# Journal of theKorean Mathematical SocietyJKMS

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

• ### 2020-07-01

#### Radii problems for the generalized Mittag-Leffler functions

Anuja Prajapati

Abstract : In this paper our aim is to find various radii problems of the generalized Mittag-Leffler function for three different kinds of normalization by using their Hadamard factorization in such a way that the resulting functions are analytic. The basic tool of this study is the Mittag-Leffler function in series. Also we have shown that the obtained radii are the smallest positive roots of some functional equations.

• ### 2021-11-01

#### Multiplicity of solutions for quasilinear Schr\"{o}dinger type equations with the concave-convex nonlinearities

In Hyoun Kim, Yun-Ho Kim, Chenshuo Li, Kisoeb Park

Abstract : We deal with the following elliptic equations: \begin{equation*} \left\{ \begin{array}{ll} \displaystyle -\text{div}(\varphi^{\prime}(|\nabla z|^2)\nabla z) +V(x)|z|^{\alpha-2}z=\lambda \rho(x)|z|^{r-2}z + h(x,z), \\ \vspace{-3mm}\\ \displaystyle z(x) \rightarrow 0, \quad \mbox{as} \ |x| \rightarrow \infty, \end{array}\right. \mbox{in} \,\R^N, \end{equation*} where $N \geq 2$, $1 < p < q < N$, $1 < \alpha \leq p^*q^{\prime}/p^{\prime}$, $\alpha < q$, $1 < r < \min\{p,\alpha\}$, $\varphi(t)$ behaves like $t^{q/2}$ for small $t$ and $t^{p/2}$ for large $t$, and $p^{\prime}$ and $q^{\prime}$ the conjugate exponents of $p$ and $q$, respectively. Here, $V:\mathbb R^{N} \to (0,\infty)$ is a potential function and $h:\mathbb R^{N}\times\mathbb R \to \mathbb R$ is a Carath\'eodory function. The present paper is devoted to the existence of at least two distinct non-trivial solutions to quasilinear elliptic problems of Schr\"{o}dinger type, which provides a concave--convex nature to the problem. The primary tools are the well-known mountain pass theorem and a variant of Ekeland's variational principle.

• ### 2021-11-01

#### Bergman type operators on some generalized Cartan-Hartogs domains

Le He, Yanyan Tang, Zhenhan Tu

• ### 2021-01-01

#### Positively expansive maps and the limit shadowing properties

Kazuhiro Sakai

Abstract : In this paper, the notion of two-sided limit shadowing property is considered for a positively expansive open map. More precisely, let $f$ be a positively expansive open map of a compact metric space $X$. It is proved that if $f$ is topologically mixing, then it has the two-sided limit shadowing property. As a corollary, we have that if $X$ is connected, then the notions of the two-sided limit shadowing property and the average-shadowing property are equivalent.

• ### 2020-11-01

#### A $q$-queens problem V. some of our favorite pieces: queens, bishops, rooks, and nightriders

Seth Chaiken, Christopher R. H. Hanusa, Thomas Zaslavsky

Abstract : Parts~I--IV showed that the number of ways to place $q$ nonattacking queens or similar chess pieces on an $n\times n$ chessboard is a quasipolynomial function of $n$ whose coefficients are essentially polynomials in $q$. For partial queens, which have a subset of the queen's moves, we proved complete formulas for these counting quasipolynomials for small numbers of pieces and other formulas for high-order coefficients of the general counting quasipolynomials. We found some upper and lower bounds for the periods of those quasipolynomials by calculating explicit denominators of vertices of the inside-out polytope. Here we discover more about the counting quasipolynomials for partial queens, both familiar and strange, and the nightrider and its subpieces, and we compare our results to the empirical formulas found by \Kot. We prove some of \Kot's formulas and conjectures about the quasipolynomials and their high-order coefficients, and in some instances go beyond them.

• ### 2020-11-01

#### Cyclotomic quiver Hecke algebras corresponding to minuscule representations

Euiyong Park

Abstract : In the paper, we give an explicit basis of the cyclotomic quiver Hecke algebra corresponding to a minuscule representation of finite type.

## Current Issue

• ### 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

• ### General iterative algorithms for monotone inclusion, variational inequality and fixed point problems

Jong Soo Jung

J. Korean Math. Soc. 2021; 58(3): 525-552
https://doi.org/10.4134/JKMS.j180808

• ### Topological stability and shadowing property for group actions on metric spaces

Yinong Yang

J. Korean Math. Soc. 2021; 58(2): 439-449
https://doi.org/10.4134/JKMS.j200095

• ### Some finiteness results for co-associated primes of generalized local homology modules and applications

Yen Ngoc Do, Tri Minh Nguyen, Nam Tuan Tran

J. Korean Math. Soc. 2020; 57(5): 1061-1078
https://doi.org/10.4134/JKMS.j180792

• ### Weighted $L^p$-boundedness of singular integrals with rough kernel associated to surfaces

Ronghui Liu, Huoxiong Wu

J. Korean Math. Soc. 2021; 58(1): 69-90
https://doi.org/10.4134/JKMS.j190845

• ### On the scaled inverse of $(x^i-x^j)$ modulo cyclotomic polynomial of the form $\Phi_{p^s}(x)$ or $\Phi_{p^s q^t}(x)$

Jung Hee Cheon, Dongwoo Kim, Duhyeong Kim, Keewoo Lee

J. Korean Math. Soc. 2022; 59(3): 621-634
https://doi.org/10.4134/JKMS.j210446

• ### Curves orthogonal to a vector field in Euclidean spaces

Luiz C. B. da~Silva, Gilson S. Ferreira~Jr.

J. Korean Math. Soc. 2021; 58(6): 1485-1500
https://doi.org/10.4134/JKMS.j210119

• ### A Liouville theorem of an integral equation of the Chern-Simons-Higgs type

Qinghua Chen, Yayun Li, Mengfan Ma

J. Korean Math. Soc. 2021; 58(6): 1327-1345
https://doi.org/10.4134/JKMS.j200616