Proceedings of the American Mathematical Society最新文献

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A note on new weighted geometric inequalities for hypersurfaces in ℝⁿ 关于ℝⁿ中超曲面的新加权几何不等式的说明

IF 1 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society

Pub Date : 2024-04-10 DOI: 10.1090/proc/16875

Jie Wu

In this note, we prove a family of sharp weighed inequalities which involve weighted k k -th mean curvature integral and two distinct quermassintegrals for closed hypersurfaces in R n mathbb {R}^n . This inequality generalizes the corresponding result of Wei and Zhou [Bull. Lond. Math. Soc. 55 (2023), pp. 263–281] where their proof is based on earlier results of Kwong-Miao [Pacific J. Math. 267 (2014), pp. 417–422; Commun. Contemp. Math. 17 (2015), p. 1550014]. Here we present a proof which does not rely on Kwong-Miao’s results.

在本注释中，我们证明了一系列尖锐的权重不等式，它们涉及 R n mathbb {R}^n 中封闭超曲面的加权 k k -th 平均曲率积分和两个不同的质点积分。这个不等式概括了 Wei 和 Zhou [Bull. Lond. Math. Soc. 55 (2023), pp.267 (2014), pp.Contemp.Math.17 (2015), p. 1550014].这里我们提出一个不依赖邝淼结果的证明。

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引用次数: 0

The realizability problem as a special case of the infinite-dimensional truncated moment problem 作为无穷维截断矩问题特例的可实现性问题

IF 1 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society

Pub Date : 2024-04-05 DOI: 10.1090/proc/16710

Raúl E. Curto, Maria Infusino

引用次数: 0

A new lower bound for the number of conjugacy classes 共轭类数的新下限

IF 1 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society

Pub Date : 2024-04-03 DOI: 10.1090/proc/16876

Burcu Çınarcı, Thomas Keller

In 2000, Héthelyi and Külshammer [Bull. London Math. Soc. 32 (2000), pp. 668–672] proposed that if <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding="application/x-tex">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a finite group, <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a prime dividing the group order, and <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="k left-parenthesis upper G right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>G</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">k(G)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is the number of conjugacy classes of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding="application/x-tex">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, then <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="k left-parenthesis upper G right-parenthesis greater-than-or-equal-to 2 StartRoot p minus 1 EndRoot"> <mml:semantics> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>G</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>≥</mml:mo> <mml:mn>2</mml:mn> <mml:msqrt> <mml:mi>p</mml:mi> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:msqrt> </mml:mrow> <mml:annotation encoding="application/x-tex">k(G)geq 2sqrt {p-1}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, and they proved this conjecture for solvable <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding="application/x-tex">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and showed that it is sharp for those primes <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for which <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartRoot p minus 1 EndRoot"> <mml:semantics> <mml:msqrt> <mml:mi>p</mml:mi> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:msqrt> <mml:annotation encoding="application/x-tex">sqrt {p-1}</mml:annotation> </mml:semantics> </mml:math> </inl

2000 年，Héthelyi 和 Külshammer [Bull.668-672] 提出，如果 G G 是有限群，p p 是划分群阶的素数，而 k ( G ) k(G) 是 G G 的共轭类数，那么 k ( G ) ≥ 2 p - 1 k(G)geq 2sqrt {p-1} ，他们对可解的 G G 证明了这一猜想，并证明对于那些 p - 1 sqrt {p-1} 是整数的素数 p p，这一猜想是尖锐的。这引发了一系列的活动，导致了对这一结果的许多概括和变化；特别是，如今人们知道这一猜想对所有有限群都是真的。在本笔记中，我们提出了一个自然的、更强的新猜想，它对所有素数 p p 都是尖锐的，我们证明了它对可解群的适用性，而且当 p p 较大时，也适用于任意群。

引用次数: 0

Monotonicity rules for the ratio of two function series and two integral transforms 两个函数序列之比和两个积分变换的单调性规则

