# Journal of theKorean Mathematical SocietyJKMS

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

## Most Read

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• ### 2022-01-01

#### Synchronized components of a subshift

Manouchehr Shahamat

Abstract : We introduce the notion of a minimal synchronizing word; that is a synchronizing word whose proper subwords are not synchronized. This has been used to give a new shorter proof for a theorem in [6]. Also, the common synchronized components of a subshift and its derived set have been characterized.

• ### 2022-01-01

#### Regularity of the generalized Poisson operator

Pengtao Li, Zhiyong Wang, Kai Zhao

Abstract : Let $L=-\Delta+V$ be a Schr\"{o}dinger operator, where the potential $V$ belongs to the reverse H\"{o}lder class. In this paper, by the subordinative formula, we investigate the generalized Poisson operator $P^{L}_{t,\sigma}$, $0<\sigma<1$, associated with $L$. We estimate the gradient and the time-fractional derivatives of the kernel of  $P^{L}_{t,\sigma}$, respectively. As an application, we establish a Carleson measure characterization of the Campanato type space $\mathcal{C}^{\gamma}_{L}(\mathbb{R}^{n})$ via $P^{L}_{t,\sigma}$.

• ### 2022-01-01

#### Construction for self-orthogonal codes over a certain non-chain Frobenius ring

Boran Kim

Abstract : We present construction methods for free self-orthogonal (self-dual or Type II) codes over $\mathbb Z_4[v]/\langle v^2+2v \rangle$ which is one of the finite commutative local non-chain Frobenius rings of order $16$. By considering their Gray images on $\mathbb Z_4$, we give a construct method for a code over $\mathbb Z_4$. We have some new and optimal codes over $\mathbb Z_4$ with respect to the minimum Lee weight or minimum Euclidean weight.

• ### 2022-01-01

#### Parabolic quaternionic Monge-Amp\{e}re equation on compact manifolds with a flat hyperK\"ahler metric

Jiaogen Zhang

Abstract : The quaternionic Calabi conjecture was introduced by Alesker-Verbitsky, analogous to the K\"ahler case which was raised by Calabi. On a compact connected hypercomplex manifold, when there exists a  flat hyperK\"ahler metric which is compatible with the underlying hypercomplex structure, we will consider the parabolic quaternionic Monge-Amp\{e}re equation.  Our goal is to prove the long time existence and $C^{\infty}$ convergence for normalized solutions  as $t\rightarrow\infty$. As a consequence, we show that the limit function is exactly the solution of quaternionic Monge-Amp\{e}re equation, this gives a parabolic proof for the quaternionic Calabi conjecture in this special setting.

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• ### 2022-01-01

#### Katok-Hasselblatt-kinematic expansive flows

Hien Minh Huynh

Abstract : In this paper we introduce a new notion of expansive flows, which is the combination of expansivity in the sense of Katok and Hasselblatt and kinematic expansivity, named KH-kinematic expansivity. We present new properties of several variations of expansivity. A new hierarchy of expansive flows is given.

• ### 2022-01-01

#### Global nonexistence for the wave equation with boundary variable exponent nonlinearities

Tae Gab Ha, Sun-Hye Park

Abstract : This paper deals with a nonlinear wave equation with boundary damping and source terms of variable exponent nonlinearities. This work is devoted to prove a global nonexistence of solutions for a nonlinear wave equation with nonnegative initial energy as well as negative initial energy.

Chunfang Gao

## Most Read

• ### Synchronized components of a subshift

Manouchehr Shahamat

J. Korean Math. Soc. 2022; 59(1): 1-12
https://doi.org/10.4134/JKMS.j200112

• ### Regularity of the generalized Poisson operator

Pengtao Li, Zhiyong Wang, Kai Zhao

J. Korean Math. Soc. 2022; 59(1): 129-150
https://doi.org/10.4134/JKMS.j210224

• ### Construction for self-orthogonal codes over a certain non-chain Frobenius ring

Boran Kim

J. Korean Math. Soc. 2022; 59(1): 193-204
https://doi.org/10.4134/JKMS.j210357

• ### Parabolic quaternionic Monge-Amp\{e}re equation on compact manifolds with a flat hyperK\"ahler metric

Jiaogen Zhang

J. Korean Math. Soc. 2022; 59(1): 13-33
https://doi.org/10.4134/JKMS.j200626

## Most Downloaded

• ### Synchronized components of a subshift

Manouchehr Shahamat

J. Korean Math. Soc. 2022; 59(1): 1-12
https://doi.org/10.4134/JKMS.j200112

• ### Parabolic quaternionic Monge-Amp\`{e}re equation on compact manifolds with a flat hyperK\"ahler metric

Jiaogen Zhang

J. Korean Math. Soc. 2022; 59(1): 13-33
https://doi.org/10.4134/JKMS.j200626

• ### Margin-based generalization for classifications with input noise

Hi Jun Choe, Hayeong Koh, Jimin Lee

J. Korean Math. Soc. 2022; 59(2): 217-233
https://doi.org/10.4134/JKMS.j200406

• ### Hardy type estimates for Riesz transforms associated with Schr\"{o}dinger operators on the Heisenberg group

Chunfang Gao

J. Korean Math. Soc. 2022; 59(2): 235-254
https://doi.org/10.4134/JKMS.j200484