Indagationes Mathematicae-New Series最新文献

英文中文

Erratum to “Charting the q-Askey scheme. II. The q “绘制q-Askey方案”勘误表。II.q<

IF 0.6 4区数学 Q3 Mathematics

Indagationes Mathematicae-New Series

Pub Date : 2023-06-01 DOI: 10.1016/j.indag.2023.05.006

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引用次数: 0

Beatty primes from fractional powers of almost-primes 从几乎质数的分数次幂得到漂亮的质数

IF 0.6 4区数学 Q3 Mathematics

Indagationes Mathematicae-New Series

Pub Date : 2023-05-11 DOI: 10.1016/j.indag.2023.04.004

Victor Zhenyu Guo , Jinjiang Li , Min Zhang

Let $α > 1$ be irrational and of finite type, $β \in R$ . In this paper, it is proved that for $R ⩾ 13$ and any fixed $c \in (1, c_{R})$ , there exist infinitely many primes in the intersection of Beatty sequence $B_{α, β}$ and $⌊ n^{c} ⌋$ , where $c_{R}$ is an explicit constant depending on $R$ herein, $n$ is a natural number with at most $R$ prime factors, counted with multiplicity.

设α>1为无理数有限型，β∈R。在本文中，证明了对于R大于或等于13和任何固定的c∈(1,cR)，在Beatty序列Bα，β和⌊nc⌋的交集中存在无限多个素数，其中cR是一个依赖于R的显式常数，n是一个自然数，最多有R个素数因子，用多重计数。

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引用次数: 0

The Heinz type inequality, Bloch type theorem and Lipschitz characteristic of polyharmonic mappings 多调和映射的Heinz型不等式、Bloch型定理和Lipschitz特性

IF 0.6 4区数学 Q3 Mathematics

Indagationes Mathematicae-New Series

Pub Date : 2023-05-10 DOI: 10.1016/j.indag.2023.05.001

Shaolin Chen

Suppose that $f$ satisfies the following: $(1)$ the polyharmonic equation $Δ^{m} f = Δ (Δ^{m - 1} f)$ $= φ_{m}$ $(φ_{m} \in C (\bar{B^{n}}, R^{n}))$ , (2) the boundary conditions $Δ^{0} f = φ_{0}, Δ^{1} f = φ_{1}, \dots, Δ^{m - 1} f = φ_{m - 1}$ on $S^{n - 1}$ ( $φ_{j} \in C (S^{n - 1}, R^{n})$ for $j \in {0, 1, \dots, m - 1}$ and $S^{n - 1}$ denotes the boundary of the unit ball $B^{n}$ ), and $(3)$ $f (0) = 0$ , where $n \geq 3$ and $m \geq 1$ are integers. Initially, we prove a Schwarz type lemma and use it to obtain a Heinz type inequality of mappings satisfying the polyharmonic equation with the above Dirichlet boundary value conditions. Furthermore, we establish a Bloch type theorem of mappings satisfying the above polyharmonic equation, which gives an answer to an open problem in Chen an

设f满足下列条件:(1)多调和方程Δmf=Δ(Δm−1f)=φm(φm∈C(Bn¯，Rn)); (2) Sn−1上的边界条件Δ0f=φ0，Δ1f=φ1，…，Δm−1f=φm−1 (φj∈C(Sn−1,Rn)对于j∈{0,1，…，m−1}，其中Sn−1表示单位球Bn的边界);(3)f(0)=0，其中n≥3,m≥1为整数。首先，我们证明了一个Schwarz型引理，并利用它得到了在上述Dirichlet边值条件下满足多谐方程的映射的Heinz型不等式。此外，我们建立了一个满足上述多谐方程的映射的Bloch型定理，该定理给出了Chen和Ponnusamy(2019)的一个开放问题的答案。此外，我们证明了如果f是满足上述多谐方程的Bn的K-拟共形自映射，则f是Lipschitz连续的，并且对于j∈{1，…，m}， Lipschitz常数在K→1+和‖φj‖∞→0+时渐近尖锐。

