Bulletin of the
Korean Mathematical Society
BKMS
ISSN(Print) 1015-8634
ISSN(Online) 2234-3016
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2023-01-31
Multiplicative functions commutable with binary quadratic forms $x^2 \pm xy + y^2$
Poo-Sung ParkAbstract : If a multiplicative function $f$ is commutable with a quadratic form $x^2+xy+y^2$, i.e., \[ f(x^2+xy+y^2) = f(x)^2 + f(x)\,f(y) + f(y)^2, \] then $f$ is the identity function. In other hand, if $f$ is commutable with a quadratic form $x^2-xy+y^2$, then $f$ is one of three kinds of functions: the identity function, the constant function, and an indicator function for $\mathbb{N}\setminus p\mathbb{N}$ with a prime $p$.$\\ \\ \\$
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2022-09-30
A note on Artinian local rings
Kui Hu, Hwankoo Kim, Dechuan ZhouAbstract : In this note, we prove that an Artinian local ring is G-semisimple (resp., SG-semisimple, $2$-SG-semisimple) if and only if its maximal ideal is G-projective (resp., SG-projective, $2$-SG-projective). As a corollary, we obtain the global statement of the above. We also give some examples of local G-semisimple rings whose maximal ideals are $n$-generated for some positive integer $n$.
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2022-07-31
A new characterization of type $(A)$ and ruled real hypersurfaces in nonflat complex space forms
Yaning WangAbstract : In this paper, we obtain an inequality involving the squared norm of the covariant differentiation of the shape operator for a real hypersurface in nonflat complex space forms. It is proved that the equality holds for non-Hopf case if and only if the hypersurface is ruled and the equality holds for Hopf case if and only if the hypersurface is of type $(A)$.
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2022-07-31
Integral operators on Ces\`{a}ro function spaces
Kwok-Pun Ho
Abstract : This paper studies the boundedness of integral operators on the Ces\`{a}ro function spaces. As applications of the main result, we obtain the Hilbert inequalities, the boundedness of the Erd\'{e}lyi-Kober fractional integrals and the Mellin fractional integrals on the Ces\`{a}ro function spaces.
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2022-05-31
Finiteness and vanishing results on hypersurfaces with finite index in $\mathbb{R}^{n+1}$: a revision
Nguyen Van DucAbstract : In this note, we revise some vanishing and finiteness results on hypersurfaces with finite index in $\mathbb{R}^{n+1}$. When the hypersurface is stable minimal, we show that there is no nontrivial $L^{2p}$ harmonic $1$-form for some $p$. The our range of $p$ is better than those in [7]. With the same range of $p$, we also give finiteness results on minimal hypersurfaces with finite index.
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2022-05-31
Free Products Of Operator Systems
Florin PopAbstract : In this paper we introduce the notion of universal free product for operator systems and operator spaces, and prove extension results for the operator system lifting property (OSLP) and operator system local lifting property (OSLLP) to the universal free product.
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2022-07-31
B\'ezout rings and weakly B\'ezout rings
Haitham El~AlaouiAbstract : In this paper, we study some properties of B\'ezout and weakly B\'ezout rings. Then, we investigate the transfer of these notions to trivial ring extensions and amalgamated algebras along an ideal. Also, in the context of domains we show that the amalgamated is a B{\'e}zout ring if and only if it is a weakly B\'ezout ring. All along the paper, we put the new results to enrich the current literature with new families of examples of non-B\'ezout weakly B\'ezout rings.
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2022-05-31
A sharp integral inequality for compact linear Weingarten hypersurfaces
Henrique F. de~Lima, F\'{a}bio R. dos~Santos, Lucas S. RochaAbstract : We establish a sharp integral inequality related to compact (without boundary) linear Weingarten hypersurfaces (immersed) in a locally symmetric Einstein manifold and we apply it to characterize totally umbilical hypersurfaces and isoparametric hypersurfaces with two distinct principal curvatures, one which is simple, in such an ambient space. Our approach is based on the ideas and techniques introduced by Al\'{\i}as and Mel\'{e}ndez in [4] for the case of hypersurfaces with constant scalar curvature in an Euclidean round sphere.
