Bulletin of the
Korean Mathematical Society
BKMS
ISSN(Print) 1015-8634
ISSN(Online) 2234-3016
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2023-09-30
Differences of weighted composition operators on Bergman spaces induced by doubling weights
Jiale ChenAbstract : We characterize the boundedness and compactness of differences of weighted composition operators acting from weighted Bergman spaces $A^p_{\omega}$ to Lebesgue spaces $L^q(d\mu)$ for all $0<p,q<\infty$, where $\omega$ is a radial weight on the unit disk admitting a two-sided doubling condition.
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2024-01-31
On delay differential equations with meromorphic solutions of hyper-order less than one
Risto Korhonen, Yan LiuAbstract : We consider the delay differential equations \begin{equation*} b(z)w(z+1)+c(z)w(z-1)+a(z)\frac{w'(z)}{w^k(z)}=\frac{P(z,w(z))}{Q(z,w(z))}, \end{equation*} where $k\in\{1,2\}$, $a(z)$, $b(z)\not\equiv 0$, $c(z)\not\equiv 0$ are rational functions, and $P(z,w(z))$ and $Q(z,w(z))$ are polynomials in $w(z)$ with rational coefficients satisfying certain natural conditions regarding their roots. It is shown that if this equation has a non-rational meromorphic solution $w$ with hyper-order $\rho_{2}(w)
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2023-07-31
An extension of Schneider's characterization theorem for ellipsoids
Dong-Soo Kim, Young Ho KimAbstract : Suppose that $M$ is a strictly convex hypersurface in the $(n+1)$-dimensional Euclidean space ${\mathbb E}^{n+1}$ with the origin $o$ in its convex side and with the outward unit normal $N$. For a fixed point $p \in M$ and a positive constant $t$, we put $\Phi_t$ the hyperplane parallel to the tangent hyperplane $\Phi$ at $p$ and passing through the point $q=p-tN(p)$. We consider the region cut from $M$ by the parallel hyperplane $\Phi_t$, and denote by $I_p(t)$ the $(n+1)$-dimensional volume of the convex hull of the region and the origin $o$. Then Schneider's characterization theorem for ellipsoids states that among centrally symmetric, strictly convex and closed surfaces in the 3-dimensional Euclidean space ${\mathbb E}^{3}$, the ellipsoids are the only ones satisfying $I_p(t)=\phi(p)t$, where $\phi$ is a function defined on $M$. Recently, the characterization theorem was extended to centrally symmetric, strictly convex and closed hypersurfaces in ${\mathbb E}^{n+1}$ satisfying for a constant $\beta$, $I_p(t)=\phi(p)t^{\beta}$. In this paper, we study the volume $I_p(t)$ of a strictly convex and complete hypersurface in ${\mathbb E}^{n+1}$ with the origin $o$ in its convex side. As a result, first of all we extend the characterization theorem to strictly convex and closed (not necessarily centrally symmetric) hypersurfaces in ${\mathbb E}^{n+1}$ satisfying $I_p(t)=\phi(p)t^{\beta}$. After that we generalize the characterization theorem to strictly convex and complete (not necessarily closed) hypersurfaces in ${\mathbb E}^{n+1}$ satisfying $I_p(t)=\phi(p)t^{\beta}$.
