Communications of the
Korean Mathematical Society

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

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  • 2022-04-30

    Some results on $S$-accr pairs

    Ahmed Hamed, Achraf Malek

    Abstract : Let $Rsubseteq T$ be an extension of a commutative ring and $Ssubseteq R$ a multiplicative subset. We say that $(R, T)$ is an $S$-accr (a commutative ring $R$ is said to be $S$-accr if every ascending chain of residuals of the form $(I:B)subseteq (I:B^2)subseteq (I:B^3)subseteqcdots$ is $S$-stationary, where $I$ is an ideal of $R$ and $B$ is a finitely generated ideal of $R$) pair if every ring $A$ with $Rsubseteq Asubseteq T$ satisfies $S$-accr. Using this concept, we give an $S$-version of several different known results.

  • 2022-01-31

    Generalized isometry in normed spaces

    Abbas Zivari-Kazempour

    Abstract : Let $g:Xlongrightarrow Y$ and $f:Ylongrightarrow Z$ be two maps between real normed linear spaces. Then $f$ is called generalized isometry or $g$-isometry if for each $x,y in X$, $$ Vert f(g(x))-f(g(y))Vert=Vert g(x)-g(y)Vert. $$ In this paper, under special hypotheses, we prove that each generalized isometry is affine. Some examples of generalized isometry are given as well.

  • 2022-01-31

    Rings in which every ideal contained in the set of zero-divisors is a d-ideal

    Adam Anebri, Najib Mahdou, Abdeslam Mimouni

    Abstract : In this paper, we introduce and study the class of rings in which every ideal consisting entirely of zero divisors is a d-ideal, considered as a generalization of strongly duo rings. Some results including the characterization of AA-rings are given in the first section. Further, we examine the stability of these rings in localization and study the possible transfer to direct product and trivial ring extension. In addition, we define the class of $d_E$-ideals which allows us to characterize von Neumann regular rings.

  • 2022-01-31

    New generalization of the Wright series in two variables and its properties

    Abdelmajid Belafhal, Salma Chib, Talha Usman

    Abstract : The main aim of this paper is to introduce a new generalization of the Wright series in two variables, which is expressed in terms of Hermite polynomials. The properties of the freshly defined function involving its auxiliary functions and the integral representations are established. Furthermore, a Gauss-Hermite quadrature and Gaussian quadrature formulas have been established to evaluate some integral representations of our main results and compare them with our theoretical evaluations using graphical simulations.

  • 2022-10-31

    Notes on $(LCS)_n$-manifolds satisfying certain conditions

    Shyam Kishor, Pushpendra Verma

    Abstract : The object of the present paper is to study the properties of conharmonically flat $(LCS)_n$-manifold, special weakly Ricci symmetric and generalized Ricci recurrent $(LCS)_n$-manifold. The existence of such a manifold is ensured by non-trivial example.

  • 2023-10-31

    Equality in degrees of compactness: Schauder's theorem and $s$-numbers

    Asuman Guven Aksoy, Daniel Akech Thiong

    Abstract : We investigate an extension of Schauder's theorem by studying the relationship between various $s$-numbers of an operator $T$ and its adjoint $T^*$. We have three main results. First, we present a new proof that the approximation number of $T$ and $T^*$ are equal for compact operators. Second, for non-compact, bounded linear operators from $X$ to $Y$, we obtain a relationship between certain $s$-numbers of $T$ and $T^*$ under natural conditions on $X$ and $Y$. Lastly, for non-compact operators that are compact with respect to certain approximation schemes, we prove results for comparing the degree of compactness of $T$ with that of its adjoint $T^*$.

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  • 2022-07-31

    A characterization of finite factorization positive monoids

    Harold Polo

    Abstract : We provide a characterization of the emph{positive monoids} (i.e., additive submonoids of the nonnegative real numbers) that satisfy the finite factorization property. As a result, we establish that positive monoids with well-ordered generating sets satisfy the finite factorization property, while positive monoids with co-well-ordered generating sets satisfy this property if and only if they satisfy the bounded factorization property.

  • 2022-01-31

    Rational homotopy type of mapping spaces between complex projective spaces and their evaluation subgroups

    Jean-Baptiste Gatsinzi

    Abstract : We use $L_{infty}$ models to compute the rational homotopy type of the mapping space of the component of the natural inclusion $i_{n,k}: mathbb{C}P^n hookrightarrow mathbb{C}P^{n+k}$ between complex projective spaces and show that it has the rational homotopy type of a product of odd dimensional spheres and a complex projective space. We also characterize the mapping $ aut_1 mathbb{C}P^n ightarrow map ( mathbb{C}P^n, mathbb{C}P^{n+k}; i_{n,k}) $ and the resulting $G$-sequence.

  • 2022-07-31

    Infinitely many homoclinic solutions for damped vibration systems with locally defined potentials

    Wafa Selmi, Mohsen Timoumi

    Abstract : In this paper, we are concerned with the existence of infinitely many fast homoclinic solutions for the following damped vibration system $$ddot{u}(t)+q(t)dot{u}(t)-L(t)u(t)+ abla W(t,u(t))=0, forall tinmathbb{R}, leqno(1)$$ where $qin C(mathbb{R},mathbb{R})$, $Lin C(mathbb{R},mathbb{R}^{N^{2}})$ is a symmetric and positive definite matix-valued function and $Win C^{1}(mathbb{R} imesmathbb{R}^{N},mathbb{R})$. The novelty of this paper is that, assuming that $L$ is bounded from below unnecessarily coercive at infinity, and $W$ is only locally defined near the origin with respect to the second variable, we show that $(1)$ possesses infinitely many homoclinic solutions via a variant symmetric mountain pass theorem.

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  • 2022-10-31

    On functions starlike with respect to $n$-ply symmetric, conjugate and symmetric conjugate points

    Somya Malik, Vaithiyanathan Ravichandran

    Abstract : For given non-negative real numbers $\alpha_k$ with $ \sum_{k=1}^{m}\alpha_k =1$ and normalized analytic functions $f_k$, $k=1,\dotsc,m$, defined on the open unit disc, let the functions $F$ and $F_n$ be defined by $ F(z):=\sum_{k=1}^{m}\alpha_k f_k (z)$, and $F_{n}(z):=n^{-1}\sum_{j=0}^{n-1} e^{-2j\pi i/n} F(e^{2j\pi i/n} z)$. This paper studies the functions $f_k$ satisfying the subordination $zf'_{k} (z)/F_{n} (z) \prec h(z)$, where the function $h$ is a convex univalent function with positive real part. We also consider the analogues of the classes of starlike functions with respect to symmetric, conjugate, and symmetric conjugate points. Inclusion and convolution results are proved for these and related classes. Our classes generalize several well-known classes and the connections with the previous works are indicated.

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October, 2023
Vol.38 No.4

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