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2022-05-31
Application of Rothe's method to a nonlinear wave equation on graphs
Yong Lin, Yuanyuan XieAbstract : We study a nonlinear wave equation on finite connected weig\-hted graphs. Using Rothe's and energy methods, we prove the existence and uniqueness of solution under certain assumption. For linear wave equation on graphs, Lin and Xie [10] obtained the existence and uniqueness of solution. The main novelty of this paper is that the wave equation we considered has the nonlinear damping term $|u_t|^{p-1}\cdot u_t$ ($p>1$).
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2023-01-31
On Chowla's hypothesis implying that $L(s,\chi)>0$ for $s>0$ for real characters $\chi$
St\'ephane R. LouboutinAbstract : Let $L(s,\chi)$ be the Dirichlet $L$-series associated with an $f$-periodic complex function $\chi$. Let $P(X)\in {\mathbb C}[X]$. We give an expression for $\sum_{n=1}^f \chi (n)P(n)$ as a linear combination of the $L(-n,\chi)$'s for $0\leq n<\deg P(X)$. We deduce some consequences pertaining to the Chowla hypothesis implying that $L(s,\chi )>0$ for $s>0$ for real Dirichlet characters $\chi$. To date no extended numerical computation on this hypothesis is available. In fact by a result of R. C. Baker and H. L. Montgomery we know that it does not hold for almost all fundamental discriminants. Our present numerical computation shows that surprisingly it holds true for at least $65\%$ of the real, even and primitive Dirichlet characters of conductors less than $10^6$. We also show that a generalized Chowla hypothesis holds true for at least $72\%$ of the real, even and primitive Dirichlet characters of conductors less than $10^6$. Since checking this generalized Chowla's hypothesis is easy to program and relies only on exact computation with rational integers, we do think that it should be part of any numerical computation verifying that $L(s,\chi )>0$ for $s>0$ for real Dirichlet characters $\chi$. To date, this verification for real, even and primitive Dirichlet characters has been done only for conductors less than $2\cdot 10^5$.
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Uniqueness of meromorphic solutions of a certain type of difference equations
Jun-Fan Chen, Shu-Qing Lin
Bull. Korean Math. Soc. 2022; 59(4): 827-841
https://doi.org/10.4134/BKMS.b210490 -
The recurrent hypercyclicity criterion for translation $C_0$-semigroups on complex sectors
Yuxia Liang, Zhi-Yuan Xu, Ze-Hua Zhou
Bull. Korean Math. Soc. 2023; 60(2): 293-305
https://doi.org/10.4134/BKMS.b210802 -
Second main theorem with weighted counting functions and uniqueness theorem
Liu Yang
Bull. Korean Math. Soc. 2022; 59(5): 1105-1117
https://doi.org/10.4134/BKMS.b210620 -
Complete characterization of odd factors via the size, spectral radius or distance spectral radius of graphs
Shuchao Li, Shujing Miao
Bull. Korean Math. Soc. 2022; 59(4): 1045-1067
https://doi.org/10.4134/BKMS.b210613
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UN rings and group rings
Kanchan Jangra, Dinesh Udar
Bull. Korean Math. Soc. 2023; 60(1): 83-91
https://doi.org/10.4134/BKMS.b210917 -
Bach almost solitons in paraSasakian geometry
Uday Chand De, Gopal Ghosh
Bull. Korean Math. Soc. 2023; 60(3): 763-774
https://doi.org/10.4134/BKMS.b220366 -
On Chowla's hypothesis implying that $L(s,\chi)>0$ for $s>0$ for real characters $\chi$
St\'ephane R. Louboutin
Bull. Korean Math. Soc. 2023; 60(1): 1-22
https://doi.org/10.4134/BKMS.b210464 -
Residual supersingular Iwasawa theory over quadratic imaginary fields
Parham Hamidi
Bull. Korean Math. Soc. 2023; 60(4): 1035-1059
https://doi.org/10.4134/BKMS.b220461
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