Bulletin of the
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Bull. Korean Math. Soc. 2023; 60(3): 561~848
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2023-05-31
$p$-Biharmonic hypersurfaces in Einstein space and conformally flat space
Ahmed Mohammed Cherif, Khadidja MouffokiAbstract : In this paper, we present some new properties for $p$-biharmon\-ic hypersurfaces in a Riemannian manifold. We also characterize the $p$-biharmonic submanifolds in an Einstein space. We construct a new example of proper $p$-biharmonic hypersurfaces. We present some open problems.
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2023-05-31
Generalized $m$-quasi-Einstein structure in almost Kenmotsu manifolds
Mohan Khatri, Jay Prakash SinghAbstract : The goal of this paper is to analyze the generalized $m$-quasi-Einstein structure in the context of almost Kenmotsu manifolds. Firstly we showed that a complete Kenmotsu manifold admitting a generalized $m$-quasi-Einstein structure $(g,f,m,\lambda)$ is locally isometric to a hyperbolic space $\mathbb{H}^{2n+1}(-1)$ or a warped product $\widetilde{M}\times_\gamma\mathbb{R}$ under certain conditions. Next, we proved that a $(\kappa,\mu)'$-almost Kenmotsu manifold with $h'\neq0$ admitting a closed generalized $m$-quasi-Einstein metric is locally isometric to some warped product spaces. Finally, a generalized $m$-quasi-Einstein metric $(g,f,m,\lambda)$ in almost Kenmotsu 3-H-manifold is considered and proved that either it is locally isometric to the hyperbolic space $\mathbb{H}^3(-1)$ or the Riemannian product $\mathbb{H}^2(-4)\times\mathbb{R}$.
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2023-05-31
When all permutations are combinatorial similarities
Viktoriia Bilet, Oleksiy DovgosheyAbstract : Let \((X, d)\) be a semimetric space. A permutation \(\Phi\) of the set \(X\) is a combinatorial self similarity of \((X, d)\) if there is a bijective function \(f \colon d(X \times X) \to d(X \times X)\) such that \[ d(x, y) = f(d(\Phi(x), \Phi(y))) \] for all \(x\), \(y \in X\). We describe the set of all semimetrics \(\rho\) on an arbitrary nonempty set \(Y\) for which every permutation of \(Y\) is a combinatorial self similarity of \((Y, \rho)\).
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2023-05-31
The classification of $\omega$-left-symmetric algebras in low dimensions
Zhiqi Chen, Yang WuAbstract : $\omega$-left-symmetric algebras contain left-symmetric algebras as a subclass and the commutator defines an $\omega$-Lie algebra. In this paper, we classify $\omega$-left-symmetric algebras in dimension 3 up to an isomorphism based on the classification of $\omega$-Lie algebras and the technique of Lie algebras.
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2023-05-31
Bach almost solitons in paraSasakian geometry
Uday Chand De, Gopal GhoshAbstract : If a paraSasakian manifold of dimension $(2n+1)$ represents Bach almost solitons, then the Bach tensor is a scalar multiple of the metric tensor and the manifold is of constant scalar curvature. Additionally it is shown that the Ricci operator of the metric $g$ has a constant norm. Next, we characterize 3-dimensional paraSasakian manifolds admitting Bach almost solitons and it is proven that if a 3-dimensional paraSasakian manifold admits Bach almost solitons, then the manifold is of constant scalar curvature. Moreover, in dimension 3 the Bach almost solitons are steady if $r=-6$; shrinking if $r>-6$; expanding if $r
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2023-05-31
A new $q$-analogue of Van Hamme's $($G.2$)$ supercongruence for primes $p\equiv 3\pmod{4}$
Victor J. W. Guo
, Xiuguo LianAbstract : Van Hamme's (G.2) supercongruence modulo $p^4$ for primes $p\equiv 3 \pmod 4$ and $p>3$ was first established by Swisher. A $q$-analogue of this supercognruence was implicitly given by the first author and Schlosser. In this paper, we present a new $q$-analogue of Van Hamme's (G.2) supercongruence for $p\equiv 3\pmod{4}$.
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2023-05-31
System of generalized multi-valued resolvent equations: algorithmic and analytical approach
Javad Balooee, Shih-sen Chang, Jinfang TangAbstract : In this paper, under some new appropriate conditions imposed on the parameter and mappings involved in the resolvent operator associated with a $P$-accretive mapping, its Lipschitz continuity is proved and an estimate of its Lipschitz constant is computed. This paper is also concerned with the construction of a new iterative algorithm using the resolvent operator technique and Nadler's technique for solving a new system of generalized multi-valued resolvent equations in a Banach space setting. The convergence analysis of the sequences generated by our proposed iterative algorithm under some appropriate conditions is studied. The final section deals with the investigation and analysis of the notion of $H(\cdot,\cdot)$-co-accretive mapping which has been recently introduced and studied in the literature. We verify that under the conditions considered in the literature, every $H(\cdot,\cdot)$-co-accretive mapping is actually $P$-accretive and is not a new one. In the meanwhile, some important comments on $H(\cdot,\cdot)$-co-accretive mappings and the results related to them appeared in the literature are pointed out.
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2023-05-31
An altered group ring construction of the $[24,12,8]$ and $[48,24,12]$ Type II linear block code
Shefali Gupta, Dinesh UdarAbstract : In this paper, we present a new construction for self-dual codes that uses the concept of double bordered construction, group rings, and reverse circulant matrices. Using groups of orders $2,3,4,$ and $5$, and by applying the construction over the binary field and the ring $F_{2}+uF_{2}$, we obtain extremal binary self-dual codes of various lengths: $12, 16, 20, 24, 32, 40,$ and $48$. In particular, we show the significance of this new construction by constructing the unique Extended Binary Golay Code $[24,12,8]$ and the unique Extended Quadratic Residue $[48,24,12]$ Type II linear block code. Moreover, we strengthen the existing relationship between units and non-units with the self-dual codes presented in [10] by limiting the conditions given in the corollary. Additionally, we establish a relationship between idempotent and self-dual codes, which is done for the first time in the literature.
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2023-05-31
Erratum/Addendum to ``Biisometric operators and biorthogonal sequences'' [Bull. Korean Math. Soc. {\bf 56} (2019), No. 3, pp. 585--596]
Carlos Kubrusly, Nhan LevanAbstract : Erratum/Addendum to the paper ``Biisometric operators and biorthogonal sequences" [Bull. Korean Math. Soc. {\bf 56} (2019), No. 3, pp. 585--596].
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