# Journal of theKorean Mathematical SocietyJKMS

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

• ### 2022-05-01

#### The exceptional set of one prime square and five prime cubes

Yuhui Liu

Abstract : For a natural number $n$, let $R(n)$ denote the number of representations of $n$ as the sum of one square and five cubes of primes. In this paper, it is proved that the anticipated asymptotic formula for $R(n)$ fails for at most $O(N^{\frac{4}{9} + \varepsilon})$ positive integers not exceeding $N$.

• ### 2022-01-01

#### Gorenstein sequences of high socle degrees

Jung Pil Park, Yong-Su Shin

Abstract : In [4], the authors showed that if an $h$-vector $(h_0,h_1,\dots,h_e)$ with $h_1=4e-4$ and $h_i\le h_1$ is a Gorenstein sequence, then $h_1=h_i$ for every $1\le i\le e-1$ and $e\ge 6$. In this paper, we show that if an $h$-vector $(h_0,h_1,\dots,h_e)$ with $h_1=4e-4$, $h_2=4e-3$, and $h_i\le h_2$ is a Gorenstein sequence, then $h_2=h_i$ for every $2\le i\le e-2$ and $e\ge 7$. We also propose an open question that if  an $h$-vector $(h_0,h_1,\dots,h_e)$ with $h_1=4e-4$, $4e-3<h_2\le {(h_1)_{(1)}}| ^{+1}_{+1}$, and $h_2\le h_i$ is a Gorenstein sequence, then $h_2=h_i$ for every $2\le i\le e-2$ and $e\ge 6$.

• ### 2022-01-01

#### The interior gradient estimate for a class of mixed Hessian curvature equations

Jundong Zhou

Abstract : In this paper, we are concerned with a class of mixed Hessian curvature equations with non-degeneration. By using the maximum principle and constructing an auxiliary function, we obtain the interior gradient estimate of $(k-1)$-admissible solutions.

• ### 2022-05-01

#### Zeros of new Bergman kernels

Noureddine Ghiloufi, Safa Snoun

Abstract : In this paper we determine explicitly the kernels $\mathbb K_{\alpha,\beta}$ associated with new Bergman spaces $\mathcal A_{\alpha,\beta}^2(\mathbb D)$ considered recently by the first author and M. Zaway. Then we study the distribution of the zeros of these kernels essentially when $\alpha\in\mathbb N$ where the zeros are given by the zeros of a real polynomial $Q_{\alpha,\beta}$. Some numerical results are given throughout the paper.

• ### 2022-03-01

#### Ring isomorphisms between closed strings via homological mirror symmetry

Sangwook Lee

Abstract : We investigate how closed string mirror symmetry is related to homological mirror symmetry, under the presence of an explicit geometric mirror functor.

• ### 2022-03-01

#### Generalized Killing structure Jacobi operator for real hypersurfaces in complex hyperbolic two-plane Grassmannians

Hyunjin Lee, Young Jin Suh, Changhwa Woo

Abstract : In this paper, first we introduce a new notion of generalized Killing structure Jacobi operator for a real hypersurface $M$ in complex hyperbolic two-plane Grassmannians $S U_{2, m} / S\left(U_{2} \cdot U_{m}\right)$. Next we prove that there does not exist a Hopf real hypersurface in complex hyperbolic two-plane Grassmannians $S U_{2, m} / S\left(U_{2} \cdot U_{m}\right)$ with generalized Killing structure Jacobi operator.

• ### 2022-05-01

#### Birkhoff's ergodic theorems in terms of weighted inductive means

Byoung Jin Choi, Jae Hun Kim

Abstract : In this paper, we study the Birkhoff's ergodic theorem on geodesic metric spaces, especially on Hadamard spaces, using the notion of weighted inductive means. Also, we study a deterministic weighted sequence for the weighted Birkhoff's ergodic theorem in Hadamard spaces.

• ### 2022-03-01

#### Goldbach-Linnik type problems with unequal powers of primes

Li Zhu

Abstract : It is proved that every sufficiently large even integer can be represented as a sum of two squares of primes, two cubes of primes, two fourth powers of primes and 17 powers of 2.

• ### 2022-01-01

#### Grothendieck group for sequences

Xuan Yu

Abstract : For any category with a distinguished collection of sequences, such as $n$-exangulated category, category of N-complexes and category of precomplexes, we consider its Grothendieck group and similar results of Bergh-Thaule for $n$-angulated categories [1] are proven. A classification result of dense complete subcategories is given and we give a formal definition of K-groups for these categories following Grayson's algebraic approach of K-theory for exact categories [4].

• ### 2022-05-01

#### A Neumann type problem on an unbounded domain in the Heisenberg group

Shivani Dubey, Mukund Madhav Mishra, Ashutosh Pandey

Abstract : We discuss the wellposedness of the Neumann problem on a half-space for the Kohn-Laplacian in the Heisenberg group. We then construct the Neumann function and explicitly represent the solution of the associated inhomogeneous problem.

## Current Issue

• ### Katok-Hasselblatt-kinematic expansive flows

Hien Minh Huynh

J. Korean Math. Soc. 2022; 59(1): 151-170
https://doi.org/10.4134/JKMS.j210258

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

Tae Gab Ha, Sun-Hye Park

J. Korean Math. Soc. 2022; 59(1): 205-216
https://doi.org/10.4134/JKMS.j210364

• ### On cylindrical smooth rational Fano fourfolds

Nguyen Thi Anh Hang, Michael Hoff, Hoang Le Truong

J. Korean Math. Soc. 2022; 59(1): 87-103
https://doi.org/10.4134/JKMS.j210140

• ### Practical FHE parameters against lattice attacks

Jung Hee Cheon, Yongha Son, Donggeon Yhee

J. Korean Math. Soc. 2022; 59(1): 35-51
https://doi.org/10.4134/JKMS.j200650

• ### 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

• ### 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

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

Tae Gab Ha, Sun-Hye Park

J. Korean Math. Soc. 2022; 59(1): 205-216
https://doi.org/10.4134/JKMS.j210364