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Bull. Korean Math. Soc. 2023; 60(3): 561~848
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2023-05-31
MacWilliams-type identities on vectorial Boolean functions with bent components and applications
Jong Yoon HyunAbstract : In this paper, we focus on establishing the MacWilliams-type identities on vectorial Boolean functions with bent component functions. As their applications, we provide a bound for the non-existence of vectorial dual-bent functions with prescribed minimum degree, and several Gleason-type theorems are presented as well.
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2023-05-31
Extensions of multiple Lauricella and Humbert's confluent hypergeometric functions through a highly generalized Pochhammer symbol and their related properties
Ritu Agarwal, Junesang Choi, Naveen Kumar, Rakesh K. ParmarAbstract : Motivated by several generalizations of the Pochhammer \linebreak symbol and their associated families of hypergeometric functions and hypergeometric polynomials, by choosing to use a very generalized Pochhammer symbol, we aim to introduce certain extensions of the generalized Lauricella function $F_A^{(n)}$ and the Humbert's confluent hypergeometric function $\Psi^{(n)}$of $n$ variables with, as their respective particular cases, the second Appell hypergeometric function $F_2$ and the generalized Humbert's confluent hypergeometric functions $\Psi_2$ and investigate their several properties including, for example, various integral representations, finite summation formulas with an $s$-fold sum and integral representations involving the Laguerre polynomials, the incomplete gamma functions, and the Bessel and modified Bessel functions. Also, pertinent links between the major identities discussed in this article and different (existing or novel) findings are revealed.
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2023-05-31
Some results on meromorphic solutions of q-difference differential equations
Lingyun Gao, Zhenguang Gao, Manli LiuAbstract : In view of Nevanlinna theory, we investigate the meromorphic solutions of q-difference differential equations and our results give the estimates about counting function and proximity function of meromorphic solutions to these equations. In addition, some interesting results are obtained for two general equations and a class of system of q-difference differential equations.
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2023-05-31
On the hybrid mean value of generalized Dedekind sums, generalized Hardy sums and Kloosterman sums
Qing Tian, Yan WangAbstract : The main purpose of this paper is to study the hybrid mean value problem involving generalized Dedekind sums, generalized Hardy sums and Kloosterman sums. Some exact computational formulas are given by using the properties of Gauss sums and the mean value theorem of the Dirichlet L-function. A result of W. Peng and T. P. Zhang [12] is extended. The new results avoid the restriction that $q$ is a prime.
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2023-05-31
Vanishing theorems for weighted harmonic $1$-forms on smooth metric measure spaces
Xiaoli Chao, Weili WangAbstract : In this paper, we prove some vanishing theorems under the assumptions of weighted BiRic curvature or $m$-Bakry-\'{E}mery-Ricci curvature bounded from below.
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2023-05-31
Characterization of weakly cofinite local cohomology modules
Moharram Aghapournahr, Marziye HatamkhaniAbstract : Let $R$ be a commutative Noetherian ring, $\mathfrak{a}$ an ideal of $R$,$M$ an arbitrary $R$-module and $X$ a finite $R$-module. We prove a characterization for ${H} \DeclareMathOperator{\End}{End}_{\mathfrak{a}}^{i}(M)$ and ${H} \DeclareMathOperator{\End}{End}_{\mathfrak{a}}^{i}(X,M)$ to be $\mathfrak{a}$-weakly cofinite for all $i$, whenever one of the following cases holds:(a) ${ara} (\mathfrak{a})\leq 1$, (b) $\dim R/\mathfrak{a} \leq 1$ or (c) $\dim R\leq 2$. We alsoprove that, if $M$ is a weakly Laskerian $R$-module, then ${H} \DeclareMathOperator{\End}{End}_{\mathfrak{a}}^{i}(X,M)$ is $\mathfrak{a}$-weakly cofinite for all $i$, whenever $\dim X\leq 2$ or $\dim M\leq 2$ (resp.$(R,\mathfrak{m})$ a local ring and $\dim X\leq 3$ or $\dim M\leq 3$). Let $d=\dim M<\infty$, we prove an equivalent condition for top local cohomology module ${H} \DeclareMathOperator{\End}{End}_{\mathfrak{a}}^{d}(M)$ to be weakly Artinian.
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2023-05-31
Compact composition operators on Besov spaces on the unit ball
Chao ZhangAbstract : In this paper, we give new necessary and sufficient conditions for the compactness of composition operator on the Besov space and the Bloch space of the unit ball, which, to a certain extent, generalizes the results given by M. Tjani in [10].
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2023-05-31
The critical pods of planar quadratic polynomial maps of topological degree 2
Misong Chang, Sunyang Ko, Chong Gyu Lee, Sang-Min LeeAbstract : {Let $K$ be an algebraically closed field of characteristic 0 and let $f$ be a non-fibered planar quadratic polynomial map of topological degree 2 defined over $K$. We assume further that the meromorphic extension of $f$ on the projective plane has the unique indeterminacy point.} We define \emph{the critical pod of $f$} where $f$ sends a critical point to another critical point. By observing the behavior of $f$ at the critical pod, we can determine a good conjugate of $f$ which shows its statue in GIT sense.
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2023-05-31
There are no numerical radius peak $n$-linear mappings on $c_0$
Sung Guen KimAbstract : For $n\geq 2$ and a real Banach space $E$, ${\mathcal L}(^n E:E)$ denotes the space of all continuous $n$-linear mappings from $E$ to itself. Let $$\Pi(E)=\{[x^*, (x_1, \ldots, x_n)]: x^{*}(x_j)=\|x^{*}\|=\|x_j\|=1~\mbox{for}~{j=1, \ldots, n}~\}.$$ An element $[x^*, (x_1, \ldots, x_n)]\in \Pi(E)$ is called a {\em numerical radius point} of $T\in {\mathcal L}(^n E:E)$ if $|x^{*}(T(x_1, \ldots, x_n))|=v(T)$, where the numerical radius $v(T)=\sup_{[y^*, y_1, \ldots, y_n]\in \Pi(E)}\Big|y^{*}\Big(T(y_1, \ldots,y_n)\Big)\Big|$. For $T\in {\mathcal L}(^n E:E)$, we define \begin{align*} {Nradius}({T})=&\ \{[x^*, (x_1, \ldots, x_n)]\in \Pi(E): [x^*, (x_1, \ldots, x_n)]\\ &\quad \mbox{is a numerical radius point of}~T\}. \end{align*} $T$ is called a {\em numerical radius peak $n$-linear mapping} if there is a unique $[x^{*}, (x_1, \ldots, x_n)]\in \Pi(E)$ such that ${Nradius}({T})=\{\pm [x^{*}, (x_1, \ldots, x_n)]\}$. In this paper we present explicit formulae for the numerical radius of $T$ for every $T\in {\mathcal L}(^n E:E)$ for $E=c_0$ or $l_{\infty}$. Using these formulae we show that there are no numerical radius peak mappings of ${\mathcal L}(^n c_0:c_0)$.
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2023-05-31
On a Spitzer-type law of large numbers for partial sums of independent and identically distributed random variables under sub-linear expectations
Miaomiao Wang, Min Wang, Xuejun WangAbstract : In this paper, under some suitable conditions, we study the Spitzer-type law of large numbers for the maximum of partial sums of independent and identically distributed random variables in upper expectation space. Some general results on necessary and sufficient conditions of the Spitzer-type law of large numbers for the maximum of partial sums of independent and identically distributed random variables under sub-linear expectations are established, which extend the corresponding ones in classic probability space to the case of sub-linear expectation space.
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