Journal of theKorean Mathematical SocietyJKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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• 2021-05-01

Blow-up of solutions for wave equations with strong damping and variable-exponent nonlinearity

Sun-Hye Park

Abstract : In this paper we consider the following strongly damped wave equation with variable-exponent nonlinearity $$u_{tt}(x,t) - \Delta u (x,t) - \Delta u_t (x,t) = |u(x,t)|^{p(x)-2} u(x,t) ,$$ where the exponent $p(\cdot)$ of nonlinearity is a given measurable function. We establish finite time blow-up results for the solutions with non-positive initial energy and for certain solutions with positive initial energy. We extend the previous results for strongly damped wave equations with constant exponent nonlinearity to the equations with variable-exponent nonlinearity.

• 2021-03-01

Monoidal functors and exact sequences of groups for Hopf quasigroups

Jos\'{e} N. Alonso \'{A}lvarez, Jos\'{e} M. Fern\'{a}ndez Vilaboa, Ram\'{o}n Gonz\'{a}lez Rodr\'{\i}guez

Abstract : In this paper we introduce the notion of strong Galois $H$-progenerator object for a finite cocommutative Hopf quasigroup $H$ in a symmetric monoidal category ${\sf C}$. We prove that the set of isomorphism classes of strong Galois $H$-progenerator objects is a subgroup of the group of strong Galois $H$-objects introduced in \cite{JKMS}. Moreover, we show that strong Galois $H$-progenerator objects are preserved by strong symmetric monoidal functors and, as a consequence, we obtain an exact sequence involving the associated Galois groups. Finally, to the previous functors, if $H$ is finite, we find exact sequences of Picard groups related with invertible left $H$-(quasi)modules and an isomorphism $Pic(_{{\sf H}}{\sf Mod})\cong Pic({\sf C})\oplus G(H^{\ast})$ where $Pic(_{{\sf H}}{\sf Mod})$ is the Picard group of the category of left $H$-modules, $Pic({\sf C})$ the Picard group of ${\sf C}$, and $G(H^{\ast})$ the group of group-like morphisms of the dual of $H$.

• 2021-01-01

Continuous data assimilation for the three-dimensional simplified Bardina model utilizing measurements of only two components of the velocity field

Cung The Anh, Bui Huy Bach

Abstract : We study a continuous data assimilation algorithm for the three-dimensional simplified Bardina model utilizing measurements of only two components of the velocity field. Under suitable conditions on the relaxation (nudging) parameter and the spatial mesh resolution, we obtain an asymptotic in time estimate of the difference between the approximating solution and the unknown reference solution corresponding to the measurements, in an appropriate norm, which shows exponential convergence up to zero.

• 2020-11-01

Erd\H os-Ko-Rado type theorems for simplicial complexes via algebraic shifting

Younjin Kim

Abstract : In 2009, Borg~\cite{BORG13} suggested a conjecture concerning the size of a $t$-intersecting $k$-uniform family of faces of an arbitrary simplicial complex. In this paper, we give a strengthening of Borg's conjecture for shifted simplicial complexes using algebraic shifting.

• 2021-05-01

Corrigendum to A dual iterative substructuring method with a small penalty parameter'', [J. Korean Math. Soc. 54 (2017), No. 2, 461--477]

Chang-Ock Lee, Eun-Hee Park, Jongho Park

Abstract : In this corrigendum, we offer a correction to~[J. Korean Math. Soc. 54 (2017), No. 2, 461--477]. We construct a counterexample for the strengthened Cauchy--Schwarz inequality used in the original paper. In addition, we provide a new proof for Lemma~5 of the original paper, an estimate for the extremal eigenvalues of the standard unpreconditioned FETI-DP dual operator.

• 2021-01-01

Weak convergence for stationary bootstrap empirical processes of associated sequences

Eunju Hwang

Abstract : In this work the stationary bootstrap of Politis and Romano \cite{PR1994a} is applied to the empirical distribution function of stationary and associated random variables. A weak convergence theorem for the stationary bootstrap empirical processes of associated sequences is established with its limiting to a Gaussian process almost surely, conditionally on the stationary observations. The weak convergence result is proved by means of a random central limit theorem on geometrically distributed random block size of the stationary bootstrap procedure. As its statistical applications, stationary bootstrap quantiles and stationary bootstrap mean residual life process are discussed. Our results extend the existing ones of Peligrad \cite{P1998} who dealt with the weak convergence of non-random blockwise empirical processes of associated sequences as well as of Shao and Yu \cite{SY1996} who obtained the weak convergence of the mean residual life process in reliability theory as an application of the association.

• 2020-07-01

Radii problems for the generalized Mittag-Leffler functions

Anuja Prajapati

Abstract : In this paper our aim is to find various radii problems of the generalized Mittag-Leffler function for three different kinds of normalization by using their Hadamard factorization in such a way that the resulting functions are analytic. The basic tool of this study is the Mittag-Leffler function in series. Also we have shown that the obtained radii are the smallest positive roots of some functional equations.

• 2021-11-01

Symmetric and pseudo-symmetric numerical semigroups via Young diagrams and their semigroup rings

Meral Suer, Mehmet Yesil

Abstract : This paper studies Young diagrams of symmetric and pseudo-symmetric numerical semigroups and describes new operations on Young diagrams as well as numerical semigroups. These provide new decompositions of symmetric and pseudo-symmetric semigroups into a numerical semigroup and its dual. It is also given exactly for what kind of numerical semigroup $S$, the semigroup ring ${\mathbb k}[\![S]\!]$ has at least one Gorenstein subring and has at least one Kunz subring.

• 2021-11-01

Bergman type operators on some generalized Cartan-Hartogs domains

Le He, Yanyan Tang, Zhenhan Tu

Abstract : For $\mu=(\mu_1,\dots,\mu_t)$ ($\mu_j>0$), $\xi=(z_1,\dots,z_t,w)\in \mathbb{C}^{n_1}\times\cdots\times \mathbb{C}^{n_t}\times \mathbb{C}^m$, define \Omega(\mu,t)\!=\!\big\{\xi\in\mathbb{B}_{n_1}\times\cdots\times\mathbb{B}_{n_t}\times\mathbb{C}^{m}: \|w\|^2

• 2021-09-01

On semilocal Klein-Gordon-Maxwell equations

Jongmin Han, Juhee Sohn, Yeong Seok Yoo

Abstract : In this article, we study the Klein-Gordon-Maxwell equations arising from a semilocal gauge field model. This model describes the interaction of two complex scalar fields and one gauge field, and generalizes the classical Klein-Gordon equation coupled with the Maxwell electrodynamics. We prove that there exist infinitely many standing wave solutions for $p\in (2,6)$ which are radially symmetric. Here, $p$ comes from the exponent of the potential of scalar fields. We also prove the nonexistence of nontrivial solutions for the critical case $p=6$.

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