Bulletin of the
Korean Mathematical Society
BKMS
ISSN(Print) 1015-8634
ISSN(Online) 2234-3016
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2022-11-30
An associated sequence of ideals of an increasing sequence of rings
Ali Benhissi, Abdelamir DabbabiAbstract : Let ${\mathcal A}=(A_n)_{n\geq 0}$ be an increasing sequence of rings. We say that ${\mathcal I}=(I_n)_{n\geq 0}$ is an associated sequence of ideals of ${\mathcal A}$ if $I_0=A_0$ and for each $n\geq 1$, $I_n$ is an ideal of $A_n$ contained in $I_{n+1}$. We define the polynomial ring and the power series ring as follows: ${\mathcal I}[X]=\lbrace f={\sum_{i=0}^n}a_iX^i\in {\mathcal A}[X]: n\in \mathbb{N}, a_i\in I_i\rbrace$ and ${\mathcal I}[[X]]=\lbrace f={\sum_{i=0}^{+\infty}}a_iX^i\in {\mathcal A}[[X]]: a_i\in I_i\rbrace$. In this paper we study the Noetherian and the SFT properties of these rings and their consequences.
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2022-07-31
$P$-extremal functions and Bernstein-Markov properties associated to compact sets in $\mathbb R^d$
Hoang Thieu Anh, Kieu Phuong Chi, Nguyen Quang Dieu, Tang Van LongAbstract : Given a compact subset $P \subset (\mathbb R^+)^d$ and a compact set $K$ in $\mathbb C^d$. We concern with the Bernstein-Markov properties of the triple $(P,K,\mu)$ where $\mu$ is a finite positive Borel measure with compact support $K$. Our approach uses (global) $P$-extremal functions which is inspired by the classical case (when $P=\Sigma$ the unit simplex) in [7].
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2022-07-31
Uniqueness of meromorphic solutions of a certain type of difference equations
Jun-Fan Chen, Shu-Qing LinAbstract : In this paper, we study the uniqueness of two finite order transcendental meromorphic solutions $f(z)$ and $g(z)$ of the following complex difference equation $$A_{1}(z)f(z+1)+A_{0}(z)f(z)=F(z)e^{\alpha(z)}$$ when they share 0, $\infty$ CM, where $A_{1}(z),$ $A_{0}(z),$ $F(z)$ are non-zero polynomials, $\alpha(z)$ is a polynomial. Our result generalizes and complements some known results given recently by Cui and Chen, Li and Chen. Examples for the precision of our result are also supplied.
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2023-03-31
The recurrent hypercyclicity criterion for translation $C_0$-semigroups on complex sectors
Yuxia Liang, Zhi-Yuan Xu, Ze-Hua ZhouAbstract : Let $\{T_t\}_{t\in \Delta}$ be the translation semigroup with a sector $\Delta\subset \mathbb{C}$ as index set. The recurrent hypercyclicity criterion (RHCC) for the $C_0$-semigroup $\{T_t\}_{t\in \Delta}$ is established, and then the equivalent conditions ensuring $\{T_t\}_{t\in \Delta}$ satisfying the RHCC on weighted spaces of $p$-integrable and of continuous functions are presented. Especially, every chaotic semigroup $\{T_t\}_{t\in \Delta}$ satisfies the RHCC.
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2022-09-30
Second main theorem with weighted counting functions and uniqueness theorem
Liu YangAbstract : In this paper, we obtain a second main theorem for holomorphic curves and moving hyperplanes of $\mathbf{P}^{n}(\mathbf{C})$ where the counting functions are truncated multiplicity and have different weights. As its application, we prove a uniqueness theorem for holomorphic curves of finite growth index sharing moving hyperplanes with different multiple values.
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2022-07-31
Complete characterization of odd factors via the size, spectral radius or distance spectral radius of graphs
Shuchao Li, Shujing MiaoAbstract : Given a graph $G,$ a $\{1,3,\ldots,2n-1\}$-factor of $G$ is a spanning subgraph of $G$, in which each degree of vertices is one of $\{1,3,\ldots,2n-1\}$, where $n$ is a positive integer. In this paper, we first establish a lower bound on the size (resp.~the spectral radius) of $G$ to guarantee that $G$ contains a $\{1,3,\ldots,2n-1\}$-factor. Then we determine an upper bound on the distance spectral radius of $G$ to ensure that $G$ has a $\{1,3,\ldots,2n-1\}$-factor. Furthermore, we construct some extremal graphs to show all the bounds obtained in this contribution are best possible.
