Abstract : We investigate how closed string mirror symmetry is related to homological mirror symmetry, under the presence of an explicit geometric mirror functor.
Abstract : We describe a construction which takes as an input a left order of the fundamental group of a manifold, and outputs a (singular) foliation of this manifold which is analogous to a taut foliation. We investigate this construction in detail in dimension $2$, and exhibit connections to various problems in dimension $3$.
Abstract : In this paper, we study the Birkhoff's ergodic theorem on geodesic metric spaces, especially on Hadamard spaces, using the notion of weighted inductive means. Also, we study a deterministic weighted sequence for the weighted Birkhoff's ergodic theorem in Hadamard spaces.
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 : Let $a$ and $b$ be positive even integers. An even $[a,b]$-factor of a graph $G$ is a spanning subgraph $H$ such that for every vertex $v \in V(G)$, $d_H(v)$ is even and $a \le d_H(v) \le b$. Let $\kappa(G)$ be the minimum size of a vertex set $S$ such that $G-S$ is disconnected or one vertex, and let $\sigma_2(G)=\min_{uv \notin E(G)}(d(u)+d(v))$. In 2005, Matsuda proved an Ore-type condition for an $n$-vertex graph satisfying certain properties to guarantee the existence of an even $[2,b]$-factor. In this paper, we prove that for an even positive integer $b$ with $b \ge 6$, if $G$ is an $n$-vertex graph such that $n \ge b+5$, $\kappa(G) \ge 4$, and $\sigma_2(G) \ge \frac{8n}{b+4}$, then $G$ contains an even $[4,b]$-factor; each condition on $n$, $\kappa(G)$, and $\sigma_2(G)$ is sharp.
Abstract : We consider the set of points with historic behavior (which is also called the irregular set) for continuous flows and suspension flows. In this paper under the hypothesis that $(X_t)_t$ is a continuous flow on a $d$-dimensional Riemaniann closed manifold $M$ $(d \geq 2)$ with gluing orbit property, we prove that the set of points with historic behavior in a compact and invariant subset $\Delta$ of $M$ is either empty or is a Baire residual subset on $\Delta$. We also prove that the set of points with historic behavior of a suspension flows over a homeomorphism satisfyng the gluing orbit property is either empty or Baire residual and carries full topological entropy.
Abstract : For an arbitrary integer $x$, an integer of the form $T(x)\!=\!\frac{x^2+x}{2}$ is called a triangular number. Let $\alpha_1,\dots,\alpha_k$ be positive integers. A sum $\Delta_{\alpha_1,\dots,\alpha_k}(x_1,\dots,x_k)=\alpha_1 T(x_1)+\cdots+\alpha_k T(x_k)$ of triangular numbers is said to be {\it almost universal with one exception} if the Diophantine equation $\Delta_{\alpha_1,\dots,\alpha_k}(x_1,\dots,x_k)=n$ has an integer solution $(x_1,\dots,x_k)\in\mathbb{Z}^k$ for any nonnegative integer $n$ except a single one. In this article, we classify all almost universal sums of triangular numbers with one exception. Furthermore, we provide an effective criterion on almost universality with one exception of an arbitrary sum of triangular numbers, which is a generalization of ``15-theorem" of Conway, Miller, and Schneeberger.
Abstract : We study the rationality and symmetry of the Gromov-Witten invariants of the projective line twisted by certain line bundles.
Abstract : In this paper, we introduce and study regular rings relative to the hereditary torsion theory $w$ (a special case of a well-centered torsion theory over a commutative ring), called $w$-regular rings. We focus mainly on the $w$-regularity for $w$-coherent rings and $w$-Noetherian rings. In particular, it is shown that the $w$-coherent $w$-regular domains are exactly the Pr\"ufer $v$-multiplication domains and that an integral domain is $w$-Noetherian and $w$-regular if and only if it is a Krull domain. We also prove the $w$-analogue of the global version of the Serre--Auslander-Buchsbaum Theorem. Among other things, we show that every $w$-Noetherian $w$-regular ring is the direct sum of a finite number of Krull domains. Finally, we obtain that the global weak $w$-projective dimension of a $w$-Noetherian ring is 0, 1, or $\infty$.
Abstract : We discuss the wellposedness of the Neumann problem on a half-space for the Kohn-Laplacian in the Heisenberg group. We then construct the Neumann function and explicitly represent the solution of the associated inhomogeneous problem.
Jundong Zhou
J. Korean Math. Soc. 2022; 59(1): 53-69
https://doi.org/10.4134/JKMS.j200665
Nak Eun Cho, Anbhu Swaminathan, Lateef Ahmad Wani
J. Korean Math. Soc. 2022; 59(2): 353-365
https://doi.org/10.4134/JKMS.j210246
Jung Pil Park, Yong-Su Shin
J. Korean Math. Soc. 2022; 59(1): 71-85
https://doi.org/10.4134/JKMS.j200690
Huabin Chen, Qunjia Wan
J. Korean Math. Soc. 2022; 59(2): 279-298
https://doi.org/10.4134/JKMS.j210111
Huabin Chen, Qunjia Wan
J. Korean Math. Soc. 2022; 59(2): 279-298
https://doi.org/10.4134/JKMS.j210111
Sebastian Petit, Hendrik Van Maldeghem
J. Korean Math. Soc. 2023; 60(4): 907-929
https://doi.org/10.4134/JKMS.j220528
Benjamín A. Itzá-Ortiz, Rubén A. Martínez-Avendaño
J. Korean Math. Soc. 2022; 59(5): 997-1013
https://doi.org/10.4134/JKMS.j220108
J. Korean Math. Soc. 2022; 59(2): 337-352
https://doi.org/10.4134/JKMS.j210245
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