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2023-07-31
Classification of twisted product lightlike submanifolds
Sangeet Kumar, Megha PruthiAbstract : In this paper, we introduce the idea of twisted product lightlike submanifolds of semi-Riemannian manifolds and provide non-trivial examples of such lightlike submanifolds. Then, we prove the non-existence of proper isotropic or totally lightlike twisted product submanifolds of a semi-Riemannian manifold. We also show that for a twisted product lightlike submanifold of a semi-Riemannian manifold, the induced connection $\nabla$ is not a metric connection. Further, we prove that a totally umbilical $SCR$-lightlike submanifold of an indefinite Kaehler manifold $\tilde{M}$ does not admit any twisted product $SCR$-lightlike submanifold of the type $M_{\perp}\times_{\phi}M_{T}$, where $M_{\perp}$ is a totally real submanifold and $M_{T}$ is a holomorphic submanifold of $\tilde{M}$. Consequently, we obtain a geometric inequality for the second fundamental form of twisted product $SCR$-lightlike submanifolds of the type $M_{T}\times_{\phi}M_{\perp}$ of an indefinite Kaehler manifold $\tilde{M}$, in terms of the gradient of $\ln \phi$, where $\phi$ stands for the twisting function. Subsequently, the equality case of this inequality is discussed. Finally, we construct a non-trivial example of a twisted product $SCR$-lightlike submanifold in an indefinite Kaehler manifold.
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2024-03-31
On the generalized principally injective modules
Fatemeh Gholami, Zohreh Habibi, Alireza NajafizadehAbstract : Some results are generalized from principally injective rings to principally injective modules. Moreover, it is proved that the results are valid to some other extended injectivity conditions which may be defined over modules. The influence of such injectivity conditions are studied for both the trace and the reject submodules of some modules over commutative rings. Finally, a correction is given to a paper related to the subject.
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2023-09-30
On the construction of optimal linear codes of dimension four
ATSUYA KATO, TATSUYA MARUTA, KEITA NOMURAAbstract : A fundamental problem in coding theory is to find $n_q(k,d)$, the minimum length $n$ for which an $[n,k,d]_q$ code exists. We show that some $q$-divisible optimal linear codes of dimension $4$ over $\mbox{$\mathbb{F}$}_q$, which are not of Belov type, can be constructed geometrically using hyperbolic quadrics in PG$(3,q)$. We also construct some new linear codes over $\mbox{$\mathbb{F}$}_q$ with $q=7,8$, which determine $n_7(4,d)$ for $31$ values of $d$ and $n_8(4,d)$ for $40$ values of $d$.
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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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2023-11-30
Bredon homology of wallpaper groups
Ramon FloresAbstract : In this paper we compute the Bredon homology of wallpaper groups with respect to the family of finite groups and with coefficients in the complex representation ring. We provide explicit bases of the homology groups in terms of irreducible characters of the stabilizers.
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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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2023-09-30
Mixed radial-angular integrabilities for Hardy type operators
Ronghui Liu, Shuangping TaoAbstract : In this paper, we are devoted to studying the mixed radial-angular integrabilities for Hardy type operators. As an application, the upper and lower bounds are obtained for the fractional Hardy operator. In addition, we also establish the sharp weak-type estimate for the fractional Hardy operator.
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A note on the properties of pseudo-weighted Browder spectrum
Preeti Dharmarha, Sarita Kumari
Bull. Korean Math. Soc. 2023; 60(1): 123-135
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Generalized $m$-quasi-Einstein structure in almost Kenmotsu manifolds
Mohan Khatri, Jay Prakash Singh
Bull. Korean Math. Soc. 2023; 60(3): 717-732
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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
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UN rings and group rings
Kanchan Jangra, Dinesh Udar
Bull. Korean Math. Soc. 2023; 60(1): 83-91
https://doi.org/10.4134/BKMS.b210917
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Stability and topology of translating solitons for the mean curvature flow with the small $L^m$ norm of the second fundamental form
Eungmo Nam, Juncheol Pyo
Bull. Korean Math. Soc. 2023; 60(1): 171-184
https://doi.org/10.4134/BKMS.b220049 -
On semi-regular injective modules and strong dedekind rings
Renchun Qu
Bull. Korean Math. Soc. 2023; 60(4): 1071-1083
https://doi.org/10.4134/BKMS.b220516 -
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 -
Residual supersingular Iwasawa theory over quadratic imaginary fields
Parham Hamidi
Bull. Korean Math. Soc. 2023; 60(4): 1035-1059
https://doi.org/10.4134/BKMS.b220461
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