Bulletin of the
Korean Mathematical Society
BKMS
ISSN(Print) 1015-8634
ISSN(Online) 2234-3016
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2023-11-30
Operators $A$, $B$ for which the Aluthge transform $\widetilde{AB}$ is a generalised $n$-projection
Bhagwati Duggal, In Hyoun KimAbstract : A Hilbert space operator $A\in{\mathcal B(H)}$ is a generalised \linebreak $n$-projection, denoted $A\in (G-n-P)$, if ${A^*}^n=A$. $(G-n-P)$-operators $A$ are normal operators with finitely countable spectra $\sigma(A)$, subsets of the set $\{0\}\cup\{\sqrt[n+1]{1}\}$. The Aluthge transform $\tilde{A}$ of $A\in{\mathcal B(H)}$ may be $(G-n-P)$ without $A$ being $(G-n-P)$. For doubly commuting operators $A, B\in{\mathcal B(H)}$ such that $\sigma(AB)=\sigma(A)\sigma(B)$ and $\|A\|\|B\|\leq \left\|\widetilde{AB}\right\|$, $\widetilde{AB}\in (G-n-P)$ if and only if $A=\left\|\tilde{A}\right\|(A_{00}\oplus(A_{0}\oplus A_u))$ and $B=\left\|\tilde{B}\right\|(B_0\oplus B_u)$, where $A_{00}$ and $B_0$, and $A_0\oplus A_u$ and $B_u$, doubly commute, $A_{00}B_0$ and $A_0$ are 2 nilpotent, $A_u$ and $B_u$ are unitaries, $A^{*n}_u=A_u$ and $B^{*n}_u=B_u$. Furthermore, a necessary and sufficient condition for the operators $\alpha A$, $\beta B$, $\alpha \tilde{A}$ and $\beta \tilde{B}$, $\alpha=\frac{1}{\left\|\tilde{A}\right\|}$ and $\beta=\frac{1}{\left\|\tilde{B}\right\|}$, to be $(G-n-P)$ is that $A$ and $B$ are spectrally normaloid at $0$.
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2023-09-30
Weak potency and cyclic subgroup separability of certain free products and tree products
Muhammad Sufi Mohd Asri, Wan Ainun Mior Othman, Kok Bin Wong, Peng Choon WongAbstract : In this note, we shall show that the generalized free products of subgroup separable groups amalgamating a subgroup which itself is a finite extension of a finitely generated normal subgroup of both the factor groups are weakly potent and cyclic subgroup separable. Then we apply our result to generalized free products of finite extensions of finitely generated torsion-free nilpotent groups. Finally, we shall show that their tree products are cyclic subgroup separable.
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2023-11-30
Two-weight norm estimates for square functions associated to fractional Schr{\"o}dinger operators with Hardy potential
Tongxin Kang, Yang ZouAbstract : Let $d\in\mathbb{N}$ and ${\alpha}\in(0,\min\{2,d\})$. For any $a\in[a^\ast,\infty)$, the fractional Schr\"odinger operator $\mathcal{L}_a$ is defined by \begin{equation*} \mathcal{L}_a:=(-\Delta)^{{\alpha}/2}+a{|x|}^{-{\alpha}}, \end{equation*} where $a^*:=-{\frac{2^{\alpha}{\Gamma}((d+{\alpha})/4)^2}{{\Gamma}((d-{\alpha})/4)^2}}$. In this paper, we study two-weight Sobolev inequalities associated with $\mathcal{L}_a$ and two-weight norm estimates for several square functions associated with $\mathcal{L}_a$.
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2023-09-30
Single step real-valued iterative method for linear system of equations with complex symmetric matrices
Jingjing Cui, Zhengge Huang, Beibei Li, Xiaofeng XieAbstract : For solving complex symmetric positive definite linear systems, we propose a single step real-valued (SSR) iterative method, which does not involve the complex arithmetic. The upper bound on the spectral radius of the iteration matrix of the SSR method is given and its convergence properties are analyzed. In addition, the quasi-optimal parameter which minimizes the upper bound for the spectral radius of the proposed method is computed. Finally, numerical experiments are given to demonstrate the effectiveness and robustness of the propose methods.
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2023-11-30
Volume density asymptotics of central harmonic spaces
Peter Gilkey, JeongHyeong ParkAbstract : We show the asymptotics of the volume density function in the class of central harmonic manifolds can be specified arbitrarily and do not determine the geometry.
