Bulletin of the
Korean Mathematical Society
BKMS
ISSN(Print) 1015-8634
ISSN(Online) 2234-3016
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2022-11-30
Some new classes of zero-difference balanced functions and related constant composition codes
Sankhadip Roy
Abstract : Zero-difference balanced (ZDB) functions can be applied to many areas like optimal constant composition codes, optimal frequency hopping sequences etc. Moreover, it has been shown that the image set of some ZDB functions is a regular partial difference set, and hence provides strongly regular graphs. Besides, perfect nonlinear functions are zero-difference balanced functions. However, the converse is not true in general. In this paper, we use the decomposition of cyclotomic polynomials into irreducible factors over $\mathbb F_p$, where $p$ is an odd prime to generalize some recent results on ZDB functions. Also we extend a result introduced by Claude et al. [3] regarding zero-difference-$p$-balanced functions over $\mathbb F_{p^n}$. Eventually, we use these results to construct some optimal constant composition codes.
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2022-11-30
Blow up of solutions for a Petrovsky type equation with logarithmic nonlinearity
Jorge Ferreira, Nazl\i \, Irk\i l, Erhan Pi\c{s}kin, Carlos Raposo, Mohammad ShahrouziAbstract : This paper aims to investigate the initial boundary value problem of the nonlinear viscoelastic Petrovsky type equation with nonlinear damping and logarithmic source term. We derive the blow-up results by the combination of the perturbation energy method, concavity method, and differential-integral inequality technique.
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2023-01-31
On the top local cohomology and formal local cohomology modules
Shahram Rezaei, Behrouz SadeghiAbstract : Let ${\mathfrak{a}}$ and $\mathfrak{b}$ be ideals of a commutative Noetherian ring $R$ and $M$ a finitely generated $R$-module of finite dimension $d>0$. In this paper, we obtain some results about the annihilators and attached primes of top local cohomology and top formal local cohomology modules. In particular, we determine $\operatorname{Ann} (\mathfrak{b}\operatorname{H}_{\mathfrak{a}}^{d}(M))$, $\operatorname{Att} (\mathfrak{b}\operatorname{H}_{\mathfrak{a}}^{d}(M))$, $\operatorname{Ann}(\mathfrak{b}\mathfrak{F}_{\mathfrak{a}}^{d} (M))$ and $\operatorname{Att} (\mathfrak{b}\mathfrak{F}_{\mathfrak{a}}^{d} (M))$.
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2022-05-31
Strong classification of extensions of classifiable $C^{*}$-algebras
S{\o}ren Eilers, Gunnar Restorff, Efren RuizAbstract : We show that certain extensions of classifiable $C^{*}$-algebras are strongly classified by the associated six-term exact sequence in $K$-theory together with the positive cone of $K_{0}$-groups of the ideal and quotient. We use our results to completely classify all unital graph $C^{*}$-algebras with exactly one non-trivial ideal.
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2023-03-31
Rings and modules which are stable under nilpotents of their injective hulls
Nguyen Thi Thu HaAbstract : It is shown that every nilpotent-invariant module can be decomposed into a direct sum of a quasi-injective module and a square-free module that are relatively injective and orthogonal. This paper is also concerned with rings satisfying every cyclic right $R$-module is nilpotent-invariant. We prove that $R\cong R_1\times R_2$, where $R_1, R_2$ are rings which satisfy $R_1$ is a semi-simple Artinian ring and $R_2$ is square-free as a right $R_2$-module and all idempotents of $R_2$ is central. The paper concludes with a structure theorem for cyclic nilpotent-invariant right $R$-modules. Such a module is shown to have isomorphic simple modules $eR$ and $fR$, where $e,f$ are orthogonal primitive idempotents such that $eRf\ne 0$.
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2022-09-30
On the geometry of complex metallic Norden manifolds
Adara Monica Blaga, Rakesh Kumar, Rachna RaniAbstract : We study almost complex metallic Norden manifolds and their adapted connections with respect to an almost complex metallic Norden structure. We study various connections like special connection of the first type, special connection of the second type, Kobayashi-Nomizu metallic Norden type connection, Yano metallic Norden type connection etc., on almost complex metallic Norden manifolds. We establish classifications of almost complex metallic Norden manifolds by using covariant derivative of the almost complex metallic Norden structure and also by using torsion tensor on the canonical connections.
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2022-11-30
Lipschitz type characterization of Fock type spaces
Hong Rae Cho, Jeong Min HaAbstract : For setting a general weight function on $n$ dimensional complex space ${\mathbb C}^n$, we expand the classical Fock space.We define Fock type space $F^{p,q}_{\phi, t}({\mathbb C}^n)$ of entire functions with a mixed norm, where $0<p,q<\infty$ and $t\in\mathbb R$ and prove that the mixed norm of an entire function is equivalent to the mixed norm of its radial derivative on $F^{p,q}_{\phi, t}({\mathbb C}^n)$.As a result of this application, the space $F^{p,p}_{\phi, t}({\mathbb C}^n)$ is especially characterized by a Lipschitz type condition.