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引用次数: 1

Box and nabla products that are D-spaces 属于D空间的Box和nabla产品

IF 0.6 4区数学 Q3 Mathematics

Indagationes Mathematicae-New Series

Pub Date : 2023-05-03 DOI: 10.1016/j.indag.2023.04.002

H.A. Barriga-Acosta , P.M. Gartside

A space $X$ is $D$ if for every assignment, $U$ , of an open neighborhood to each point $x$ in $X$ there is a closed discrete $D$ such that $⋃ {U (x) : x \in D} = X$ . The box product, $□ X^{ω}$ , is $X^{ω}$ with topology generated by all $\prod_{n} U_{n}$ , where every $U_{n}$ is open. The nabla product, $\nabla X^{ω}$ , is obtained from $□ X^{ω}$ by quotienting out mod-finite. The weight of $X$ , $w (X)$ , is the minimal size of a base, while $d = cof ω^{ω}$ .

It is shown that there are specific compact spaces $X$ such that $□ X^{ω}$ and $\nabla X^{ω}$ are not $D$ , but in general:

(1) $□ X^{ω}$ and $\nabla X^{ω}$ are hereditarily $D$ if $X$ is scattered and either hereditarily paracompact or of finite scattered height, or if $X$ is metrizable (and $w (X) \leq d$ for $□ X^{ω}$ );

(2) $\nabla X^{ω}$ is hereditarily $D$ if $X$ is first countable and

空间X是D，如果对于X中每个点X的开邻域的每一个赋值U，都有一个闭的离散D，使得⋃{U（X）:X∈D}=X。盒子产品，□Xω，是拓扑由所有πnUn生成的Xω，其中每个Un是开的。nabla乘积，ŞXω，由□Xω的模有限商。X的权重w（X）是基的最小大小，而d=cofω。证明了存在特定的紧致空间X，使得□Xω和ŞXω不是D，但一般来说：（1）□如果X是散射的并且是可遗传的仿紧的或者是有限散射高度的，或者如果X是可度量的（并且w（X）≤D□Xω）；（2）如果X是第一可数且w（X）≤ω1，或一致地如果X是一可数且|X|≤c，或w（X；和（3）□如果X是紧致的并且是第一可数的或者w（X）≤ω1，则Xω一致为D。

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引用次数: 0

Minimal surfaces and Schwarz lemma 极小曲面与Schwarz引理

IF 0.6 4区数学 Q3 Mathematics

Indagationes Mathematicae-New Series

Pub Date : 2023-05-01 DOI: 10.1016/j.indag.2023.01.002

David Kalaj

We prove a sharp Schwarz lemma type inequality for the Weierstrass–Enneper parameterization of minimal disks. It states the following. If

F : D \to Σ

is a conformal harmonic parameterization of a minimal disk

Σ \subset R^{3}

, where

D

is the unit disk and

| Σ | = π R^{2}

, then

| F_{x} (z) | (1 - {| z |}^{2}) \leq R

. If for some

z

the previous inequality is equality, then the surface is an affine image of a disk, and

F

is linear up to a Möbius transformation of the unit disk.

我们证明了最小盘的Weierstrass-Enneper参数化的尖锐Schwarz引理型不等式。它陈述如下。若F:D→Σ是最小盘的共形调和参数化Σ∧R3，其中D为单位盘，|Σ|=πR2，则|Fx(z)|(1−|z|2)≤R。如果对于某个z，前面的不等式是相等的，那么曲面是一个圆盘的仿射像，F是线性的，直到单位圆盘的Möbius变换。

