Abstract : 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.
Abstract : 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].
Abstract : 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.
Abstract : 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.
Abstract : 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.
Abstract : 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.
Abstract : 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.
Abstract : 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 $\mathbb{F}_q$.
Abstract : This paper establishes the {Baum--Katz} type theorem and the {Marcinkiewicz--Zymund} type strong law of large numbers for sequences of coordinatewise negatively associated and identically distributed random vectors $\{X,X_n,n\ge1\}$ taking values in a Hilbert space $H$ with general normalizing constants $b_n=n^{\alpha}\widetilde L(n^{\alpha})$, where $\widetilde L(\cdot)$ is the de Bruijn conjugate of a slowly varying function $L(\cdot).$ The main result extends and unifies many results in the literature. The sharpness of the result is illustrated by two examples.
Abstract : Zero-difference balanced (ZDB) functions can be applied to many areas like optimal constant composition codes, optimal frequency hopping sequences etc. Moreover, it has been shown that the image set of some ZDB functions is a regular partial difference set, and hence provides strongly regular graphs. Besides, perfect nonlinear functions are zero-difference balanced functions. However, the converse is not true in general. In this paper, we use the decomposition of cyclotomic polynomials into irreducible factors over $\mathbb F_p$, where $p$ is an odd prime to generalize some recent results on ZDB functions. Also we extend a result introduced by Claude et al. [3] regarding zero-difference-$p$-balanced functions over $\mathbb F_{p^n}$. Eventually, we use these results to construct some optimal constant composition codes.
Sunben Chiu, Pingzhi Yuan, Tao Zhou
Bull. Korean Math. Soc. 2023; 60(4): 863-872
https://doi.org/10.4134/BKMS.b220166
Xiaoying Wu
Bull. Korean Math. Soc. 2022; 59(3): 725-743
https://doi.org/10.4134/BKMS.b210427
Rosihan M. Ali, Sushil Kumar, Vaithiyanathan Ravichandran
Bull. Korean Math. Soc. 2023; 60(2): 281-291
https://doi.org/10.4134/BKMS.b210368
Jun Ho Lee
Bull. Korean Math. Soc. 2022; 59(3): 697-707
https://doi.org/10.4134/BKMS.b210422
Enkhbayar Azjargal, Zorigt Choinkhor, Nyamdavaa Tsegmid
Bull. Korean Math. Soc. 2023; 60(4): 1131-1139
https://doi.org/10.4134/BKMS.b220595
Yu Wang
Bull. Korean Math. Soc. 2023; 60(4): 1025-1034
https://doi.org/10.4134/BKMS.b220460
Weiguo Lu, Ce Xu, Jianing Zhou
Bull. Korean Math. Soc. 2023; 60(4): 985-1001
https://doi.org/10.4134/BKMS.b220447
Chunxu Xu, Tao Yu
Bull. Korean Math. Soc. 2023; 60(4): 957-969
https://doi.org/10.4134/BKMS.b220428
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