Communications of the
Korean Mathematical Society
CKMS
ISSN(Print) 1225-1763
ISSN(Online) 2234-3024
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2023-07-31
Generic lightlike submanifolds of semi-Riemannian product manifolds
Nand Kishor Jha, Jatinder Kaur, Sangeet Kumar, Megha PruthiAbstract : We introduce the study of generic lightlike submanifolds of a semi-Riemannian product manifold. We establish a characterization theorem for the induced connection on a generic lightlike submanifold to be a metric connection. We also find some conditions for the integrability of the distributions associated with generic lightlike submanifolds and discuss the geometry of foliations. Then we search for some results enabling a generic lightlike submanifold of a semi-Riemannian product manifold to be a generic lightlike product manifold. Finally, we examine minimal generic lightlike submanifolds of a semi-Riemannian product manifold.
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2023-01-31
Hyperbolic structure of pointwise inverse pseudo-orbit tracing property for $C^1$ diffeomorphisms
Manseob LeeAbstract : We deal with a type of inverse pseudo-orbit tracing property with respect to the class of continuous methods, as suggested and studied by Pilyugin \cite{P1}. In this paper, we consider a continuous method induced through the diffeomorphism of a compact smooth manifold, and using the concept, we proved the following: (i) If a diffeomorphism $f$ of a compact smooth manifold $M$ has the robustly pointwise inverse pseudo-orbit tracing property, $f$ is structurally stable. (ii) For a $C^1$ generic diffeomorphism $f$ of a compact smooth manifold $M$, if $f$ has the pointwise inverse pseudo-orbit tracing property, $f$ is structurally stable. (iii) If a diffeomorphism $f$ has the robustly pointwise inverse pseudo-orbit tracing property around a transitive set $\Lambda$, then $\Lambda$ is hyperbolic for $f$. Finally, (iv) for $C^1$ generically, if a diffeomorphism $f$ has the pointwise inverse pseudo-orbit tracing property around a locally maximal transitive set $\Lambda$, then $\Lambda$ is hyperbolic for $f$. In addition, we investigate cases of volume preserving diffeomorphisms.
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2022-10-31
Another characterization of the norming set of $T\in {\mathcal L}(^2l_{\infty}^2)$
Sung Guen KimAbstract : In this paper we present another characterization of the \linebreak norming set of $T\in {\mathcal L}(^2l_{\infty}^2)$ in terms of $\qopname\relax o{Norm}(T)\cap \Omega$ whose proofs are more systematic than those of Kim \cite{K1}, where $\Omega=\big\{\big((1, 1), (1, 1)\big)$, $\big((1, 1), (1, -1)\big)$, $\big((1, -1), (1, 1)\big)$, $\big((1, -1), (1, -1)\big)\big\}$.
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2023-01-31
Pr\"ufer conditions vs EM conditions
Emad Abuosba, Mariam Al-Azaizeh, Manal GhanemAbstract : In this article we relate the six Pr\"{u}fer conditions with the EM conditions. We use the EM-conditions to prove some cases of equivalence of the six Pr\"{u}fer conditions. We also use the Pr\"{u}fer conditions to answer some open problems concerning EM-rings.
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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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2023-01-31
Terracini loci of codimension $1$ and a criterion for partially symmetric tensors
Edoardo BallicoAbstract : The Terracini $t$-locus of an embedded variety $X\subset \mathbb{P}^r$ is the set of all cardinality $t$ subsets of the smooth part of $X$ at which a certain differential drops rank, i.e., the union of the associated double points is linearly dependent. We give an easy to check criterion to exclude some sets from the Terracini loci. This criterion applies to tensors and partially symmetric tensors. We discuss the non-existence of codimension $1$ Terracini $t$-loci when $t$ is the generic $X$-rank.
