Abstract : The $t$-wise intersection is a useful property of a linear code due to its many applications. Recently, the second author determined the $t$-wise intersection of a relative two-weight code. By using this result and generalizing the finite projective geometry method, we will present the $t$-wise intersection of a relative three-weight code and its applications in this paper.
Abstract : In this work, we consider constacyclic and cyclic self-dual codes over the rings $R_k$. We start with theoretical existence results for constacyclic and cyclic self-dual codes of any length over $R_k$ and then construct cyclic self-dual codes over $R_1 = \F_2+u\F_2$ of even lengths from lifts of binary cyclic self-dual codes. We classify all free cyclic self-dual codes over $R_1$ of even lengths for which non-trivial such codes exist. In particular we demonstrate that our constructions provide a counter example to a claim made by Batoul et al. in \cite{Batoul} and we explain why their claim fails.
Abstract : The aim in this note is to describe some classes of rings in relation to factorization by prime radical, upper nilradical, and Jacobson radical. We introduce the concepts of {\it tpr} ring, {\it tunr} ring, and {\it tjr} ring in the process, respectively. Their ring theoretical structures are investigated in relation to various sorts of factor rings and extensions. We also study the structure of noncommutative tpr (tunr, tjr) rings of minimal order, which can be a base of constructing examples of various ring structures. Various sorts of structures of known examples are studied in relation with the topics of this note.
Abstract : In this paper, we study the value distribution of the derivative of a Dirichlet $L$-function $L'(s,\chi)$ at the $a$-points $\rho_{a,\chi}=\beta_{a,\chi}+i\gamma_{a,\chi}$ of $L(s,\chi).$ We give an asymptotic formula for the sum $$\sum_{\rho_{a,\chi};\ 0
Abstract : The purpose of this paper is twofold. The first is to show that two meromorphic functions $f$ and $g$ must be linked by a quasi-M\"{o}bius transformation if they share a pair of small functions regardless of multiplicity and share other three pairs of small functions with multiplicities truncated to level 4. We also show a quasi-M\"{o}bius transformation between two meromorphic functions if they share four pairs of small functions with multiplicities truncated by $4$, where all zeros with multiplicities at least $k> 865$ are omitted. Moreover the explicit M\"{o}bius-transformation between such $f$ and $g$ is given. Our results are improvement of some recent results.
Abstract : We give some sufficient conditions for the null and infinite derivatives of the Riesz-N{\'a}gy-Tak{\'a}cs (RNT) singular function. Using these conditions, we show that the Hausdorff dimension of the set of the infinite derivative points of the RNT singular function coincides with its packing dimension which is positive and less than 1 while the Hausdorff dimension of the non-differentiability set of the RNT singular function does not coincide with its packing dimension 1.
Abstract : In this paper, we present nonlinear differential equations arising from the generating function of the Eulerian polynomials. In addition, we give explicit formulae for the Eulerian polynomials which are derived from our nonlinear differential equations.
Abstract : In this paper, the limit behavior of solution for the Schr\"{o}d\-inger equation with random dispersion and time-dependent nonlinear loss/gain: $idu + \frac{1}{\varepsilon} m(\frac{t}{\varepsilon^2})\partial_{xx}udt + |u|^{2\sigma}u dt + i\varepsilon a(t)|u|^{2\sigma_{0}}udt = 0$ is studied. Combining stochastic Strichartz-type estimates with $L^2$ norm estimates, we first derive the global existence for $L^2$ and $H^1$ solution of the stochastic Schr\"{o}dinger equation with white noise dispersion and time-dependent loss/gain:~$idu + \Delta{u} \circ d\beta + |u|^{2\sigma}u dt + ia(t)|u|^{2\sigma_{0}}udt = 0$. Secondly, we prove rigorously the global diffusion-approximation limit of the solution for the former as $\varepsilon\rightarrow0$ in one-dimensional $L^2$ subcritical and critical cases.
Abstract : We consider weighted Hardy spaces on bidisk ${\mathbb D}^2$ which generalize the weighted Bergman spaces $A_\alpha^2({\mathbb D}^2)$. Let $z,w$ be coordinate functions and $T_{\overline{z}^Nw}$ Toeplitz operator with symbol $\overline{z}^Nw$. In this paper, we study the reducing subspaces of $T_{\overline{z}^Nw}$ on the weighted Hardy spaces.
Abstract : This paper presents a systematic study of the abstract harmonic analysis over spaces of complex measures on homogeneous spaces of compact groups. Let $G$ be a compact group and $H$ be a closed subgroup of $G$. Then we study abstract harmonic analysis of complex measures over the left coset space $G/H$.
Duranta Chutia, Rajib Haloi
Bull. Korean Math. Soc. 2022; 59(3): 757-780
https://doi.org/10.4134/BKMS.b210469
Dongli Liu, Jian Tan, Jiman Zhao
Bull. Korean Math. Soc. 2022; 59(3): 547-566
https://doi.org/10.4134/BKMS.b201019
Joungmin Song
Bull. Korean Math. Soc. 2022; 59(3): 609-615
https://doi.org/10.4134/BKMS.b210096
Imsoon Jeong, Gyu Jong Kim, Changhwa Woo
Bull. Korean Math. Soc. 2023; 60(4): 849-861
https://doi.org/10.4134/BKMS.b220152
Rosihan M. Ali, Sushil Kumar, Vaithiyanathan Ravichandran
Bull. Korean Math. Soc. 2023; 60(2): 281-291
https://doi.org/10.4134/BKMS.b210368
Sunben Chiu, Pingzhi Yuan, Tao Zhou
Bull. Korean Math. Soc. 2023; 60(4): 863-872
https://doi.org/10.4134/BKMS.b220166
Rita Hibschweiler
Bull. Korean Math. Soc. 2023; 60(4): 1061-1070
https://doi.org/10.4134/BKMS.b220471
Imsoon Jeong, Gyu Jong Kim, Changhwa Woo
Bull. Korean Math. Soc. 2023; 60(4): 849-861
https://doi.org/10.4134/BKMS.b220152
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