Indagationes Mathematicae-New Series最新文献

英文中文

Non-self-intersective Dragon curves 非自相交的龙曲线

IF 0.8 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2025-03-24 DOI: 10.1016/j.indag.2025.03.006

Shigeki Akiyama , Yuichi Kamiya , Fan Wen

Let us fold a strip of paper many times in the same direction, and then unfold it to form a fixed angle

θ

at all creases. The resulting shape is called the Dragon curve with the unfolding angle

θ

. When

0 \leq θ < 90 °

, the corresponding Dragon curve has a self-intersection. When

θ = 180 °

, the corresponding Dragon curve is a straight line, which has no self-intersection. In this paper, we will show that any Dragon curve whose unfolding angle is greater than

99.3438 °

and less than

180 °

has no self-intersection.

让我们将一张纸沿同一方向折叠多次，然后将其展开，在所有折痕处形成一个固定的角度θ。得到的形状称为展开角为θ的龙曲线。当0≤θ<；90°时，对应的龙曲线有自交。当θ=180°时，对应的龙曲线为直线，没有自交。在本文中，我们将证明任何展开角大于99.3438°且小于180°的Dragon曲线都不存在自交。

引用次数: 0

On arithmetically defined hyperbolic 5-manifolds arising from maximal orders in definite Q-algebras 定q代数中由极大阶产生的算术定义双曲5流形

IF 0.8 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2025-03-13 DOI: 10.1016/j.indag.2025.03.001

Joachim Schwermer

Using the quaternionic formalism for the description of the group of isometries of hyperbolic 5-space we consider arithmetically defined 5-dimensional hyperbolic manifolds which are non-compact but of finite volume. They arise from maximal orders

Λ

in the central simple algebra

M_{2} (D)

of degree 4 where

D

denotes a definite quaternion

Q

-algebra. The affine

Z

-group scheme

S L_{Λ}

determines an integral structure for the algebraic

Q

-group

G = S L_{Λ} \times_{Z} Q

obtained by base change. The group

G

is an inner form of the special linear

Q

-group

S L_{4}

. Each torsion-free subgroup

Γ \subset S L_{Λ} (Z)

determines a hyperbolic 5-manifold, to be denoted

X_{G} / Γ

. Given a principal congruence subgroup

Γ (p^{e})

, we determine the number of ends and the dimensions of the cohomology groups at infinity of the manifold

X_{G} / Γ (p^{e})

利用四元数的形式描述了双曲5空间的等距群，考虑了非紧的有限体积的算术定义的五维双曲流形。它们起源于4次中心简单代数M2(D)的最大阶Λ，其中D表示一个确定的四元数q代数。仿射z群方案SLΛ决定了由碱基变化得到的代数q群G=SLΛ×ZQ的一个积分结构。群G是特殊线性q群SL4的内形式。每个无扭转子群Γ∧SLΛ(Z)决定一个双曲5流形，表示为XG/Γ。给定一个主同余子群Γ（pe），我们确定了流形XG/Γ（pe）无穷远处的上同调群的端数和维数。

引用次数: 0

Degrees of join-distributivity via Bruns–Lakser towers 通过Bruns-Lakser塔的联合分配度

IF 0.8 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2025-03-11 DOI: 10.1016/j.indag.2025.02.005

G. Bezhanishvili , F. Dashiell Jr. , M.A. Moshier , J. Walters-Wayland

We utilize the Bruns–Lakser completion to introduce Bruns–Lakser towers of a meet-semilattice. This machinery enables us to develop various hierarchies inside the class of bounded distributive lattices, which measure

κ

-degrees of distributivity of bounded distributive lattices and their Dedekind–MacNeille completions. We also use Priestley duality to obtain a dual characterization of the resulting hierarchies. Among other things, this yields a natural generalization of Esakia’s representation of Heyting lattices to proHeyting lattices.