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2023-05-31
System of generalized multi-valued resolvent equations: algorithmic and analytical approach
Javad Balooee, Shih-sen Chang, Jinfang TangAbstract : In this paper, under some new appropriate conditions imposed on the parameter and mappings involved in the resolvent operator associated with a $P$-accretive mapping, its Lipschitz continuity is proved and an estimate of its Lipschitz constant is computed. This paper is also concerned with the construction of a new iterative algorithm using the resolvent operator technique and Nadler's technique for solving a new system of generalized multi-valued resolvent equations in a Banach space setting. The convergence analysis of the sequences generated by our proposed iterative algorithm under some appropriate conditions is studied. The final section deals with the investigation and analysis of the notion of $H(\cdot,\cdot)$-co-accretive mapping which has been recently introduced and studied in the literature. We verify that under the conditions considered in the literature, every $H(\cdot,\cdot)$-co-accretive mapping is actually $P$-accretive and is not a new one. In the meanwhile, some important comments on $H(\cdot,\cdot)$-co-accretive mappings and the results related to them appeared in the literature are pointed out.
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2024-01-31
Rotationally symmetric solutions of the prescribed higher mean curvature spacelike equations in Minkowski spacetime
Man XuAbstract : In this paper we consider the existence of rotationally symmetric entire solutions for the prescribed higher mean curvature spacelike equations in Minkowski spacetime. As a first step, we study the associated 0-Dirichlet problems on a ball, and then we prove that all possible solutions can be extended to $+\infty$. The proof of our main results are based upon the topological degree methods and the standard prolongability theorem of ordinary differential equations.
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2023-07-31
A model of retirement and consumption-portfolio choice
Junkee Jeon, Hyeng Keun KooAbstract : In this study we propose a model of optimal retirement, consumption and portfolio choice of an individual agent, which encompasses a large class of the models in the literature, and provide a methodology to solve the model. Different from the traditional approach, we consider the problems before and after retirement simultaneously and identify the difference in the dual value functions as the utility value of lifetime labor. The utility value has an option nature, namely, it is the maximized value of choosing the retirement time optimally and we discover it by solving a variational inequality. Then, we discover the dual value functions by using the utility value. We discover the value function and optimal policies by establishing a duality between the value function and the dual value function. The model and approach offer a significant advantage for computation of optimal policies for a large class of problems.
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2023-11-30
Anti-flips of the blow-ups of the projective spaces at torus invariant points
Hiroshi Sato, Shigehito TsuzukiAbstract : We explicitly construct the smooth toric Fano variety which is isomorphic to the blow-up of the projective space at torus invariant points in codimension one by anti-flips.
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2023-05-31
A new $q$-analogue of Van Hamme's $($G.2$)$ supercongruence for primes $p\equiv 3\pmod{4}$
Victor J. W. Guo
, Xiuguo LianAbstract : Van Hamme's (G.2) supercongruence modulo $p^4$ for primes $p\equiv 3 \pmod 4$ and $p>3$ was first established by Swisher. A $q$-analogue of this supercognruence was implicitly given by the first author and Schlosser. In this paper, we present a new $q$-analogue of Van Hamme's (G.2) supercongruence for $p\equiv 3\pmod{4}$.
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Modified cyclotomic polynomials
Ae-Kyoung Cha, Miyeon Kwon, Ki-Suk Lee, Seong-Mo Yang
Bull. Korean Math. Soc. 2022; 59(6): 1511-1522
https://doi.org/10.4134/BKMS.b210864 -
Starlike functions associated with a petal shaped domain
Kush Arora, S. Sivaprasad Kumar
Bull. Korean Math. Soc. 2022; 59(4): 993-1010
https://doi.org/10.4134/BKMS.b210602 -
Zero sums of dual Toeplitz products on the orthogonal complement of the Dirichlet space
Young Joo Lee
Bull. Korean Math. Soc. 2023; 60(1): 161-170
https://doi.org/10.4134/BKMS.b220042 -
Approximate projection algorithms for solving equilibrium and multivalued variational inequality problems in Hilbert space
Nguyen Minh Khoa, Tran Van Thang
Bull. Korean Math. Soc. 2022; 59(4): 1019-1044
https://doi.org/10.4134/BKMS.b210607
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On delay differential equations with meromorphic solutions of hyper-order less than one
Risto Korhonen, Yan Liu
Bull. Korean Math. Soc. 2024; 61(1): 229-246
https://doi.org/10.4134/BKMS.b230089 -
Time analyticity for the heat equation under Bakry-\'Emery Ricci curvature condition
Ling Wu
Bull. Korean Math. Soc. 2023; 60(6): 1673-1685
https://doi.org/10.4134/BKMS.b220830 -
Commutators of the maximal functions on Banach function spaces
Müjdat Ağcayazı, Pu Zhang
Bull. Korean Math. Soc. 2023; 60(5): 1391-1408
https://doi.org/10.4134/BKMS.b220724 -
Pricing American lookback options under a stochastic volatility model
Donghyun Kim, Junhui Woo, Ji-Hun Yoon
Bull. Korean Math. Soc. 2023; 60(2): 361-388
https://doi.org/10.4134/BKMS.b220134
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