Journal of the
Korean Mathematical Society

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

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  • 2021-05-01

    A finite difference/finite volume method for solving the fractional diffusion wave equation

    Yinan Sun, Tie Zhang

    Abstract : In this paper, we present and analyze a fully discrete numerical method for solving the time-fractional diffusion wave equation: $\partial^\beta_tu-\hbox{div}(a\nabla u)=f$, $1

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  • 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.

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  • 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

    Complete $f$-moment convergence for extended negatively dependent random variables under sub-linear expectations

    Chao Lu, Rui Wang, Xuejun Wang, Yi Wu

    Abstract : In this paper, we investigate the complete $f$-moment convergence for extended negatively dependent (END, for short) random variables under sub-linear expectations. We extend some results on complete $f$-moment convergence from the classical probability space to the sub-linear expectation space. As applications, we present some corollaries on complete moment convergence for END random variables under sub-linear expectations.

  • 2020-11-01

    Existence, multiplicity and regularity of solutions for the fractional $p$-Laplacian equation

    Yun-Ho Kim

    Abstract : We are concerned with the following elliptic equations: \begin{equation*} \begin{cases} (-\Delta)_p^su=\lambda f(x,u) \quad \textmd{in} \ \ \Omega,\\ u= 0\quad \text{on}\ \ \mathbb{R}^N\backslash\Omega, \end{cases} \end{equation*} where $\lambda$ are real parameters, $(-\Delta)_p^s$ is the fractional $p$-Laplacian operator, $0

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  • 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.

  • 2020-07-01

    On the $C$-projective vector fields on Randers spaces

    Mehdi Rafie-Rad, Azadeh Shirafkan

    Abstract : A characterization of the $C$-projective vector fields on a Randers space is presented in terms of ${\bf\Xi}$-curvature. It is proved that the ${\bf\Xi}$-curvature is invariant for $C$-projective vector fields. The dimension of the algebra of the $C$-projective vector fields on an $n$-dimensional Randers space is at most $n(n+2)$. The generalized Funk metrics on the $n$-dimensional Euclidean unit ball $\mathbb{B}^n(1)$ are shown to be explicit examples of the Randers metrics with a $C$-projective algebra of maximum dimension $n(n+2)$. Then, it is also proved that an $n$-dimensional Randers space has a $C$-projective algebra of maximum dimension $n(n+2)$ if and only if it is locally Minkowskian or (up to re-scaling) locally isometric to the generalized Funk metric. A new projective invariant is also introduced.

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  • 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.

  • 2021-07-01

    Prime knots with arc index 12 up to 16 crossings

    Gyo Taek Jin, Hyuntae Kim, Seungwoo Lee, Hun Joo Myung

    Abstract : We obtain the list of prime knots with arc index 12 up to 16 crossings and their minimal grid diagrams. This is a continuation of the works \cite{Jin2006} and \cite{Jin2011} in which Cromwell matrices were generated to obtain minimal grid diagrams of all prime knots up to arc index 11. We provide minimal grid diagrams of the prime alternating knots with arc index 12. They are the 10 crossing prime alternating knots. The full list of 19,513 prime knots of arc index 12 up to 16 crossings and their minimal grid diagrams can be found in the arXiv~\cite{Jin2020}.

  • 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 $H$.

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May, 2022
Vol.59 No.3

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