我们利用Bruns-Lakser完成引入Bruns-Lakser塔楼的半格子结构。这种机制使我们能够在有界分布格类中发展各种层次结构，这些层次结构测量有界分布格的分布度及其Dedekind-MacNeille补全。我们还使用普利斯特利对偶性来获得所得层次的对偶特征。除此之外，这产生了Esakia的Heyting格表示到proHeyting格的自然推广。

引用次数: 0

Exercises on the Kepler ellipses through a fixed point in space, after Otto Laporte 以奥托·拉波特（Otto Laporte）的名字命名，在空间中的一个固定点上练习开普勒椭圆

IF 0.8 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2025-03-07 DOI: 10.1016/j.indag.2025.02.004

G.J. Heckman

This article has a twofold purpose. On the one hand I would like to draw attention to some nice exercises on the Kepler laws, due to Otto Laporte from 1970. Our discussion here has a more geometric flavor than the original analytic approach of Laporte.

On the other hand it serves as an addendum to a paper of mine from 1998 on the quantum integrability of the Kovalevsky top. Later I learned that this integrability result had been obtained already long before by Laporte in 1933.

这篇文章有双重目的。一方面，我想让大家注意一些关于开普勒定律的很好的练习，这是1970年Otto Laporte提出的。我们这里的讨论比拉波特原来的解析方法更有几何色彩。另一方面，它是我1998年关于Kovalevsky顶的量子可积性的论文的补充。后来我才知道，这个可积性结果早在1933年拉波特就已经得到了。

引用次数: 0

Bounds for asymptotic characters of simple Lie groups 单李群的渐近特征的界

IF 0.8 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2025-02-25 DOI: 10.1016/j.indag.2025.02.003

Pavel Etingof , Eric Rains

An important function attached to a complex simple Lie group

G

is its asymptotic character

X (λ, x)

(where

λ, x

are real (co)weights of

G

) – the Fourier transform in

x

of its Duistermaat–Heckman function

D H_{λ} (p)

(continuous limit of weight multiplicities). It is shown in Garibaldi et al. that the best

λ

-independent upper bound

- c (G)

for

{inf}_{x} Re X (λ, x)

for fixed

λ

is strictly negative. We quantify this result by providing a lower bound for

c (G)

in terms of

dim G

. We also provide upper and lower bounds for

D H_{λ} (0)

when

| λ | = 1

. This allows us to show that

| X (λ, x) | \leq C (G) {| λ |}^{- 1} {| x |}^{- 1}

for some constant

C (G)

depending only on

G

, which implies the conjecture in Remark 17.16 of Garibaldi et al. We also show that

c (S L_{n}) \leq {(\frac{4}{π^{2}})}^{n - 2}

. Finally, in the appendix we prove Conjecture 1 in Coquereaux and Zuber (2018) about Mittag-Leffler type sums for

G

附在复单李群G上的一个重要函数是它的渐近特征X(λ， X)（其中λ， X是G的实（co）权）-它的Duistermaat-Heckman函数DHλ(p)（权复数的连续极限）在X中的傅里叶变换。Garibaldi等人证明，对于固定λ的infxReX(λ,x)，最佳λ无关上界- c(G)是严格负的。我们通过用dimG给出c(G)的下界来量化这个结果。当|λ|=1时，我们还给出了DHλ(0)的上界和下界。这允许我们证明|X(λ， X)|≤C(G)|λ|−1| X |−1对于某常数C(G)只依赖于G，这暗示了Garibaldi等人在备注17.16中的猜想。我们还证明了c(SLn)≤(4π2)n−2。最后，在附录中，我们证明了Coquereaux和Zuber（2018）关于G的Mittag-Leffler型和的猜想1。

引用次数: 0

Exponentially-improved asymptotics for q-difference equations: 2ϕ0 and qPI q差分方程的指数改进渐近性：20和qPI

IF 0.8 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2025-02-11 DOI: 10.1016/j.indag.2025.02.002

Nalini Joshi , Adri Olde Daalhuis

Usually when solving differential or difference equations via series solutions one encounters divergent series in which the coefficients grow like a factorial. Surprisingly, in the

q

-world the

n

th coefficient is often of the size

q^{- \frac{1}{2} n (n - 1)}

, in which

q \in (0, 1)

is fixed. Hence, the divergence is much stronger, and one has to introduce alternative Borel and Laplace transforms to make sense of these formal series. We will discuss exponentially-improved asymptotics for the basic hypergeometric function

_{2} ϕ_{0}

and for solutions of the

q

-difference first Painlevé equation

q P_{I}

. These are optimal truncated expansions, and re-expansions in terms of new

q

-hyperterminant functions. The re-expansions do incorporate the Stokes phenomena.

