Communications of the
Korean Mathematical Society
CKMS
ISSN(Print) 1225-1763
ISSN(Online) 2234-3024
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2023-04-30
Warped product pseudo-slant submanifolds of a Kenmotsu manifold
Mohammad ShuaibAbstract : For a pseudo-slant submanifold of a Kenmotsu manifold, we have worked out conditions in terms its canonical structure tensors, $T$ and $F$, and its shape operator so that it reduces to a warped product submanifold.
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2024-01-31
3-Hom-Lie superbialgebras and 3-Hom-Lie classical Yang-Baxter equations
Issam Bartouli, Imed Basdouri, Gaith Chaabane, Mohamed Fadous, Jean LerbetAbstract : 3-Lie algebras are in close relationships with many fields. In this paper we are concerned with the study of 3-Hom-Lie super algebras, the concepts of 3-Hom-Lie coalgebras and how they make a 3-Hom-Lie superbialgebras, we study the structures of such categories of algebras and the relationships between each others. We study a super twisted 3-ary version of the Yang-Baxter equation, called the super 3-Lie classical Hom-Yang-Baxter equation (3-Lie CHYBE), which is a general form of 3-Lie classical Yang-Baxter equation and prove that the superbialgebras induced by the solutions of the super 3-Lie CHYBE induce the coboundary local cocycle 3-Hom-Lie superbialgebras.
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2023-07-31
Energy decay for a viscoelastic equation with Balakrishnan-Taylor damping involving infinite memory and nonlinear time-varying delay terms in dynamical boundary
soufiane Benkouider, Abita RahmouneAbstract : In this paper, we study the initial-boundary value problem for viscoelastic wave equations of Kirchhoff type with Balakrishnan--Taylor damping terms in the presence of the infinite memory and external time-varying delay. For a certain class of relaxation functions and certain initial data, we prove that the decay rate of the solution energy is similar to that of relaxation function which is not necessarily of exponential or polynomial type. Also, we show another stability with $g$ satisfying some general growth at infinity.
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2023-07-31
Eigenvalue comparison for the discrete $(3,3)$~conjugate boundary value problem
Jun Ji, Bo YangAbstract : In this paper, we consider a boundary value problem for a sixth order difference equation. We prove the monotone behavior of the eigenvalue of the problem as the coefficients in the difference equation change values and the existence of a positive solution for a class of problems.
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2023-07-31
The pseudospectra of bounded linear operators on quasi normed space
Aymen ammar, Ameni Bouchekoua, Nawrez LazragAbstract : In this paper, we introduce the pseudospectra of bounded linear operators on quasi normed space and study its proprieties. Beside that, we establish the relationship between the pseudospectra of a sequence of bounded linear operators and its limit.
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2023-07-31
Continuous Welch bounds with applications
K. MAHESH KRISHNAAbstract : Let $(\Omega, \mu)$ be a measure space and $\{\tau_\alpha\}_{\alpha\in \Omega}$ be a normalized continuous Bessel family for a finite dimensional Hilbert space $\mathcal{H}$ of dimension $d$. If the diagonal $\Delta := \{(\alpha, \alpha):\alpha \in \Omega\}$ is measurable in the measure space $\Omega\times \Omega$, then we show that \begin{align*} &\ \sup _{\alpha, \beta \in \Omega, \alpha\neq \beta}|\langle \tau_\alpha, \tau_\beta\rangle |^{2m}\\ \geq&\ \frac{1}{(\mu\times\mu)((\Omega\times\Omega)\setminus\Delta)}\left[\frac{ \mu(\Omega)^2}{{d+m-1 \choose m}}-(\mu\times\mu)(\Delta)\right],~\quad \forall m \in \mathbb{N}. \end{align*} This improves 48 years old celebrated result of Welch [41]. We introduce the notions of continuous cross correlation and frame potential of Bessel family and give applications of continuous Welch bounds to these concepts. We also introduce the notion of continuous Grassmannian frames.
