スレタイ箱入り無数目を語る部屋34(あほ二人の”アナグマの姿焼き"Part8ｗ)

前スレが1000近く又は1000超えになったので、新スレを立てる
(”ヘンテコスレ”が別にあります https://rio2016.5ch.io/test/read.cgi/math/1711570726/ 箱入り無数目を語る部屋19 )

https://rio2016.5ch.io/test/read.cgi/math/1788330573/
前スレ スレタイ箱入り無数目を語る部屋33(あほ二人の”アナグマの姿焼き"Part7ｗ)

(参考)時枝記事
https://imgur.com/uMqtRwr
時枝 箱入り無数目（数学セミナー201511月号の記事）の最初
https://imgur.com/YAdz2Mz
時枝 箱入り無数目（数学セミナー201511月号の記事）の後

数学セミナー201511月号「箱入り無数目」
https://rio2016.5ch.io/test/read.cgi/math/1620904362/401-406 純粋・応用数学（含むガロア理論）8 より
１．時枝問題（数学セミナー201511月号の記事）の最初の設定はこうだった。
「箱がたくさん，可算無限個ある.箱それぞれに，私が実数を入れる.
どんな実数を入れるかはまったく自由，例えばn番目の箱にe^nを入れてもよいし，すべての箱にπを入れてもよい.
もちろんでたらめだって構わない.そして箱をみな閉じる.
今度はあなたの番である.片端から箱を開けてゆき中の実数を覗いてよいが，一つの箱は開けずに閉じたまま残さねばならぬとしよう.
どの箱を閉じたまま残すかはあなたが決めうる.
勝負のルールはこうだ. もし閉じた箱の中の実数をピタリと言い当てたら，あなたの勝ち. さもなくば負け.
勝つ戦略はあるでしょうか?」

２．続けて時枝はいう
　私たちのやろうとすることはQのコーシー列の集合を同値関係で類別してRを構成するやりかた(の冒頭)に似ている.
但しもっときびしい同値関係を使う.
実数列の集合 R^Nを考える.
s = (s1，s2，s3 ，・・・)，s'=(s'1， s'2， s'3，・・・ )∈R^Nは，ある番号から先のしっぽが一致する∃n0：n >= n0 → sn＝ s'n とき同値s 〜 s'と定義しよう(いわばコーシーのべったり版).
念のため推移律をチェックすると，sとs'が1962番目から先一致し，s'とs"が2015番目から先一致するなら，sとs"は2015番目から先一致する.
〜は R^N を類別するが，各類から代表を選び，代表系を袋に蓄えておく.
幾何的には商射影 R^N→ R^N/〜の切断を選んだことになる.
任意の実数列s に対し，袋をごそごそさぐってそいつと同値な(同じファイパーの)代表r= r(s)をちょうど一つ取り出せる訳だ.
sとrとがそこから先ずっと一致する番号をsの決定番号と呼び，d = d(s)と記す.
つまりsd，sd+1，sd+2,・・・を知ればsの類の代表r は決められる.
更に，何らかの事情によりdが知らされていなくても，あるD>=d についてsD+1， sD+2，sD+3，・・・
が知らされたとするならば，それだけの情報で既に r = r(s)は取り出せ， したがってd= d(s)も決まり，
結局sd (実はsd，sd+1，・・・，sD ごっそり)が決められることに注意しよう.
(補足)
sD+1， sD+2，sD+3，・・・：ここでD+1などは下付添え字

つづく

Fri, 18 Sep 2026 (showing 12 of 12 entries )
[1] arXiv:2609.20675 [pdf, html, other]
Limit theorems for Coulomb gases on a Jordan curve in an external potential
Kurt Johansson, Thomas Wolfs
Comments: 45 pages
Subjects: Complex Variables (math.CV)
[2] arXiv:2609.20607 [pdf, html, other]
On Simply Connected Domains Supporting an Unbounded Analytic Function with Bounded Derivative
Cameron MacMahon
Comments: 15 Pages, 4 Figures
Subjects: Complex Variables (math.CV)
[3] arXiv:2609.20288 [pdf, other]
Coefficient estimates and Hankel determinant for the class of leaf shaped starlike function
Shantanu Panja, Abhijit Banerjee, Sujoy Majumder
Subjects: Complex Variables (math.CV)
[4] arXiv:2609.20256 [pdf, html, other]
Sendov's conjecture holds for every degree n≥10200000
Teng Zhang
Comments: 29 pages. All comments are welcome!
Subjects: Complex Variables (math.CV)
[5] arXiv:2609.20196 [pdf, html, other]
Rigidity of symmetric holomorphic functions on infinite-dimensional sequence spaces
David Feldman, Jon Bannon
Comments: Comments welcome!
Subjects: Complex Variables (math.CV)

