Bulletin of the
Korean Mathematical Society
BKMS
ISSN(Print) 1015-8634
ISSN(Online) 2234-3016
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2024-03-31
Six dimensional almost complex torus manifolds with Euler number six
Donghoon Jang, Jiyun ParkAbstract : An almost complex torus manifold is a $2n$-dimensional compact connected almost complex manifold equipped with an effective action of a real $n$-dimensional torus $T^n \simeq (S^1)^n$ that has fixed points. For an almost complex torus manifold, there is a labeled directed graph which contains information on weights at the fixed points and isotropy spheres. Let $M$ be a 6-dimensional almost complex torus manifold with Euler number 6. We show that two types of graphs occur for $M$, and for each type of graph we construct such a manifold $M$, proving the existence. Using the graphs, we determine the Chern numbers and the Hirzebruch $\chi_y$-genus of $M$.
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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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2023-03-31
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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2023-01-31
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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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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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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2022-11-30
The $H^1$-uniform attractor for the 2D non-autonomous tropical climate model on some unbounded domains
Pigong Han, Keke Lei, Chenggang Liu, Xuewen WangAbstract : In this paper, we study the uniform attractor of the 2D non-autonomous tropical climate model in an arbitrary unbounded domain on which the Poincar\'e inequality holds. We prove that the uniform attractor is compact not only in the $L^2$-spaces but also in the $H^1$-spaces. Our proof is based on the concept of asymptotical compactness. Finally, for the quasiperiodical external force case, the dimension estimates of such a uniform attractor are also obtained.
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2022-05-31
Free Products Of Operator Systems
Florin PopAbstract : In this paper we introduce the notion of universal free product for operator systems and operator spaces, and prove extension results for the operator system lifting property (OSLP) and operator system local lifting property (OSLLP) to the universal free product.
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2022-07-31
Approximate projection algorithms for solving equilibrium and multivalued variational inequality problems in Hilbert space
Nguyen Minh Khoa, Tran Van ThangAbstract : In this paper, we propose new algorithms for solving equilibrium and multivalued variational inequality problems in a real Hilbert space. The first algorithm for equilibrium problems uses only one approximate projection at each iteration to generate an iteration sequence converging strongly to a solution of the problem underlining the bifunction is pseudomonotone. On the basis of the proposed algorithm for the equilibrium problems, we introduce a new algorithm for solving multivalued variational inequality problems. Some fundamental experiments are given to illustrate our algorithms as well as to compare them with other algorithms.
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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 -
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 -
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
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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 -
Some one-dimensional Noetherian domains and G-projective modules
Kui Hu, Hwankoo Kim, Dechuan Zhou
Bull. Korean Math. Soc. 2023; 60(6): 1453-1461
https://doi.org/10.4134/BKMS.b220513 -
Single step real-valued iterative method for linear system of equations with complex symmetric matrices
Jingjing Cui, Zhengge Huang, Beibei Li, Xiaofeng Xie
Bull. Korean Math. Soc. 2023; 60(5): 1181-1199
https://doi.org/10.4134/BKMS.b220524 -
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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