Communications of the
Korean Mathematical Society

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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  • 2022-04-30

    Subclasses of analytic functions defined by Lommel operator

    c{S}ahsene Altinkaya, Rizwan Salim Badar, Khalida Inayat Noor

    Abstract : We use convolution techniques to define certain classes of starlike functions which are associated with Lommel operator. Some inclusion results are investigated. It is also shown that these classes are invariant under Bernardi integral operator.

  • 2022-10-31

    Riemannian submersions whose total space is endowed with a torse-forming vector field

    \c{S}emsi Eken~Meri\c{c}, Erol K{\i}l{\i}\c{c}

    Abstract : In the present paper, a Riemannian submersion $\pi$ between Riemannian manifolds such that the total space of $\pi$ endowed with a torse-forming vector field $\nu$ is studied. Some remarkable results of such a submersion whose total space is Ricci soliton are given. Moreover, some characterizations about any fiber of $\pi$ or the base manifold $B$ to be an almost quasi-Einstein are obtained.

  • 2022-07-31

    Semi-neutral groupoids and $BCK$-algebras

    Hee Sik Kim, Joseph Neggers, Young Joo Seo

    Abstract : In this paper, we introduce the notion of a left-almost-zero groupoid, and we generalize two axioms which play important roles in the theory of $BCK$-algebra using the notion of a projection. Moreover, we investigate a Smarandache disjointness of semi-leftoids.

  • 2022-01-31

    $mu$-countably compactness and $mumathcal{H}$-countably compactness

    Zuhier Altawallbeh, Ibrahim Jawarneh

    Abstract : We define and study the notion of $mu$-countably compact linebreak spaces in generalized topology and $mumathcal{H}$-countably compact spaces which are considered with respect to a hereditary class $mathcal{H}$. Some interesting properties and relations are provided in the paper. Moreover, some preservation of functions properties are studied and investigated.

  • 2022-10-31

    Circle approximation using parametric polynomial curves of high degree in explicit form

    Young Joon Ahn

    Abstract : In this paper we present a full circle approximation method using parametric polynomial curves with algebraic coefficients which are curvature continuous at both endpoints. Our method yields the $n$-th degree parametric polynomial curves which have a total number of $2n$ contacts with the full circle at both endpoints and the midpoint. The parametric polynomial approximants have algebraic coefficients involving rational numbers and radicals for degree higher than four. We obtain the exact Hausdorff distances between the circle and the approximation curves.

  • 2023-07-31

    Local-global principle and generalized local cohomology modules

    Bui Thi Hong Cam, Nguyen Minh Tri, Do Ngoc Yen

    Abstract : Let $\mathcal{M}$ be a stable Serre subcategory of the category of $R$-modules. We introduce the concept of $\mathcal{M}$-minimax $R$-modules and investigate the local-global principle for generalized local cohomology modules that concerns to the $\mathcal{M}$-minimaxness. We also provide the $\mathcal{M}$-finiteness dimension $f^{\mathcal{M}}_I(M,N)$ of $M,N$ relative to $I$ which is an extension the finiteness dimension $f_I(N)$ of a finitely generated $R$-module $N$ relative to $I$.

  • 2022-04-30

    A note on static manifolds and almost Ricci solitons

    Reihaneh Ahmadzadeh, Hajar Ghahremani-Gol

    Abstract : In this short paper, we investigate the existence of non-trivial almost Ricci solitones on static manifolds. As a result we show any compact nontrivial static manifold is isometric to a Euclidean sphere.

  • 2023-07-31

    On nonnil-SFT rings

    Ali Benhissi, Abdelamir Dabbabi

    Abstract : The purpose of this paper is to introduce a new class of rings containing the class of SFT-rings and contained in the class of rings with Noetherian prime spectrum. Let $A$ be a commutative ring with unit and $I$ be an ideal of $A$. We say that $I$ is SFT if there exist an integer $k\geq 1$ and a finitely generated ideal $F\subseteq I$ of $A$ such that $x^k\in F$ for every $x\in I$. The ring $A$ is said to be nonnil-SFT, if each nonnil-ideal (i.e., not contained in the nilradical of $A$) is SFT. We investigate the nonnil-SFT variant of some well known theorems on SFT-rings. Also we study the transfer of this property to Nagata's idealization and the amalgamation algebra along an ideal. Many examples are given. In fact, using the amalgamation construction, we give an infinite family of nonnil-SFT rings which are not SFT.

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  • 2023-04-30

    Results associated with the Schwarz lemma on the boundary

    B\"{u}lent Nafi \"{O}rnek

    Abstract : In this paper, some estimations will be given for the analytic functions belonging to the class $\mathcal{R}\left( \alpha \right) $. In these estimations, an upper bound and a lower bound will be determined for the first coefficient of the expansion of the analytic function $h(z)$ and the modulus of the angular derivative of the function $\frac{zh^{\prime }(z)}{ h(z)}$, respectively. Also, the relationship between the coefficients of the analytical function $h(z)$ and the derivative mentioned above will be shown.

  • 2023-01-31

    On lightlike hypersurfaces of cosymplectic space form

    Ejaz Sabir Lone, Pankaj Pandey

    Abstract : The main purpose of this paper is to study the lightlike hypersurface $(M,\bar{g})$ of cosymplectic space form $\bar{M}(c)$. In this paper, we computed the Gauss and Codazzi formulae of $(M,\bar{g})$ of cosymplectic manifold $(\bar{M},g)$. We showed that we can't obtain screen semi-invariant lightlike hypersurface (SCI-LH) of $\bar{M}(c)$ with parallel second fundamental form $h$, parallel screen distribution and $c\neq 0$. We showed that if second fundamental form $h$ and local second fundamental form $B$ are parallel, then $(M,\bar{g})$ is totally geodesic. Finally we showed that if $(M,\bar{g})$ is umbilical, then cosymplectic manifold $(\bar{M},g)$ is flat.

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October, 2023
Vol.38 No.4

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