Bulletin of the
Korean Mathematical Society
BKMS
ISSN(Print) 1015-8634
ISSN(Online) 2234-3016
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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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2023-07-31
Annihilator ideals of simple modules of restricted quantized enveloping algebra
Yu WangAbstract : Let $U$ be the restricted quantized enveloping algebra $\widetilde{U}_q(\mathfrak{sl}_2)$ over an algebraically closed field of characteristic zero, where $q$ is a primitive $l$-th root of unity (with $l$ being odd and greater than $1$). In this paper we show that any indecomposable submodule of $U$ under the adjoint action is generated by finitely many special elements. Using this result we describe all ideals of $U$. Moreover, we classify annihilator ideals of simple modules of $U$ by generators.
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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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2022-05-31
Constructions of regular sparse anti-magic squares
Guangzhou Chen
, Wen Li, Bangying Xin, Ming ZhongAbstract : For positive integers $n$ and $d$ with $d
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2023-01-31
The nilpotency of the prime radical of a Goldie module
John A. Beachy, Mauricio Medina-B\'arcenasAbstract : With the notion of prime submodule defined by F. Raggi et al. we prove that the intersection of all prime submodules of a Goldie module $M$ is a nilpotent submodule provided that $M$ is retractable and $M^{(\Lambda)}$-projective for every index set $\Lambda$. This extends the well known fact that in a left Goldie ring the prime radical is nilpotent.
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2022-11-30
Biharmonic hypersurfaces with recurrent operators in the Euclidean space
Esmaiel Abedi, Najma MosadeghAbstract : We show how some of well-known recurrent operators such as recurrent curvature operator, recurrent Ricci operator, recurrent Jacobi operator, recurrent shape and Weyl operators have the significant role for biharmonic hypersurfaces to be minimal in the Euclidean space.
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2023-01-31
UN rings and group rings
Kanchan Jangra, Dinesh UdarAbstract : A ring $R$ is called a UN ring if every non unit of it can be written as product of a unit and a nilpotent element. We obtain results about lifting of conjugate idempotents and unit regular elements modulo an ideal $I$ of a UN ring $R$. Matrix rings over UN rings are discussed and it is obtained that for a commutative ring $R$, a matrix ring $M_n(R)$ is UN if and only if $R$ is UN. Lastly, UN group rings are investigated and we obtain the conditions on a group $G$ and a field $K$ for the group algebra $KG$ to be UN. Then we extend the results obtained for $KG$ to the group ring $RG$ over a ring $R$ (which may not necessarily be a field).
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2023-07-31
Dynamics of random dynamical systems
Enkhbayar Azjargal, Zorigt Choinkhor, Nyamdavaa TsegmidAbstract : In this paper, we introduce the concept of $\omega$-expansive of random map on compact metric spaces $\mathcal{P}$. Also we introduce the definitions of positively, negatively shadowing property and shadowing property for two-sided RDS. Then we show that if $\varphi$ is $\omega$-expansive and has the shadowing property for $\omega$, then $\varphi$ is topologically stable for $\omega$.
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2022-11-30
On the Pocklington-Peralta square root algorithm in finite fields
Chang Heon Kim, Namhun Koo, Soonhak KwonAbstract : We present a new square root algorithm in finite fields which is a variant of the Pocklington-Peralta algorithm. We give the complexity of the proposed algorithm in terms of the number of operations (multiplications) in finite fields, and compare the result with other square root algorithms, the Tonelli-Shanks algorithm, the Cipolla-Lehmer algorithm, and the original Pocklington-Peralta square root algorithm. Both the theoretical estimation and the implementation result imply that our proposed algorithm performs favorably over other existing algorithms. In particular, for the NIST suggested field P-224, we show that our proposed algorithm is significantly faster than other proposed algorithms.
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2023-01-31
Lens spaces admitting minimal symplectic fillings with the second Betti number one
Heesang Park, Dongsoo ShinAbstract : We classify lens spaces with the Milnor fillable contact structure that admit minimal symplectic fillings whose second Betti numbers are one.
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Pricing American lookback options under a stochastic volatility model
Donghyun Kim, Junhui Woo, Ji-Hun Yoon
Bull. Korean Math. Soc. 2023; 60(2): 361-388
https://doi.org/10.4134/BKMS.b220134 -
Computation of Wedderburn decomposition of groups algebras from their subalgebra
Gaurav Mittal, Rajendra Kumar Sharma
Bull. Korean Math. Soc. 2022; 59(3): 781-787
https://doi.org/10.4134/BKMS.b210478 -
On complete convergence for weighted sums of coordinatewise negatively associated random vectors in Hilbert spaces
Vu Thi Ngoc Anh, Nguyen Thi Thanh Hien
Bull. Korean Math. Soc. 2022; 59(4): 879-895
https://doi.org/10.4134/BKMS.b210509 -
Some remarks on problems of subset sum
Min Tang, Hongwei Xu
Bull. Korean Math. Soc. 2022; 59(6): 1339-1348
https://doi.org/10.4134/BKMS.b210262
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On semi-regular injective modules and strong dedekind rings
Renchun Qu
Bull. Korean Math. Soc. 2023; 60(4): 1071-1083
https://doi.org/10.4134/BKMS.b220516 -
On the $p$-adic valuation of generalized harmonic numbers
Çağatay Altuntaş
Bull. Korean Math. Soc. 2023; 60(4): 933-955
https://doi.org/10.4134/BKMS.b220399 -
Existence of the continued fractions of $\sqrt{d}$ and its applications
Jun Ho Lee
Bull. Korean Math. Soc. 2022; 59(3): 697-707
https://doi.org/10.4134/BKMS.b210422 -
Complex symmetric weighted composition-differentiation operators on $H^2$
Lian Hu, Songxiao Li, Rong Yang
Bull. Korean Math. Soc. 2023; 60(5): 1141-1154
https://doi.org/10.4134/BKMS.b220215
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