Abstract : In this erratum, we offer a correction to [J. Korean Math. Soc. 57 (2020), No. 6, pp. 1435--1449]. Theorem 1 in the original paper has three assertions (i)-(iii), but we add (iv) after having clarified the argument.
Abstract : Using the results in the paper [12], we give an estimate for the first positive and negative Dirac eigenvalue on a 7-dimensional Sasakian spin manifold. The limiting case of this estimate can be attained if the manifold under consideration admits a Sasakian Killing spinor. By imposing the eta-Einstein condition on Sasakian manifolds of higher dimensions $2m+1 \geq 9$, we derive some new Dirac eigenvalue inequalities that improve the recent results in [12, 13].
Abstract : In this paper, using the theory of majorization, we discuss the Schur $m$ power convexity for $L$-conjugate means of $n$ variables and the Schur convexity for weighted $L$-conjugate means of $n$ variables. As applications, we get several inequalities of general mean satisfying Schur convexity, and a few comparative inequalities about $n$ variables Gini mean are established.
Abstract : The main objective of this paper is to develop a concrete inverse formula of the system induced by the fourth-order finite difference method for two-point boundary value problems with Robin boundary conditions. This inverse formula facilitates to make a fast algorithm for solving the problems. Our numerical results show the efficiency and accuracy of the proposed method, which is implemented by the Thomas algorithm.
Abstract : We describe the Gorenstein derived categories of Gorenstein rings via the homotopy categories of Gorenstein injective modules. We also introduce the concept of Gorenstein cosilting complexes and study its basic properties. This concept is generalized by cosilting complexes in relative homological methods. Furthermore, we investigate the existence of the relative version of the Bongartz's theorem and construct a Bongartz's complement for a Gorenstein precosilting complex.
Abstract : Let $C$ be a curve and $V \to C$ an orthogonal vector bundle of rank $r$. For $r \le 6$, the structure of $V$ can be described using tensor, symmetric and exterior products of bundles of lower rank, essentially due to the existence of exceptional isomorphisms between $\mathrm{Spin} (r , \mathbb C)$ and other groups for these $r$. We analyze these structures in detail, and in particular use them to describe moduli spaces of orthogonal bundles. Furthermore, the locus of isotropic vectors in $V$ defines a quadric subfibration $Q_V \subset \mathbb P V$. Using familiar results on quadrics of low dimension, we exhibit isomorphisms between isotropic Quot schemes of $V$ and certain ordinary Quot schemes of line subbundles. In particular, for $r \le 6$ this gives a method for enumerating the isotropic subbundles of maximal degree of a general $V$, when there are finitely many.
Abstract : In this paper we study a pointwise version of Walters topological stability in the class of homeomorphisms on a compact metric space. We also show that if a sequence of homeomorphisms on a compact metric space is uniformly expansive with the uniform shadowing property, then the limit is expansive with the shadowing property and so topologically stable. Furthermore, we give examples to illustrate our results.
Abstract : It is shown that every continuum-wise expansive $C^1$ generic vector field $X$ on a compact connected smooth manifold $M$ satisfies Axiom A and has no cycles, and every continuum-wise expansive homoclinic class of a $C^1$ generic vector field $X$ on a compact connected smooth manifold $M$ is hyperbolic. Moreover, every continuum-wise expansive $C^1$ generic divergence-free vector field $X$ on a compact connected smooth manifold $M$ is Anosov.
Abstract : In this paper, we investigate the portfolio optimization problem under the SVCEV model, which is a hybrid model of constant elasticity of variance (CEV) and stochastic volatility, by taking into account of minimum-entropy robustness. The Hamilton-Jacobi-Bellman (HJB) equation is derived and the first two orders of optimal strategies are obtained by utilizing an asymptotic approximation approach. We also derive the first two orders of practical optimal strategies by knowing that the underlying Ornstein-Uhlenbeck process is not observable. Finally, we conduct numerical experiments and sensitivity analysis on the leading optimal strategy and the first correction term with respect to various values of the model parameters.
Abstract : Let $R$ be a commutative ring with identity and $S$ a multiplicative subset of $R$. In this paper, we introduce and study the notions of $u$-$S$-pure $u$-$S$-exact sequences and uniformly $S$-absolutely pure modules which extend the classical notions of pure exact sequences and absolutely pure modules. And then we characterize uniformly $S$-von Neumann regular rings and uniformly $S$-Noetherian rings using uniformly $S$-absolutely pure modules.
Benjamín A. Itzá-Ortiz, Rubén A. Martínez-Avendaño
J. Korean Math. Soc. 2022; 59(5): 997-1013
https://doi.org/10.4134/JKMS.j220108
Kitae Kim, Hyang-Sook Lee, Seongan Lim, Jeongeun Park, Ikkwon Yie
J. Korean Math. Soc. 2022; 59(6): 1047-1065
https://doi.org/10.4134/JKMS.j210496
Jung Hee Cheon, Dongwoo Kim, Duhyeong Kim, Keewoo Lee
J. Korean Math. Soc. 2022; 59(3): 621-634
https://doi.org/10.4134/JKMS.j210446
Yuhui Liu
J. Korean Math. Soc. 2022; 59(3): 439-448
https://doi.org/10.4134/JKMS.j190679
Benjamín A. Itzá-Ortiz, Rubén A. Martínez-Avendaño
J. Korean Math. Soc. 2022; 59(5): 997-1013
https://doi.org/10.4134/JKMS.j220108
Byoung Jin Choi, Jae Hun Kim
J. Korean Math. Soc. 2022; 59(3): 549-570
https://doi.org/10.4134/JKMS.j210239
Xing Yu Song, Ling Wu
J. Korean Math. Soc. 2023; 60(5): 1023-1041
https://doi.org/10.4134/JKMS.j220589
Hojoo Lee
J. Korean Math. Soc. 2023; 60(1): 71-90
https://doi.org/10.4134/JKMS.j220095
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd