Journal of the
Korean Mathematical Society
JKMS
ISSN(Print) 0304-9914
ISSN(Online) 2234-3008
Most Read
HOME
VIEW ARTICLES
Most Read
VIEW ARTICLES
Most Read
-
2023-01-01
Rational homology disk smoothings and Lefschetz fibrations
Hakho ChoiAbstract : In this article, we generalize the results discussed in \cite{MR2783383} by introducing a genus to generic fibers of Lefschetz fibrations. That is, we give families of relations in the mapping class groups of genus-1 surfaces with boundaries that represent rational homology disk smoothings of weighted homogeneous surface singularities whose resolution graphs are $3$-legged with a bad central vertex.
-
2023-01-01
Simple zeros of $L$-functions and the Weyl-type subconvexity
Peter Jaehyun Cho
, Gyeongwon OhAbstract : Let $f$ be a self-dual primitive Maass or modular forms for level $4$. For such a form $f$, we define \begin{align*} N_f^s(T)\!:=\!|\{\rho \in \mathbb{C} : |\Im(\rho)| \leq T, \text{ $\rho$ is a non-trivial simple zero of $L_f(s)$} \}|. \end{align*} We establish an omega result for $N_f^s(T)$, which is $N_f^s(T)=\Omega \big( T^{\frac{1}{6}-\epsilon} \big)$ for any $\epsilon>0$. For this purpose, we need to establish the Weyl-type subconvexity for $L$-functions attached to primitive Maass forms by following a recent work of Aggarwal, Holowinsky, Lin, and Qi.
-
2023-11-01
Low rank orthogonal bundles and quadric fibrations
Insong Choe, George H. HitchingAbstract : 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.
-
2022-09-01
Fourier transform of anisotropic mixed-norm Hardy spaces with applications to Hardy--Littlewood inequalities
Jun Liu, Yaqian Lu, Mingdong ZhangAbstract : Let $\vec{p}\in(0,1]^n$ be an $n$-dimensional vector and $A$ a dilation. Let $H_A^{\vec{p}}(\mathbb{R}^n)$ denote the anisotropic mixed-norm Hardy space defined via the radial maximal function. Using the known atomic characterization of $H_{A}^{\vec{p}}(\mathbb{R}^n)$ and establishing a uniform estimate for corresponding atoms, the authors prove that the Fourier transform of $f\in H_A^{\vec{p}}(\mathbb{R}^n)$ coincides with a continuous function $F$ on $\mathbb{R}^n$ in the sense of tempered distributions. Moreover, the function $F$ can be controlled pointwisely by the product of the Hardy space norm of $f$ and a step function with respect to the transpose matrix of $A$. As applications, the authors obtain a higher order of convergence for the function $F$ at the origin, and an analogue of Hardy--Littlewood inequalities in the present setting of $H_A^{\vec{p}}(\mathbb{R}^n)$.
-
2023-09-01
Erratum to ``Pseudo-Riemannian Sasaki solvmanifolds'' [J. Korean Math. Soc. 60 (2023), No. 1, pp. 115--141]
Diego Conti, Federico A. Rossi, Romeo Segnan DalmassoAbstract : In this erratum, we offer a correction to [J. Korean Math. Soc. 60 (2023), No. 1, pp. 115--141]. We rectify Theorem 5.7 and Table 1 of the original paper.
-
2023-09-01
Infinite families of congruences modulo $2$ for $2$-core and $13$-core partitions
Ankita Jindal, Nabin Kumar MeherAbstract : A partition of $n$ is called a $t$-core partition if none of its hook number is divisible by $t$. In 2019, Hirschhorn and Sellers [5] obtained a parity result for $3$-core partition function $a_3(n)$. Motivated by this result, both the authors [8] recently proved that for a non-negative integer $\alpha$, $a_{3^{\alpha} m}(n)$ is almost always divisible by an arbitrary power of $2$ and $3$ and $a_{t}(n)$ is almost always divisible by an arbitrary power of $p_i^j$, where $j$ is a fixed positive integer and $t= p_1^{a_1}p_2^{a_2}\cdots p_m^{a_m}$ with primes $p_i \geq 5.$ In this article, by using Hecke eigenform theory, we obtain infinite families of congruences and multiplicative identities for $a_2(n)$ and $a_{13}(n)$ modulo $2$ which generalizes some results of Das [2].
-
2022-11-01
$(\mathcal{F}, \mathcal{A})$-Gorenstein flat homological dimensions
V\'ictor BecerrilAbstract : In this paper we develop the homological properties of the Gorenstein $(\mathcal{L}, \mathcal{A})$-flat $R$-modules $\mathcal{GF}_{(\mathcal{F} (R), \mathcal{A})}$ proposed by Gillespie, \linebreak where the class $\mathcal{A} \subseteq \mathrm{Mod} (R^{\mathrm{op}})$ sometimes corresponds to a duality pair $(\mathcal{L}, \mathcal{A})$. We study the weak global and finitistic dimensions that come with the class $\mathcal{GF}_{(\mathcal{F} (R), \mathcal{A})}$ and show that over a $(\mathcal{L}, \mathcal{A})$-Gorenstein ring, the functor $-\otimes _R-$ is left balanced over $\mathrm{Mod} (R^{\mathrm{op}}) \times \mathrm{Mod} (R)$ by the classes $\mathcal{GF}_{(\mathcal{F} (R^{\mathrm{op}}), \mathcal{A})} \times \mathcal{GF}_{(\mathcal{F} (R), \mathcal{A})}$. When the duality pair is $(\mathcal{F} (R), \mathcal{FP}Inj (R^{\mathrm{op}}))$ we recover the G. Yang's result over a Ding-Chen ring, and we see that is new for $(\mathrm{Lev} (R), \mathrm{AC} (R^{\mathrm{op}}))$ among others.
