The Moduli Space of Polynomial Maps and Their Fixed-Point Multipliers: II. Improvement to the Algorithm and Monic Centered Polynomials

We consider the set $\mathrm{MC}_d$ of monic centered polynomials of one complex variable with degree $d \geq 2$, and study the map $\widehat{\Phi}_d:\mathrm{MC}_d\to \widetilde{\Lambda}_d \subset \mathbb{C}^d / \mathfrak{S}_d$ which maps each $f \in \mathrm{MC}_d$ to its unordered collection of fixed-point multipliers. We give an explicit formula for counting the number of elements of each fiber $\widehat{\Phi}_d^{-1}\left(\bar{\lambda}\right)$ for every $\bar{\lambda} \in \widetilde{\Lambda}_d$. This formula contains no induction process, and is a drastic improvement of our previous result which gave a rather long algorithm with some induction processes for counting the number of elements of each fiber.Comment: 18 page

The Moduli Space of Polynomial Maps and Their Fixed-Point Multipliers

We consider the family $\mathrm{MP}_d$ of affine conjugacy classes of polynomial maps of one complex variable with degree $d \geq 2$, and study the map $\Phi_d:\mathrm{MP}_d\to \widetilde{\Lambda}_d \subset \mathbb{C}^d / \mathfrak{S}_d$ which maps each $f \in \mathrm{MP}_d$ to the set of fixed-point multipliers of $f$. We show that the local fiber structure of the map $\Phi_d$ around $\bar{\lambda} \in \widetilde{\Lambda}_d$ is completely determined by certain two sets $\mathcal{I}(\lambda)$ and $\mathcal{K}(\lambda)$ which are subsets of the power set of $\{1,2,\ldots,d \}$. Moreover for any $\bar{\lambda} \in \widetilde{\Lambda}_d$, we give an algorithm for counting the number of elements of each fiber $\Phi_d^{-1}\left(\bar{\lambda}\right)$ only by using $\mathcal{I}(\lambda)$ and $\mathcal{K}(\lambda)$. It can be carried out in finitely many steps, and often by hand.Comment: 40pages; Revised expression in Introduction a little, and added proofs for some propositions; results unchange

多項式写像のモジュライ空間とその固定点における微分係数

京都大学0048新制・論文博士博士(理学)乙第13201号論理博第1560号新制||理||1635(附属図書館)京都大学大学院理学研究科数学・数理解析専攻(主査)教授 宍倉 光広, 教授 泉 正己, 教授 國府 寛司学位規則第4条第2項該当Doctor of ScienceKyoto UniversityDFA

The moduli space of polynomial maps and their fixed-point multipliers

於 城崎国際アートセンター(2019年10月21日-10月25日)2019年度科学研究費補助金 基盤研究(S)(課題番号15H05738, 代表 金銅誠之), 2019年度科学研究費補助金 基盤研究(S)(課題番号16H06337, 代表 高橋篤史), 2019年度科学研究費補助金 基盤研究(S)(課題番号17H06127, 代表 齋藤政彦)Date : Oct. 21, 2019 (Mon) - Oct. 25, 2019 (Fri). Venue : Kinosaki International Arts Center.Kinosaki Algebraic Geometry Symposium 2019 is partially supported by Grantin-Aid for Scientific Research (S) 15H05738, (S) 16H06337, and (S) 17H06127. Organizers: Hiraku Kawanoue (Chubu University), Takashi Kishimoto (Saitama University), Shingo Taki (Tokai University

Classification by Nurses’ Work Values and Their Characteristics: Latent Profile Analysis of Nurses Working in Japanese Hospitals

This study aimed to classify nurses with similar work values into subgroups by examining their intrinsic, extrinsic, social, and prestige work values. Additionally, we clarified the characteristics of the obtained subgroups using personal attributes, work engagement, and life satisfaction. Using a cross-sectional observational study design, we randomly sampled 52 hospitals in the Tohoku region of Japan and conducted a self-administered questionnaire survey with 2600 nurses. Latent profile analysis was performed to identify the number of subgroups. Of the 1627 collected questionnaires, 1587 were regarded as valid. The latent profile analysis revealed the following five subgroups with strong statistical significance: (1) self-oriented, (2) low, (3) medium-low, (4) medium-high, and (5) high types. The means of work engagement and life satisfaction gradually increased from the (2) low- to (5) high-type subgroups. There were significant differences among the subgroups in terms of marital status, child status, and job title. The (5) high-type subgroup had many nurses with job titles, high work engagement, and high life satisfaction. The (2) low-type subgroup included many nurses who were young, had few years of experience, were married, had children, and had low levels of work engagement and life satisfaction. Preregistration: This study was not registered