For a set x, let ${\cal S}\left$ be the set of all permutations of x. We prove in ZF several results concerning this notion, among which are the following: For all sets x such that ${\cal S}\left$ is Dedekind infinite, $\left| {{{\cal S}_{{\rm{fin}}}}\left} \right| < \left| {{\cal S}\left} \right|$ and there are no finite-to-one functions from ${\cal S}\left$ into ${{\cal S}_{{\rm{fin}}}}\left$, where ${{\cal S}_{{\rm{fin}}}}\left$ denotes the set of all permutations of x which move only finitely many elements. For all sets (...) x such that ${\cal S}\left$ is Dedekind infinite, $\left| {{\rm{seq}}\left} \right| < \left| {{\cal S}\left} \right|$ and there are no finite-to-one functions from ${\cal S}\left$ into seq, where seq denotes the set of all finite sequences of elements of x. For all infinite sets x such that there exists a permutation of x without fixed points, there are no finite-to-one functions from ${\cal S}\left$ into x. For all sets x, $|{[x]^2}| < \left| {{\cal S}\left} \right|$. (shrink)

For a set x, let S(x) be the set of all permutations of x. We prove by the method of permutation models that the following statements are consistent with ZF: (1) There is an infinite set x such that |p(x)|<|S(x)|<|seq^1-1(x)|<|seq(x)|, where p(x) is the powerset of x, seq(x) is the set of all finite sequences of elements of x, and seq^1-1(x) is the set of all finite sequences of elements of x without repetition. (2) There is a Dedekind infinite set (...) x such that |S(x)|<|[x]^3| and such that there exists a surjection from x onto S(x). (3) There is an infinite set x such that there is a finite-to-one function from S(x) into x. (shrink)

It is proved in (without the axiom of choice) that for all infinite cardinals and all natural numbers, where is the cardinality of the set of permutations with exactly non‐fixed points of a set which is of cardinality.

A partition is finitary if all its members are finite. For a set A, $\mathscr {B}(A)$ denotes the set of all finitary partitions of A. It is shown consistent with $\mathsf {ZF}$ (without the axiom of choice) that there exist an infinite set A and a surjection from A onto $\mathscr {B}(A)$. On the other hand, we prove in $\mathsf {ZF}$ some theorems concerning $\mathscr {B}(A)$ for infinite sets A, among which are the following: (1) If there is a finitary (...) partition of A without singleton blocks, then there are no surjections from A onto $\mathscr {B}(A)$ and no finite-to-one functions from $\mathscr {B}(A)$ to A. (2) For all $n\in \omega $, $|A^n|<|\mathscr {B}(A)|$. (3) $|\mathscr {B}(A)|\neq |\mathrm {seq}(A)|$, where $\mathrm {seq}(A)$ is the set of all finite sequences of elements of A. (shrink)

For a cardinal, we write for the cardinality of the set of permutations with finitely many non‐fixed points of a set which is of cardinality. We investigate the relationships between and for an arbitrary infinite cardinal in (without the axiom of choice). It is proved in that for all infinite cardinals, and we show that this is the best possible result.

For a set M, let |M| denote the cardinality of M. A family F is called strongly almost disjoint if there is an n∈ω such that |A∩B|<n for any two distinct elements A, B of F. It is shown in ZF (without the axiom of choice) that, for all infinite sets M and all strongly almost disjoint families F⊆P(M), |F|<|P(M)| and there are no finite-to-one functions from P(M) into F, where P(M) denotes the power set of M.

The factorial of a cardinal, denoted by, is the cardinality of the set of all permutations of a set which is of cardinality. We give a condition that makes the cardinal equality provable without the axiom of choice. In fact, we prove in that, for all cardinals, if and there is a permutation without fixed points on a set which is of cardinality, then.

It is proved in $\mathsf {ZF}$ (without the axiom of choice) that, for all infinite sets M, there are no surjections from $\omega \times M$ onto $\operatorname {\mathrm {\mathscr {P}}}(M)$.