通常在用级数解解微分或差分方程时，会遇到系数像阶乘一样增长的发散级数。令人惊讶的是，在q世界中，第n个系数的大小通常为q−12n(n−1)，其中q∈(0,1)是固定的。因此，散度要强得多，我们必须引入另一种波雷尔和拉普拉斯变换来理解这些形式级数。我们将讨论基本超几何函数20的指数改进渐近性和q-差分第一painlevel方程qPI的解。这些是最优的截断展开式，以及新的q-超终止函数的再展开式。重新扩展确实包含了斯托克斯现象。

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引用次数: 0

The S3-symmetric q-Onsager algebra and its Lusztig automorphisms s3对称q-Onsager代数及其Lusztig自同构

IF 0.8 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2025-02-11 DOI: 10.1016/j.indag.2025.02.001

Paul Terwilliger

The

q

-Onsager algebra

O_{q}

is defined by two generators and two relations, called the

q

-Dolan/Grady relations. In 2019, Baseilhac and Kolb introduced two automorphisms of

O_{q}

, now called the Lusztig automorphisms. Recently, we introduced a generalization of

O_{q}

called the

S_{3}

-symmetric

q

-Onsager algebra

O_{q}

. The algebra

O_{q}

has six distinguished generators, said to be standard. The standard

O_{q}

-generators can be identified with the vertices of a regular hexagon, such that nonadjacent generators commute and adjacent generators satisfy the

q

-Dolan/Grady relations. In the present paper we do the following: (i) for each standard

O_{q}

-generator we construct an automorphism of

O_{q}

called a Lusztig automorphism; (ii) we describe how the six Lusztig automorphisms of

O_{q}

are related to each other; (iii) we describe what happens if a finite-dimensional irreducible

O_{q}

-module is twisted by a Lusztig automorphism; (iv) we give a detailed example involving an irreducible

O_{q}

-module with dimension 5.

q-Onsager代数Oq由两个生成器和两个关系定义，称为q-Dolan/Grady关系。2019年，Baseilhac和Kolb引入了Oq的两个自同构，现在称为Lusztig自同构。最近，我们介绍了Oq的一种推广，称为s3对称q-Onsager代数Oq。代数Oq有六个不同的生成器，据说是标准的。标准的oq生成器可以用正六边形的顶点来标识，使得非相邻生成器可交换，相邻生成器满足q-Dolan/Grady关系。在本文中，我们做了以下工作：(i)对于每个标准的Oq生成器，我们构造了一个Oq的自同构，称为Lusztig自同构；（ii）描述了Oq的六个Lusztig自同构之间的相互关系；（iii）描述了有限维不可约oq模被Lusztig自同构扭曲时的情形；（iv）我们给出了一个涉及维数为5的不可约oq模的详细例子。

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引用次数: 0

Binary quadratic forms with the same value set 具有相同值集的二元二次型

IF 0.8 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2025-02-07 DOI: 10.1016/j.indag.2025.01.005

Étienne Fouvry , Peter Koymans

Given a binary quadratic form

F \in Z [X, Y]

, we define its value set

F (Z^{2})

to be

{F (x, y) : (x, y) \in Z^{2}}

. If

F, G \in Z [X, Y]

are two binary quadratic forms, we give necessary and sufficient conditions on

F

and

G

for

F (Z^{2}) = G (Z^{2})

给定一个二元二次型F∈Z[X，Y]，定义其值集F（Z2）为{F(X，Y):(X，Y)∈Z2}。若F，G∈Z[X，Y]是两个二元二次型，给出F(Z2)=G（Z2）的F和G的充分必要条件。

