The present study critically evaluates whether school leadership influences student learning homogenously regardless of school contexts. It examined relationships between four principal leadership variables (envisioning, instructional management, promoting professional development, empowerment) and two types of student outcomes (enjoyment in learning science, science achievement,) in different school contexts (in terms of the availability of science resources, quality of science teachers, and school socioeconomic status (SES)). The sample comprised 248,620 students and 9,370 principals in 35 developed countries who participated in the Programme (...) for International Student Assessment (PISA) 2015. Latent profile analysis (LPA) showed that schools operated in three types of school contexts with different levels of science resources, proportion of quality science teachers, and school SES. There were also differences in the pattern of leadership practices across the three types of school contexts. Three-level hierarchical linear modeling (HLM) showed that among the four leadership variables, only instructional management was positively associated with students’ enjoyment of science in schools with less science resources and quality science teachers. Therefore, instructional management had compensatory effects for students in less-endowed schools. In contrast, principal leadership related to envisioning, teacher professional development, and empowerment was not positively related to students’ science learning in all three school contexts. (shrink)

Ben shu yi Ming ru Li Cai de jiang xue huo dong yu xue pai jian gou wei zhong xin, tan tao cong shi liu shi ji chu dao shi qi shi ji mo li xue qun ti zhong xin xing xue shuo he xue pai de chan sheng, chuan bo, kuo zhan yu chuan cheng de mo shi, bing zhuo zhong cong si xiang shi de jiao du jie shi zhe zhong mo shi chan sheng he yun xing (...) de si xiang gen yuan yu nei zai dong li. Quan shu zheng wen gong qi zhang, zhu yao nei rong fen wei shang xia liang bian, shang bian yi hong guan zong lun de fang shi, cong li xue jing dian "Da xue" de wen ben bian dong he quan shi jing zheng qie ru, tan tao zhong wan Ming li xue xue shuo he xue pai jian gou de li lun gen ju; xia bian yi Li Cai de "zhi xiu" xue shuo ji qi jiang xue huo dong zuo wei ge an yan jiu, tan tao li xue xue shuo he xue pai de chuan bo ji chuan cheng de she hui hua tu jing. (shrink)

We give a survey of current research on Gödel’s incompleteness theorems from the following three aspects: classifications of different proofs of Gödel’s incompleteness theorems, the limit of the applicability of Gödel’s first incompleteness theorem, and the limit of the applicability of Gödel’s second incompleteness theorem.

In this paper, we examine the limit of applicability of Gödel’s first incompleteness theorem. We first define the notion “$\textsf {G1}$ holds for the theory $T$”. This paper is motivated by the following question: can we find a theory with a minimal degree of interpretation for which $\textsf {G1}$ holds. To approach this question, we first examine the following question: is there a theory T such that Robinson’s $\mathbf {R}$ interprets T but T does not interpret $\mathbf {R}$ and $\textsf (...) {G1}$ holds for T? In this paper, we show that there are many such theories based on Jeřábek’s work using some model theory. We prove that for each recursively inseparable pair $\langle A,B\rangle $, we can construct a r.e. theory $U_{\langle A,B\rangle }$ such that $U_{\langle A,B\rangle }$ is weaker than $\mathbf {R}$ w.r.t. interpretation and $\textsf {G1}$ holds for $U_{\langle A,B\rangle }$. As a corollary, we answer a question from Albert Visser. Moreover, we prove that for any Turing degree $\mathbf {0}< \mathbf {d}<\mathbf {0}^{\prime }$, there is a theory T with Turing degree $\mathbf {d}$ such that $\textsf {G1}$ holds for T and T is weaker than $\mathbf {R}$ w.r.t. Turing reducibility. As a corollary, based on Shoenfield’s work using some recursion theory, we show that there is no theory with a minimal degree of Turing reducibility for which $\textsf {G1}$ holds. (shrink)

LetZ2,Z3, andZ4denote 2nd, 3rd, and 4thorder arithmetic, respectively. We let Harrington’s Principle, HP, denote the statement that there is a realxsuch that everyx-admissible ordinal is a cardinal inL. The known proofs of Harrington’s theorem “$Det\left$implies 0♯exists” are done in two steps: first show that$Det\left$implies HP, and then show that HP implies 0♯exists. The first step is provable inZ2. In this paper we show thatZ2+ HP is equiconsistent with ZFC and thatZ3+ HP is equiconsistent with ZFC + there exists a remarkable (...) cardinal. As a corollary,Z3+ HP does not imply 0♯exists, whereas Z4+ HP does. We also study strengthenings of Harrington’s Principle over 2ndand 3rdorder arithmetic. (shrink)

In this work, we aim at understanding incompleteness in an abstract way via metamathematical properties of formal theories. We systematically examine the relationships between the following twelve important metamathematical properties of arithmetical theories: Rosser, EI (effectively inseparable), RI (recursively inseparable), TP (Turing persistent), EHU (essentially hereditarily undecidable), EU (essentially undecidable), Creative, |$\textbf{0}^{\prime }$| (theories with Turing degree |$\textbf{0}^{\prime }$|⁠), REW (all RE sets are weakly representable), RFD (all recursive functions are definable), RSS (all recursive sets are strongly representable), RSW (all (...) recursive sets are weakly representable). Given any two properties |$P$| and |$Q$| in the above list, we examine whether |$P$| implies |$Q$|⁠. (shrink)

Ben shu dui Zhongguo zhe xue xue ke ji zhe xue shi yan jiu de fang fa lun deng wen ti jin xing le tan tao yu fen xi.

Remarkable cardinals were introduced by Schindler, who showed that the existence of a remarkable cardinal is equiconsistent with the assertion that the theory of L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L}$$\end{document} is absolute for proper forcing :176–184, 2000). Here, we study the indestructibility properties of remarkable cardinals. We show that if κ is remarkable, then there is a forcing extension in which the remarkability of κ becomes indestructible by all <κ-closed ≤κ-distributive forcing and all two-step iterations of (...) the form Add∗R˙\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Add*\dot{\mathbb R}}$$\end{document}, where R˙\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\dot{\mathbb R}}$$\end{document} is forced to be <κ-closed and ≤κ-distributive. In the process, we introduce the notion of a remarkable Laver function and show that every remarkable cardinal carries such a function. We also show that remarkability is preserved by the canonical forcing of the GCH. (shrink)

ABSTRACT We use Gödel’s incompleteness theorems as a case study for investigating mathematical depth. We examine the philosophical question of what the depth of Gödel’s incompleteness theorems consists in. We focus on the methodological study of the depth of Gödel’s incompleteness theorems, and propose three criteria to account for the depth of the incompleteness theorems: influence, fruitfulness, and unity. Finally, we give some explanations for our account of the depth of Gödel’s incompleteness theorems.

This paper belongs to the research on the limit of the first incompleteness theorem. Effectively inseparable (EI) theories can be viewed as an effective version of essentially undecidable (EU) theories, and EI is stronger than EU. We examine this question: Are there minimal effectively inseparable theories with respect to interpretability? We propose tEI, the theory version of EI. We first prove that there are no minimal tEI theories with respect to interpretability (i.e., for any tEI theory T, we can effectively (...) find a theory which is tEI and strictly weaker than T with respect to interpretability). By a theorem due to Pour-EI, we have that tEI is equivalent with EI. Thus, there are no minimal EI theories with respect to interpretability. Also, we prove that there are no minimal finitely axiomatizable EI theories with respect to interpretability. (shrink)

In this paper, we prove that: if κ is supercompact and the math formula Hypothesis holds, then there is a proper class of regular cardinals in math formula which are measurable in math formula. Woodin also proved this result independently [11]. As a corollary, we prove Woodin's Local Universality Theorem. This work shows that under the assumption of the math formula Hypothesis and supercompact cardinals, large cardinals in math formula are reflected to be large cardinals in math formula in a (...) local way, and reveals the huge difference between math formula-supercompact cardinals and supercompact cardinals under the math formula Hypothesis. (shrink)

Williams puts forward and develops his theory of integrity on the basis of criticizing utilitarianism and Kantian ethics as too demanding to make enough room for personal projects. Instead, his integrity theory advocates that we should act out of commitments with which we deeply identify ourselves. In doing so, we express who we really are and make our life meaningful. If not so, our integrity would be violated and we may lose ourselves. Such a description of the self in moral (...) life is criticized as solipsism for that it makes the relationship between one’s projects and himself only be regulated by himself. This paper aims to point out that such criticism is inappropriate. To show the inaccuracy of the criticism, the author will analyze the relationship between the self and others in two aspects. The first aspect is about the structure of formation of desires and others, and the second one is about the action responsibility and others. After analysis, in the first aspect of desires, the self needs others to form and stabilize desires, beliefs and motivations to cooperate with others. Others help the self to sustain the sense of reality to prevent the self from forming wishful thinking. As to action, others’ need for response is an important element in ascribing the self’s action responsibility. The self acquires self-conception, self-cognition and self-identity through the interaction with others. Thus, others play an essential role in Williams’ theory of integrity. Although there are some flaws in Williams’ integrity theory, to reexamine his theory is conducive to our understanding of moral life. (shrink)

This paper examines the influence of CEO career horizon problems on corporate social responsibility. We assume that as CEOs are getting older, they tend to disengage in CSR due to their shorter career horizons. We further argue that high levels of industry-level discretion and blockholder ownership amplify the negative effects of CEO age on CSR. Using a panel sample of US-based firms over 2004–2009, we do not find the main effect of CEO age on CSR, but find support for the (...) moderating effects, such that CEO age is negatively associated with CSR when there are high levels of ILD and blockholder ownership. Therefore, results suggest that CEO career horizon problems matter for CSR when CEOs have sufficient discretion over the firm’s strategic decisions and outside blockholders put more pressure on CEOs to engage in financial earning management. (shrink)

The product presentation videos on E-commerce platforms have a significant influence on consumers' purchase decisions, and enterprises have focused on choosing the type of product presentation videos. Based on the resource matching theory, mental imagery theory and cue utilization theory, this study investigated the influence of product presentation videos type on consumers' purchase intention and the moderating effect of product rating. Through three pre-experiments and two formal experiments, the results showed that the product usage video has a stronger effect on (...) consumers' purchase intention more than the product appearance video, which is mediated by perceived diagnosticity and mental imagery. In addition, product rating moderated the influence of product presentation videos type on consumers' purchase intention. The product usage video would improve consumers' purchase intention more than the product appearance video when the product rating is high; however, there is no significant difference in the impact of two types of videos on consumers' purchase intention when the product rating is low. This study supplements the research on product presentation videos and provides a reference for online retailers to select effective product presentation videos. (shrink)

We show that for any ω-r.e. degree d and n-r.e. degree b with d

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Liver transplantation (LT) activities during the COVID-19 pandemic have been curtailed in many countries. The impact of various policies restricting LT on outcomes of potential LT candidates is unclear. We studied all patients on the nationwide LT waitlists in Hong Kong and Singapore between January 2016 and May 2020. We used continuous time Markov chains to model the effects of different scenarios and varying durations of disruption on LT candidates.

Physical literacy has received considerable attention in the field of physical education and physical activity worldwide. According to recent studies, the level of physical fitness among Chinese university students is gradually decreasing. This study aims to examine the impact of the PF level on PA and PL, as well as the relationships among PF, PA, and PL, in Chinese university students. Participants comprised 798 university students in Chongqing, China. Participants completed the tests of vital capacity, cardiorespiratory fitness, muscular strength, and (...) flexibility, according to the National Physical Fitness Measurement Standards Manual, as well as questionnaires on PA and PL. The independent t-tests were conducted to examine sex differences in the evaluated variables, and the Pearson’s correlation between each PF test and PL attributes and PA was calculated according to sex. In addition, the independent t-tests were conducted to determine whether the PF level had an effect on PL attributes and PA at various intensities. Significant sex differences were found in the PF domains of vital capacity, muscular strength, and aerobic fitness, with higher scores in men than in women, but not in the PF domain of flexibility and total PL score. Furthermore, the PF domains of muscular strength and aerobic fitness were significantly and positively correlated with the PL attributes of confidence and physical competence in both men and women, while the PF domains of vital capacity and aerobic fitness were significantly and positively correlated with the PL attribute of motivation in men. In addition, PL was significantly and positively associated with cardiorespiratory fitness, vital capacity, muscular strength, and flexibility among participants in the fit group. These findings support advocating for increased participation in PA in university students and using PL as a tool to improve PF components. (shrink)

ABSTRACT We show that there is a polynomial over the rational number field corresponding to each propositional formula in a given many-valued logic. To decide whether a propositional formula can be deduced from a finite set of such formulas (deduction problem), we only need to decide whether a polynomial vanishes on an algebraic variety. By using Wu's method, an algorithm for this problem is presented.

Medical devices have been long used for odiagnostic, therapeutic or rehabilitation purposes. Currently, they can range from a low-cost portable device that is often used for personal health monitoring to high-end sophisticated equipment that can only be operated by trained professionals. Depending on the functional purposes, there are different certification or compliance markings on the device when it is sold. One common certification marking is the Conformité Européenne affixation but this has a range of certification mark numbering for a variety (...) of functional purposes. While the regulators and medical device manufacturers understand the associated significance and clinical implications, these may not be apparent to the professionals and the general public. With portable healthcare devices and mobile applications gaining popularity, better awareness of certification marking will be needed. Particularly, there are differences in the allowed functional purposes and the associated cost derivations of devices with a seemingly similar nature. A preferred approach such as an easy-to-understand notation next to any certification marking on a device can aid in differentiation without the need to digest mountainous regulatory details. (shrink)

During the past few years significant progress has been made in our understanding of the structure and function of the proteins involved in eukaryotic DNA replication. Data from several laboratories suggest that, in contrast to prokaryotic DNA replication, two distinct DNA polymerases are required for eukaryotic DNA replication, i.e. DNA polymerase delta for the synthesis of the leading strand and DNA polymerase alpha for the lagging strand. Several accessory proteins analogous to prokaryotic replication factors have been identified and some of (...) these are specific for pol delta whereas others affect both DNA replicases. The replicases and their accessory proteins appear to be highly conserved in eukaryotes, as homologous proteins have been found in species ranging from humans to yeast. (shrink)

During the past few years significant progress has been made in our understanding of the structure and function of the proteins involved in eukaryotic DNA replication. Data from several laboratories suggest that, in contrast to prokaryotic DNA replication, two distinct DNA polymerases are required for eukaryotic DNA replication, i.e. DNA polymerase delta for the synthesis of the leading strand and DNA polymerase alpha for the lagging strand. Several accessory proteins analogous to prokaryotic replication factors have been identified and some of (...) these are specific for pol delta whereas others affect both DNA replicases. The replicases and their accessory proteins appear to be highly conserved in eukaryotes, as homologous proteins have been found in species ranging from humans to yeast. (shrink)

Precision medicine (PM) aims to revolutionise healthcare, but little is known about the role religion and spirituality might play in the ethical discourse about PM. This Perspective reports the outcomes of a knowledge exchange fora with religious authorities in Singapore about data sharing for PM. While the exchange did not identify any foundational religious objections to PM, ethical concerns were raised about the possibility for private industry to profiteer from social resources and the potential for genetic discrimination by private health (...) insurers. According to religious authorities in Singapore, sharing PM data with private industry will require a clear public benefit and robust data governance that incorporates principles of transparency, accountability and oversight. (shrink)

Social desirability bias (SDB) is one of the main concerns in self-reported studies that measures explicit attitudes such as ethics research. Although SDB was introduced since the early 1950s, little effort has been made to understand the necessity of including an SDB scale in studies of sensitive topics such as ethics. The purpose of this paper was to (1) identify whether current ethics-related studies considered SDB when conducting their research and (2) ascertain whether SDB was a significant variable in such (...) studies. This investigation takes the form of a systematic review of articles published within the last 20 years in well-known business ethics journals (2000–2019). We found that (a) only 13.67% of ethics research measured SDB; (b) although the majority of the reviewed articles were from the West, researchers in Asia have also made significant progress in recent years in measuring SDB in their studies; (c) SDB was used mainly as a control variable and as such researchers preferred scales with fewer items; and (d) SDB was unavoidable even when using online surveys. Based on our findings, we attempt to provide an overview of SDB in ethics research and encourage ethics researchers who adopt self-reported surveys to include an SDB measurement in their studies to control SDB. (shrink)

Planning ability is important in everyday functioning, and a key measure to assess the preparation and execution of plans is the Tower of London task. Previous studies indicate that older adults are often less accurate than the young on the ToL and that there may be cultural differences in performance on the task. However, potential interactions between age and culture have not previously been explored. In the current study we examined the effects of age on ToL performance in an Asian (...) culture and a Western culture. We also explored whether working memory, age, education, and socioeconomic status explained variance in ToL performance across these two cultures. Results indicated that age effects on ToL performance were greater in the Malaysian sample. Subsequent moderated mediation analysis revealed differences between the two cultures, in that the age-related variance in ToL accuracy was accounted for by WM capacity at low and medium education levels only in the Malaysian sample. Demographic variables could not explain additional variance in ToL speed or accuracy. These results may reflect cultural differences in the familiarity and cognitive load of carrying out complex planning tasks. (shrink)

