Communications of the
Korean Mathematical Society
CKMS
ISSN(Print) 1225-1763
ISSN(Online) 2234-3024
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2022-07-31
The Drazin inverse of the sum of two products
Safae Alaoui~Chrifi, Abdelaziz TajmouatiAbstract : In this paper, for bounded linear operators $A,B,C$ satisfying $[AB,B]=[BC,B]=[AB,BC]=0$ we study the Drazin invertibility of the sum of products formed by the three operators $A,B$ and $C$. In particular, we give an explicit representation of the anti-commutator ${A,B}=AB+BA$. Also we give some conditions for which the sum $A+C$ is Drazin invertible.
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2022-07-31
Study of gradient solitons in three dimensional Riemannian manifolds
Gour Gopal Biswas, Uday Chand DeAbstract : We characterize a three-dimensional Riemannian manifold endowed with a type of semi-symmetric metric $P$-connection. At first, it is proven that if the metric of such a manifold is a gradient $m$-quasi-Einstein metric, then either the gradient of the potential function $psi$ is collinear with the vector field $P$ or, $lambda=-(m+2)$ and the manifold is of constant sectional curvature $-1$, provided $Ppsi eq m$. Next, it is shown that if the metric of the manifold under consideration is a gradient $ho$-Einstein soliton, then the gradient of the potential function is collinear with the vector field $P$. Also, we prove that if the metric of a 3-dimensional manifold with semi-symmetric metric $P$-connection is a gradient $omega$-Ricci soliton, then the manifold is of constant sectional curvature $-1$ and $lambda+mu=-2$. Finally, we consider an example to verify our results.
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2024-04-30
Parallel shrinking projection method for fixed point and generalized equilibrium problems on Hadamard manifold
HAMMED ANUOLUWAPO ABASS
, KAZEEM OLAWALE OYEWOLEAbstract : In this article, we propose a shrinking projection algorithm for solving a finite family of generalized equilibrium problem which is also a fixed point of a nonexpansive mapping in the setting of Hadamard manifolds. Under some mild conditions, we prove that the sequence generated by the proposed algorithm converges to a common solution of a finite family of generalized equilibrium problem and fixed point problem of a nonexpansive mapping. Lastly, we present some numerical examples to illustrate the performance of our iterative method. Our results extends and improve many related results on generalized equilibrium problem from linear spaces to Hadamard manifolds. The result discuss in this article extends and complements many related results in the literature.
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2022-07-31
Estimates for the norm of a multilinear form on $mathbb{R}^n$ with the $l_p$-norm
Sung Guen KimAbstract : In this paper, we present some estimates for the norm of a multilinear form $Tin {mathcal L}(^ml_{p}^n)$ for $1leq pleqinfty$ and $n, mgeq 2.$
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2022-07-31
Semi-neutral groupoids and $BCK$-algebras
Hee Sik Kim, Joseph Neggers, Young Joo SeoAbstract : In this paper, we introduce the notion of a left-almost-zero groupoid, and we generalize two axioms which play important roles in the theory of $BCK$-algebra using the notion of a projection. Moreover, we investigate a Smarandache disjointness of semi-leftoids.
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2022-07-31
Geometric distance fitting of parabolas in $mathbb{R}^3$
Ik Sung KimAbstract : We are interested in the problem of fitting a parabola to a set of data points in $mathbb{ R}^3 $. It can be usually solved by minimizing the geometric distances from the fitted parabola to the given data points. In this paper, a parabola fitting algorithm will be proposed in such a way that the sum of the squares of the geometric distances is minimized in~$mathbb{R}^3$. Our algorithm is mainly based on the steepest descent technique which determines an adequate number $ lambda $ such that $h ( lambda ) = Q ( u - lambda abla Qigl( u igr) ) < Q ( u)$. Some numerical examples are given to test our algorithm.
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2024-04-30
Some properties of critical point equations metrics on the statistical manifolds
Hajar Ghahremani-Gol, Mohammad Amin SedghiAbstract : The aim of this paper is to investigate some properties of the critical points equations on the statistical manifolds. We obtain some geometric equations on the statistical manifolds which admit critical point equations. We give a relation only between potential function and difference tensor for a CPE metric on the statistical manifolds to be Einstein.
