# Journal of theKorean Mathematical SocietyJKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

• ### 2021-01-01

#### Weighted projective lines with weight permutation

Lina Han, Xintian Wang

Abstract : Let $\mathbb X$ be a weighted projective line defined over the algebraic closure $k=\overline{\mathbb F}_q$ of the finite field $\bbf_q$ and $\sigma$ be a weight permutation of $\mathbb X$. By folding the category coh-$\mathbb{X}$ of coherent sheaves on $\mathbb X$ in terms of the Frobenius twist functor induced by $\sigma$, we obtain an $\bbf_q$-category, denoted by coh-$(\mathbb{X},\sigma;q)$. We then prove that $\coh(\mathbb{X},\sigma;q)$ is derived equivalent to the valued canonical algebra associated with $(\bbX,\sigma)$.

• ### 2020-11-01

Imed Abid

Abstract : We study bifurcation for the following fractional Schr\"{o}dinger equation \begin{eqnarray*}\left\{ \begin{array}{rlll} (-\Delta)^{s}u+V(x)u& = \lambda\,f(u)& \hbox{in}\,\Omega \\ u&>0& \hbox{in}\,\Omega\\ u &=0 &\hbox{in}\,\R^n\setminus\Omega \\ \end{array} \right. \end{eqnarray*} where $0 Show More • ### 2021-07-01 #### Numerical solutions for one and two dimensional nonlinear problems related to dispersion managed solitons Younghoon Kang, Eunjung Lee, Young-Ran Lee Abstract : We study behavior of numerical solutions for a nonlinear eigenvalue problem on$\R^n$that is reduced from a dispersion managed nonlinear Schr\"{o}dinger equation. The solution operator of the free Schr\"{o}dinger equation in the eigenvalue problem is implemented via the finite difference scheme, and the primary nonlinear eigenvalue problem is numerically solved via Picard iteration. Through numerical simulations, the results known only theoretically, for example the number of eigenpairs for one dimensional problem, are verified. Furthermore several new characteristics of the eigenpairs, including the existence of eigenpairs inherent in zero average dispersion two dimensional problem, are observed and analyzed. Show More • ### 2021-03-01 #### Parameter Marcinkiewicz integral and its commutator on generalized Orlicz-Morrey spaces Guanghui Lu Abstract : The aim of this paper is to mainly establish the sufficient and necessary conditions for the boundedness of the commutator$\mathcal{M}^{\rho}_{\Omega, b}$which is generated by the parameter Marcinkiwicz integral$\mathcal{M}^{\rho}_{\Omega}$and the Lipschitz function$b$on generalized Orlicz-Morrey space$L^{\Phi,\varphi}(\mathbb{R}^{d})$in the sense of the Adams type result (or Spanne type result). Moreover, the necessary conditions for the parameter Marcinkiewizcz integral$\mathcal{M}^{\rho}_{\Omega}$on the$L^{\Phi,\varphi}(\mathbb{R}^{d})$, and the commutator$[b,\mathcal{M}^{\rho}_{\Omega}]$generated by the$\mathcal{M}^{\rho}_{\Omega}$and the space$\mathrm{BMO}$on the$L^{\Phi,\varphi}(\mathbb{R}^{d})$, are also obtained, respectively. Show More • ### 2021-03-01 #### A graded minimal free resolution of the$m$-th order symbolic power of a star configuration in$\mathbb P^n$Jung Pil Park, Yong-Su Shin Abstract : In \cite{S:3} the author finds a graded minimal free resolution of the$2$-nd order symbolic power of a star configuration in$\P^n$of any codimension$r$. In this paper, we find that of any$m$-th order symbolic power of a star configuration in$\P^n$of codimension$2$, which generalizes the result of Galetto, Geramita, Shin, and Van Tuyl in \cite[Theorem 5.3]{GGSV:1}. Furthermore, we extend it to the$m$-th order symbolic power of a star configuration in$\P^n$of any codimension$r$for$m=3,4$, which also generalizes the result of Biermann et al. in \cite[Corollaries 4.6 and 5.7]{BDGMNORS}. We also suggest how to find a graded minimal free resolution of the$m$-th order symbolic power of a star configuration in$\P^n$of any codimension$r$for$m\ge 5$. Show More • ### 2021-01-01 #### Strong hypercyclicity of Banach space operators Mohammad Ansari, Karim Hedayatian, Bahram Khani-Robati Abstract : A bounded linear operator$T$on a separable infinite dimensional Banach space$X$is called strongly hypercyclic if $$X\backslash\{0\}\subseteq \bigcup_{n=0}^{\infty}T^n(U)$$ for all nonempty open sets$U\subseteq X$. We show that if$T$is strongly hypercyclic, then so are$T^n$and$cT$for every$n\ge 2$and each unimodular complex number$c$. These results are similar to the well known Ansari and Le\'{o}n-M\"{u}ller theorems for hypercyclic operators. We give some results concerning multiplication operators and weighted composition operators. We also present a result about the invariant subset problem. Show More • ### 2021-01-01 #### Mathematical analysis of an SIR'' epidemic model in a continuous reactor - deterministic and probabilistic approaches Miled El Hajji, Sayed Sayari, Abdelhamid Zaghdani Abstract : In this paper, a mathematical dynamical system involving both deterministic (with or without delay) and stochastic SIR'' epidemic model with nonlinear incidence rate in a continuous reactor is considered. A