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2022-07-31
Colocalization of generalized local homology modules
Marziyeh HatamkhaniAbstract : Let $R$ be a commutative Noetherian ring and $I$ an ideal of $R$. In this paper, we study colocalization of generalized local homology modules. We intend to establish a dual case of local-global principle for the finiteness of generalized local cohomology modules. Let $M$ be a finitely generated $R$-module and $N$ a representable $R$-module. We introduce the notions of the representation dimension $r^I (M, N)$ and artinianness dimension $a^I (M, N)$ of $M,N$ with respect to $I$ by $r^I (M, N)= \inf\{i\in \mathbb{N}_0 : H^I_i(M,N) \text{ is not representable}\}$ and $a^I (M, N)= \inf\{i\in \mathbb{N}_0 : H^I_i(M,N)\text{ is not artinian}\}$ and we show that $a^I (M, N)=r^I (M, N)$ $=\inf\{r^{IR_{\mathfrak{p}}}(M_{\mathfrak{p}},_{\mathfrak{p}}N) : \mathfrak{p}\in \operatorname{Spec}(R)\}\geq \inf\{a^{IR_{\mathfrak{p}}}(M_{\mathfrak{p}},_{\mathfrak{p}}N) : \mathfrak{p}\in \operatorname{Spec}(R)\}$. Also, in the case where $R$ is semi-local and $N$ a semi discrete linearly compact $R$-module such that $N/\bigcap_{t>0} I^tN$ is artinian we prove that $\inf\{i: H^I_i(M,N) \text{ is not minimax}\}\!=\!\inf\{r^{IR_{\mathfrak{p}}}(M_{\mathfrak{p}},_{\mathfrak{p}}N) : \mathfrak{p}\in \operatorname{Spec}(R)\setminus\operatorname{Max}(R)\}.$
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2022-05-31
On toric Hamiltonian $T$-spaces with anti-symplectic involutions
Jin Hong KimAbstract : The aim of this paper is to deal with the realization problem of a given Lagrangian submanifold of a symplectic manifold as the fixed point set of an anti-symplectic involution. To be more precise, let $(X, \omega, \mu)$ be a toric Hamiltonian $T$-space, and let $\Delta=\mu(X)$ denote the moment polytope. Let $\tau$ be an anti-symplectic involution of $X$ such that $\tau$ maps the fibers of $\mu$ to (possibly different) fibers of $\mu$, and let $p_0$ be a point in the interior of $\Delta$. If the toric fiber $\mu^{-1}(p_0)$ is real Lagrangian with respect to $\tau$, then we show that $p_0$ should be the origin and, furthermore, $\Delta$ should be centrally symmetric.
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2022-11-30
Irreducibility of the moduli space for the quotient singularity $\frac{1}{2k+1}(k+1,1,2k)$
Seung-Jo JungAbstract : A 3-fold quotient terminal singularity is of the type $\frac{1}{r}(b,1$, $-1)$ with $\gcd(r,b)=1$. In \cite{Terminal}, it is proved that the economic resolution of a 3-fold terminal quotient singularity is isomorphic to a distinguished component of a moduli space $\mathcal M_{\theta}$ of $\theta$-stable $G$-constellations for a suitable $\theta$. This paper proves that each connected component of the moduli space $\\mathcal M_{\theta}$ has a torus fixed point and classifies all torus fixed points on $\mathcal M_{\theta}$. By product, we show that for $\frac{1}{2k+1}(k+1,1,-1)$ case the moduli space $\mathcal M_{\theta}$ is irreducible.
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Integrability of an almost complex structure on $S^4\times_f V^2$
Jong Taek Cho, Sun Hyang Chun, Yunhee Euh
Bull. Korean Math. Soc. 2022; 59(4): 801-810
https://doi.org/10.4134/BKMS.b200606 -
The third Hermitian-Toeplitz and Hankel determinants for parabolic starlike functions
Rosihan M. Ali, Sushil Kumar, Vaithiyanathan Ravichandran
Bull. Korean Math. Soc. 2023; 60(2): 281-291
https://doi.org/10.4134/BKMS.b210368 -
An associated sequence of ideals of an increasing sequence of rings
Ali Benhissi, Abdelamir Dabbabi
Bull. Korean Math. Soc. 2022; 59(6): 1349-1357
https://doi.org/10.4134/BKMS.b210425 -
$P$-extremal functions and Bernstein-Markov properties associated to compact sets in $\mathbb R^d$
Hoang Thieu Anh, Kieu Phuong Chi, Nguyen Quang Dieu, Tang Van Long
Bull. Korean Math. Soc. 2022; 59(4): 811-825
https://doi.org/10.4134/BKMS.b210341
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On the structure of certain subset of Farey sequence
Xing-Wang Jiang, Ya-Li Li
Bull. Korean Math. Soc. 2023; 60(4): 915-931
https://doi.org/10.4134/BKMS.b220396 -
Some results on 2-strongly Gorenstein projective modules and related rings
Dong Chen, Kui Hu
Bull. Korean Math. Soc. 2023; 60(4): 895-903
https://doi.org/10.4134/BKMS.b220392 -
Hypersurfaces with prescribed mean curvature in measure metric space
Zhengmao Chen
Bull. Korean Math. Soc. 2023; 60(4): 1085-1100
https://doi.org/10.4134/BKMS.b220531 -
A model of retirement and consumption-portfolio choice
Junkee Jeon, Hyeng Keun Koo
Bull. Korean Math. Soc. 2023; 60(4): 1101-1129
https://doi.org/10.4134/BKMS.b220553
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