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ON q-ANALOGUES OF ZETA FUNCTIONS OF ROOT SYSTEMS 关于根系统的ZETA函数的q-相似性
IF 0.4 4区 数学 Q3 MATHEMATICS Pub Date : 2023-01-01 DOI: 10.2206/kyushujm.76.451
Masakimi Kato
. Komori, Matsumoto and Tsumura introduced a zeta function ζ r ( s , (cid:49)) associated with a root system (cid:49) . In this paper, we introduce a q -analogue of this zeta function, denoted by ζ r ( s , a , (cid:49) ; q ) , and investigate its properties. We show that a ‘Weyl group symmetric’ linear combination of ζ r ( s , a , (cid:49) ; q ) can be written as a multiple integral over a torus involving functions ψ s . For positive integers k , functions ψ k can be regarded as q -analogues of the periodic Bernoulli polynomials. When (cid:49) is of type A 2 or A 3 , the linear combinations can be expressed as the functions ψ k , which are q -analogues of explicit expressions of Witten’s volume formula. We also introduce a two-parameter deformation of the zeta function ζ r ( s , (cid:49)) and study its properties. ,
Komori、Matsumoto和Tsumura引入了与根系(cid:49)相关的ζr(s,(cid:49))函数。在本文中,我们引入了这个ζ函数的q-类似物,表示为ζr(s,a,(cid:49);q),并研究其性质。我们证明了ζr(s,a,(cid:49)的“Weyl群对称”线性组合;q)可以写成包含函数ψs的环面上的多重积分。对于正整数k,函数ψk可以看作周期伯努利多项式的q-类似物。当(cid:49)是A2或A3型时,线性组合可以表示为函数ψk,它是Witten体积公式显式表达式的q-类似物。我们还引入了ζr(s,(cid:49))的双参数变形,并研究了它的性质,
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引用次数: 1
LINEAR OPERATORS WITH EMPTY SPECTRUM 具有空谱的线性算子
4区 数学 Q3 MATHEMATICS Pub Date : 2023-01-01 DOI: 10.2206/kyushujm.77.63
Morisuke HASUMI, Michio SETO
In this note we are interested in showing a simple property which characterizes linear operators having empty spectrum on complex Banach spaces. Although it is rather well known that such operators exist, the current literature deals with very few such examples,only as an exercise topic. Our characterization says that such operators are in one-to-one correspondence with injective quasinilpotent operators. This means that the purely unbounded property of linear operators can be reduced to the bounded one. In fact, we obtain a simple way to test and construct examples of such operators and then proceed to make observations of some interest from the function-theoretic point of view. For instance, we define an analogue of the order in the theory of entire functions and show the existence of operators of all order types.
在这篇笔记中,我们感兴趣的是给出复巴拿赫空间上具有空谱的线性算子的一个简单性质。虽然这类运算符的存在是众所周知的,但目前的文献很少涉及这类例子,只是作为一个练习主题。我们的刻画表明这样的算子与内射拟幂算子是一一对应的。这意味着线性算子的纯无界性质可以简化为有界性质。事实上,我们获得了一种简单的方法来测试和构造这些算子的例子,然后从函数论的角度进行一些有趣的观察。例如,我们在全函数理论中定义了阶的类比,并证明了所有阶类型算子的存在性。
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引用次数: 0
CURVE SHORTENING FLOWS ON ROTATIONAL SURFACES GENERATED BY MONOTONE CONVEX FUNCTIONS 由单调凸函数生成的旋转表面上的曲线缩短流
4区 数学 Q3 MATHEMATICS Pub Date : 2023-01-01 DOI: 10.2206/kyushujm.77.179
Naotoshi FUJIHARA
In this paper, we study curve shortening flows on rotational surfaces in ℝ3. We assume that the surfaces have negative Gauss curvatures and that some condition related to the Gauss curvature and the curvature of an embedded curve holds on them. Under these assumptions, we prove that the curve remains a graph over the parallels of the rotational surface along the flow. Also, we prove the comparison principle and the long-time existence of the flow.
