# Journal of theKorean Mathematical SocietyJKMS

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

• ### 2022-03-01

#### Green's additive complement problem for $k$-th powers

Yuchen Ding, Li-Yuan Wang

Abstract : Let $k\geqslant 2$ be an integer, $S^k=\{1^k,2^k,3^k,\ldots\}$ and $B=\{b_1,b_2,b_3,\ldots\}$ be an additive complement of $S^k$, which means all sufficiently large integers can be written as the sum of an element of $S^k$ and an element of $B$. In this paper we prove that $$\limsup_{n\rightarrow \infty}\frac{\Gamma\left(2-\frac{1}{k}\right)^{\frac{k}{k-1}}\Gamma\left(1+\frac{1}{k}\right) ^{\frac{k}{k-1}}n^{\frac{k}{k-1}}-b_n}{n} \geqslant \frac{k}{2(k-1)}\frac{\Gamma\left(2-\frac{1}{k}\right)^2}{\Gamma\left(2-\frac{2}{k}\right)},$$ where $\Gamma(\cdot)$ is Euler's Gamma function.

• ### 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.

• ### 2022-03-01

#### Moment estimate and existence for the solution of neutral stochastic functional differential equation

Huabin Chen, Qunjia Wan

Abstract : In this paper, the existence and uniqueness for the global solution of neutral stochastic functional differential equation is investigated under the locally Lipschitz condition and the contractive condition. The implicit iterative methodology and the Lyapunov-Razumikhin theorem are used. The stability analysis for such equations is also applied. One numerical example is provided to illustrate the effectiveness of the theoretical results obtained.

• ### 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.

• ### 2022-05-01

#### On weighted compactness of commutators of bilinear fractional maximal operator

Qianjun He, Juan Zhang

## Current Issue

• ### 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

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

Yuhui Liu

J. Korean Math. Soc. 2022; 59(3): 439-448
https://doi.org/10.4134/JKMS.j190679

• ### Gorenstein sequences of high socle degrees

Jung Pil Park, Yong-Su Shin

J. Korean Math. Soc. 2022; 59(1): 71-85
https://doi.org/10.4134/JKMS.j200690