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2023-10-31
The flow-curvature of curves in a geometric surface
Mircea CrasmareanuAbstract : For a fixed parametrization of a curve in an orientable two-dimensional Riemannian manifold, we introduce and investigate a new frame and curvature function. Due to the way of defining this new frame as being the time-dependent rotation in the tangent plane of the standard Frenet frame, both these new tools are called flow.
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2024-01-31
RNA foldings and stuck knots
Jose Ceniceros, Mohamed Elhamdadi, Josef Komissar, Hitakshi LahraniAbstract : We study RNA foldings and investigate their topology using a combination of knot theory and embedded rigid vertex graphs. Knot theory has been helpful in modeling biomolecules, but classical knots emphasize a biomolecule's entanglement while ignoring their intrachain interactions. We remedy this by using stuck knots and links, which provide a way to emphasize both their entanglement and intrachain interactions. We first give a generating set of the oriented stuck Reidemeister moves for oriented stuck links. We then introduce an algebraic structure to axiomatize the oriented stuck Reidemeister moves. Using this algebraic structure, we define a coloring counting invariant of stuck links and provide explicit computations of the invariant. Lastly, we compute the counting invariant for arc diagrams of RNA foldings through the use of stuck link diagrams.
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2024-04-30
On a special class of matrix rings
Arnab BhattacharjeeAbstract : In this paper, we continue to explore an idea presented in \cite{bhatt2020} and introduce a new class of matrix rings called \emph{staircase} matrix rings which has applications in noncommutative ring theory. We show that these rings preserve the notions of reduced, symmetric, reversible, IFP, reflexive, abelian rings, etc.
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2024-01-31
Generalized $\eta$-Ricci solitons on para-Kenmotsu manifolds associated to the Zamkovoy connection
Shahroud azamiAbstract : In this paper, we study para-Kenmotsu manifolds admitting generalized $\eta$-Ricci solitons associated to the Zamkovoy connection. We provide an example of generalized $\eta$-Ricci soliton on a para-Kenmotsu manifold to prove our results.
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Certain image formulas of $(p,\nu)$--extended Gauss' hypergeometric function and related Jacobi transforms
Purnima Chopra, Mamta Gupta, Kanak Modi
Commun. Korean Math. Soc. 2022; 37(4): 1055-1072
https://doi.org/10.4134/CKMS.c210344 -
Commutativity criteria of prime rings involving two endomorphisms
Souad Dakir, Abdellah Mamouni, Mohammed Tamekkante
Commun. Korean Math. Soc. 2022; 37(3): 659-667
https://doi.org/10.4134/CKMS.c210240 -
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 -
On graded $(m, n)$-closed submodules
Rezvan Varmazyar
Commun. Korean Math. Soc. 2023; 38(4): 993-999
https://doi.org/10.4134/CKMS.c220338
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Convergence of sequences in generalized topological spaces via filter
Julio C. Ramos-Fernández, Ennis Rosas, Margot Salas-Brown
Commun. Korean Math. Soc. 2023; 38(3): 901-911
https://doi.org/10.4134/CKMS.c220251 -
On a uniqueness question of meromorphic functions and partial shared values
Imrul Kaish, Rana Mondal
Commun. Korean Math. Soc. 2024; 39(1): 105-116
https://doi.org/10.4134/CKMS.c210304 -
A characterization of zero divisors and topological divisors of zero in $C[a,b]$ and $\ell^\infty$
Harish Chandra, Anurag Kumar Patel
Commun. Korean Math. Soc. 2023; 38(2): 451-459
https://doi.org/10.4134/CKMS.c220108 -
Riemann solitons on $(\kappa, \mu)$-almost cosymplectic manifolds
Prakasha Doddabhadrappla Gowda, Devaraja Mallesha Naik, Amruthalakshmi Malleshrao Ravindranatha, Venkatesha Venkatesha
Commun. Korean Math. Soc. 2023; 38(3): 881-892
https://doi.org/10.4134/CKMS.c220243
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