引用次数: 0

Dunkl symmetric coherent pairs of measures. An application to Fourier Dunkl–Sobolev expansions 敦克尔对称相干测度对。傅里叶Dunkl-Sobolev展开的应用

IF 0.8 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2025-02-04 DOI: 10.1016/j.indag.2025.01.006

Mabrouk Sghaier , Francisco Marcellán , Sabrine Hamdi

<div><div>Let <math><msub><mrow><mi>T</mi></mrow><mrow><mi>μ</mi></mrow></msub></math> be the Dunkl operator. A pair of symmetric measures <math><mrow><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow></math> supported on a symmetric subset of the real line is said to be a symmetric Dunkl-coherent pair if the corresponding sequences of monic orthogonal polynomials <math><msub><mrow><mrow><mo>{</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>}</mo></mrow></mrow><mrow><mi>n</mi><mo>≥</mo><mn>0</mn></mrow></msub></math> and <math><msub><mrow><mrow><mo>{</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>}</mo></mrow></mrow><mrow><mi>n</mi><mo>≥</mo><mn>0</mn></mrow></msub></math> (resp.) satisfy <math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>μ</mi></mrow></msub><msub><mrow><mi>P</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><msub><mrow><mi>μ</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub></mrow></mfrac><mo>−</mo><msub><mrow><mi>σ</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><mfrac><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>μ</mi></mrow></msub><msub><mrow><mi>P</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><msub><mrow><mi>μ</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow></mfrac><mo>,</mo><mspace></mspace><mspace></mspace><mi>n</mi><mo>≥</mo><mn>2</mn><mo>,</mo></mrow></math>where <math><msub><mrow><mrow><mo>{</mo><msub><mrow><mi>σ</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>}</mo></mrow></mrow><mrow><mi>n</mi><mo>≥</mo><mn>1</mn></mrow></msub></math> is a sequence of non-zero complex numbers and <math><mrow><msub><mrow><mi>μ</mi></mrow><mrow><mn>2</mn><mi>n</mi></mrow></msub><mo>=</mo><mn>2</mn><mi>n</mi><mo>,</mo><msub><mrow><mi>μ</mi></mrow><mrow><mn>2</mn><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>=</mo><mn>2</mn><mi>n</mi><mo>−</mo><mn>1</mn><mo>+</mo><mn>2</mn><mi>μ</mi><mo>,</mo><mi>n</mi><mo>≥</mo><mn>1</mn><mo>.</mo></mrow></math></div><div>In this contribution we focus the attention on the sequence <math><msub><mrow><mrow><mo>{</mo><msubsup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow><mrow><mrow><mo>(</mo><mi>λ</mi><mo>,</mo><mi>μ</mi><mo>)</mo></mrow></mrow></msubsup><mo>}</mo></mrow></mrow><mrow><mi>n</mi><mo>≥</mo><mn>0</mn></mrow></msub></math> of monic orthogonal polynomials with respect to the Dunkl–Sobolev inner product <math><mrow><mo><</mo><mi>p</mi><mo>,</mo><mi>q</mi><msub><mrow><mo>></mo></mrow><mrow><mi>s</mi><mo>,</mo><mi>μ</mi></mrow></msub><mo>=</mo><mrow><mo>〈</mo><mi>u</mi><mo>,</mo><mi>p</mi>

设t为Dunkl算子。如果一元正交多项式{Pn}n≥0和{Rn}n≥0 （resp.）对应的序列满足Rn(x)=TμPn+1(x)μn+1 - σn−1TμPn−1(x)μn−1,n≥2，则在实线的对称子集上支持的一对对称测度（u,v）称为对称敦克尔相干对，其中{σn}n≥1是一个非零复数序列，且μ2n=2n,μ2n−1=2n−1+2μ,n≥1。在这篇贡献中，我们将注意力集中在关于Dunkl-Sobolev内积<；p,q>s,μ= < u,pq > +λ < v,TμpTμq >,λ>0,p，q∈p的单正交多项式序列{Sn(λ,μ)}n≥0。对于合适的光滑函数f，使f∈W21(R,u,v,μ)={f;||f||u2+λ||Tμf||v2<∞}，给出了一种计算傅里叶- sobolev型展开式的系数的算法。最后给出了两个说明性的数值算例。