ABSTRACTFilm clips are widely used in emotion research due to their relatively high ecological validity. Although researchers have established various film clip sets for different cultures, the few that exist related to Chinese culture do not adequately address positive emotions. The main purposes of the present study were to establish a standardised database of Chinese emotional film clips that could elicit more categories of reported positive emotions compared to the existing databases and to expand the available film clips that can (...) be used as neutral materials. Two experiments were conducted to construct the database. In experiment 1, 111 film clips were selected from more than one thousand Chinese movies for preliminary screening. After 315 participants viewed and evaluated these film clips, 39 excerpts were selected for further validation. In experiment 2, 147 participants watched and rated these 39 film clips, as well as another 8 excerpts chosen from the existing databases, to compare their validit... (shrink)

The collection contains published and unpublished essays, lecture transcripts, notes, poems, etc., often with handwritten edits and comments. Topics vary, with a focus on Chinese philosophy, comparison of Chinese and Western thought, contemporary intellectual and social reform movements, biographical reflections and self-criticism. The collection may reflect how 20th century political developments, especially the Cultural Revolution, impacted Feng Youlan's thought.

This paper explores how managers’ and supervisors’ equity incentives impact the likelihood of committing corporate fraud in Chinese-listed firms. Previous research has shown that corporate fraud in China is a widespread phenomenon and has severe consequences for affected firms and executives. However, our understanding of the reasons that fraud is committed in a Chinese setting has been very limited thus far. This is an increasingly important topic, because corporate governance is rapidly changing in China, and it is unclear whether adopting (...) the executive compensation practices of the West is appropriate for Chinese firms. We show that managers’ equity incentives increase their propensity to commit corporate fraud. We also find that this effect is more pronounced for state-owned firms. However, we find a negative but not significant relationship between the equity incentives of the supervisory board and the incidence of fraud. (shrink)

A function is boundedly finite-to-one if there is a natural number $k$ such that each point has at most $k$ inverse images. In this paper, we prove in $\textsf{ZF}$ (i.e. the Zermelo–Fraenkel set theory without the axiom of choice) several results concerning this notion, among which are the following: (1)For each infinite set $A$ and natural number $n$, there is no boundedly finite-to-one function from $\mathcal{S}(A)$ to $\mathcal{S}_{\leq n}(A)$, where $\mathcal{S}(A)$ is the set of all permutations of $A$ and $\mathcal{S}_{\leq (...) n}(A)$ is the set of all permutations of $A$ moving at most $n$ points. (2) For each infinite set $A$, there is no boundedly finite-to-one function from $\mathcal{B}(A)$ to $\textrm{fin}(A)$, where $\mathcal{B}(A)$ is the set of all partitions of $A$ such that every block is finite and $\textrm{fin}(A)$ is the set of all finite subsets of $A$. (shrink)

Di 1 juan. San song tang zi xu -- di 2-3 juan. Zhongguo zhe xue shi -- di 4-5 juan. Zhen yuan liu shu -- di 6 juan. Zhongguo zhe xue jian shi [translation of Short history of Chinese philosophy] -- di 7-9 juan. Zhongguo zhe xue shi xin bian -- di 10 juan. Zhe xue lun wen ji.

本书选取冯友兰作品中关于哲思的经典篇目,讲述作者对人生诸多领域的思考,对诸多人生问题的剖析,处处洋溢着丰富的智慧与哲人的洞见.

Compare with other professions, teachers are reported to have a higher risk of poor mental health. This study examined the relationships between emotional intelligence, perceived organizational justice, and mental health among Chinese high school teachers. Three hundred and eighty-one high school teachers, with their age range between 21 and 50 years, were administered the Emotional Intelligence Scale, Perceived Organizational Justice Scale, and Mental Health Scale. The result found that emotional intelligence and perceived organizational justice directly influence the mental health of (...) high school teachers. In addition, perceived organizational justice mediated the association between emotional intelligence and mental health. Moreover, the present study analyzes the different role of subtypes of perceived organizational justice on the relationships between emotional intelligence and mental health, and the results showed that the mediating effects of perceived distributive justice and interactive justice on emotional intelligence and mental health are not significant, only the perceived procedural justice mediated the relationships between emotional intelligence and teachers’ mental health. The results are discussed in a conceptual context. (shrink)

