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)

Online shopping for customized garments has become the fastest-growing field of the Chinese eBusiness market. Most consumers not only limit themselves to buying standardized garments but also want to buy garments customized to their preferences. This phenomenon has pushed the fashion textile and apparel industry to change its supply chain operations to meet the customization demand. Besides, the fashion textile and apparel industry also want to study how different channel factors will affect consumers' perceived value and further influence consumers' purchasing (...) decisions. We initiated this study and empirically tested more than 200 experienced consumers. This study collaborated with a fashion textile and apparel company that aims to implement customized product lines soon. Based on the perceived value theory and risk management theory, we investigated whether product involvement and channel identification on supply chain design will affects potential customized product consumers' purchasing decisions. The findings reveal that channel recognition affects consumer decisions by having a positive impact on their perceived value. The perceived risk and shopping channel involvement of consumers have a negative impact on their perceived values and channel selections. In addition, product involvement has a moderating effect on the relationship between channel's perceived risk, perceived values, and channel selections as well. (shrink)

Based upon the demarcation between Elementalism and Atomism Chemistry from the perspective of the long-term history of chemistry, the authors re-examine the Berthollet-Proust controversy on the three types of chemical compounds, pointing out that Berthollet proposed the law of indefinite proportions by deduction, while Proust proposed the law of definite proportions by induction. The controversy is beyond the framework of affinity chemistry and entail a synthesis of meta-chemical thinking and experiments. Proust’s discovery of the law of definite proportions not only (...) function as Bacon’s “instances of lamp” to invoke Dalton and other atomism chemists to envision atomism, but also served as a bridge linking the two meta-chemistries. John Dalton, the third choice, envisioned his atomism by abduction. The case study on “the Berthollet-Proust controversy and Dalton’s resolution” mandates a reinvestigation of the crucial role of the system of experiments and the evolution of chemistry according to the demarcation between the established branches of Elementalism and Atomism Chemistry. (shrink)

Journal of Mathematical Logic, Ahead of Print. Bagaria and Magidor introduced the notion of almost strong compactness, which is very close to the notion of strong compactness. Boney and Brooke-Taylor asked whether the least almost strongly compact cardinal is strongly compact. Goldberg gives a positive answer in the case [math] holds from below and the least almost strongly compact cardinal has uncountable cofinality. In this paper, we give a negative answer for the general case. Our result also gives an affirmative (...) answer to a question of Bagaria and Magidor. (shrink)

Wheels are the key components of a train, and the shape of the wheel flange should be maintained to ensure the security of train operations. As a method to maintain the shape at the cost of the diameter size, reprofiling has significant impacts on the lifecycle of a train. A wheel model is built in this paper based on the analysis of the wheel wear features and datasets from Taiyuan locomotives. With the decision variables T i, T i ′, which (...) describe the reprofiling strategy, we formulate a multiobjective optimization problem simultaneously minimizing the reprofiling numbers and maximizing the serving years. To find the solutions of the multiobjective model, the NSGA-II is extended with an alteration of the crowding distance calculation and genetic operators. The improved NSGA-II performs better than other approaches. Meanwhile, outstanding solutions with longer servicing years and less reprofiling are listed in this paper. Our study reveals the relationship between the diameter, flange thickness, and their individual attrition rates and proposes a wear model, multiobjective model, and improved NSGA-II. Compared with existing reprofiling strategies, the strategy recommended in our work can significantly increase the lifecycle of the wheel coupled with a low repair frequency. (shrink)

As one of the important 21st-century skills, collaborative problem solving (CPS) has caught much attention in the assessment area. Two initiative approaches have been created: the human-to-human and human-to-agent modes. Between the two modes, the human-to-human interaction is much closer to the real-world situation and its process stream data can reveal more detailed information about the cognitive processes. In order to measure CPS ability effectively by this mode, how to extract indicators from the data and model it is crucial, while (...) the existing methods all have some disadvantages. In the present study, we proposed a new paradigm for extracting indicators and modeling the dyad data in the human-to-human mode. Specifically, both individual and group indicators were extracted from the data stream, which served as evidence for demonstrating CPS skills. In addition, a within-item multidimensional Rasch model was used to fit the dyad data. To test the validity of the paradigm, we developed five tasks following the asymmetric mechanism and integrated them into an online testing platform. Four hundred thirty-four students from China participated in the assessment and the online platform recorded their crucial actions with time stamps. The new paradigm was used to deal with the generated process stream data. Results showed that the model fitted well. The item parameter estimates and fitting indexes were acceptable, and students were well differentiated. In general, the new paradigm of extracting indicators and modeling the dyad data is feasible for improving the human-to-human assessment of CPS. Finally, the limitations of the current study and further research directions are discussed. (shrink)

湖南省优秀社科学术著作资助出版湖南省第九届优秀社科著作出版立项项目湘潭大学学术著作出版资助本论文是湘潭大学博士科研项目成果项目编号04QDB12.

In this paper, we characterize the possible cofinalities of the least $\lambda $ -strongly compact cardinal. We show that, on the one hand, for any regular cardinal, $\delta $, that carries a $\lambda $ -complete uniform ultrafilter, it is consistent, relative to the existence of a supercompact cardinal above $\delta $, that the least $\lambda $ -strongly compact cardinal has cofinality $\delta $. On the other hand, provably the cofinality of the least $\lambda $ -strongly compact cardinal always carries a (...) $\lambda $ -complete uniform ultrafilter. (shrink)