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2022-07-31
A robust numerical technique for solving non-linear Volterra integro-differential equations with boundary layer
Firat Cakir, Musa Cakir, Hayriye Guckir~CakirAbstract : In this paper, we study a first-order non-linear singularly perturbed Volterra integro-differential equation (SPVIDE). We discretize the problem by a uniform difference scheme on a Bakhvalov-Shishkin mesh. The scheme is constructed by the method of integral identities with exponential basis functions and integral terms are handled with interpolating quadrature rules with remainder terms. An effective quasi-linearization technique is employed for the algorithm. We establish the error estimates and demonstrate that the scheme on Bakhvalov-Shishkin mesh is $O(N^{-1})$ uniformly convergent, where $N$ is the mesh parameter. The numerical results on a couple of examples are also provided to confirm the theoretical analysis.
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2024-01-31
Conformal Ricci soliton on paracontact metric $(k,\mu)$-manifolds with Schouten-van Kampen connection
PARDIP MANDAL, MOHAMMAD HASAN SHAHID, SARVESH KUMAR YADAVAbstract : The main object of the present paper is to study conformal Ricci soliton on paracontact metric $(k,\mu)$-manifolds with respect to Schouten-van Kampen connection. Further, we obtain the result when paracontact metric $(k,\mu)$-manifolds with respect to Schouten-van Kampen connection satisfying the condition $\overset{\star}{C}(\xi,U)\cdot\overset{\star}{S}=0$. Finally we characterized concircular curvature tensor on paracontact metric $(k,\mu)$-manifolds with respect to Schouten-van Kampen connection.
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2023-10-31
On the rational cohomology of mapping spaces and their realization problem
Abdelhadi ZaimAbstract : Let $f:X\rightarrow Y$ be a map between simply connected CW-complexes of finite type with $X$ finite. In this paper, we prove that the rational cohomology of mapping spaces map$(X,Y;f)$ contains a polynomial algebra over a generator of degree $N$, where $ N= $ max$ \lbrace i, \pi_{i }(Y)\otimes \mathbb{Q}\neq 0 \rbrace$ is an even number. Moreover, we are interested in determining the rational homotopy type of map$\left( \mathbb{S}^{n}, \mathbb{C} P^{m};f\right) $ and we deduce its rational cohomology as a consequence. The paper ends with a brief discussion about the realization problem of mapping spaces.
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2023-10-31
Laplace transform and Hyers-Ulam stability of differential equation for logistic growth in a population model
Ponmana Selvan Arumugam, Ganapathy Gandhi, Saravanan Murugesan, Veerasivaji RamachandranAbstract : In this paper, we prove the Hyers-Ulam stability and Mittag-Leffler-Hyers-Ulam stability of a differential equation of Logistic growth in a population by applying Laplace transforms method.
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A characterization of finite factorization positive monoids
Harold Polo
Commun. Korean Math. Soc. 2022; 37(3): 669-679
https://doi.org/10.4134/CKMS.c210270 -
Notes on $(LCS)_n$-manifolds satisfying certain conditions
Shyam Kishor, Pushpendra Verma
Commun. Korean Math. Soc. 2022; 37(4): 1171-1180
https://doi.org/10.4134/CKMS.c210172 -
Semi-neutral groupoids and $BCK$-algebras
Hee Sik Kim, Joseph Neggers, Young Joo Seo
Commun. Korean Math. Soc. 2022; 37(3): 649-658
https://doi.org/10.4134/CKMS.c210236 -
Estimates for certain shifted convolution sums involving Hecke eigenvalues
Guodong Hua
Commun. Korean Math. Soc. 2023; 38(2): 319-330
https://doi.org/10.4134/CKMS.c210366
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Geometry of generalized Berger-type deformed metric on $B$-manifold
ABDERRAHIM ZAGANE
Commun. Korean Math. Soc. 2023; 38(4): 1281-1298
https://doi.org/10.4134/CKMS.c230049 -
Nonnil-$S$-coherent rings
Najib Mahdou, El Houssaine Oubouhou
Commun. Korean Math. Soc. 2024; 39(1): 45-58
https://doi.org/10.4134/CKMS.c230065 -
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 -
Spacetimes admitting divergence free $m$-projective curvature tensor
Uday Chand De, Dipankar Hazra
Commun. Korean Math. Soc. 2024; 39(1): 201-210
https://doi.org/10.4134/CKMS.c230105
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