mixed braidoid equivalence, we formulate and prove the analogue of the Alexander and the Markov theorems for mixed knotoids. We also formulate and prove the analogue of the Alexander theorem for mixed pseudo knotoids.
Abstract : In this paper, we consider a boundary value problem for a sixth order difference equation. We prove the monotone behavior of the eigenvalue of the problem as the coefficients in the difference equation change values and the existence of a positive solution for a class of problems.
Abstract : In this paper, for the bounded solution of the non-densely defined non-autonomous evolution equation, we present the condition for asymptotic periodicity by using the circular spectral theory of functions on the half line and the extrapolation theory of non-densely defined evolution equation.
Abstract : In this paper, we prove Pascal's hexagon theorem by elementary tools only. We follow the well-known route to prove the theorem by Bez\'{o}ut's theorem, explaining all the details in elementary argument. In particular, we prove a toy version of Study's lemma.
Abstract : In the present study, we consider some curvature properties of generalized $B$-curvature tensor on Kenmotsu manifold. Here first we describe certain vanishing properties of generalized $B$ curvature tensor on Kenmostu manifold. Later we formulate generalized $B$ pseudo-symmetric condition on Kenmotsu manifold. Moreover, we also characterize generalized $B$ $\phi$-recurrent Kenmotsu manifold.
Abstract : In this paper, the concept of a maximal chain of ideals is introduced. Some properties of such chains are studied. We introduce some other concepts related to a maximal chain of ideals such as the $n$-maximal ideal, the maximal dimension of a ring $S$ $(M.\dim(S))$, the maximal depth of an ideal $K$ of $S$ $(M.d(K))$ and maximal height of an ideal $K(M.d(K))$.
Abstract : Parallel conics have interesting area and chord properties. In this paper, we study such properties of conics and conic hypersurfaces. First of all, we characterize conics in the plane with respect to the above mentioned properties. Finally, we establish some characterizations of hypersurfaces with centrally symmetric hyperplane sections.
Abstract : In this paper, we give sufficient conditions for the generalized Ornstein-Uhlenbeck operators perturbed by regular potentials and inverse square potentials \begin{align*} A_{\Phi,G,V,c} = \Delta-\nabla \Phi\cdot\nabla+G\cdot \nabla-V+c|x|^{-2} \end{align*} with a suitable domain generates a quasi-contractive, positive and analytic $C_{0}$-semigroup in $L^{p}(\mathbb{R}^{N},e^{-\Phi(x)}dx)$, $1
Abstract : In this paper we prove the existence of nontrivial weak solutions to the boundary value problem \begin{align*} - G_1 u & =u^3 + f(x,y,u) \quad \text{ in } \Omega ,\\ u &\geq 0 \quad \text{ in } \Omega ,\\ u & =0 \quad \text{ on } \partial\Omega , \end{align*} where $\Omega $ is a bounded domain with smooth boundary in $\mathbb{R}^3$, $G_1 $ is a Grushin type operator, and $f(x,y,u)$ is a lower order perturbation of $u^3$ with $f(x,y,0)=0$. The nonlinearity involved is of critical exponent, which differs from the existing results in \cite{Tri:2018,TriLuyen:2020}.
Junghyun Hong, Jongmin Lee, Ho Park
Commun. Korean Math. Soc. 2023; 38(1): 89-96
https://doi.org/10.4134/CKMS.c220015
Dong Hyun Cho
Commun. Korean Math. Soc. 2022; 37(3): 749-763
https://doi.org/10.4134/CKMS.c210264
Goutam Kumar Ghosh
Commun. Korean Math. Soc. 2023; 38(2): 377-387
https://doi.org/10.4134/CKMS.c210303
Tamem Al-Shorman, Malik Bataineh, Ece Yetkin Celikel
Commun. Korean Math. Soc. 2023; 38(2): 365-376
https://doi.org/10.4134/CKMS.c220169
OM P. AHUJA, Asena \c{C}etinkaya, NAVEEN KUMAR JAIN
Commun. Korean Math. Soc. 2023; 38(4): 1111-1126
https://doi.org/10.4134/CKMS.c230002
Shiv Sharma Shukla, Vipul Singh
Commun. Korean Math. Soc. 2023; 38(4): 1191-1213
https://doi.org/10.4134/CKMS.c220309
Nand Kishor Jha, Jatinder Kaur, Sangeet Kumar, Megha Pruthi
Commun. Korean Math. Soc. 2023; 38(3): 847-863
https://doi.org/10.4134/CKMS.c220039
Asuman Guven Aksoy, Daniel Akech Thiong
Commun. Korean Math. Soc. 2023; 38(4): 1127-1139
https://doi.org/10.4134/CKMS.c230003
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