Bulletin of the
Korean Mathematical Society
BKMS
ISSN(Print) 1015-8634
ISSN(Online) 2234-3016
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2023-01-31
On the top local cohomology and formal local cohomology modules
Shahram Rezaei, Behrouz SadeghiAbstract : Let ${\mathfrak{a}}$ and $\mathfrak{b}$ be ideals of a commutative Noetherian ring $R$ and $M$ a finitely generated $R$-module of finite dimension $d>0$. In this paper, we obtain some results about the annihilators and attached primes of top local cohomology and top formal local cohomology modules. In particular, we determine $\operatorname{Ann} (\mathfrak{b}\operatorname{H}_{\mathfrak{a}}^{d}(M))$, $\operatorname{Att} (\mathfrak{b}\operatorname{H}_{\mathfrak{a}}^{d}(M))$, $\operatorname{Ann}(\mathfrak{b}\mathfrak{F}_{\mathfrak{a}}^{d} (M))$ and $\operatorname{Att} (\mathfrak{b}\mathfrak{F}_{\mathfrak{a}}^{d} (M))$.
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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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2022-07-31
Starlike functions associated with a petal shaped domain
Kush Arora, S. Sivaprasad Kumar
Abstract : In this paper, we establish some radius results and inclusion relations for starlike functions associated with a petal-shaped domain.
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2022-07-31
On the existence of the Tweedie power parameter implicit estimator
Abdelaziz Ghribi, Aymen Hassin, Afif MasmoudiAbstract : A special class of exponential dispersion models is the class of Tweedie distributions. This class is very significant in statistical modeling as it includes a number of familiar distributions such as Gaussian, Gamma and compound Poisson. A Tweedie distribution has a power parameter $p$, a mean $m$ and a dispersion parameter $\phi$. The value of the power parameter lies in identifying the corresponding distribution of the Tweedie family. The basic objective of this research work resides in investigating the existence of the implicit estimator of the power parameter of the Tweedie distribution. A necessary and sufficient condition on the mean parameter $m$, suggesting that the implicit estimator of the power parameter $p$ exists, was established and we provided some asymptotic properties of this estimator.
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2023-01-31
S-curvature and geodesic orbit property of invariant $(\alpha_{1},\alpha_{2})$-metrics on spheres
Huihui An, Zaili Yan, Shaoxiang ZhangAbstract : Geodesic orbit spaces are homogeneous Finsler spaces whose geodesics are all orbits of one-parameter subgroups of isometries. Such Finsler spaces have vanishing S-curvature and hold the Bishop-Gromov volume comparison theorem. In this paper, we obtain a complete description of invariant $(\alpha_{1},\alpha_{2})$-metrics on spheres with vanishing S-curvature. Also, we give a description of invariant geodesic orbit $(\alpha_{1},\alpha_{2})$-metrics on spheres. We mainly show that a ${\mathrm S}{\mathrm p}(n+1)$-invariant $(\alpha_{1},\alpha_{2})$-metric on $\mathrm{S}^{4n+3}={\mathrm S}{\mathrm p}(n+1)/{\mathrm S}{\mathrm p}(n)$ is geodesic orbit with respect to ${\mathrm S}{\mathrm p}(n+1)$ if and only if it is ${\mathrm S}{\mathrm p}(n+1){\mathrm S}{\mathrm p}(1)$-invariant. As an interesting consequence, we find infinitely many Finsler spheres with vanishing S-curvature which are not geodesic orbit spaces.
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2024-03-31
Wavelet characterizations of variable Hardy-Lorentz spaces
Yao HeAbstract : In this paper, let $q\in(0,1]$. We establish the boundedness of intrinsic $g$-functions from the Hardy-Lorentz spaces with variable exponent ${H}^{p(\cdot),q}(\mathbb R^{n})$ into Lorentz spaces with variable exponent ${L}^{p(\cdot),q}(\mathbb R^{n})$. Then, for any $q\in(0,1]$, via some estimates on a discrete Littlewood-Paley $g$-function and a Peetre-type maximal function, we obtain several equivalent characterizations of ${H}^{p(\cdot),q}(\mathbb R^{n})$ in terms of wavelets.