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2022-05-31
Computation of Wedderburn decomposition of groups algebras from their subalgebra
Gaurav Mittal, Rajendra Kumar SharmaAbstract : In this paper, we show that under certain conditions the Wedderburn decomposition of a finite semisimple group algebra $\mathbb{F}_qG$ can be deduced from a subalgebra $\mathbb{F}_q(G/H)$ of factor group $G/H$ of $G$, where $H$ is a normal subgroup of $G$ of prime order $P$. Here, we assume that $q=p^r$ for some prime $p$ and the center of each Wedderburn component of $\mathbb{F}_qG$ is the coefficient field $\mathbb{F}_q$.
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2023-03-31
Pricing American lookback options under a stochastic volatility model
Donghyun Kim, Junhui Woo, Ji-Hun YoonAbstract : In this study, we deal with American lookback option prices on dividend-paying assets under a stochastic volatility (SV) model. By using the asymptotic analysis introduced by Fouque et al. [17] and the Laplace-Carson transform (LCT), we derive the explicit formula for the option prices and the free boundary values with a finite expiration whose volatility is driven by a fast mean-reverting Ornstein-Uhlenbeck process. In addition, we examine the numerical implications of the SV on the American lookback option with respect to the model parameters and verify that the obtained explicit analytical option price has been obtained accurately and efficiently in comparison with the price obtained from the Monte-Carlo simulation.
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2022-11-30
Some remarks on problems of subset sum
Min Tang, Hongwei XuAbstract : Let $A=\{a_1<a_2<\cdots\}$ be a sequence of integers and let $P(A)=\left\{\sum \varepsilon_ia_i: a_i\in A, \varepsilon_i=0\text{ or }1, \sum \varepsilon_i<\infty\right\}$. Burr posed the following question: Determine conditions on integers sequence $B$ that imply either the existence or the non-existence of $A$ for which $P(A)$ is the set of all non-negative integers not in $B$. In this paper, we focus on some problems of subset sum related to Burr's question.
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2022-11-30
Blow up of solutions for a Petrovsky type equation with logarithmic nonlinearity
Jorge Ferreira, Nazl\i \, Irk\i l, Erhan Pi\c{s}kin, Carlos Raposo
, Mohammad ShahrouziAbstract : This paper aims to investigate the initial boundary value problem of the nonlinear viscoelastic Petrovsky type equation with nonlinear damping and logarithmic source term. We derive the blow-up results by the combination of the perturbation energy method, concavity method, and differential-integral inequality technique.
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On the greatest common divisor of binomial coefficients
Sunben Chiu, Pingzhi Yuan, Tao Zhou
Bull. Korean Math. Soc. 2023; 60(4): 863-872
https://doi.org/10.4134/BKMS.b220166 -
A generalization of $w$-linked extensions
Xiaoying Wu
Bull. Korean Math. Soc. 2022; 59(3): 725-743
https://doi.org/10.4134/BKMS.b210427 -
Existence of the continued fractions of $\sqrt{d}$ and its applications
Jun Ho Lee
Bull. Korean Math. Soc. 2022; 59(3): 697-707
https://doi.org/10.4134/BKMS.b210422 -
Rings with a right duo factor ring by an ideal contained in the center
Jeoung Soo Cheon, Tai Keun Kwak, Yang Lee, Zhelin Piao, Sang Jo Yun
Bull. Korean Math. Soc. 2022; 59(3): 529-545
https://doi.org/10.4134/BKMS.b201014
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Dynamics of random dynamical systems
Enkhbayar Azjargal, Zorigt Choinkhor, Nyamdavaa Tsegmid
Bull. Korean Math. Soc. 2023; 60(4): 1131-1139
https://doi.org/10.4134/BKMS.b220595 -
Annihilator ideals of simple modules of restricted quantized enveloping algebra
Yu Wang
Bull. Korean Math. Soc. 2023; 60(4): 1025-1034
https://doi.org/10.4134/BKMS.b220460 -
Some relations on parametric linear Euler sums
Weiguo Lu, Ce Xu, Jianing Zhou
Bull. Korean Math. Soc. 2023; 60(4): 985-1001
https://doi.org/10.4134/BKMS.b220447 -
Toeplitz-type operators on the Fock space $F_{\alpha}^{2}$
Chunxu Xu, Tao Yu
Bull. Korean Math. Soc. 2023; 60(4): 957-969
https://doi.org/10.4134/BKMS.b220428
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