profound qualitative analysis is given. It is proved that, for both deterministic models, if$\R_d > 1$, then the endemic equilibrium is globally asymptotically stable. However, if$\R_d \leq 1$, then the disease-free equilibrium is globally asymptotically stable. Concerning the stochastic model, the Feller's test combined with the canonical probability method were used in order to conclude on the long-time dynamics of the stochastic model. The results improve and extend the results obtained for the deterministic model in its both forms. It is proved that if$\R_s > 1$, the disease is stochastically permanent with full probability. However, if$\R_s \leq 1$, then the disease dies out with full probability. Finally, some numerical tests are done in order to validate the obtained results. Show More • ### 2021-05-01 #### Kenmotsu manifolds satisfying the Fischer-Marsden equation Sudhakar Kr Chaubey, Uday Chand De, Young Jin Suh Abstract : The present paper deals with the study of Fischer-Marsden conjecture on a Kenmotsu manifold. It is proved that if a Kenmotsu metric satisfies$\mathfrak{L}^{*}_{g}(\lambda)=0$on a$(2n+1)$-dimensional Kenmotsu manifold$M^{2n+1}$, then either$\xi \lambda=- \lambda$or$M^{2n+1}$is Einstein. If$n=1$,$M^3$is locally isometric to the hyperbolic space$H^{3}(-1)$. • ### 2021-05-01 #### On$\mathbb{Z}_p\mathbb{Z}_p[u]/\langle u^k\rangle$-cyclic codes and their weight enumerators Maheshanand Bhaintwal, Soumak Biswas Abstract : In this paper we study the algebraic structure of$\mathbb{Z}_p\mathbb{Z}_p[u]/\langle u^k\rangle$-cyclic codes, where$u^k=0$and$p$is a prime. A$\mathbb{Z}_p\mathbb{Z}_p[u]/\langle u^k\rangle$-linear code of length$(r+s)$is an$R_k$-submodule of$\mathbb{Z}_p^r \times R_k^s$with respect to a suitable scalar multiplication, where$R_k = \mathbb{Z}_p[u]/\langle u^k\rangle$. Such a code can also be viewed as an$R_k$-submodule of$\mathbb{Z}_p[x]/\langle x^r-1\rangle \times R_k[x]/\langle x^s-1\rangle$. A new Gray map has been defined on$\mathbb{Z}_p[u]/\langle u^k\rangle$. We have considered two cases for studying the algebraic structure of$\mathbb{Z}_p\mathbb{Z}_p[u]/\langle u^k\rangle$-cyclic codes, and determined the generator polynomials and minimal spanning sets of these codes in both the cases. In the first case, we have considered$(r,p)=1$and$(s,p)\neq 1$, and in the second case we consider$(r,p)=1$and$(s,p)=1$. We have established the MacWilliams identity for complete weight enumerators of$\mathbb{Z}_p\mathbb{Z}_p[u]/\langle u^k\rangle$-linear codes. Examples have been given to construct$\mathbb{Z}_p\mathbb{Z}_p[u]/\langle u^k\rangle$-cyclic codes, through which we get codes over$\mathbb{Z}_p$using the Gray map. Some optimal$p$-ary codes have been obtained in this way. An example has also been given to illustrate the use of MacWilliams identity. Show More • ### 2021-03-01 #### Symplectic fillings of quotient surface singularities and minimal model program Hakho Choi, Heesang Park, Dongsoo Shin Abstract : We prove that every minimal symplectic filling of the link of a quotient surface singularity can be obtained from its minimal resolution by applying a sequence of rational blow-downs and symplectic antiflips. We present an explicit algorithm inspired by the minimal model program for complex 3-dimensional algebraic varieties. ## Current Issue ### July, 2022 Vol.59 No.4 ## Most Read • ### Stabilized-penalized collocated finite volume scheme for incompressible biofluid flows Nasserdine Kechkar, Mohammed Louaar J. Korean Math. Soc. 2022; 59(3): 519-548 https://doi.org/10.4134/JKMS.j210211 • ### A deep learning algorithm for optimal investment strategies under Merton's framework Daeyung Gim, Hyungbin Park J. Korean Math. Soc. 2022; 59(2): 311-335 https://doi.org/10.4134/JKMS.j210168 • ### Constructions of Segal algebras in$L^1(G)$of LCA groups$G$in which a generalized Poisson summation formula holds Jyunji Inoue, Sin-Ei Takahasi J. Korean Math. Soc. 2022; 59(2): 367-377 https://doi.org/10.4134/JKMS.j210290 • ### Boundedness of Calder\'{o}n-Zygmund operators on inhomogeneous product Lipschitz spaces Shaoyong He, Taotao Zheng J. Korean Math. Soc. 2022; 59(3): 469-494 https://doi.org/10.4134/JKMS.j210115 ## Most Downloaded • ### A deep learning algorithm for optimal investment strategies under Merton's framework Daeyung Gim, Hyungbin Park J. Korean Math. Soc. 2022; 59(2): 311-335 https://doi.org/10.4134/JKMS.j210168 • ### Maximal invariance of topologically almost continuous iterative dynamics Byungik Kahng J. Korean Math. Soc. 2022; 59(1): 105-127 https://doi.org/10.4134/JKMS.j210201 • ### Stabilized-penalized collocated finite volume scheme for incompressible biofluid flows Nasserdine Kechkar, Mohammed Louaar J. Korean Math. Soc. 2022; 59(3): 519-548 https://doi.org/10.4134/JKMS.j210211 • ### Green's additive complement problem for$k\$-th powers

Yuchen Ding, Li-Yuan Wang

J. Korean Math. Soc. 2022; 59(2): 299-309
https://doi.org/10.4134/JKMS.j210123