Abstract : In this paper, we study the $n$-dimensional M\"obius transformation. We obtain several conjugacy invariants and give a conjugacy classification for $n$-dimensional M\"obius transformation.
Abstract : Let $R$ be a commutative ring with nonzero identity and $M$ be an $R$-module. In this paper, we first introduce the concept of $S$-idempotent element of $R$. Then we give a relation between $S$-idempotents of $R$ and clopen sets of $S$-Zariski topology. After that we define $S$-pure ideal which is a generalization of the notion of pure ideal. In fact, every pure ideal is $S$-pure but the converse may not be true. Afterwards, we show that there is a relation between $S$-pure ideals of $R$ and closed sets of $S$-Zariski topology that are stable under generalization.
Abstract : Let $T$ be a bilinear Calder\'{o}n-Zygmund operator, $$b\in \cup_{q>1}L_{loc}^{q}(G).$$ We firstly obtain a constructive proof of the weak factorisation of Hardy spaces. Then we establish the characterization of $BMO$ spaces by the boundedness of the commutator $[b, T]_{j}$ in variable Lebesgue spaces.
Abstract : In this note, we study a comparison principle for elliptic obstacle problems of $p$-Laplacian type with $L^1$-data. As a consequence, we improve some known regularity results for obstacle problems with zero Dirichlet boundary conditions.
Abstract : Let $\mathcal{S}$ be a Serre class in the category of modules and $\mathfrak{a}$ an ideal of a commutative Noetherian ring $R$. We study the containment of Tor modules, Koszul homology and local homology in $\mathcal{S}$ from below. With these results at our disposal, by specializing the Serre class to be Noetherian or zero, a handful of conclusions on Noetherianness and vanishing of the foregoing homology theories are obtained. We also determine when $\mathrm{Tor}_{s+t}^R(R/\mathfrak{a},X)\cong\mathrm{Tor}_{s}^R(R/\mathfrak{a},\mathrm{H}_{t}^\mathfrak{a}(X))$.
Abstract : In this paper, we prove that any orthogonal almost complex structure on a warped product manifold of any oriented closed surface and a round 4-sphere for a concircular warping function on the sphere is never integrable. This gives a partial answer to Calabi's problem.
Abstract : This note is devoted to establishing the variation continuity of the one-dimensional discrete uncentered multilinear maximal operator. The above result is based on some refine variation estimates of the above maximal functions on monotone intervals. The main result essentially improves some known ones.
Abstract : We study some factorization properties of the idealization $R$(+)$M$ of a module $M$ in a commutative ring $R$ which is not necessarily a domain. We show that $R$(+)$M$ is ACCP if and only if $R$ is ACCP and $M$ satisfies ACC on its cyclic submodules. We give an example to show that the BF property is not necessarily preserved in idealization, and give some conditions under which $R$(+)$M$ is a BFR. We also characterize the idealization rings which are UFRs.
Abstract : In this paper, we consider the set of periodic shadowable points for homeomorphisms of a compact metric space, and we prove that this set satisfies some properties such as invariance and being a $G_{\delta}$ set. Then we investigate implication relations related to sets consisting of shadowable points, periodic shadowable points and uniformly expansive points, respectively. Assume that the set of periodic points and the set of periodic shadowable points of a homeomorphism on a compact metric space are dense in $X$. Then we show that a homeomorphism has the periodic shadowing property if and only if so is the restricted map to the set of periodic shadowable points. We also give some examples related to our results.
Abstract : A regular $t$-balanced Cayley map on a group $\Gamma$ is an embedding of a Cayley graph on $\Gamma$ into a surface with certain special symmetric properties. We completely classify regular $t$-balanced Cayley maps for a class of split metacyclic $2$-groups.
Seung-Jo Jung
Bull. Korean Math. Soc. 2022; 59(6): 1409-1422
https://doi.org/10.4134/BKMS.b210797
Jin Hong Kim
Bull. Korean Math. Soc. 2022; 59(3): 671-683
https://doi.org/10.4134/BKMS.b210406
Kui Hu, Hwankoo Kim, Dechuan Zhou
Bull. Korean Math. Soc. 2022; 59(5): 1317-1325
https://doi.org/10.4134/BKMS.b210759
Poo-Sung Park
Bull. Korean Math. Soc. 2023; 60(1): 75-81
https://doi.org/10.4134/BKMS.b210915
Juan Huang, Tai Keun Kwak, Yang Lee, Zhelin Piao
Bull. Korean Math. Soc. 2023; 60(5): 1321-1334
https://doi.org/10.4134/BKMS.b220692
Thu Thuy Hoang, Hong Nhat Nguyen, Duc Thoan Pham
Bull. Korean Math. Soc. 2023; 60(2): 461-473
https://doi.org/10.4134/BKMS.b220190
Karim Bouchannafa, Moulay Abdallah Idrissi, Lahcen Oukhtite
Bull. Korean Math. Soc. 2023; 60(5): 1281-1293
https://doi.org/10.4134/BKMS.b220654
Sangeet Kumar, Megha Pruthi
Bull. Korean Math. Soc. 2023; 60(4): 1003-1016
https://doi.org/10.4134/BKMS.b220452
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