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Bull. Korean Math. Soc. 2023; 60(2): 281~560
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2023-03-31
The third Hermitian-Toeplitz and Hankel determinants for parabolic starlike functions
Rosihan M. Ali, Sushil Kumar, Vaithiyanathan RavichandranAbstract : A normalized analytic function $f$ is parabolic starlike if $w(z)$ $:=zf'(z)/f(z)$ maps the unit disk into the parabolic region $\{w: \operatorname{Re} w>|w-1|\}$. Sharp estimates on the third Hermitian-Toeplitz determinant are obtained for parabolic starlike functions. In addition, upper bounds on the third Hankel determinants are also determined.
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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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2023-03-31
Conjugacy classification of $n$-dimensional M\"obius group
Binlin Dai, Zekun LiAbstract : In this paper, we study the $n$-dimensional M\"obius transformation. We obtain several conjugacy invariants and give a conjugacy classification for $n$-dimensional M\"obius transformation.
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2023-03-31
Prime-producing polynomials related to class number one problem of number fields
Jun Ho LeeAbstract : First, we recall the results for prime-producing polynomials related to class number one problem of quadratic fields. Next, we give the relation between prime-producing cubic polynomials and class number one problem of the simplest cubic fields and then present the conjecture for the relations. Finally, we numerically compare the ratios producing prime values for several polynomials in some interval.
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2023-03-31
Some integral inequalities for the Laplacian with density on weighted manifolds with boundary
Fanqi ZengAbstract : In this paper, we derive a Reilly-type inequality for the Laplacian with density on weighted manifolds with boundary. As its applications, we obtain some new Poincar\'{e}-type inequalities not only on weighted manifolds, but more interestingly, also on their boundary. Furthermore, some mean-curvature type inequalities on the boundary are also given.
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2023-03-31
Rings and modules which are stable under nilpotents of their injective hulls
Nguyen Thi Thu HaAbstract : It is shown that every nilpotent-invariant module can be decomposed into a direct sum of a quasi-injective module and a square-free module that are relatively injective and orthogonal. This paper is also concerned with rings satisfying every cyclic right $R$-module is nilpotent-invariant. We prove that $R\cong R_1\times R_2$, where $R_1, R_2$ are rings which satisfy $R_1$ is a semi-simple Artinian ring and $R_2$ is square-free as a right $R_2$-module and all idempotents of $R_2$ is central. The paper concludes with a structure theorem for cyclic nilpotent-invariant right $R$-modules. Such a module is shown to have isomorphic simple modules $eR$ and $fR$, where $e,f$ are orthogonal primitive idempotents such that $eRf\ne 0$.
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2023-03-31
$\Delta$-transitivity for semigroup actions
Tiaoying ZengAbstract : In this paper, we study $\Delta$-transitivity, $\Delta$-weak mixing and $\Delta$-mixing for semigroup actions and give several characterizations of them, which generalize related results in the literature.
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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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2023-03-31
Hankel determinants for starlike functions with respect to symmetrical points
Nak Eun Cho, Young Jae Sim, Derek K. ThomasAbstract : We prove sharp bounds for Hankel determinants for starlike functions $f$ with respect to symmetrical points, i.e., $f$ given by $f(z)=z+\sum_{n=2}^{\infty}a_nz^n$ for $z\in \mathbb{D}$ satisfying $$ Re\dfrac{zf'(z)}{f(z)-f(-z)}>0, \quad z\in \mathbb{D}. $$ We also give sharp upper and lower bounds when the coefficients of $f$ are real.
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2023-03-31
Model structures and recollements induced by duality pairs
Wenjing Chen, Ling Li, Yanping RaoAbstract : Let $(\mathcal{L}, \mathcal{A})$ be a complete duality pair. We give some equivalent characterizations of Gorenstein $(\mathcal{L}, \mathcal{A})$-projective modules and construct some model structures associated to duality pairs and Frobenius pairs. Some rings are described by Frobenius pairs. In addition, we investigate special Gorenstein $(\mathcal{L}, \mathcal{A})$-projective modules and construct some model structures and recollements associated to them.
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