Communications of the
Korean Mathematical Society
CKMS
ISSN(Print) 1225-1763
ISSN(Online) 2234-3024
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2023-04-30
Estimates for certain shifted convolution sums involving Hecke eigenvalues
Guodong HuaAbstract : In this paper, we obtain certain estimates for averages of shifted convolution sums involving Hecke eigenvalues of classical holomorphic cusp forms. This generalizes some results of L\"{u} and Wang in this direction.
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2023-04-30
A simple proof for a result on $n$-Jordan homomorphisms
Choonkil Park, Abbas Zivari-KazempourAbstract : In this short note, we give a simple proof of the main theorem of \cite{Cheshmavar} which states that every $n$-Jordan homomorphism $h:A\longrightarrow B$ between two commutative algebras $A$ and $B$ is an $n$-homomorphism.
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2022-04-30
A fundamental theorem of calculus for the $M_{alpha}$-integral
Abraham Perral RaccaAbstract : This paper presents a fundamental theorem of calculus, an integration by parts formula and a version of equiintegrability convergence theorem for the $M_{alpha}$-integral using the $M_{alpha}$-strong Lusin condition. In the convergence theorem, to be able to relax the condition of being point-wise convergent everywhere to point-wise convergent almost everywhere, the uniform $M_{alpha}$-strong Lusin condition was imposed.
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2023-04-30
On the Characterization of $F_{0}$-spaces
Mahmoud BenkhalifaAbstract : Let $X$ be a simply connected rationally elliptic space such that $H^{2}(X; {\mathbb Q})\neq0$. In this paper, we show that if $ H^{2n}(X^{[2n-2]}; {\mathbb Q})=0$ or if $\pi_{2n}(X^{2n}) \otimes {\mathbb Q}=0$ for all $n$, then $X$ is an $F_{0}$-space.
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2023-04-30
Simple formulations on circulant matrices with alternating Fibonacci
Sugi GuritmanAbstract : In this article, an alternating Fibonacci sequence is defined from a second-order linear homogeneous recurrence relation with constant coefficients. Then, the determinant, inverse, and eigenvalues of the circulant matrices with entries in the first row having the formation of the sequence are formulated explicitly in a simple way. In this study, the method for deriving the formulation of the determinant and inverse is simply using traditional elementary row or column operations. For the eigenvalues, the known formulation from the case of general circulant matrices is simplified by considering the specialty of the sequence and using cyclic group properties. We also propose algorithms for the formulation to show how efficient the computations are.
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2023-01-31
On the 2-absorbing submodules and zero-divisor graph of equivalence classes of zero divisors
Shiroyeh Payrovi, Yasaman SadatrasulAbstract : Let $R$ be a commutative ring, $M$ be a Noetherian $R$-module, and $N$ a 2-absorbing submodule of $M$ such that $r(N :_{R} M)= \mathfrak p$ is a prime ideal of $R$. The main result of the paper states that if $N=Q_1\cap\cdots\cap Q_n$ with $r(Q_i:_RM)=\mathfrak p_i$, for $i=1,\ldots, n$, is a minimal primary decomposition of $N$, then the following statements are true. \begin{itemize} \item[(i)] $\mathfrak p=\mathfrak p_k$ for some $1 \leq k \leq n$. \item[(ii)] For each $j=1,\ldots,n$ there exists $m_j \in M$ such that ${\mathfrak p}_j=(N :_{R} m_{j})$. \item[(iii)] For each $i,j=1,\ldots,n$ either $\mathfrak p_{i} \subseteq \mathfrak p_{j}$ or $\mathfrak p_{j} \subseteq \mathfrak p_{i}$. \end{itemize} Let $\Gamma_E(M)$ denote the zero-divisor graph of equivalence classes of zero divisors of $M$. It is shown that $\{Q_1\cap\cdots\cap Q_{n-1}, Q_1\cap\cdots\cap Q_{n-2},\ldots , Q_1\}$ is an independent subset of $V(\Gamma_E(M))$, whenever the zero submodule of $M$ is a 2-absorbing submodule and $Q_1\cap\cdots\cap Q_n=0$ is its minimal primary decomposition. Furthermore, it is proved that $\Gamma_E(M)[(0 :_{R} M)]$, the induced subgraph of $\Gamma_E(M)$ by $(0 :_{R} M)$, is complete.