Actions are usually generalized among social group members. Importantly, the efficiency of an action with respect to achieving an external target determines action understanding, and it may have different degrees of social relevance to social groups. Thus, this study explored the role of action efficiency in action generalization. We used computer animations to simulate actions in social groups initiated by visual action cues or category labels, and we measured differences in response times between identifying actions that were and were not (...) consistent with group members, without explicit requirements regarding generalization. It was found that in both visually introduced and explicitly labeled social groups, when the group members acted inefficiently toward the external object, perceivers identified group‐consistent actions faster than group‐inconsistent actions, indicating that the exemplars' common inefficient actions are generalized to the unknown ingroup member, accordingly facilitating the identification of expected consistent inefficient action (Experiment 1). As this effect was not present when removing social group cues, it was determined to be specific to social groups (Experiment 2). Importantly, such generalization was not observed when the identical action was deemed efficient toward the external object (Experiment 3) and was specific to the demonstration of the action being completed by multiple group members rather than being repeated twice by one group member, supporting the group‐based inference and ruling out the possibility of the increased memorability of inefficient actions leading to more generalization relative to efficient actions (Experiment 4). Therefore, the efficiency of an action bounds the generalization of the action across social group members through a process that is spontaneous and implicit. This constrained action generalization may be due to inefficient actions being represented as culture‐specific conventional forms. (shrink)

Anxious major depressive disorder is a common subtype of major depressive disorder; however, its unique neural mechanism is not well-understood currently. Using multimodal MRI data, this study examined common and specific alterations of amygdala subregions between patients with and without anxiety. No alterations were observed in the gray matter volume or intra-region functional integration in either patient group. Compared with the controls, both patient groups showed decreased functional connectivity between the left superficial amygdala and the left putamen, and between the (...) right superficial amygdala and the bilateral anterior cingulate cortex and medial orbitofrontal cortex, while only patients with anxiety exhibited decreased activity in the bilateral laterobasal and superficial amygdala. Moreover, the decreased activity correlated negatively with the Hamilton depression scale scores in the patients with anxiety. These findings provided insights into the pathophysiologic processes of anxious major depressive disorder and may help to develop new and effective treatment programs. (shrink)

Background and aimThe postpartum depression literacy of perinatal women is closely related to the occurrence, recognition, and treatment of postpartum depression, therefore valid instruments for evaluating the level of PoDLi are of great significance for both research and clinical practice. This study aimed to cross-culturally adapt the postpartum depression literacy scale into Chinese and to test its psychometric properties among Chinese perinatal women.Materials and methodsA cross-sectional study was conducted from April to May 2022 in a tertiary hospital in Hangzhou, Zhejiang (...) Province, China. 619 out of the 650 perinatal women that were approached via a convenience sampling method completed the Chinese version of the PoDLiS. Content validity [the content validity index of items and scale-level content validity index ] was evaluated by an expert panel. Psychometric properties, including item analysis, structure validity, convergent and discriminant validity, reliability, criterion validity, and floor/ceiling effect were examined.ResultsThe final version of C-PoDLiS is a six-factor structure consisting of 27 items, which explained 61.00% of the total variance. Adequate content validity was ensured by the expert panel. The modified confirmatory factor analysis model revealed that the 6-factor model fitted the data well. The total Cronbach’s α was 0.862, the total McDonald’s ω was 0.869, and the test-retest reliability coefficient was 0.856. Results of convergent validity and discriminant validity provided good or acceptable psychometric support. Significant correlations between scores of the C-PoDLiS and Mental health literacy scale and Attitudes toward seeking professional psychological help short form scale supported good concurrent and predictive validity, respectively. No floor/ceiling effect was found.ConclusionThe C-PoDLiS was demonstrated to be a sound instrument with good reliability and validity for evaluating Chinese perinatal women’s PoDLi levels. Its use in the future can facilitate data aggregation and outcome comparisons across different studies on this topic. (shrink)