Communications of the
Korean Mathematical Society
CKMS

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

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  • 2022-07-31

    A note on maximal hypersurfaces in a generalized Robertson-Walker spacetime

    Henrique Fernandes de~Lima

    Abstract : In this note, we apply a maximum principle related to vo-lu-me growth of a complete noncompact Riemannian manifold, which was recently obtained by Al'{i}as, Caminha and do Nascimento in~cite{Alias-Caminha-Nascimento}, to es-ta-blish new uniqueness and nonexistence results concerning maximal spacelike hypersurfaces immersed in a generalized Robertson-Walker (GRW) spacetime obeying the timelike convergence condition. A study of entire solutions for the maximal hypersurface equation in GRW spacetimes is also made and, in particular, a new Calabi-Bernstein type result is presented.

  • 2023-10-31

    Formulas and relations for Bernoulli-type numbers and polynomials derive from Bessel function

    Selin Selen OZBEK SIMSEK, Yilmaz SIMSEK

    Abstract : The main purpose of this paper is to give some new identities and properties related to Bernoulli type numbers and polynomials associated with the Bessel function of the first kind. We give symmetric properties of the Bernoulli type numbers and polynomials. Moreover, using generating functions and the Fa \`{a} di Bruno's formula, we derive some new formulas and relations related to not only these polynomials, but also the Bernoulli numbers and polynomials and the Euler numbers and polynomials.

  • 2023-07-31

    Results concerning semi-symmetric metric $F$-connections on the Hsu-$B$ manifolds

    Uday Chand De, Aydin Gezer, Cagri Karaman

    Abstract : In this paper, we firstly construct a Hsu-$B$ manifold and give some basic results related to it. Then, we address a semi-symmetric metric $F$-connection on the Hsu-$B$ manifold and obtain the curvature tensor fields of such connection, and study properties of its curvature tensor and torsion tensor fields.

  • 2023-04-30

    A note on statistical manifolds with torsion

    Hwajeong Kim

    Abstract : Given a linear connection $\nabla$ and its dual connection $\nabla^*$, we discuss the situation where $\nabla +\nabla^* = 0$. We also discuss statistical manifolds with torsion and give new examples of some type for linear connections inducing the statistical manifolds with non-zero torsion.

  • 2023-04-30

    Singular and Marcinkiewicz integral operators on product domains

    Badriya Al-Azri, Ahmad Al-Salman

    Abstract : In this paper, we prove $L^{p}$ estimates of a class of singular integral operators on product domains along surfaces defined by mappings that are more general than polynomials and convex functions. We assume that the kernels are in $L(\log L)^{2}(\mathbb{S}^{n-1}\times \mathbb{S}^{m-1})$. Furthermore, we\ prove $L^{p}$ estimates of the related class of Marcinkiewicz integral operators. Our results extend as well as improve previously known results.

  • 2023-10-31

    Space of homeomorphisms under regular topology

    Mir Aaliya, Sanjay Mishra

    Abstract : In this paper, we attempt to study several topological properties for the function space ${H(X)}$, space of self-homeomorphisms on a metric space endowed with the regular topology. We investigate its metrizability and countability and prove their coincidence at $X$ compact. Furthermore, we prove that the space ${H(X)}$ endowed with the regular topology is a topological group when $X$ is a metric, almost $P$-space. Moreover, we prove that the homeomorphism spaces of increasing and decreasing functions on $\mathbb R$ under regular topology are open subspaces of $H(\mathbb R)$ and are homeomorphic.

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  • 2023-01-31

    Ricci $\rho$-soliton in a perfect fluid spacetime with a gradient vector field

    Dibakar Dey, Pradip Majhi

    Abstract : In this paper, we studied several geometrical aspects of a perfect fluid spacetime admitting a Ricci $\rho$-soliton and an $\eta$-Ricci $\rho$-soliton. Beside this, we consider the velocity vector of the perfect fluid space time as a gradient vector and obtain some Poisson equations satisfied by the potential function of the gradient solitons.

  • 2024-01-31

    On strongly quasi $J$-ideals of commutative rings

    El Mehdi Bouba , Yassine EL-khabchi, Mohammed Tamekkante

    Abstract : Let $R$ be a commutative ring with identity. In this paper, we introduce a new class of ideals called the class of strongly quasi $J$-ideals lying properly between the class of $J$-ideals and the class of quasi $J$-ideals. A proper ideal $I$ of $R$ is called a strongly quasi $J$-ideal if, whenever $a$, $b\in R$ and $ab\in I$, then $a^{2}\in I$ or $b\in {\rm Jac}(R)$. Firstly, we investigate some basic properties of strongly quasi $J$-ideals. Hence, we give the necessary and sufficient conditions for a ring $R$ to contain a strongly quasi $J$-ideals. Many other results are given to disclose the relations between this new concept and others that already exist. Namely, the primary ideals, the prime ideals and the maximal ideals. Finally, we give an idea about some strongly quasi $J$-ideals of the quotient rings, the localization of rings, the polynomial rings and the trivial rings extensions.

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  • 2023-07-31

    Fractional integration and differentiation of the $(p,q)$--extended modified Bessel function of the second kind and integral transforms

    Purnima Chopra, Mamta Gupta, Kanak Modi

    Abstract : Our aim is to establish certain image formulas of the $(p,q)$--extended modified Bessel function of the second kind $M_{\nu,p,q} (z)$ by employing the Marichev-Saigo-Maeda fractional calculus (integral and differential) operators including their composition formulas and using certain integral transforms involving $(p,q)$--extended modified Bessel function of the second kind $M_{\nu,p,q} (z)$. Corresponding assertions for the Saigo's, Riemann-Liouville (R-L) and Erd\'elyi-Kober (E-K) fractional integral and differential operators are deduced. All the results are represented in terms of the Hadamard product of the $(p,q)$--extended modified Bessel function of the second kind $M_{\nu,p,q} (z)$ and Fox-Wright function $_{r}\Psi_{s}(z)$.

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  • 2023-07-31

    Existence and nonexistence of solutions for a class of Hamiltonian strongly degenerate elliptic system

    Nguyen Viet Tuan

    Abstract : In this paper, we study the existence and nonexistence of solutions for a class of Hamiltonian strongly degenerate elliptic system with subcritical growth \begin{equation*} \begin{cases} -\Delta_\lambda u -\mu v =|v|^{p-1}v &\;\text{ in } \Omega,\\ -\Delta_\lambda v -\mu u=|u|^{q-1}u &\;\text{ in } \Omega,\\ u = v = 0 &\;\text{ on } \partial\Omega, \end{cases} \end{equation*} where $p, q>1$ and $\Omega$ is a smooth bounded domain in $\mathbb{R}^N$, $N\ge 3$. Here $\Delta_\lambda$ is the strongly degenerate elliptic operator. The existence of at least a nontrivial solution is obtained by variational methods while the nonexistence of positive solutions are proven by a contradiction argument.

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April, 2024
Vol.39 No.2

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