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2022-04-30
A note on generalizations of Bailey's identity involving products of generalized hypergeometric series
Adem Kilicman, Shantha Kumari Kurumujji, Arjun K. RathieAbstract : In the theory of hypergeometric and generalized hypergeometric series, the well-known and very useful identity due to Bailey (which is a generalization of the Preece's identity) plays an important role. The aim of this research paper is to provide generalizations of Bailey's identity involving products of generalized hypergeometric series in the most general form. A few known, as well as new results, have also been obtained as special cases of our main findings.
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2022-04-30
On rings whose essential maximal right ideals are GP-injective
Jeonghee Jeong, Nam Kyun KimAbstract : In this paper, we continue to study the von Neumann regularity of rings whose essential maximal right ideals are GP-injective. It is proved that the following statements are equivalent: (1) $R$ is strongly regular; (2) $R$ is a 2-primal ring whose essential maximal right ideals are GP-injective; (3) $R$ is a right (or left) quasi-duo ring whose essential maximal right ideals are GP-injective. Moreover, it is shown that $R$ is strongly regular if and only if $R$ is a strongly right (or left) bounded ring whose essential maximal right ideals are GP-injective. Finally, we prove that a PI-ring whose essential maximal right ideals are GP-injective is strongly $pi$-regular.
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2022-01-31
A note on modular equations of signature 2 and their evaluations
Belakavadi Radhakrishna Srivatsa Kumar, Arjun Kumar Rathie, Nagara Vinayaka Udupa Sayinath, ShruthiAbstract : In his notebooks, Srinivasa Ramanujan recorded several modular equations that are useful in the computation of class invariants, continued fractions and the values of theta functions. In this paper, we prove some new modular equations of signature 2 by well-known and useful theta function identities of composite degrees. Further, as an application of this, we evaluate theta function identities.
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2022-01-31
On some new type of generating functions of generalized Poisson-Charlier polynomials
Shakeel Ahmed, Mumtaz Ahmad KhanAbstract : The present paper concerns with a study of certain generating functions and summation formulas of generalized Poisson-Charlier polynomials. Some special cases are also discussed.
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Functions subordinate to the exponential function
Priya G. Krishnan, Vaithiyanathan Ravichandran, Ponnaiah Saikrishnan
Commun. Korean Math. Soc. 2023; 38(1): 163-178
https://doi.org/10.4134/CKMS.c220087 -
Chen invariants and statistical submanifolds
Hitoshi Furuhata, Izumi Hasegawa, Naoto Satoh
Commun. Korean Math. Soc. 2022; 37(3): 851-864
https://doi.org/10.4134/CKMS.c210185 -
Infinitely many homoclinic solutions for different classes of fourth-order differential equations
Mohsen Timoumi
Commun. Korean Math. Soc. 2022; 37(1): 137-161
https://doi.org/10.4134/CKMS.c200474 -
Some results on the geometry of a non-conformal deformation of a metric
Nour Elhouda Djaa, Abderrahim Zagane
Commun. Korean Math. Soc. 2022; 37(3): 865-879
https://doi.org/10.4134/CKMS.c210207
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Miao-Tam equation on almost coK"{a}hler manifolds
Tarak Mandal
Commun. Korean Math. Soc. 2022; 37(3): 881-891
https://doi.org/10.4134/CKMS.c210225 -
Yamabe and Riemann solitons on Lorentzian para-Sasakian manifolds
Shruthi Chidananda, Venkatesha Venkatesha
Commun. Korean Math. Soc. 2022; 37(1): 213-228
https://doi.org/10.4134/CKMS.c200365 -
Local-global principle and generalized local cohomology modules
Bui Thi Hong Cam, Nguyen Minh Tri, Do Ngoc Yen
Commun. Korean Math. Soc. 2023; 38(3): 649-661
https://doi.org/10.4134/CKMS.c220160 -
Uniform distributions on curves and quantization
Joseph Rosenblatt, Mrinal Kanti Roychowdhury
Commun. Korean Math. Soc. 2023; 38(2): 431-450
https://doi.org/10.4134/CKMS.c210434
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