Bulletin of the
Korean Mathematical Society
BKMS
ISSN(Print) 1015-8634
ISSN(Online) 2234-3016
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2024-01-31
Topological sensitivity and its stronger forms on semiflows
Ruchi Das, Devender Kumar, Mohammad SalmanAbstract : In this paper we introduce and study the notions of topological sensitivity and its stronger forms on semiflows and on product semiflows. We give a relationship between multi-topological sensitivity and thick topological sensitivity on semiflows. We prove that for a Urysohn space $X$, a syndetically transitive semiflow $(T,X,\pi)$ having a point of proper compact orbit is syndetic topologically sensitive. Moreover, it is proved that for a $T_3$ space $X$, a transitive, nonminimal semiflow $(T,X,\pi)$ having a dense set of almost periodic points is syndetic topologically sensitive. Also, wherever necessary examples/counterexamples are given.
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2024-03-31
Six dimensional almost complex torus manifolds with Euler number six
Donghoon Jang, Jiyun ParkAbstract : An almost complex torus manifold is a $2n$-dimensional compact connected almost complex manifold equipped with an effective action of a real $n$-dimensional torus $T^n \simeq (S^1)^n$ that has fixed points. For an almost complex torus manifold, there is a labeled directed graph which contains information on weights at the fixed points and isotropy spheres. Let $M$ be a 6-dimensional almost complex torus manifold with Euler number 6. We show that two types of graphs occur for $M$, and for each type of graph we construct such a manifold $M$, proving the existence. Using the graphs, we determine the Chern numbers and the Hirzebruch $\chi_y$-genus of $M$.
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2024-03-31
Certain differential identities in prime rings with anti-automorphisms
Abbas Hussain Shikeh, Mohammad Aslam SiddeequeAbstract : The objective of this paper is to study some central identities involving generalized derivations and anti-automorphisms in prime rings. Using the tools of the theory of functional identities, several known results have been generalized as well as improved.
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2024-03-31
Large time convergence for a chemotaxis model with degenerate local sensing and consumption
Philippe LAURENCOTAbstract : Convergence to a steady state in the long term limit is established for global weak solutions to a chemotaxis model with degenerate local sensing and consumption, when the motility function is $C^1$-smooth on $[0,\infty)$, vanishes at zero, and is positive on $(0,\infty)$. A condition excluding that the large time limit is spatially homogeneous is also provided. These results extend previous ones derived for motility functions vanishing algebraically at zero and rely on a completely different approach.
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2024-03-31
Wavelet characterizations of variable Hardy-Lorentz spaces
Yao HeAbstract : In this paper, let $q\in(0,1]$. We establish the boundedness of intrinsic $g$-functions from the Hardy-Lorentz spaces with variable exponent ${H}^{p(\cdot),q}(\mathbb R^{n})$ into Lorentz spaces with variable exponent ${L}^{p(\cdot),q}(\mathbb R^{n})$. Then, for any $q\in(0,1]$, via some estimates on a discrete Littlewood-Paley $g$-function and a Peetre-type maximal function, we obtain several equivalent characterizations of ${H}^{p(\cdot),q}(\mathbb R^{n})$ in terms of wavelets.
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2024-03-31
Sharp bounds of fifth coefficient and Hermitian-Toeplitz determinants for Sakaguchi classes
SURYA GIRI, S. SIVAPRASAD KUMARAbstract : For the classes of analytic functions $f$ defined on the unit disk satisfying $$\frac{2 z {f}'(z)}{f(z) - f(-z)} \prec \varphi(z) \quad \text{and} \quad \frac{(2 z {f}'(z))'}{(f(z) - f(-z))'} \prec \varphi(z) , $$ denoted by $\mathcal{S}^*_s(\varphi)$ and $\mathcal{C}_s(\varphi)$, respectively, the sharp bound of the $n^{th}$ Taylor coefficients are known for $n=2$, $3$ and $4$. In this paper, we obtain the sharp bound of the fifth coefficient. Additionally, the sharp lower and upper estimates of the third order Hermitian Toeplitz determinant for the functions belonging to these classes are determined. The applications of our results lead to the establishment of certain new and previously known results.
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2024-03-31
Geometric inequalities for affine connections on Riemannian manifolds
Huiting Chang, Fanqi ZengAbstract : Using a Reilly type integral formula due to Li and Xia \cite{LiXia2017}, we prove several geometric inequalities for affine connections on Riemannian manifolds. We obtain some general De Lellis-Topping type inequalities associated with affine connections. These not only permit to derive quickly many well-known De Lellis-Topping type inequalities, but also supply a new De Lellis-Topping type inequality when the $1$-Bakry-\'{E}mery Ricci curvature is bounded from below by a negative function. On the other hand, we also achieve some Lichnerowicz type estimate for the first (nonzero) eigenvalue of the affine Laplacian with the Robin boundary condition on Riemannian manifolds.
