Canadian Mathematical Bulletin最新文献

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A generalization of immanants based on partition algebra characters 基于分区代数字符的常量概化

Canadian Mathematical Bulletin

Pub Date : 2024-04-01 DOI: 10.4153/s0008439524000249

John M. Campbell

We introduce a generalization of immanants of matrices, using partition algebra characters in place of symmetric group characters. We prove that our immanant-like function on square matrices, which we refer to as the recombinant, agrees with the usual definition for immanants for the special case whereby the vacillating tableaux associated with the irreducible characters correspond, according to the Bratteli diagram for partition algebra representations, to the integer partition shapes for symmetric group characters. In contrast to previously studied variants and generalizations of immanants, as in Temperley–Lieb immanants and f-immanants, the sum that we use to define recombinants is indexed by a full set of partition diagrams, as opposed to permutations.

我们用分割代数字符代替对称群字符，引入了矩阵高程的一般化。我们证明，我们在正方形矩阵上的伊曼函数--我们称之为重组函数--在特殊情况下与伊曼的通常定义一致，在这种情况下，与不可还原字符相关的空位表象，根据分割代数表示的布拉泰利图，对应于对称群字符的整数分割形状。与之前研究过的 "訇 "的变体和概括（如滕伯里-李布 "訇 "和 f-"訇"）不同，我们用来定义重组子的和是以一整套分区图为索引的，而不是以排列为索引的。

引用次数: 0

Existence of singular rotationally symmetric gradient Ricci solitons in higher dimensions 高维奇异旋转对称梯度利玛窦孤子的存在性

Canadian Mathematical Bulletin

Pub Date : 2024-03-21 DOI: 10.4153/s0008439524000237

Kin Ming Hui

By using fixed point argument, we give a proof for the existence of singular rotationally symmetric steady and expanding gradient Ricci solitons in higher dimensions with metric $g=frac {da^2}{h(a^2)}+a^2g_{S^n}$ for some function h where $g_{S^n}$ is the standard metric on the unit sphere $S^n$ in $mathbb {R}^n$ for any $nge 2$. More precisely, for any $lambda ge 0$ and $c_0>0$, we prove that there exist infinitely many solutions ${hin C^2((0,infty );mathbb {R}^+)}$ for the equation $2r^2h(r)h_{rr}

通过使用定点论证，我们证明了奇异旋转对称稳定和扩展梯度里奇孤子在更高维度上的存在性，其度量$g=frac {da^2}{h(a^2)}+a^2g_{S^n}$ 为某个函数h，其中$g_{S^n}$是任意$nge 2$的$mathbb {R}^n$ 中单位球$S^n$上的标准度量。更确切地说，对于任意 $lambda ge 0$ 和 $c_0>0$，我们证明存在无穷多个解 ${hin C^2((0,infty )；方程$2r^2h(r)h_{rr}(r)=(n-1)h(r)(h(r)-1)+rh_r(r)(rh_r(r)-lambda r-(n-1))}$, $h(r)>；0$, in $(0,infty )$ satisfying $underset {substack {rto 0}}{lim },r^{sqrt {n}-1}h(r)=c_0$ 并证明了原点附近全局奇异解的高阶渐近行为。我们还从该方程在原点附近的渐近行为出发，找到了该方程唯一全局奇异解存在的条件。

引用次数: 0

OMEGA RESULTS FOR THE ERROR TERM IN THE SQUARE-FREE DIVISOR PROBLEM FOR SQUARE-FULL INTEGERS 平方整数无平方除数问题中误差项的欧米伽结果

Canadian Mathematical Bulletin

Pub Date : 2024-03-20 DOI: 10.4153/s0008439524000225

Debika Banerjee, Makoto Minamide

引用次数: 0

ALMOST SURE CONVERGENCE OF THE NORM OF LITTLEWOOD POLYNOMIALS Littlewood 多项式规范的几乎确定收敛性

Canadian Mathematical Bulletin

Pub Date : 2024-03-15 DOI: 10.4153/s0008439524000213

Yongjiang Duan, Xiang Fang, NA Zhan

引用次数: 0

IDEALS WITH COMPONENTWISE LINEAR POWERS 具有分量线性幂的理想

Canadian Mathematical Bulletin

Pub Date : 2024-03-12 DOI: 10.4153/s0008439524000201

Takayuki Hibi, Somayeh Moradi

引用次数: 0

A class of Hessian quotient equations in de Sitter space 德西特空间中的一类黑森商数方程

Canadian Mathematical Bulletin

Pub Date : 2024-03-06 DOI: 10.4153/s0008439524000183

Jinyu Gao, Guanghan Li, Kuicheng Ma

In this paper, we consider the closed spacelike solution to a class of Hessian quotient equations in de Sitter space. Under mild assumptions, we obtain an existence result using standard degree theory based on a priori estimates.