IF 1 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society

Pub Date : 2024-04-03 DOI: 10.1090/proc/16728

Zhong-Xuan Mao, Jing-Feng Tian

In this paper, we investigate the monotonicity of the functions <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="t right-arrow from bar StartFraction sigma-summation Underscript k equals 0 Overscript normal infinity Endscripts a Subscript k Baseline w Subscript k Baseline left-parenthesis t right-parenthesis Over sigma-summation Underscript k equals 0 Overscript normal infinity Endscripts b Subscript k Baseline w Subscript k Baseline left-parenthesis t right-parenthesis EndFraction"> <mml:semantics> <mml:mrow> <mml:mi>t</mml:mi> <mml:mo stretchy="false">↦</mml:mo> <mml:mfrac> <mml:mrow> <mml:munderover> <mml:mo>∑</mml:mo> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:mi mathvariant="normal">∞</mml:mi> </mml:munderover> <mml:msub> <mml:mi>a</mml:mi> <mml:mi>k</mml:mi> </mml:msub> <mml:msub> <mml:mi>w</mml:mi> <mml:mi>k</mml:mi> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:mrow> <mml:munderover> <mml:mo>∑</mml:mo> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:mi mathvariant="normal">∞</mml:mi> </mml:munderover> <mml:msub> <mml:mi>b</mml:mi> <mml:mi>k</mml:mi> </mml:msub> <mml:msub> <mml:mi>w</mml:mi> <mml:mi>k</mml:mi> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:mfrac> </mml:mrow> <mml:annotation encoding="application/x-tex">t mapsto frac {sum _{k=0}^infty a_k w_k(t)}{sum _{k=0}^infty b_k w_k(t)}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="x right-arrow from bar StartFraction integral Subscript alpha Superscript beta Baseline f left-parenthesis t right-parenthesis w left-parenthesis t comma x right-parenthesis normal d t Over integral Subscript alpha Superscript beta Baseline g left-parenthesis t right-parenthesis w left-parenthesis t comma x right-parenthesis normal d t EndFraction"> <mml:semantics> <mml:mrow> <mml:mi>x</mml:mi> <mml:mo stretchy="false">↦</mml:mo> <mml:mfrac> <mml:mrow> <mml:msubsup> <mml:mo>∫</mml:mo> <mml:mi>α</mml:mi> <mml:mi>β</mml:mi> </mml:msubsup> <mml:mi>f</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mi>w</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>,</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mrow> <mml:mi mathvariant="normal">d</mml:mi> </mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> <mml:mrow> <mml:msubsup> <mml:mo>∫</mml:mo> <mml:mi>α</mml:mi> <mml:mi>β</mml:mi> </mml:msubsup> <mml:mi>g</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy="false">)

在本文中、我们研究了函数 t ↦ ∑ k = 0 ∞ a k w k ( t ) ∑ k = 0 ∞ b k w k ( t ) 的单调性。t ) t （映射到 frac {sum _{k=0}^infty a_k w_k(t)}{sum _{k=0}^infty b_k w_k(t)} and x ↦ ∫ α β f ( t ) w ( t 、x ) d t ∫ α β g ( t ) w ( t , x ) d t x mapsto frac {int _alpha ^beta f(t) w(t,x) mathrm {d} t}{int _alpha ^beta g(t) w(t,x) mathrm {d} t} ，重点是一元函数的情况。重点关注 a k / b k a_k/b_k 和 f ( t ) / g ( t ) f(t)/g(t) 的单调性发生一次变化的情况。这些结果还为两个幂级数、两个 Z mathcal {Z} -变换、两个离散拉普拉斯变换、两个离散梅林变换、两个拉普拉斯变换和两个梅林变换的比率的单调性提供了启示。最后，我们利用这些单调性规则来介绍特殊函数和随机阶数领域的一些应用。

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引用次数: 0

On the canonicity of the singularities of quotients of the Fulton-MacPherson compactification 论富尔顿-麦克弗森紧凑化商数奇点的可控性

IF 1 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society

Pub Date : 2024-04-03 DOI: 10.1090/proc/16859

Sophie Kriz

We prove that quotients of the Fulton-MacPherson compactification of configuration spaces of smooth projective varieties of dimension > 1 >1 by permutation groups have canonical singularities.

我们证明，维数> 1 >1的光滑射影变种的配置空间的富尔顿-麦克弗森紧凑化的商具有典范奇异性。

引用次数: 0

The strong Lefschetz property of Gorenstein algebras generated by relative invariants 相对不变式生成的戈伦斯坦代数的强列夫谢茨性质

IF 1 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society

Pub Date : 2024-04-03 DOI: 10.1090/proc/16870

Takahiro Nagaoka, Akihito Wachi

We prove the strong Lefschetz property for Artinian Gorenstein algebras generated by the relative invariants of prehomogeneous vector spaces of commutative parabolic type.

