Communications of the
Korean Mathematical Society
CKMS
ISSN(Print) 1225-1763
ISSN(Online) 2234-3024
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2022-04-30
Some results on $S$-accr pairs
Ahmed Hamed, Achraf MalekAbstract : 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.
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2022-01-31
Generalized isometry in normed spaces
Abbas Zivari-KazempourAbstract : 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.
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2022-01-31
Rings in which every ideal contained in the set of zero-divisors is a d-ideal
Adam Anebri, Najib Mahdou, Abdeslam MimouniAbstract : 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.
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2022-01-31
New generalization of the Wright series in two variables and its properties
Abdelmajid Belafhal, Salma Chib, Talha UsmanAbstract : 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.
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2022-10-31
Notes on $(LCS)_n$-manifolds satisfying certain conditions
Shyam Kishor, Pushpendra VermaAbstract : 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.
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2023-10-31
Equality in degrees of compactness: Schauder's theorem and $s$-numbers
Asuman Guven Aksoy, Daniel Akech ThiongAbstract : 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 PoloAbstract : 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.
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2022-01-31
Rational homotopy type of mapping spaces between complex projective spaces and their evaluation subgroups
Jean-Baptiste GatsinziAbstract : 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.
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2022-07-31
Infinitely many homoclinic solutions for damped vibration systems with locally defined potentials
Wafa Selmi, Mohsen TimoumiAbstract : 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 RavichandranAbstract : 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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Geometric properties on $(j,k)$-symmetric functions related to starlike and convex function
Priyabrat Gochhayat, Anuja Prajapati
Commun. Korean Math. Soc. 2022; 37(2): 455-472
https://doi.org/10.4134/CKMS.c210072 -
Co-uniform and hollow $S$-acts over monoids
Roghaieh Khosravi, Mohammad Roueentan
Commun. Korean Math. Soc. 2022; 37(2): 347-358
https://doi.org/10.4134/CKMS.c210114 -
Decompositions of graded maximal submodules
Fida Moh'd
Commun. Korean Math. Soc. 2022; 37(1): 1-15
https://doi.org/10.4134/CKMS.c200428 -
A translation of an analogue of Wiener space with its applications on their product spaces
Dong Hyun Cho
Commun. Korean Math. Soc. 2022; 37(3): 749-763
https://doi.org/10.4134/CKMS.c210264
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S-coherent property in trivial extension and in amalgamated duplication
MOHAMED CHHITI, SALAH EDDINE MAHDOU
Commun. Korean Math. Soc. 2023; 38(3): 705-714
https://doi.org/10.4134/CKMS.c220260 -
Oriented transformations on a finite chain: another description
Vítor Hugo Fernandes
Commun. Korean Math. Soc. 2023; 38(3): 725-731
https://doi.org/10.4134/CKMS.c220272 -
Jordan $\mathcal{G}_n$-derivations on path algebras
Abderrahim Adrabi, Driss Bennis, Brahim Fahid
Commun. Korean Math. Soc. 2022; 37(4): 957-967
https://doi.org/10.4134/CKMS.c210346 -
A note on defectless extensions of henselian valued fields
Azadeh Nikseresht
Commun. Korean Math. Soc. 2022; 37(1): 65-74
https://doi.org/10.4134/CKMS.c210016
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