在本文中，我们考虑了德西特空间中一类 Hessian 商方程的封闭空间解。在温和的假设条件下，我们利用基于先验估计的标准度理论得到了一个存在性结果。

引用次数: 0

Linear independence of series related to the Thue–Morse sequence along powers 与 Thue-Morse 序列相关的序列沿幂级数的线性独立性

Canadian Mathematical Bulletin

Pub Date : 2024-03-06 DOI: 10.4153/s0008439524000195

Michael Coons, Yohei Tachiya

The Thue–Morse sequence ${t(n)}_{ngeqslant 0}$ is the indicator function of the parity of the number of ones in the binary expansion of nonnegative integers n, where $t(n)=1$ (resp. $=0$) if the binary expansion of n has an odd (resp. even) number of ones. In this paper, we generalize a recent result of E. Miyanohara by showing that, for a fixed Pisot or Salem number $beta>sqrt {varphi }=1.272019ldots $, the set of the numbers $$begin{align*}1,quad sum_{ngeqslant1}frac{t(n)}{beta^{n}},quad sum_{ngeqslant1}frac{t(n^2)}{beta^{n}},quad dots, quad sum_{ngeqslant1}frac{t(n^k)}{beta^{n}},quad dots end{align*}$$is linearly independent over the field $mathbb {Q}(beta )$, where $varphi :=(1+sqrt {5})/2$ is the golden ratio. Our result yields that for any integer $kgeqslant 1$<

Thue-Morse 序列 ${t(n)}_{ngeqslant 0}$ 是非负整数 n 的二进制展开中 1 的个数奇偶性的指示函数，其中如果 n 的二进制展开中 1 的个数为奇数（或偶数），则 $t(n)=1$（或 $=0$）。在本文中，我们推广了宫之原（E. Miyanohara）最近的一个结果，证明对于一个固定的皮索特（Pisot）或萨利姆（Salem）数 $beta>sqrt {varphi }=1.272019ldots $, the set of the numbers $$begin{align*}1,quad sum_{ngeqslant1}frac{t(n)}{beta^{n}},quad sum_{ngeqslant1}frac{t(n^2)}{beta^{n}}、quad dots, quad sum_{ngeqslant1}frac{t(n^k)}{beta^{n}}, quad dots end{align*}$$ 是线性独立于域 $mathbb {Q}(beta )$, 其中 $varphi ：=(1+sqrt {5})/2$ 是黄金分割率。我们的结果表明，对于任意整数 $kgeqslant 1$，并且对于 mathbb {Q}(beta )$ 中的任意 $a_1,a_2,ldots ,a_k 都不为零，序列 {$a_1t(n)+a_2t(n^2)+cdots +a_kt(n^k)}_{ngeqslant 1}$ 最终不可能是周期性的。

引用次数: 0

Moments of the central L-values of the Asai lifts 浅井升降机中心 L 值的矩

Canadian Mathematical Bulletin

Pub Date : 2024-03-04 DOI: 10.4153/s0008439524000171

Wenzhi Luo

We study some analytic properties of the Asai lifts associated with cuspidal Hilbert modular forms, and prove sharp bounds for the second moment of their central L-values.

我们研究了与尖顶希尔伯特模态相关的浅井提升的一些分析性质，并证明了其中心 L 值第二矩的锐界。

引用次数: 0

On the Complexity of Extending the Convergence Domain of Newton’s Method Under the Weak Majorant Condition 论弱马约兰特条件下扩展牛顿方法收敛域的复杂性

Canadian Mathematical Bulletin

Pub Date : 2024-03-01 DOI: 10.4153/s000843952400016x

Ioannis K. Argyros, S. George

引用次数: 0

Hausdorff operators on some classical spaces of analytic functions 一些经典解析函数空间上的豪斯多夫算子

Canadian Mathematical Bulletin

Pub Date : 2024-02-29 DOI: 10.4153/s0008439524000158

Huayou Xie, Qingze Lin

In this note, we start on the study of the sufficient conditions for the boundedness of Hausdorff operators $$ begin{align*}(mathcal{H}_{K,mu}f)(z):=int_{mathbb{D}}K(w)f(sigma_w(z))dmu(w)end{align*} $$on three important function spaces (i.e., derivative Hardy spaces, weighted Dirichlet spaces, and Bloch type spaces), which is a continuation of the previous works of Mirotin et al. Here, $mu $ is a positive Radon measure, K is a $mu $-measurable function on the open unit disk $mathbb {D}$, and $sigma _w(z)$ is the classical Möbius transform of $mathbb {D}$.

在本论文中，我们首先研究 Hausdorff 算子 $$ （begin{align*}(mathcal{H}_{K,mu}f)(z):=int_{mathbb{D}}K(w)f(sigma_w(z))dmu(w)）有界性的充分条件。这里，$mu $ 是一个正的拉顿度量，K 是开放单位盘 $mathbb {D}$ 上的一个 $mu $ 可度量函数，$sigma _w(z)$ 是 $mathbb {D}$ 的经典莫比乌斯变换。

引用次数: 0

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