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2024-03-31
Geometric inequalities for affine connections on Riemannian manifolds
Huiting Chang, Fanqi ZengAbstract : Using a Reilly type integral formula due to Li and Xia \cite{LiXia2017}, we prove several geometric inequalities for affine connections on Riemannian manifolds. We obtain some general De Lellis-Topping type inequalities associated with affine connections. These not only permit to derive quickly many well-known De Lellis-Topping type inequalities, but also supply a new De Lellis-Topping type inequality when the $1$-Bakry-\'{E}mery Ricci curvature is bounded from below by a negative function. On the other hand, we also achieve some Lichnerowicz type estimate for the first (nonzero) eigenvalue of the affine Laplacian with the Robin boundary condition on Riemannian manifolds.
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2022-11-30
Lipschitz type characterization of Fock type spaces
Hong Rae Cho, Jeong Min HaAbstract : For setting a general weight function on $n$ dimensional complex space ${\mathbb C}^n$, we expand the classical Fock space.We define Fock type space $F^{p,q}_{\phi, t}({\mathbb C}^n)$ of entire functions with a mixed norm, where $0<p,q<\infty$ and $t\in\mathbb R$ and prove that the mixed norm of an entire function is equivalent to the mixed norm of its radial derivative on $F^{p,q}_{\phi, t}({\mathbb C}^n)$.As a result of this application, the space $F^{p,p}_{\phi, t}({\mathbb C}^n)$ is especially characterized by a Lipschitz type condition.
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2024-03-31
Large time convergence for a chemotaxis model with degenerate local sensing and consumption
Philippe LAURENCOTAbstract : Convergence to a steady state in the long term limit is established for global weak solutions to a chemotaxis model with degenerate local sensing and consumption, when the motility function is $C^1$-smooth on $[0,\infty)$, vanishes at zero, and is positive on $(0,\infty)$. A condition excluding that the large time limit is spatially homogeneous is also provided. These results extend previous ones derived for motility functions vanishing algebraically at zero and rely on a completely different approach.
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2022-05-31
On toric Hamiltonian $T$-spaces with anti-symplectic involutions
Jin Hong KimAbstract : The aim of this paper is to deal with the realization problem of a given Lagrangian submanifold of a symplectic manifold as the fixed point set of an anti-symplectic involution. To be more precise, let $(X, \omega, \mu)$ be a toric Hamiltonian $T$-space, and let $\Delta=\mu(X)$ denote the moment polytope. Let $\tau$ be an anti-symplectic involution of $X$ such that $\tau$ maps the fibers of $\mu$ to (possibly different) fibers of $\mu$, and let $p_0$ be a point in the interior of $\Delta$. If the toric fiber $\mu^{-1}(p_0)$ is real Lagrangian with respect to $\tau$, then we show that $p_0$ should be the origin and, furthermore, $\Delta$ should be centrally symmetric.
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On the existence of the Tweedie power parameter implicit estimator
Abdelaziz Ghribi, Aymen Hassin, Afif Masmoudi
Bull. Korean Math. Soc. 2022; 59(4): 979-991
https://doi.org/10.4134/BKMS.b210590 -
On weakly $S$-prime submodules
Hani A. Khashan, Ece Yetkin~Celikel
Bull. Korean Math. Soc. 2022; 59(6): 1387-1408
https://doi.org/10.4134/BKMS.b210784 -
Complex symmetric weighted composition-differentiation operators on $H^2$
Lian Hu, Songxiao Li, Rong Yang
Bull. Korean Math. Soc. 2023; 60(5): 1141-1154
https://doi.org/10.4134/BKMS.b220215 -
Continuous data assimilation for the three-dimensional Leray-$\alpha$ model with stochastically noisy data
Bui Kim My
, Tran Quoc TuanBull. Korean Math. Soc. 2023; 60(1): 93-111
https://doi.org/10.4134/BKMS.b210919
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Anti-flips of the blow-ups of the projective spaces at torus invariant points
Hiroshi Sato, Shigehito Tsuzuki
Bull. Korean Math. Soc. 2023; 60(6): 1705-1714
https://doi.org/10.4134/BKMS.b220864 -
Mixed radial-angular integrabilities for Hardy type operators
Ronghui Liu, Shuangping Tao
Bull. Korean Math. Soc. 2023; 60(5): 1409-1425
https://doi.org/10.4134/BKMS.b220726 -
Results on the algebraic differential independence of the Riemann zeta function and the Euler gamma function
Xiao-Min Li, Yi-Xuan Li
Bull. Korean Math. Soc. 2023; 60(6): 1651-1672
https://doi.org/10.4134/BKMS.b220813 -
Volume density asymptotics of central harmonic spaces
Peter Gilkey, JeongHyeong Park
Bull. Korean Math. Soc. 2023; 60(6): 1539-1553
https://doi.org/10.4134/BKMS.b220735
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