本文研究了在旋转曲面上的曲线缩短流。我们假设曲面具有负高斯曲率,并且与高斯曲率和嵌入曲线的曲率有关的某些条件适用于它们。在这些假设下,我们证明了曲线仍然是沿流动的旋转表面的平行线上的图形。并证明了比较原理和流的长期存在性。
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引用次数: 1
REMARKABLE RELATIONS BETWEEN THE CENTRAL BINOMIAL SERIES, EULERIAN POLYNOMIALS, AND POLY-BERNOULLI NUMBERS, LEADING TO STEPHAN'S OBSERVATION 中心二项式级数、欧拉多项式和多伯努利数之间的显著关系,导致了斯蒂芬的观察
4区 数学 Q3 MATHEMATICS Pub Date : 2023-01-01 DOI: 10.2206/kyushujm.77.149
Beáta BÉNYI, Toshiki MATSUSAKA
The central binomial series at negative integers are expressed as a linear combination of values of certain two polynomials. We show that one of the polynomials is a special value of the bivariate Eulerian polynomial and the other polynomial is related to the anti-diagonal sum of poly-Bernoulli numbers. As an application, we prove Stephan's observation from 2004.
中心二项式级数在负整数处被表示为两个多项式值的线性组合。我们证明了其中一个多项式是二元欧拉多项式的一个特殊值,另一个多项式与多元伯努利数的反对角和有关。作为应用,我们证明了Stephan从2004年开始的观察。
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引用次数: 0
ASYMPTOTIC EXPANSION OF OSCILLATORY INTEGRALS WITH SINGULAR PHASES 奇异相位振荡积分的渐近展开式
4区 数学 Q3 MATHEMATICS Pub Date : 2023-01-01 DOI: 10.2206/kyushujm.77.319
Joe KAMIMOTO, Hiromichi MIZUNO
The purpose of this article is to describe the singularities of one-dimensional oscillatory integrals, whose phases have a certain singularity, in the form of an asymptotic expansion. In the case of the Laplace integral, an analogous result is also given.
本文的目的是用渐近展开的形式描述相位具有一定奇异性的一维振荡积分的奇异性。对于拉普拉斯积分,也给出了类似的结果。
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引用次数: 0
RICCI-BOURGUIGNON AND GRADIENT SOLITONS ON REAL HYPERSURFACES IN THE COMPLEX QUADRIC 复二次型实超曲面上的Ricci-bourguignon孤子和梯度孤子
4区 数学 Q3 MATHEMATICS Pub Date : 2023-01-01 DOI: 10.2206/kyushujm.77.331
Hyunjin LEE, Eunmi PAK, Young Jin SUH
By using the property of generalized pseudo-anti-commuting, Ric Φ + Φ Ric = f Φ, for real hypersurfaces in the complex quadric Qm = SOm+2/SO2SOm, we give a complete classification of Ricci-Bourguignon soliton Hopf real hypersurfaces in the complex quadric Qm. Then, as an application, we show a complete classification of Hopf Ricci-Bourguignon gradient solitons in the complex quadric Qm.
利用复二次型Qm = SOm+2/SO2SOm的广义伪反可交换Ric Φ + Φ Ric = f Φ的性质,给出了复二次型Qm中Ricci-Bourguignon孤子Hopf实超曲面的完全分类。然后,作为应用,我们给出了复二次型Qm中Hopf Ricci-Bourguignon梯度孤子的完全分类。
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引用次数: 0
THE DESCRIPTION OF THE CAPELLI ELEMENTS WITH A PARAMETER FOR CLASSICAL LIE ALGEBRAS IN TERMS OF SYMMETRIZED DETERMINANT 用对称行列式描述经典李代数的带参数capelli元
4区 数学 Q3 MATHEMATICS Pub Date : 2023-01-01 DOI: 10.2206/kyushujm.77.43
Shotaro KAWATA
We construct the Capelli elements Ck(u) = C(1k)(u) (k = 1, . . . , n) with a parameter u for the symplectic Lie algebras and orthogonal Lie algebras. They correspond to factorial Schur functions with parameter u attached to the column partitions (1k). We also give explicit formulas for Ck(u) arising from the expansion of Cn(u) = C(1n)(u) with respect to the parameter u. We use the Jacobi-Trudi formula for the factorial Schur functions Rλ(x; u) to construct the higher Capelli elements Cλ(u). They are expressed as determinants of matrices whose entries are Capelli elements Ck(u) attached to the column partitions.
