Communications of the
Korean Mathematical Society
CKMS
ISSN(Print) 1225-1763
ISSN(Online) 2234-3024
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2024-01-31
On a uniqueness question of meromorphic functions and partial shared values
Imrul Kaish, Rana MondalAbstract : 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.
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2022-10-31
Knotoids, pseudo knotoids, Braidoids and pseudo braidoids on the torus
Ioannis DiamantisAbstract : 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.
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2023-07-31
Eigenvalue comparison for the discrete $(3,3)$~conjugate boundary value problem
Jun Ji, Bo YangAbstract : 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.
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2023-10-31
Circular spectrum and asymptotic periodic solutions to a class of non-densely defined evolution equations
Le Anh Minh, Nguyen Ngoc VienAbstract : 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.
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2022-10-31
Pascal's hexagon theorem reproved by elementary tools only
Insong ChoeAbstract : 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.
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2023-07-31
Certain study of generalized $B$ curvature tensor within the framework of Kenmotsu manifold
Rahuthanahalli Thimmegowda Naveen Kumar, Basavaraju Phalaksha Murthy, Puttasiddappa Somashekhara, Venkatesha VenkateshaAbstract : 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.
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2023-04-30
Maximal chain of ideals and $n$-maximal ideal
Hemin A. Ahmad, Parween A. HummadiAbstract : 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 $K(M.d(K))$.
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2024-01-31
Some characterizations of conics and hypersurfaces with centrally symmetric hyperplane sections
Shin-Ok Bang, Dong Seo Kim, Dong-Soo Kim, Wonyong KimAbstract : 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.
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2024-01-31
On the generalized Ornstein-Uhlenbeck operators with regular and singular potentials in weighted $L^{p}$-spaces
Imen Metoui
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
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2023-01-31
Existence theorems for critical degenerate equations involving the Grushin operators
Huong Thi Thu Nguyen, Tri Minh NguyenAbstract : 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}.
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Generalizing some Fibonacci--Lucas relations
Junghyun Hong, Jongmin Lee, Ho Park
Commun. Korean Math. Soc. 2023; 38(1): 89-96
https://doi.org/10.4134/CKMS.c220015 -
A translation of an analogue of Wiener space with its applications on their product spaces
Dong Hyun Cho
Commun. Korean Math. Soc. 2022; 37(3): 749-763
https://doi.org/10.4134/CKMS.c210264 -
Two linear polynomials shared by an entire function and its linear differential polynomials
Goutam Kumar Ghosh
Commun. Korean Math. Soc. 2023; 38(2): 377-387
https://doi.org/10.4134/CKMS.c210303 -
On graded $J$-ideals over graded rings
Tamem Al-Shorman, Malik Bataineh, Ece Yetkin Celikel
Commun. Korean Math. Soc. 2023; 38(2): 365-376
https://doi.org/10.4134/CKMS.c220169
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Analytic functions with conic domains associated with certain generalized $q$-integral operator
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 -
Transversal lightlike submersions from indefinite Sasakian manifolds onto lightlike manifolds
Shiv Sharma Shukla, Vipul Singh
Commun. Korean Math. Soc. 2023; 38(4): 1191-1213
https://doi.org/10.4134/CKMS.c220309 -
Generic lightlike submanifolds of semi-Riemannian product manifolds
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 -
Equality in degrees of compactness: Schauder's theorem and $s$-numbers
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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