Abstract : 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.
Abstract : This paper is concerned with the study of spacetimes satisfying $\mathrm{div}\mathcal{M}=0$, where ``div" denotes the divergence and $\mathcal{M}$ is the $m$-projective curvature tensor. We establish that a perfect fluid spacetime with $\mathrm{div}\mathcal{M}=0$ is a generalized Robertson-Walker spacetime and vorticity free; whereas a four-dimensional perfect fluid spacetime becomes a Robertson-Walker spacetime. Moreover, we establish that a Ricci recurrent spacetime with $\mathrm{div}\mathcal{M}=0$ represents a generalized Robertson-Walker spacetime.
Abstract : In this paper, for the bounded solution of the non-densely defined non-autonomous evolution equation, we present the condition for asymptotic periodicity by using the circular spectral theory of functions on the half line and the extrapolation theory of non-densely defined evolution equation.
Abstract : Let $S$ be a semigroup. We determine the complex-valued solutions of the following functional equation \[f(xy)+\mu (y)f(\sigma (y)x) = 2f(x)g(y),\ x,y\in S,\] where $\sigma:S\rightarrow S$ is an automorphism, and $\mu :S\rightarrow \mathbb{C}$ is a multiplicative function such that $\mu (x\sigma (x))=1$ for all $x\in S$.
Abstract : In this paper, we investigate the dimension and the structure of the centralizer of a square matrix with entries from an arbitrary field.
Abstract : 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.
Abstract : The aim of the present paper is to study complete lifts of a semi-symmetric non-metric connection from a Riemannian manifold to its tangent bundles. Some curvature properties of a Riemannian manifold to its tangent bundles with respect to such a connection have been investigated.
Abstract : Let $ G_{k,n}(\h) $ for $ 2\leq k
Abstract : 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.
Abstract : For each positive integer $ n $, a square congruence graph $ S(n) $ is the graph with vertex set $ H=\left\lbrace 1,2,3,\ldots,n\right\rbrace $ and two vertices $ a , b $ are adjacent if they are distinct and $ a^{2}\equiv b^{2}\pmod n$. In this paper we investigate some structural properties of square congruence graph and we obtain the relationship between clique number, chromatic number and maximum degree of square congruence graph. Also we study square congruence graph with $ p $ vertices or $ 2p $ vertices for any prime number $ p$.
Guodong Hua
Commun. Korean Math. Soc. 2023; 38(2): 319-330
https://doi.org/10.4134/CKMS.c210366
Asmaa Orabi Mohammed, Medhat Ahmed Rakha, Arjun K. Rathie
Commun. Korean Math. Soc. 2023; 38(3): 807-819
https://doi.org/10.4134/CKMS.c220217
Hieu Van Ha, Duong Quang Hoa, Vu Anh Le
Commun. Korean Math. Soc. 2022; 37(4): 1181-1197
https://doi.org/10.4134/CKMS.c210308
Ejaz Sabir Lone, Pankaj Pandey
Commun. Korean Math. Soc. 2023; 38(1): 223-234
https://doi.org/10.4134/CKMS.c220011
Ali Benhissi, Abdelamir Dabbabi
Commun. Korean Math. Soc. 2024; 39(1): 71-77
https://doi.org/10.4134/CKMS.c230111
Hyojun An, Hyungjin Huh
Commun. Korean Math. Soc. 2023; 38(4): 1091-1100
https://doi.org/10.4134/CKMS.c220362
Md. Adud, BIKASH CHAKRABORTY
Commun. Korean Math. Soc. 2024; 39(1): 117-125
https://doi.org/10.4134/CKMS.c230016
Souad DAKIR, Hajar EL MIR, Abdellah MAMOUNI
Commun. Korean Math. Soc. 2024; 39(1): 1-10
https://doi.org/10.4134/CKMS.c230052
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