引用次数: 0

On moments of the error term of the multivariable kth divisor functions 多变量第k因子函数误差项的矩

IF 0.8 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2025-01-30 DOI: 10.1016/j.indag.2025.01.003

Zhen Guo, Xin Li

<div><div>Suppose <math><mrow><mi>k</mi><mo>⩾</mo><mn>3</mn></mrow></math> is an integer. Let <math><mrow><msub><mrow><mi>τ</mi></mrow><mrow><mi>k</mi></mrow></msub><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mrow></math> be the number of ways <math><mi>n</mi></math> can be written as a product of <math><mi>k</mi></math> fixed factors. For any fixed integer <math><mrow><mi>r</mi><mo>⩾</mo><mn>2</mn></mrow></math>, we have the asymptotic formula <math><mrow><munder><mrow><mo>∑</mo></mrow><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>⋯</mo><mspace></mspace><mo>,</mo><msub><mrow><mi>n</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>⩽</mo><mi>x</mi></mrow></munder><msub><mrow><mi>τ</mi></mrow><mrow><mi>k</mi></mrow></msub><mrow><mo>(</mo><msub><mrow><mi>n</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>⋯</mo><msub><mrow><mi>n</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>)</mo></mrow><mo>=</mo><msup><mrow><mi>x</mi></mrow><mrow><mi>r</mi></mrow></msup><munderover><mrow><mo>∑</mo></mrow><mrow><mi>ℓ</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>r</mi><mrow><mo>(</mo><mi>k</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></mrow></munderover><msub><mrow><mi>d</mi></mrow><mrow><mi>r</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>ℓ</mi></mrow></msub><msup><mrow><mrow><mo>(</mo><mo>log</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mi>ℓ</mi></mrow></msup><mo>+</mo><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>x</mi></mrow><mrow><mi>r</mi><mo>−</mo><mn>1</mn><mo>+</mo><msub><mrow><mi>α</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>+</mo><mi>ɛ</mi></mrow></msup><mo>)</mo></mrow><mo>,</mo></mrow></math>where <math><msub><mrow><mi>d</mi></mrow><mrow><mi>r</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>ℓ</mi></mrow></msub></math> and <math><mrow><mn>0</mn><mo><</mo><msub><mrow><mi>α</mi></mrow><mrow><mi>k</mi></mrow></msub><mo><</mo><mn>1</mn></mrow></math> are computable constants. In this paper we study the mean square of <math><mrow><msub><mrow><mi>Δ</mi></mrow><mrow><mi>r</mi><mo>,</mo><mi>k</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math> and give upper bounds for <math><mrow><mi>k</mi><mo>⩾</mo><mn>4</mn></mrow></math> and an asymptotic formula for the mean square of <math><mrow><msub><mrow><mi>Δ</mi></mrow><mrow><mi>r</mi><mo>,</mo><mn>3</mn></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math>. We also get an upper bound for the third power moment of <math><mrow><msub><mrow><mi>Δ</mi></mrow><mrow><mi>r</mi><mo>,</mo><mn>3</mn></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math>. Moreover, we study the first power moment of <math><mrow><msub><mrow><mi>Δ</mi></mrow><mrow><mi>r</mi><mo>,</mo><mn>3</mn></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math> and then give a result for the sign

假设k大于或等于3是一个整数。设τk(n)是n可以写成k个固定因子的乘积的方法个数。对于任何固定整数r大于或等于2，我们有渐近公式∑n1，⋯nr≤xτk(n1⋯nr)=xr∑r =0r(k−1)dr,k, r(logx) r +O（xr−1+αk+ æ），其中dr，k， r和0<；αk<；1是可计算常数。在本文中，我们研究Δr，k(x)的均方并给出k小于或等于4的上限和Δr，3(x)的均方的渐近公式。我们也得到了Δr 3(x)的三次幂矩的上界。此外，我们还研究了Δr，3(x)的一阶幂矩，并给出了它的符号变化的结果。

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全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

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