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2024-03-31
Timelike tubular surfaces of Weingarten types and linear Weingarten types in Minkowski 3-space
He Chenghong, Sun He-JunAbstract : Let $K$, $H$, $K_{II}$ and $H_{II}$ be the Gaussian curvature, the mean curvature, the second Gaussian curvature and the second mean curvature of a timelike tubular surface $T_\gamma(\alpha)$ with the radius $\gamma$ along a timelike curve $\alpha(s)$ in Minkowski 3-space $E_{1}^3$. We prove that $T_\gamma(\alpha)$ must be a $(K,H)$-Weingarten surface and a $(K,H)$-linear Weingarten surface. We also show that $T_{\gamma}(\alpha)$ is $(X,Y)$-Weingarten type if and only if its central curve is a circle or a helix, where $(X,Y)$ $\in$ $\{(K,K_{II})$, $(K,H_{II})$, $(H,K_{II})$, $(H,H_{II})$, $(K_{II}$, $H_{II}) \}$. Furthermore, we prove that there exist no timelike tubular surfaces of $(X,Y)$-linear Weingarten type, $(X,Y,Z)$-linear Weingarten type and $(K,H,K_{II},H_{II})$-linear Weingarten type along a timelike curve in $E_{1}^3$, where $(X,Y,Z)\in\{(K,H,K_{II})$, $(K,H,H_{II})$, $(K,K_{II},H_{II})$, $(H$, $K_{II},H_{II})\}$.
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2024-03-31
The boundedness of bilinear pseudodifferential operators in Triebel-Lizorkin and Besov spaces with variable exponents
Yin Liu, Lushun WangAbstract : In this paper, using the Fourier transform, inverse Fourier transform and Littlewood-Paley decomposition technique, we prove the boundedness of bilinear pseudodifferential operators with symbols in the bilinear H\"{o}rmander class $BS_{1,1}^m$ in variable Triebel-Lizorkin spaces and variable Besov spaces.
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2024-03-31
Bj\"{o}rling problem for zero mean curvature surfaces in the three-dimensional light cone
Joseph Cho, So Young Kim, Dami Lee, Wonjoo Lee, Seong-Deog YangAbstract : We solve the Bj\"{o}rling problem for zero mean curvature surfaces in the three-dimensional light cone. As an application, we construct and classify all rotational zero mean curvature surfaces.
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Most Read
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A generalization of ${\mathcal A}_2$-groups
Junqiang Zhang
Bull. Korean Math. Soc. 2022; 59(4): 951-960
https://doi.org/10.4134/BKMS.b210562 -
On right regularity of commutators
Da Woon Jung, Chang Ik Lee, Yang Lee, Sangwon Park, Sung Ju Ryu, Hyo Jin Sung
Bull. Korean Math. Soc. 2022; 59(4): 853-868
https://doi.org/10.4134/BKMS.b210495 -
Unique range sets without Fujimoto's hypothesis
Bikash Chakraborty
Bull. Korean Math. Soc. 2022; 59(5): 1247-1253
https://doi.org/10.4134/BKMS.b210700 -
Some polynomials with unimodular roots
Art\= uras Dubickas
Bull. Korean Math. Soc. 2022; 59(5): 1269-1277
https://doi.org/10.4134/BKMS.b210728
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Constructions of regular sparse anti-magic squares
Guangzhou Chen
, Wen Li, Bangying Xin, Ming ZhongBull. Korean Math. Soc. 2022; 59(3): 617-642
https://doi.org/10.4134/BKMS.b210281 -
Regular $t$-balanced Cayley maps on split metacyclic $2$-groups
Haimiao Chen, Jingrui Zhang
Bull. Korean Math. Soc. 2024; 61(1): 13-27
https://doi.org/10.4134/BKMS.b220811 -
Integral operators on Ces\`{a}ro function spaces
Kwok-Pun Ho
Bull. Korean Math. Soc. 2022; 59(4): 905-915
https://doi.org/10.4134/BKMS.b210522 -
Periodic shadowable points
Namjip Koo, Hyunhee Lee, Nyamdavaa Tsegmid
Bull. Korean Math. Soc. 2024; 61(1): 195-205
https://doi.org/10.4134/BKMS.b230071
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