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2022-07-31
A note on maximal hypersurfaces in a generalized Robertson-Walker spacetime
Henrique Fernandes de~LimaAbstract : In this note, we apply a maximum principle related to vo-lu-me growth of a complete noncompact Riemannian manifold, which was recently obtained by Al'{i}as, Caminha and do Nascimento in~cite{Alias-Caminha-Nascimento}, to es-ta-blish new uniqueness and nonexistence results concerning maximal spacelike hypersurfaces immersed in a generalized Robertson-Walker (GRW) spacetime obeying the timelike convergence condition. A study of entire solutions for the maximal hypersurface equation in GRW spacetimes is also made and, in particular, a new Calabi-Bernstein type result is presented.
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2022-07-31
Quantization for a probability distribution generated by an infinite iterated function system
Lakshmi Roychowdhury, Mrinal Kanti RoychowdhuryAbstract : Quantization for probability distributions concerns the best approximation of a $d$-dimensional probability distribution $P$ by a discrete probability with a given number $n$ of supporting points. In this paper, we have considered a probability measure generated by an infinite iterated function system associated with a probability vector on $mathbb R$. For such a probability measure $P$, an induction formula to determine the optimal sets of $n$-means and the $n$th quantization error for every natural number $n$ is given. In addition, using the induction formula we give some results and observations about the optimal sets of $n$-means for all $ngeq 2$.
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2024-04-30
Utilizing coupling strategy to generate a new simple 7d hyperchaotic system and its circuit application
Saad Fawzi Al-AzzawiAbstract : By utilizing coupling the strategy in the 5D Sprott B system, a new no equilibrium 7D hyperchaotic system is introduced. Despite the proposed system being simple with twelve-term, including solely two cross product nonlinearities, it displays extremely rich dynamical features such as hidden attractors and the dissipative and conservative nature. Besides, this system has largest Kaplan-Yorke dimension compared with to the work available in the literature. The dynamical properties are fully investigated via Matlab 2021 software from several aspects of phase portraits, Lyapunov exponents, Kaplan-Yorke dimension, offset boosting and so on. Moreover, the corresponding circuit is done through Multisim 14.2 software and preform to verify the new 7D system. The numerical simulations wit carryout via both software are agreement which indicates the efficiency of the proposed system.
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An improved global well-posedness result for the modified Zakharov equations in 1-D
Agus L. Soenjaya
Commun. Korean Math. Soc. 2022; 37(3): 735-748
https://doi.org/10.4134/CKMS.c210218 -
Mean values of derivatives of quadratic prime Dirichlet $L$-functions in function fields
Hwanyup Jung
Commun. Korean Math. Soc. 2022; 37(3): 635-648
https://doi.org/10.4134/CKMS.c210205 -
On the semi-local convergence of contraharmonic-mean Newton's method (CHMN)
Ioannis K. Argyros, Manoj Kumar Singh
Commun. Korean Math. Soc. 2022; 37(4): 1009-1023
https://doi.org/10.4134/CKMS.c210306 -
Golden para-contact metric manifolds
Gherici Beldjilali, Habib Bouzir
Commun. Korean Math. Soc. 2022; 37(4): 1209-1219
https://doi.org/10.4134/CKMS.c210383
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Some characterizations of conics and hypersurfaces with centrally symmetric hyperplane sections
Shin-Ok Bang, Dong Seo Kim, Dong-Soo Kim, Wonyong Kim
Commun. Korean Math. Soc. 2024; 39(1): 211-221
https://doi.org/10.4134/CKMS.c230119 -
Maximal chain of ideals and $n$-maximal ideal
Hemin A. Ahmad, Parween A. Hummadi
Commun. Korean Math. Soc. 2023; 38(2): 331-340
https://doi.org/10.4134/CKMS.c220097 -
Eigenvalue comparison for the discrete $(3,3)$~conjugate boundary value problem
Jun Ji, Bo Yang
Commun. Korean Math. Soc. 2023; 38(3): 925-935
https://doi.org/10.4134/CKMS.c210430 -
Circular spectrum and asymptotic periodic solutions to a class of non-densely defined evolution equations
Le Anh Minh, Nguyen Ngoc Vien
Commun. Korean Math. Soc. 2023; 38(4): 1153-1162
https://doi.org/10.4134/CKMS.c230015
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