Abstract : In this paper, we introduce relative Rota-Baxter systems on Leibniz algebras and give some characterizations and new constructions. Then we construct a graded Lie algebra whose Maurer-Cartan elements are relative Rota-Baxter systems. This allows us to define a cohomology theory associated with a relative Rota-Baxter system. Finally, we study formal deformations and extendibility of finite order deformations of a relative Rota-Baxter system in terms of the cohomology theory.
Abstract : For each connected and simply connected three-dimensional non-unimodular Lie group, we classify the left invariant Lorentzian metrics up to automorphism, and study the extent to which curvature can be altered by a change of metric. Thereby we obtain the Ricci operator, the scalar curvature, and the sectional curvatures as functions of left invariant Lorentzian metrics on each of these groups. Our study is a continuation and extension of the previous studies done in [3] for Riemannian metrics and in [1] for Lorentzian metrics on unimodular Lie groups.
Abstract : Let $E$ be an elliptic curve defined over $\mathbb{Q}$ of conductor $N$, $c$ the Manin constant of $E$, and $m$ the product of Tamagawa numbers of $E$ at prime divisors of $N$. Let $K$ be an imaginary quadratic field where all prime divisors of $N$ split in $K$, $P_K$ the Heegner point in $E(K)$, and ${\rm III}(E/K)$ the Shafarevich-Tate group of $E$ over $K$. Let $2u_K$ be the number of roots of unity contained in $K$. Gross and Zagier conjectured that if $P_K$ has infinite order in $E(K)$, then the integer $ c \cdot m \cdot u_K \cdot |{\rm III}(E/K)|^{\frac{1}{2}}$ is divisible by $|E(\mathbb{Q})_{\rm{tor}} |$. In this paper, we prove that this conjecture is true if $E(\mathbb{Q})_{\rm{tor}} \cong \mathbb{Z}/2\mathbb{Z}$ or $\mathbb{Z}/4\mathbb{Z}$ except for two explicit families of curves. Further, we show these exceptions can be removed under Stein--Watkins conjecture.
Abstract : In this paper we give the first steps toward the study of the Harbourne-Hirschowitz condition and the anticanonical orthogonal property for regular surfaces. To do so, we consider the Kodaira dimension of the surfaces and study the cases based on the Enriques-Kodaira classification.
Abstract : In this paper we give conditions on a matrix which guarantee that it is similar to a centrosymmetric matrix. We use this conditions to show that some $4 \times 4$ and $6 \times 6$ Toeplitz matrices are similar to centrosymmetric matrices. Furthermore, we give conditions for a matrix to be similar to a matrix which has a centrosymmetric principal submatrix, and conditions under which a matrix can be dilated to a matrix similar to a centrosymmetric matrix.
Abstract : We prove that the two-step flag variety $\mathcal{F}\ell(1,n;n+1)$ carries a non-displaceable and non-monotone Lagrangian Gelfand--Zeitlin fiber diffeomorphic to $S^3 \times T^{2n-4}$ and a continuum family of non-displaceable Lagrangian Gelfand--Zeitlin torus fibers when $n > 2$.
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 : We introduce the notions of symbolic expansivity and symbolic shadowing for homeomorphisms on non-metrizable compact spaces which are generalizations of expansivity and shadowing, respectively, for metric spaces. The main result is to generalize the Smale's spectral decomposition theorem to symbolically expansive homeomorphisms with symbolic shadowing on non-metrizable compact Hausdorff totally disconnected spaces.
Abstract : Let $\varphi: \mathbb{R}^n\times[0,\infty)\to[0,\infty)$ be a growth function and $H^{\varphi}(\mathbb{R}^n)$ the Musielak--Orlicz Hardy space defined via the non-tangential grand maximal function. A general summability method, the so-called $\theta$-summability is considered for multi-dimensional Fourier transforms in $H^{\varphi}(\mathbb{R}^n)$. Precisely, with some assumptions on $\theta$, the authors first prove that the maximal operator of the $\theta$-means is bounded from $H^{\varphi}(\mathbb{R}^n)$ to $L^{\varphi}(\mathbb{R}^n)$. As consequences, some norm and almost everywhere convergence results of the $\theta$-means, which generalizes the well-known Lebesgue's theorem, are then obtained. Finally, the corresponding conclusions of some specific summability methods, such as Bochner--Riesz, Weierstrass and Picard--Bessel summations, are also presented.
Abstract : Striking result of Vyb\'{\i}ral \cite{VYBIRAL} says that Schur product of positive matrices is bounded below by the size of the matrix and the row sums of Schur product. Vyb\'{\i}ral used this result to prove the Novak's conjecture. In this paper, we define Schur product of matrices over arbitrary C*-algebras and derive the results of Schur and Vyb\'{\i}ral. As an application, we state C*-algebraic version of Novak's conjecture and solve it for commutative unital C*-algebras. We formulate P\'{o}lya-Szeg\H{o}-Rudin question for the C*-algebraic Schur product of positive matrices.
Jangwon Ju
J. Korean Math. Soc. 2023; 60(5): 931-957
https://doi.org/10.4134/JKMS.j220231
Hyenho Lho
J. Korean Math. Soc. 2023; 60(3): 479-501
https://doi.org/10.4134/JKMS.j210448
Lei Qiao, Kai Zuo
J. Korean Math. Soc. 2022; 59(4): 821-841
https://doi.org/10.4134/JKMS.j210774
Shivani Dubey, Mukund Madhav Mishra, Ashutosh Pandey
J. Korean Math. Soc. 2022; 59(3): 635-648
https://doi.org/10.4134/JKMS.j210462
Gyu Whan Chang
J. Korean Math. Soc. 2022; 59(3): 571-594
https://doi.org/10.4134/JKMS.j210419
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
Yoosik Kim
J. Korean Math. Soc. 2023; 60(5): 1109-1133
https://doi.org/10.4134/JKMS.j230098
HeeSook Park
J. Korean Math. Soc. 2023; 60(4): 823-833
https://doi.org/10.4134/JKMS.j220345
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