Journal of the
Korean Mathematical Society

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

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  • 2021-07-01

    Even $2$-universal quadratic forms of rank $5$

    Yun-Seong Ji, Myeong Jae Kim, Byeong-Kweon Oh

    Abstract : A (positive definite integral) quadratic form is called {\it even $2$-universal} if it represents all even quadratic forms of rank $2$. In this article, we prove that there are at most $55$ even $2$-universal even quadratic forms of rank $5$. The proofs of even $2$-universalities of some candidates will be given so that exactly $20$ candidates remain unproven.

  • 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

    Positively expansive maps and the limit shadowing properties

    Kazuhiro Sakai

    Abstract : In this paper, the notion of two-sided limit shadowing property is considered for a positively expansive open map. More precisely, let $f$ be a positively expansive open map of a compact metric space $X$. It is proved that if $f$ is topologically mixing, then it has the two-sided limit shadowing property. As a corollary, we have that if $X$ is connected, then the notions of the two-sided limit shadowing property and the average-shadowing property are equivalent.

  • 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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  • 2020-09-01

    Examples of simply reducible groups

    Yongzhi Luan

    Abstract : Simply reducible groups are important in physics and chemistry, which contain some of the important groups in condensed matter physics and crystal symmetry. By studying the group structures and irreducible representations, we find some new examples of simply reducible groups, namely, dihedral groups, some point groups, some dicyclic groups, generalized quaternion groups, Heisenberg groups over prime field of characteristic $2$, some Clifford groups, and some Coxeter groups. We give the precise decompositions of product of irreducible characters of dihedral groups, Heisenberg groups, and some Coxeter groups, giving the Clebsch-Gordan coefficients for these groups. To verify some of our results, we use the computer algebra systems GAP and SAGE to construct and get the character tables of some examples.

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  • 2020-07-01

  • 2020-07-01

    Interpolation of surfaces with geodesics

    Hyun Chol Lee, Jae Won Lee, Dae Won Yoon

    Abstract : In this paper, we introduce a new method to construct a parametric surface in terms of curves and points lying on Euclidean 3-space, called a $C^0$-Hermite surface interpolation. We also prove the existence of a $C^0$-Hermite interpolation of isoparametric surfaces with the so-called marching scale functions, and give some examples. Finally, we construct ruled surfaces and surfaces foliated by a circle as an isoparametric surface.

  • 2020-07-01

    Infinitely many solutions for fractional Schr\"odinger equation with superquadratic conditions or combined nonlinearities

    Mohsen Timoumi

    Abstract : We obtain infinitely many solutions for a class of fractional Schr\"odinger equation, where the nonlinearity is superquadratic or involves a combination of superquadratic and subquadratic terms at infinity. By using some weaker conditions, our results extend and improve some existing results in the literature.

  • 2021-11-01

    Curves orthogonal to a vector field in Euclidean spaces

    Luiz C. B. da~Silva, Gilson S. Ferreira~Jr.

    Abstract : A curve is rectifying if it lies on a moving hyperplane orthogonal to its curvature vector. In this work, we extend the main result of [Chen 2017, Tamkang J. Math. {\bf 48}, 209] to any space dimension: we prove that rectifying curves are geodesics on hypercones. We later use this association to characterize rectifying curves that are also slant helices in three-dimensional space as geodesics of circular cones. In addition, we consider curves that lie on a moving hyperplane normal to (i) one of the normal vector fields of the Frenet frame and to (ii) a rotation minimizing vector field along the curve. The former class is characterized in terms of the constancy of a certain vector field normal to the curve, while the latter contains spherical and plane curves. Finally, we establish a formal mapping between rectifying curves in an $(m+2)$-dimensional space and spherical curves in an $(m+1)$-dimensional space.

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  • 2020-11-01

    A $q$-queens problem V. some of our favorite pieces: queens, bishops, rooks, and nightriders

    Seth Chaiken, Christopher R. H. Hanusa, Thomas Zaslavsky

    Abstract : Parts~I--IV showed that the number of ways to place $q$ nonattacking queens or similar chess pieces on an $n\times n$ chessboard is a quasipolynomial function of $n$ whose coefficients are essentially polynomials in $q$. For partial queens, which have a subset of the queen's moves, we proved complete formulas for these counting quasipolynomials for small numbers of pieces and other formulas for high-order coefficients of the general counting quasipolynomials. We found some upper and lower bounds for the periods of those quasipolynomials by calculating explicit denominators of vertices of the inside-out polytope. Here we discover more about the counting quasipolynomials for partial queens, both familiar and strange, and the nightrider and its subpieces, and we compare our results to the empirical formulas found by \Kot. We prove some of \Kot's formulas and conjectures about the quasipolynomials and their high-order coefficients, and in some instances go beyond them.

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July, 2022
Vol.59 No.4

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