Journal of the
Korean Mathematical Society

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

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  • 2022-07-01

    Finite $p$-groups whose normal closures of non-normal subgroups have two orders

    Lifang Wang

    Abstract : We describe the structure of finite $p$-groups in which all normal closures of non-normal subgroups have two orders for $p>2$.

  • 2022-09-01

    Bailey pairs and strange identities

    Jeremy Lovejoy

    Abstract : Zagier introduced the term ``strange identity" to describe an asymptotic relation between a certain $q$-hypergeometric series and a partial theta function at roots of unity. We show that behind Zagier's strange identity lies a statement about Bailey pairs. Using the iterative machinery of Bailey pairs then leads to many families of multisum strange identities, including Hikami's generalization of Zagier's identity.

  • 2022-09-01

    New congruences for $\ell$-regular overpartitions

    Ankita Jindal, Nabin K. Meher

    Abstract : For a positive integer $\ell$, $\overline{A}_{\ell}(n)$ denotes the number of overpartitions of $n$ into parts not divisible by $\ell$. In this article, we find certain Ramanujan-type congruences for $\overline{A}_{ r \ell}(n)$, when $r\in\{8, 9\}$ and we deduce infinite families of congruences for them. Furthermore, we also obtain Ramanujan-type congruences for $\overline{A}_{ 13}(n)$ by using an algorithm developed by Radu and Sellers [15].

  • 2023-09-01

    Continuum-wise expansiveness for $C^1$ generic vector fields

    Manseob Lee

    Abstract : It is shown that every continuum-wise expansive $C^1$ generic vector field $X$ on a compact connected smooth manifold $M$ satisfies Axiom A and has no cycles, and every continuum-wise expansive homoclinic class of a $C^1$ generic vector field $X$ on a compact connected smooth manifold $M$ is hyperbolic. Moreover, every continuum-wise expansive $C^1$ generic divergence-free vector field $X$ on a compact connected smooth manifold $M$ is Anosov.

  • 2022-11-01

    The Difference of Hyperharmonic Numbers via Geometric and Analytic Methods

    \c{C}a\u{g}atay Altunta\c{s} , Haydar G\"{o}ral, Do\u{g}a Can Sertba\c{s}

    Abstract : Our motivation in this note is to find equal hyperharmonic numbers of different orders. In particular, we deal with the integerness property of the difference of hyperharmonic numbers. Inspired by finiteness results from arithmetic geometry, we see that, under some extra assumption, there are only finitely many pairs of orders for two hyperharmonic numbers of fixed indices to have a certain rational difference. Moreover, using analytic techniques, we get that almost all differences are not integers. On the contrary, we also obtain that there are infinitely many order values where the corresponding differences are integers.

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  • 2023-07-01

    Generalized hexagons embedded in metasymplectic spaces

    Sebastian Petit, Hendrik Van Maldeghem

    Abstract : We consider thick generalized hexagons fully embedded in metasymplectic spaces, and we show that such an embedding either happens in a point residue (giving rise to a full embedding inside a dual polar space of rank 3), or happens inside a symplecton (giving rise to a full embedding in a polar space of rank 3), or is isometric (that is, point pairs of the hexagon have the same mutual position whether viewed in the hexagon or in the metasymplectic space--these mutual positions are \emph{equality, collinearity, being special, opposition}). In the isometric case, we show that the hexagon is always a Moufang hexagon, its little projective group is induced by the collineation group of the metasymplectic space, and the metasymplectic space itself admits central collineations (hence, in symbols, it is of type $\mathsf{F_{4,1}}$). We allow non-thick metasymplectic spaces without non-thick lines and obtain a full classification of the isometric embeddings in this case.

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  • 2022-05-01

    Construction of a solution of split equality variational inequality problem for pseudomonotone mappings in Banach spaces

    Getahun Bekele Wega

    Abstract : The purpose of this paper is to introduce an iterative algorithm for approximating a solution of split equality variational inequality problem for pseudomonotone mappings in the setting of Banach spaces. Under certain conditions, we prove a strong convergence theorem for the iterative scheme produced by the method in real reflexive Banach spaces. The assumption that the mappings are uniformly continuous and sequentially weakly continuous on bounded subsets of Banach spaces are dispensed with. In addition, we present an application of our main results to find solutions of split equality minimum point problems for convex functions in real reflexive Banach spaces. Finally, we provide a numerical example which supports our main result. Our results improve and generalize many of the results in the literature.

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  • 2023-05-01

    Two-sided estimates for transition probabilities of symmetric Markov chains on ${ \mathbb{Z} }^d$

    Zhi-He Chen

    Abstract : In this paper, we are mainly concerned with two-sided estimates for transition probabilities of symmetric Markov chains on ${ \mathbb{Z}  }^d$, whose one-step transition probability is comparable to $|x-y|^{-d}\phi_j(|x-y|)^{-1}$ with $\phi_j$ being a positive regularly varying function on $[1,\infty)$ with index $\alpha\in [2,\infty)$. For upper bounds, we directly apply the comparison idea and the Davies method, which considerably improves the existing arguments in the literature; while for lower bounds the relation with the corresponding continuous time symmetric Markov chains are fully used. In particular, our results answer one open question mentioned in the paper by Murugan and Saloff-Coste (2015).

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  • 2022-07-01

    A note on the zeros of Jensen polynomials

    Young-One Kim, Jungseob Lee

    Abstract : Sufficient conditions for the Jensen polynomials of the derivatives of a real entire function to be hyperbolic are obtained. The conditions are given in terms of the growth rate and zero distribution of the function. As a consequence some recent results on Jensen polynomials, relevant to the Riemann hypothesis, are extended and improved.

  • 2023-07-01

    Preresolving subcategories in extriangulated categories

    Songsong Liu, Jiaqun Wei

    Abstract : In this paper, we introduce and study preresolving subcategories in an extriangulated category~$\mathscr{C}$. Let $\mathcal{Y}$ be a $\mathcal{Z}$-preresolving subcategory of $\mathscr{C}$ admitting a $\mathcal{Z}$-proper $\xi$-generator $\mathcal{X}$. We give the characterization of $\mathcal{Z}\text{-}{\rm proper}~\mathcal{Y}$-resolution dimension of an object in $\mathscr{C}$. Next, for an object $A$ in $\mathscr{C}$, if the $\mathcal{Z}\text{-}{\rm proper}~\mathcal{Y}$-resolution~dimension of $A$ is at most $n$, then all ``$n$-$\mathcal{X}$-syzygies" of $A$ are objects in $\mathcal{Y}$. Finally, we prove that $A$ has a $\mathcal{Z}$-proper $\mathcal{X}$-resolution if and only if $A$ has a $\mathcal{Z}$-proper $\mathcal{Y}$-resolution. As an application, we introduce $(\mathcal{X},\mathcal{Z})$-Gorenstein~subcategory $\mathcal{GX}_{\mathcal{Z}}(\xi)$ of $\mathscr{C}$ and prove that $\mathcal{GX}_{\mathcal{Z}}(\xi)$ is both $\mathcal{Z}$-resolving subcategory and $\mathcal{Z}$-coresolving subcategory of $\mathscr{C}$.

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Current Issue

November, 2023
Vol.60 No.6

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