-
2022-11-01
Maximal domains of solutions for analytic quasilinear differential equations of first order
Chong-Kyu Han, Taejung KimAbstract : We study the real-analytic continuation of local real-analytic solutions to the Cauchy problems of quasi-linear partial differential equations of first order for a scalar function. By making use of the first integrals of the characteristic vector field and the implicit function theorem we determine the maximal domain of the analytic extension of a local solution as a single-valued function. We present some examples including the scalar conservation laws that admit global first integrals so that our method is applicable.
-
2022-09-01
Multiple solutions of a perturbed Yamabe-type equation on graph
Yang LiuAbstract : Let $u$ be a function on a locally finite graph $G=(V, E)$ and $\Omega$ be a bounded subset of $V$. Let $\varepsilon>0$, $p>2$ and $0\leq\lambda<\lambda_1(\Omega)$ be constants, where $\lambda_1(\Omega)$ is the first eigenvalue of the discrete Laplacian, and $h: V\rightarrow\mathbb{R}$ be a function satisfying $h\geq 0$ and $h\not\equiv 0$. We consider a perturbed Yamabe equation, say\begin{equation*}\left\{\begin{array}{lll} -\Delta u-\lambda u=|u|^{p-2}u+\varepsilon h, &{\rm in}& \Omega,\\ u=0,&{\rm on}&\partial\Omega,\end{array}\ri.\end{equation*}where $\Omega$ and $\partial\Omega$ denote the interior and the boundary of $\Omega$, respectively. Using variational methods,we prove thatthere exists some positive constant $\varepsilon_0>0$ such that for all $\varepsilon\in(0,\varepsilon_0)$, the above equationhas two distinct solutions. Moreover, we consider a more general nonlinear equation\begin{equation*}\left\{\begin{array}{lll} -\Delta u=f(u)+\varepsilon h, &{\rm in}& \Omega,\\ u=0, &{\rm on}&\partial\Omega,\end{array}\ri.\end{equation*}and prove similar result for certain nonlinear term $f(u)$.
-
2022-09-01
Dynamic behavior of cracked beams and shallow arches
Semion Gutman, Junhong Ha, Sudeok ShonAbstract : We develop a rigorous mathematical framework for studying dynamic behavior of cracked beams and shallow arches. The governing equations are derived from the first principles, and stated in terms of the subdifferentials of the bending and the axial potential energies. The existence and the uniqueness of the solutions is established under various conditions. The corresponding mathematical tools dealing with vector-valued functions are comprehensively developed. The motion of beams and arches is studied under the assumptions of the weak and strong damping. The presence of cracks forces weaker regularity results for the arch motion, as compared to the beam case.
Most Read
-
On solvability of a class of degenerate Kirchhoff equations with logarithmic nonlinearity
U\u{g}ur Sert
J. Korean Math. Soc. 2023; 60(3): 565-586
https://doi.org/10.4134/JKMS.j220129 -
A note on unicity of meromorphic functions in several variables
yezhou Li, heqing sun
J. Korean Math. Soc. 2023; 60(4): 859-876
https://doi.org/10.4134/JKMS.j220473 -
Weak Herz-type Hardy spaces with variable exponents and applications
Souad Ben Seghier
J. Korean Math. Soc. 2023; 60(1): 33-69
https://doi.org/10.4134/JKMS.j210764 -
On uniformly $S$-absolutely pure modules
Xiaolei Zhang
J. Korean Math. Soc. 2023; 60(3): 521-536
https://doi.org/10.4134/JKMS.j220055
Most Downloaded
-
Simple zeros of $L$-functions and the Weyl-type subconvexity
Peter Jaehyun Cho
, Gyeongwon OhJ. Korean Math. Soc. 2023; 60(1): 167-193
https://doi.org/10.4134/JKMS.j220242 -
The exceptional set of one prime square and five prime cubes
Yuhui Liu
J. Korean Math. Soc. 2022; 59(3): 439-448
https://doi.org/10.4134/JKMS.j190679 -
A deep learning algorithm for optimal investment strategies under Merton's framework
Daeyung Gim, Hyungbin Park
J. Korean Math. Soc. 2022; 59(2): 311-335
https://doi.org/10.4134/JKMS.j210168 -
A note on unicity of meromorphic functions in several variables
yezhou Li, heqing sun
J. Korean Math. Soc. 2023; 60(4): 859-876
https://doi.org/10.4134/JKMS.j220473
Editorial Office
✕
JKMS
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd