Jing Zhang

The classical Halpern–Läuchli theorem states that for any finite coloring of a finite product of finitely branching perfect trees of height ω, there exist strong subtrees sharing the same level set such that tuples in the product of the strong subtrees consisting of elements lying on the same level get the same color. Relative to large cardinals, we establish the consistency of a tail cone version of the Halpern–Läuchli theorem at a large cardinal (see Theorem 3.1), which, roughly speaking, deals with many colorings simultaneously and diagonally. Among other applications, we generalize a polarized partition relation on rational numbers due to Laver and Galvin to one on linear orders of larger saturation.

For achieving the sustainable development goals, green development has been raised to a high position for cities in China. The economic development in Northwest China is slow, the ecological environment is fragile, and the mineral resources are rich. Only through green development can we realize the comprehensive income of regional production development, rich life, and good ecology. This paper measures the green development efficiency of 30 prefecture-level cities in Northwest China by using DEA-SBM model of unexpected output, explores the differences and causes of green development efficiency from the perspective of time and space through convergence coefficient, coordination matrix, GIS, and other methods, and empirically tests the impact of industrial structure, technological progress, and other driving factors on green development efficiency by using panel Tobit model. The results show that, on the whole, the efficiency of green development in Northwest China is low, path dependence is serious and unbalanced, the coordinated development effect of different regions is weak, and the spillover effect of core urban agglomerations has not been effectively exerted; from the perspective of driving factors, economic development, population density, traffic situation, and education investment can significantly improve the efficiency of urban green development, and the second is that the proportion of industries significantly hinders the improvement of green development efficiency, while the impact of scientific and technological innovation is not significant. Based on the empirical results, this paper believes that the harmonious development of natural environment and economic society can be realized only by improving the coordinated development effect among cities, implementing the optimization and upgrading of industrial structure, introducing excellent talents, and promoting the technological upgrading.

We study algorithmic randomness notions via effective versions of almost-everywhere theorems from analysis and ergodic theory. The effectivization is in terms of objects described by a computably enumerable set, such as lower semicomputable functions. The corresponding randomness notions are slightly stronger than Martin–Löf randomness.We establish several equivalences. Given a ML-random realz, the additional randomness strengths needed for the following are equivalent.all effectively closed classes containingzhave density 1 atz.all nondecreasing functions with uniformly left-c.e. increments are differentiable atz.zis a Lebesgue point of each lower semicomputable integrable function.We also consider convergence of left-c.e. martingales, and convergence in the sense of Birkhoff’s pointwise ergodic theorem. Lastly, we study randomness notions related to density of${\rm{\Pi }}_n^0$and${\rm{\Sigma }}_1^1$classes at a real.

According to conceptual metaphor theory, individuals are thought to understand or express abstract concepts by using referents in the physical world—right and left for moral and immoral, for example. In this research, we used a modified Stroop paradigm to explore how abstract moral concepts are metaphorically translated onto physical referents in Chinese culture using the Chinese language. We presented Chinese characters related to moral and immoral abstract concepts in either non-distorted or distorted positions or rotated to the right or to the left. When we asked participants to identify the Chinese characters, they more quickly and accurately identified morally positive characters if they were oriented upright or turned to the right and more quickly and accurately identified immoral characters when the characters were distorted or rotated left. These results support the idea that physical cues are used in metaphorically encoding social abstractions and moral norms and provided cross-cultural validation for conceptual metaphor theory, which would predict our results.

Modernization is the common pursuit of human society, and culture, especially the advanced culture of choice determines the direction of modernization. Advanced culture is all the fine blend of history and culture, the crystallization of human civilization, is the sublimation of the spirit of the times, is the modernization and social development, cohesion and internal thrust. The proletariat as a ruling party, the ability to choose the guidelines of advanced culture and always represent the forward direction, determine their own country and the nation's rise and fall. History shows that the selection and modern culture to grasp the relationship between the grasp of understanding of China's modernization, "the main line." Prosperity in the 21st century socialist advanced culture, and thus China's modernization drive, we must correctly grasp of Marxism in China's advanced culture and the relationship between several aspects of selection, with the developing Marxism to promote China's modernization. Modernization is the common target of the human beings, however, the culture selection especially the advanced culture selection takes the key role for the direction of the modernization. The advanced culture, as the assembly of all excellent historical cultures, is the cohesive and promoting force of the modernization construction and social development. The Communist Party as the proletariat ruling party will determine its, the country and the nations' rise and decline whether to select the advanced culture as the guide for going forward. It has been proved to grasp the relations between the selection of culture and modernization, then to take the "main line" of China modernization, so it is necessary to push on Chinese modernization with the advanced culture Marxism