我们证明了由交换抛物线类型的前同调向量空间的相对不变式生成的阿尔廷戈伦斯坦代数的强列夫谢茨性质。

引用次数: 0

Global smooth solutions in a chemotaxis system modeling immune response to a solid tumor 模拟实体瘤免疫反应的趋化系统中的全局平滑解

IF 1 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society

Pub Date : 2024-04-03 DOI: 10.1090/proc/16867

Youshan Tao, Michael Winkler

This manuscript studies a no-flux initial-boundary value problem for a four-component chemotaxis system that has been proposed as a model for the response of cytotoxic T-lymphocytes to a solid tumor. In contrast to classical Keller-Segel type situations focusing on two-component interplay of chemotaxing populations with a signal directly secreted by themselves, the presently considered system accounts for a certain indirect mechanism of attractant evolution. Despite the presence of a zero-order exciting nonlinearity of quadratic type that forms a core mathematical feature of the model, the manuscript asserts the global existence of classical solutions for initial data of arbitrary size in three-dimensional domains.

本手稿研究了一个四成分趋化系统的无流动初始边界值问题，该系统已被提出作为细胞毒性 T 淋巴细胞对实体瘤反应的模型。与经典的凯勒-西格尔（Keller-Segel）型情况不同，目前考虑的系统侧重于趋化群体与自身直接分泌的信号之间的双组分相互作用，并考虑了某种吸引物演变的间接机制。尽管该模型的核心数学特征是存在二次型零阶激励非线性，但手稿仍断言，对于三维域中任意大小的初始数据，经典解在全局上是存在的。

引用次数: 0

Bounds for syzygies of monomial curves 单项式曲线对称性的界限

IF 1 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society

Pub Date : 2024-04-03 DOI: 10.1090/proc/16862

Giulio Caviglia, Alessio Moscariello, Alessio Sammartano

Let Γ ⊆ N Gamma subseteq mathbb {N} be a numerical semigroup. In this paper, we prove an upper bound for the Betti numbers of the semigroup ring of Γ Gamma which depends only on the width of Γ Gamma , that is, the difference between the largest and the smallest generator of Γ Gamma . In this way, we make progress towards a conjecture of Herzog and Stamate [J. Algebra 418 (2014), pp. 8–28]. Moreover, for 4-generated numerical semigroups, the first significant open case, we prove the Herzog-Stamate bound for all but finitely many values of the width.

让 Γ ⊆ N Gamma subseteq mathbb {N} 是一个数字半群。在本文中，我们证明了 Γ Gamma 的半群环的贝蒂数的上界，它只取决于 Γ Gamma 的宽度，即 Γ Gamma 的最大生成器和最小生成器之间的差值。这样，我们在实现赫尔佐格和斯塔马特的猜想方面取得了进展[《代数学杂志》418 (2014)，第 8-28 页]。此外，对于 4 代数值半群--第一个重要的开放情形--我们证明了赫尔佐格-斯塔马特对除有限多个宽度值之外的所有宽度值的约束。

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引用次数: 0

Global dynamics of a nonlocal reaction-diffusion-advection two-species phytoplankton model 非局部反应-扩散-平流双物种浮游植物模型的全球动力学研究

IF 1 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society

Pub Date : 2024-04-03 DOI: 10.1090/proc/16873

Danhua Jiang, Shiyuan Cheng, Yun Li, Zhi-Cheng Wang

We continue our study on the global dynamics of a non- local reaction-diffusion-advection system modeling the population dynamics of two competing phytoplankton species in a eutrophic environment, where the species depend solely on light for their metabolism. In our previous works, we proved that system (1.1) is a strongly monotone dynamical system with respect to a non-standard cone, and some competitive exclusion results were obtained. In this paper, we aim to demonstrate the existence of coexistence steady state as well as competitive exclusion. Our results highlight that advection in dispersal strategy can lead to transitions between various competitive outcomes.

我们继续研究一个非局部反应-扩散-平流系统的全局动力学，该系统建模了在富营养化环境中两个相互竞争的浮游植物物种的种群动力学，其中物种的新陈代谢完全依赖于光。在之前的研究中，我们证明了系统（1.1）是一个关于非标准锥的强单调动力系统，并得到了一些竞争排斥结果。本文旨在证明共存稳态以及竞争排斥的存在。我们的结果突出表明，分散策略中的平流可导致各种竞争结果之间的转换。

引用次数: 0

Spectral bounds for periodic Jacobi matrices 周期性雅可比矩阵的谱边界

IF 1 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society

Pub Date : 2024-03-29 DOI: 10.1090/proc/16874

Burak Hati̇noğlu

We consider periodic Jacobi operators and obtain upper and lower estimates on the sizes of the spectral bands. Our proofs are based on estimates on the logarithmic capacities and connections between the Chebyshev polynomials and logarithmic capacity of compact subsets of the real line.

我们考虑了周期性雅可比算子，并获得了谱带大小的上下限估计值。我们的证明基于对对数容量的估计以及切比雪夫多项式与实线紧凑子集的对数容量之间的联系。

引用次数: 0

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