我们构造Capelli元素Ck(u) = C(1k)(u) (k = 1,…, n),参数为u,适用于辛李代数和正交李代数。它们对应于带参数u的阶乘Schur函数,附加到列分区(1k)上。我们还给出了Ck(u)的显式公式,由Cn(u) = C(1n)(u)关于参数u展开而产生。我们使用Jacobi-Trudi公式来表示阶乘Schur函数Rλ(x;u)来构造更高的Capelli元素Cλ(u)。它们被表示为矩阵的行列式,其条目是附加到列分区上的Capelli元素Ck(u)。
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引用次数: 0
SECOND MAIN THEOREMS AND ALGEBRAIC DEPENDENCE OF MEROMORPHIC MAPPINGS ON PARABOLIC MANIFOLDS WITH MOVING TARGETS 具有运动目标的抛物流形上亚纯映射的第二个主要定理和代数依赖关系
4区 数学 Q3 MATHEMATICS Pub Date : 2023-01-01 DOI: 10.2206/kyushujm.77.203
Si Duc QUANG, Nguyen Van AN, Pham Duc THOAN
The purpose of this paper is twofold. The first is to give some forms of the second main theorem in Nevanlinna theory for meromorphic mappings from parabolic manifolds intersecting moving targets in general position with truncated counting functions, which are improvements of some recent results. The second is to apply the above forms to the proof of an algebraic dependence theorem for meromorphic mappings on parabolic manifolds sharing moving targets regardless of multiplicity.
本文的目的是双重的。首先给出了用截断计数函数与运动目标相交的抛物流形亚纯映射的Nevanlinna理论中第二个主要定理的一些形式,是对最近一些结果的改进。二是将上述形式应用于抛物流形上共享运动目标的亚纯映射的代数依赖定理的证明。
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引用次数: 0
QUALITATIVE PROPERTIES FOR ELLIPTIC PROBLEMS WITH CKN OPERATORS 具有CKN算子的椭圆型问题的定性性质
4区 数学 Q3 MATHEMATICS Pub Date : 2023-01-01 DOI: 10.2206/kyushujm.77.385
Huyuan CHEN, Yishan ZHENG
The purpose of this paper is to study the basic properties of a degenerate operator with critical gradient and critical Hardy term, controlled by two free parameters. This operator arises from the critical Caffarelli-Kohn-Nirenberg inequality. We analyze the fundamental solutions in a weighted distributional identity and obtain the Liouville theorem for the Lane-Emden equation with that operator, by using the classification of singular solutions with isolated singularities of the related Poisson problem in a bounded domain containing the origin.
研究了一类由两个自由参数控制的具有临界梯度和临界Hardy项的退化算子的基本性质。该算子由临界卡法瑞利-科恩-尼伦伯格不等式产生。利用相关泊松问题在包含原点的有界域上的孤立奇异解分类,分析了一类加权分布恒等式的基本解,得到了一类带该算子的Lane-Emden方程的Liouville定理。
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引用次数: 1
ACTION OF <i>E</i><sub>2 </sub>ON HECKE EIGENFORMS &lt;i&gt; /i&gt;&lt;sub&gt;2 &lt;/sub&gt;对HECKE特征形式的作用
4区 数学 Q3 MATHEMATICS Pub Date : 2023-01-01 DOI: 10.2206/kyushujm.77.401
Hui XUE, Naveen PRABHATH
We determine when the modified Rankin-Cohen bracket of the Eisenstein series of weight two and a Hecke eigenform is again an eigenform.
我们确定权值2和Hecke特征型的爱森斯坦级数的修正Rankin-Cohen括号何时又是特征型。
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引用次数: 0
期刊
Kyushu Journal of Mathematics
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