We study the structural rainbow Ramsey theory at uncountable cardinals. Compared to the usual rainbow Ramsey theory, the variation focuses on finding a rainbow subset that not only is of a certain cardinality but also satisfies certain structural constraints, such as being stationary or closed in its supremum. In the process of dealing with cardinals greater than ω1, we uncover some connections between versions of Chang's Conjectures and instances of rainbow Ramsey partition relations, addressing a question raised in [18].

Errors are inevitable in an increasingly risky and dynamic entrepreneurial environment. The error management and the error climate perceived by the members are crucial to the subsequent innovation behaviors. Maintaining and improving the psychological capital of entrepreneurs under errors is not only the psychological activities of entrepreneurs themselves but also a critical management process in which an organization can influence the psychological factors and behaviors of entrepreneurs through error management climate. In the context of Chinese culture, this study explores the influence of error management climate on entrepreneurial self-efficacy and innovation behavior under the boundary condition of Zhongyong thinking. Two hundred ninety samples of Chinese entrepreneurs are empirically analyzed in this study, and results show that: error management climate and entrepreneurial self-efficacy have significant positive effects on entrepreneurs’ innovation behavior; entrepreneurial self-efficacy mediates the relationship between error management climate and innovation behavior; and Zhongyong thinking plays moderating roles in the process of error management climate influencing innovation behavior. This study complements the entrepreneurship literature with its focus on error management climate as an essential antecedent of entrepreneurial self-efficacy, and promotes an understanding of how Chinese practitioners promote innovative behavior from a cultural perspective.

Student–teacher relationships have been examined by many studies. However, an omission still exists, the existing scales are not appropriate for studying STRs in private colleges because of the special character of these schools. This paper presents the development and validation of Private-College Student–Teacher Relationship Scale, the first instrument to evaluate student–teacher relationships in private colleges. The PCSTRS has six dimensions: trust, interaction, intimacy, care, approval, and comfort. In our main study, the validity and reliability of the six-factor PCSTRS model were demonstrated. The result of internal consistency coefficient indicated the high reliability of the scale, and the result of concurrent validity indicated the significant correlational relationships between the PCSTRS with other STR measures. In supplementary study, the PCSTRS was administered to 360 participants to confirm the applicability of PCSTRS and investigate the relation of STRs and students’ traits, performance, and wellbeing, as well as the differences between the private school and the public school in this relation; the analyses revealed that there were significant differences in trust, intimacy, and care between private and public colleges; positive correlations were found between STRs and self-esteem, self-efficacy, academic performance, extracurricular activity involvement, and subjective wellbeing. Present research firstly develops the PCSTRS, examined the reliability and validity, and provides the proposed nomological network among related constructs.

We investigate the interaction between compactness principles and guessing principles in the Radin forcing extensions. In particular, we show that in any Radin forcing extension with respect to a measure sequence on [Formula: see text], if [Formula: see text] is weakly compact, then [Formula: see text] holds. This provides contrast with a well-known theorem of Woodin, who showed that in a certain Radin extension over a suitably prepared ground model relative to the existence of large cardinals, the diamond principle fails at a strongly inaccessible Mahlo cardinal. Refining the analysis of the Radin extensions, we consistently demonstrate a scenario where a compactness principle, stronger than the diagonal stationary reflection principle, holds yet the diamond principle fails at a strongly inaccessible cardinal, improving a result from [O. B. -Neria, Diamonds, compactness, and measure sequences, J. Math. Log. 19(1) (2019) 1950002].