Communications of the
Korean Mathematical Society
CKMS
ISSN(Print) 1225-1763
ISSN(Online) 2234-3024
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2022-07-31
Miao-Tam equation on almost coK"{a}hler manifolds
Tarak MandalAbstract : In the present paper, we have studied Miao-Tam equation on three dimensional almost coK"{a}hler manifolds. We have also proved that there does not exist non-trivial solution of Miao-Tam equation on the said manifolds if the dimension is greater than three. Also we give an example to verify the deduced results.
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2023-04-30
Uniform distributions on curves and quantization
Joseph Rosenblatt, Mrinal Kanti RoychowdhuryAbstract : The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus to make an approximation of a continuous probability distribution by a discrete distribution. It has broad application in signal processing and data compression. In this paper, first we define the uniform distributions on different curves such as a line segment, a circle, and the boundary of an equilateral triangle. Then, we give the exact formulas to determine the optimal sets of $n$-means and the $n$th quantization errors for different values of $n$ with respect to the uniform distributions defined on the curves. In each case, we further calculate the quantization dimension and show that it is equal to the dimension of the object; and the quantization coefficient exists as a finite positive number. This supports the well-known result of Bucklew and Wise \cite{BW}, which says that for a Borel probability measure $P$ with non-vanishing absolutely continuous part the quantization coefficient exists as a finite positive number.
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2023-04-30
The measurability of Hewitt-Stromberg measures and dimensions
Zied Douzi, Bilel Selmi, Haythem ZyoudiAbstract : The aim of this paper is to study the descriptive set-theoretic complexity of the Hewitt-Stromberg measure and dimension maps.
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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 ModiAbstract : 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
Oriented transformations on a finite chain: another description
Vítor Hugo FernandesAbstract : Following the new description of an oriented full transformation on a finite chain given recently by Higgins and Vernitski in [4], in this short note we present a refinement of this description which is extendable to partial transformations and to injective partial transformations.
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2023-10-31
Some classes of operators related to $(m, n)$-paranormal and $(m, n)^*$-paranormal operators
SHINE LAL ENOSE, RAMYA PERUMAL, PRASAD THANKARAJANAbstract : In this paper, we study new classes of operators $k$-quasi $(m, n)$-paranormal operator, $k$-quasi $(m, n)^*$-paranormal operator, $k$-qu\-asi $(m, n)$-class~ $\mathcal{Q}$ operator and $k$-quasi $(m, n)$-class~ $\mathcal{Q^{*}}$ operator which are the generalization of $(m, n)$-paranormal and $(m, n)^*$-paranormal operators. We give matrix characterizations for $k$-quasi $(m, n)$-paranormal and $k$-quasi $(m, n)^*$-paranormal operators. Also we study some properties of $k$-quasi $(m, n)$-class~ $\mathcal{Q}$ operator and $k$-quasi $(m, n)$-class~ $\mathcal{Q}^*$ operators. Moreover, these classes of composition operators on $L^2$ spaces are characterized.
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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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2023-07-31
On nonnil-SFT rings
Ali Benhissi, Abdelamir DabbabiAbstract : The purpose of this paper is to introduce a new class of rings containing the class of SFT-rings and contained in the class of rings with Noetherian prime spectrum. Let $A$ be a commutative ring with unit and $I$ be an ideal of $A$. We say that $I$ is SFT if there exist an integer $k\geq 1$ and a finitely generated ideal $F\subseteq I$ of $A$ such that $x^k\in F$ for every $x\in I$. The ring $A$ is said to be nonnil-SFT, if each nonnil-ideal (i.e., not contained in the nilradical of $A$) is SFT. We investigate the nonnil-SFT variant of some well known theorems on SFT-rings. Also we study the transfer of this property to Nagata's idealization and the amalgamation algebra along an ideal. Many examples are given. In fact, using the amalgamation construction, we give an infinite family of nonnil-SFT rings which are not SFT.
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2023-07-31
$\star$-conformal Ricci solitons on almost coK\"{a}hler manifolds
Tarak Mandal, Avijit SarkarAbstract : The main intention of the current paper is to characterize certain properties of $\star$-conformal Ricci solitons on non-coK\"ahler $(\kappa,\mu)$-almost coK\"{a}hler manifolds. At first, we find that there does not exist $\star$-conformal Ricci soliton if the potential vector field is the Reeb vector field $\theta$. We also prove that the non-coK\"ahler $(\kappa,\mu)$-almost coK\"ahler manifolds admit $\star$-conformal Ricci solitons if the potential vector field is the infinitesimal contact transformation. It is also studied that there does not exist $\star$-conformal gradient Ricci solitons on the said manifolds. An example has been constructed to verify the obtained results.
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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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On Noetherian pseudo-prime spectrum of a topological le-module
Anjan Kumar Bhuniya, Manas Kumbhakar
Commun. Korean Math. Soc. 2023; 38(1): 1-9
https://doi.org/10.4134/CKMS.c210057 -
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 -
Generalized Padovan sequences
Jhon J. Bravo, Jose L. Herrera
Commun. Korean Math. Soc. 2022; 37(4): 977-988
https://doi.org/10.4134/CKMS.c210367 -
A question about maximal non $\phi$-chained subrings
Atul Gaur, Rahul Kumar
Commun. Korean Math. Soc. 2023; 38(1): 11-19
https://doi.org/10.4134/CKMS.c210272
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The dimension graph for modules over commutative rings
Shiroyeh Payrovi
Commun. Korean Math. Soc. 2023; 38(3): 733-740
https://doi.org/10.4134/CKMS.c220273 -
A question about maximal non $\phi$-chained subrings
Atul Gaur, Rahul Kumar
Commun. Korean Math. Soc. 2023; 38(1): 11-19
https://doi.org/10.4134/CKMS.c210272 -
Hyers-Ulam stability of fractional stochastic differential equations with random impulse
Dumitru Baleanu, Banupriya Kandasamy, Ramkumar Kasinathan, Ravikumar Kasinathan, Varshini Sandrasekaran
Commun. Korean Math. Soc. 2023; 38(3): 967-982
https://doi.org/10.4134/CKMS.c220231 -
A study of differential identities on $\sigma$-prime rings
Adnan Abbasi, Md Arshad Madni, Muzibur Rahman Mozumder
Commun. Korean Math. Soc. 2023; 38(3): 679-693
https://doi.org/10.4134/CKMS.c220240
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