[6] arXiv:2609.19896 [pdf, html, other]
The Reciprocal Problem on Weighted Bergman Spaces
Guangfu Cao, Li He, Shuqing Zhang
Subjects: Complex Variables (math.CV); Functional Analysis (math.FA)
[7] arXiv:2609.19829 [pdf, html, other]
On φ-Normality of Harmonic Mappings and Their Families
Gopal Datt, Ritesh Pal
Subjects: Complex Variables (math.CV)
[8] arXiv:2609.19733 [pdf, html, other]
Weak Asymptotic Symmetry of Quasisymmetric Embeddings on Quasilines
Katsuhiko Matsuzaki, Fei Tao
Subjects: Complex Variables (math.CV)
[9] arXiv:2609.19609 [pdf, html, other]
Target Geometry in Prescribed-Value Schwarz Lemmas for Harmonic Maps
Miljan Knežević, Miodrag Mateljević
Comments: 64 pages
Subjects: Complex Variables (math.CV)
[10] arXiv:2609.19522 [pdf, html, other]
Holomorphic motions, Assouad dimension and quasiconformal mappings
Katheryn Menssen, Malik Younsi
Comments: 23 pages
Subjects: Complex Variables (math.CV)

Subjects: Complex Variables (math.CV)
[11] arXiv:2609.20652 (cross-list from math.OA) [pdf, html, other]
Toeplitz C∗-algebras on radially weighted Fock spaces: commutativity and spectral representation
Khalid Bdarneh
Subjects: Operator Algebras (math.OA); Complex Variables (math.CV)
[12] arXiv:2609.20024 (cross-list from math.DS) [pdf, html, other]
Stability and Logarithmic Foliations on Complex Projective Spaces
Víctor León, Bruno Scárdua
Subjects: Dynamical Systems (math.DS); Complex Variables (math.CV)
Thu, 17 Sep 2026 (showing 7 of 7 entries )
[13] arXiv:2609.19126 [pdf, html, other]
Beyond Sendov's conjecture: the quadratic Tang--Zhang inequality
Teng Zhang
Comments: 26 pages,3 figures. All comments are welcome!
Subjects: Complex Variables (math.CV)
[14] arXiv:2609.18785 [pdf, html, other]
Non-tangential ranges of holomorphic functions at Plessner points
Oleg Ivrii
Comments: 18 pages
Subjects: Complex Variables (math.CV)

arXiv:2609.20024 (cross-list from math.DS) [pdf, html, other]
Stability and Logarithmic Foliations on Complex Projective Spaces
Víctor León, Bruno Scárdua
Subjects: Dynamical Systems (math.DS); Complex Variables (math.CV)
We study Lyapunov-type stability for invariant algebraic divisors of codimension-one
holomorphic foliations on complex projective spaces. Motivated by the notion of L-stability
introduced in \cite{LeonScardua2018} for plane singularities, we define a projective
stability condition which is compatible with the logarithmic setting and controls leafwise
holonomy along the regular part of the invariant divisor, while discarding any stability
requirement inside prescribed neighborhoods of its singular locus.
Our main result then is a global projective counterpart of the local
classification in \cite{LeonScardua2018}: for a maximal invariant algebraic divisor, projective
L-stability together with non-dicritical non-nodal generalized-curve singularities
on a generic plane section forces the ambient foliation to be globally logarithmic.
As an application we obtain a topological rigidity consequence on P2 for logarithmic foliations
under mild generic conditions. The proof of the main theorem is based on propagating
the consequences of the stability hypothesis through the reduction tree by means of
an explicit Dulac transport argument, together with the classification of
L-stable groups of germs of one-dimensional complex diffeomorphisms.

#1 Limit theorems for Coulomb gases on a Jordan curve in an external potential [PDF] [Copy] [Kimi] [REL]
Authors: Kurt Johansson, Thomas Wolfs

We consider a Coulomb gas on a Jordan curve γ
in an external potential V
at inverse temperature β>0
and obtain an asymptotic expansion of the free energy up to o(1)
and a central limit theorem for linear statistics. We focus on the one-cut regime, where the density of the weighted equilibrium measure of γ
in V
is strictly positive on γ
. The constant term in the (normalized) expansion consists of two parts: the Fredholm determinant of a generalized Grunsky operator and the Dirichlet energy of the logarithm of the density of the weighted equilibrium measure of γ
. The coefficient of the latter vanishes for β=2
. The variance of the fluctuations of the linear statistics only depends on the Dirichlet energy of the test function and is therefore independent of V
. Essential in our approach is that the generalized Grunsky operator and the accompanying equilibrium parametrization allow us to transport the particles on the curve in the external potential to a reference object in a way that preserves the equilibrium measure. In our setting, the unit circle is the natural reference object.