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引用次数: 2

A decomposition property for an MX/G/ MX/G/<mm的分解性质

IF 0.6 4区数学 Q3 Mathematics

Indagationes Mathematicae-New Series

Pub Date : 2023-05-01 DOI: 10.1016/j.indag.2023.05.002

Igor Kleiner, E. Frostig, David Perry

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引用次数: 0

Sums of even powers of k-regulous functions k-正则函数的偶幂和

IF 0.6 4区数学 Q3 Mathematics

Indagationes Mathematicae-New Series

Pub Date : 2023-05-01 DOI: 10.1016/j.indag.2022.12.004

Juliusz Banecki, Tomasz Kowalczyk

We provide an example of a nonnegative $k$ -regulous function on $R^{n}$ for $k \geq 1$ and $n \geq 2$ which cannot be written as a sum of squares of $k$ -regulous functions. We then obtain lower bounds for Pythagoras numbers $p_{2 d} (R^{k} (R^{n}))$ of $k$ -regulous functions on $R^{n}$ for $k \geq 1$ and $n \geq 2$ . We also prove that the second Pythagoras number of the ring of 0-regulous functions $R^{0} (X)$ on an irreducible 0-regulous affine variety $X$ is finite and bounded from above by $2^{dim X}$ .

我们给出了当k≥1和n≥2时Rn上的非负k-正则函数不能写成k-正则函数的平方和的例子。然后，我们得到了k-正则函数在Rn上对于k≥1和n≥2的毕达哥拉斯数p2d(Rk(Rn))的下界。证明了不可约的0-正则仿射变量X上的0-正则函数环R0(X)的第二毕达哥拉斯数是有限的，并以2dimX为上界。

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引用次数: 4

Box and nabla products that are D-spaces Box和nabla产品是d空间

IF 0.6 4区数学 Q3 Mathematics

Indagationes Mathematicae-New Series

Pub Date : 2023-05-01 DOI: 10.1016/j.indag.2023.04.002

H. Barriga-Acosta, P. Gartside

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引用次数: 0

Complex Monge–Ampère equations for plurifinely plurisubharmonic functions 多维亚调和函数的复Monge–Ampère方程

IF 0.6 4区数学 Q3 Mathematics

Indagationes Mathematicae-New Series

Pub Date : 2023-05-01 DOI: 10.1016/j.indag.2022.12.008

Nguyen Xuan Hong , Hoang Van Can , Nguyen Thi Lien , Pham Thi Lieu

This paper studies the complex Monge–Ampère equations for $F$ -plurisubharmonic functions in bounded $F$ -hyperconvex domains. We give sufficient conditions for this equation to solve for measures with a singular part.

本文研究了有界f -超凸域上f -多次调和函数的复monge - ampantere方程。给出了该方程解具有奇异部分测度的充分条件。

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引用次数: 1

Intermittency generated by attracting and weakly repelling fixed points 由固定点吸引和弱排斥产生的间歇性

IF 0.6 4区数学 Q3 Mathematics

Indagationes Mathematicae-New Series

Pub Date : 2023-05-01 DOI: 10.1016/j.indag.2022.12.002

Benthen Zeegers

Recently for a class of critically intermittent random systems a phase transition was found for the finiteness of the absolutely continuous invariant measure. The systems for which this result holds are characterized by the interplay between a superexponentially attracting fixed point and an exponentially repelling fixed point. In this article we consider a closely related family of random systems with exponentially fast attraction to and polynomially fast repulsion from two fixed points, and show that such a phase transition still exists. The method of the proof however is different and relies on the construction of a suitable invariant set for the transfer operator.

最近发现了一类临界间歇随机系统的绝对连续不变测度有限的相变。这个结果成立的系统的特点是一个超指数吸引不动点和一个指数排斥不动点之间的相互作用。本文考虑了一类密切相关的随机系统，它们对两个不动点具有指数级快速吸引和多项式级快速排斥，并证明了这样的相变仍然存在。然而，证明的方法是不同的，它依赖于为转移算子构造一个合适的不变量集。

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引用次数: 0

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