Bulletin of the
Korean Mathematical Society
BKMS
ISSN(Print) 1015-8634
ISSN(Online) 2234-3016
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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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2023-11-30
Second main theorem for meromorphic mappings on $p$-parabolic manifolds intersecting hypersurfaces in subgeneral position
Yuehuan ZhuAbstract : In this paper, we give an improvement for the second main theorems of algebraically non-degenerate meromorphic maps from generalized $ p $-parabolic manifolds into projective varieties intersecting hypersurfaces in subgeneral position with some index, which extends the results of Han [6] and Chen-Thin [3].
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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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2023-11-30
Some one-dimensional Noetherian domains and G-projective modules
Kui Hu, Hwankoo Kim, Dechuan ZhouAbstract : Let $R$ be a one-dimensional Noetherian domain with quotient field $K$ and $T$ be the integral closure of $R$ in $K$. In this note we prove that if the conductor ideal $(R:_KT)$ is a nonzero prime ideal, then every finitely generated reflexive (and hence finitely generated $G$-projective) $R$-module is isomorphic to a direct sum of some ideals.
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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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2023-11-30
Results on the algebraic differential independence of the Riemann zeta function and the Euler gamma function
Xiao-Min Li, Yi-Xuan LiAbstract : In 2010, Li-Ye [13, Theorem 0.1] proved that \begin{equation}\nonumber P\left(\zeta(z),\zeta'(z),\ldots,\zeta^{(m)}(z),\Gamma(z),\Gamma'(z),\Gamma^{''}(z)\right) \not\equiv 0\quad\text{in }\ \mathbb{C}, \end{equation} where $m$ is a non-negative integer, and $P(u_{0},u_{1}, \ldots, u_{m},v_{0},v_{1},v_{2})$ is any non-trivial polynomial in its arguments with coefficients in the field $\mathbb{C}$. Later on, Li-Ye [15, Theorem 1] proved that \begin{equation}\nonumber P\left(z,\Gamma(z),\Gamma'(z),\ldots,\Gamma^{(n)}(z), \zeta(z)\right)\not\equiv 0 \end{equation} in $z\in \mathbb{C}$ for any non-trivial distinguished polynomial $P(z,u_0, u_1,\ldots$, $u_n, v)$ with coefficients in a set $L_\delta$ of the zero function and a class of non-zero functions $f$ from $\mathbb{C}$ to $\mathbb{C}\cup\{\infty\}$ (cf. [15, Definition 1]). In this paper, we prove that $P\left(z,\zeta(z),\zeta'(z),\ldots,\zeta^{(m)}(z),\Gamma(z),\Gamma'(z),\ldots,\Gamma^{(n)}(z)\right)\not\equiv 0$ in $z\in\mathbb{C}$, where $m$ and $n$ are two non-negative integers, and $$P(z, u_0,u_1,\ldots,u_m,v_0,v_1,\ldots,v_n)$$ is any non-trivial polynomial in the $m+n+2$ variables $$u_0,u_1,\ldots,u_m,v_0,v_1,\ldots,v_n$$ with coefficients being meromorphic functions of order less than one, and the polynomial $P(z, u_0,u_1,\ldots,u_m,v_0,v_1,\ldots,v_n)$ is a distinguished polynomial in the $n+1$ variables $v_0,v_1,\ldots, v_n$. The question studied in this paper is concerning the conjecture of Markus from [16]. The main results obtained in this paper also extend the corresponding results from Li-Ye [12] and improve the corresponding results from Chen-Wang [5] and Wang-Li-Liu-Li [23], respectively.
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2023-09-30
On the determinant of a dual periodic singular fiber
Cheng Gong, Jun Lu, Sheng-Li TanAbstract : Let $F$ be a periodic singular fiber of genus $g$ with dual fiber $F^*$, and let $T$ (resp.~$T^*$) be the set of the components of $F$ (resp.~$F^*$) by removing one component with multiplicity one. We give a formula to compute the determinant $|\det T\,|$ of the intersect form of $T$. As a consequence, we prove that $|\det T\,|=|\det T^*\,|$. As an application, we compute the Mordell-Weil group of a fibration $f:S\to \mathbb P^1$ of genus $2$ with two singular fibers.
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2023-11-30
Homogeneous geodesics in homogeneous sub-Finsler manifolds
Zaili Yan, Tao ZhouAbstract : In this paper, we mainly study the problem of the existence of homogeneous geodesics in sub-Finsler manifolds. Firstly, we obtain a characterization of a homogeneous curve to be a geodesic. Then we show that every compact connected homogeneous sub-Finsler manifold and Carnot group admits at least one homogeneous geodesic through each point. Finally, we study a special class of $\ell^{p}$-type bi-invariant metrics on compact semi-simple Lie groups. We show that every homogeneous curve in such a metric space is a geodesic. Moreover, we prove that the Alexandrov curvature of the metric space is neither non-positive nor non-negative.
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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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Blow up of solutions for a Petrovsky type equation with logarithmic nonlinearity
Jorge Ferreira, Nazl\i \, Irk\i l, Erhan Pi\c{s}kin, Carlos Raposo
, Mohammad ShahrouziBull. Korean Math. Soc. 2022; 59(6): 1495-1510
https://doi.org/10.4134/BKMS.b210853 -
Some new classes of zero-difference balanced functions and related constant composition codes
Sankhadip Roy
Bull. Korean Math. Soc. 2022; 59(6): 1327-1337
https://doi.org/10.4134/BKMS.b210183 -
On the top local cohomology and formal local cohomology modules
Shahram Rezaei, Behrouz Sadeghi
Bull. Korean Math. Soc. 2023; 60(1): 149-160
https://doi.org/10.4134/BKMS.b220003 -
Strong classification of extensions of classifiable $C^{*}$-algebras
S{\o}ren Eilers, Gunnar Restorff, Efren Ruiz
Bull. Korean Math. Soc. 2022; 59(3): 567-608
https://doi.org/10.4134/BKMS.b210047
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Existence of the continued fractions of $\sqrt{d}$ and its applications
Jun Ho Lee
Bull. Korean Math. Soc. 2022; 59(3): 697-707
https://doi.org/10.4134/BKMS.b210422 -
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 -
Fixed-width partitions according to the parity of the even parts
John Maxwell Campbell
Bull. Korean Math. Soc. 2023; 60(4): 1017-1024
https://doi.org/10.4134/BKMS.b220457 -
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
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