Alcohol use disorder is one of the most common substance use disorders contributing to both behavioral and cognitive impairments in patients with AUD. Recent neuroimaging studies point out that AUD is a typical disorder featured by altered functional connectivity. However, the details about how voxel-wise functional coordination remain unknown. Here, we adopted a newly proposed method named functional connectivity density to depict altered voxel-wise functional coordination in AUD. The novel functional imaging technique, FCD, provides a comprehensive analytical method for brain's (...) “scale-free” networks. We applied resting-state functional MRI toward subjects to obtain their FCD, including global FCD, local FCD, and long-range FCD. Sixty-one patients with AUD and 29 healthy controls were recruited, and patients with AUD were further divided into alcohol-related cognitive impairment group and non-cognitive impairment group. All subjects were asked to stay stationary during the scan in order to calculate the resting-state gFCD, lFCD, and lrFCD values, and further investigate the abnormal connectivity alterations among AUD-NCI, ARCI, and HC. Compared to HC, both AUD groups exhibited significantly altered gFCD in the left inferior occipital lobe, left calcarine, altered lFCD in right lingual, and altered lrFCD in ventromedial frontal gyrus. It is notable that gFCD of the ARCI group was found to be significantly deviated from AUD-NCI and HC in left medial frontal gyrus, which changes probably contributed by the impairment in cognition. In addition, no significant differences in gFCD were found between ARCI and HC in left parahippocampal, while ARCI and HC were profoundly deviated from AUD-NCI, possibly reflecting a compensation of cognition impairment. Further analysis showed that within patients with AUD, gFCD values in left medial frontal gyrus are negatively correlated with MMSE scores, while lFCD values in left inferior occipital lobe are positively related to ADS scores. In conclusion, patients with AUD exhibited significantly altered functional connectivity patterns mainly in several left hemisphere brain regions, while patients with AUD with or without cognitive impairment also demonstrated intergroup FCD differences which correlated with symptom severity, and patients with AUD cognitive impairment would suffer less severe alcohol dependence. This difference in symptom severity probably served as a compensation for cognitive impairment, suggesting a difference in pathological pathways. These findings assisted future AUD studies by providing insight into possible pathological mechanisms. (shrink)

BackgroundTemporal lobe epilepsy is the most prevalent refractory focal epilepsy and is more likely accompanied by cognitive impairment. The fully understanding of the neuronal activity underlying TLE is of great significance.ObjectiveThis study aimed to comprehensively explore the potential brain activity abnormalities affected by TLE and detect whether the changes were associated with cognition.MethodsSix static intrinsic brain activity indicators [amplitude of low-frequency fluctuation, fractional ALFF, regional homogeneity, degree centrality, global signal correlation, and voxel-mirrored homotopic connectivity ] and their corresponding dynamic indicators, (...) such as dynamic ALFF, dynamic fALFF, dynamic ReHo, dynamic DC, dynamic VMHC, and dynamic GSCorr, in 57 patients with unilateral TLE and 42 healthy volunteers were compared. Correlation analyses were also performed between these indicators in areas displaying group differences and cognitive function, epilepsy duration, and severity.ResultsMarked overlap was present among the abnormal brain regions detected using various static and dynamic indicators, primarily including increased ALFF/dALFF/fALFF in the bilateral medial temporal lobe and thalamus, decreased ALFF/dALFF/fALFF in the frontal lobe contralateral to the epileptogenic side, decreased fALFF, ReHo, dReHo, DC, dDC, GSCorr, dGSCorr, and VMHC in the temporal neocortex ipsilateral to the epileptogenic foci, decreased dReHo, dDC, dGSCorr, and dVMHC in the occipital lobe, and increased ALFF, fALFF, dfALFF, ReHo, and DC in the supplementary motor area ipsilateral to the epileptogenic foci. Furthermore, most IBA indicators in the abnormal brain region significantly correlated with the duration of epilepsy and several cognitive scale scores.ConclusionThe combined application of static and dynamic IBA indicators could comprehensively reveal more real abnormal neuronal activity and the impairment and compensatory mechanisms of cognitive function in TLE. Moreover, it might help in the lateralization of epileptogenic foci and exploration of the transmission and inhibition pathways of epileptic activity. (shrink)

BackgroundThe COVID-19 pandemic has changed the healthcare landscape drastically. Stricken by sharp surges in morbidity and mortality with resource and manpower shortages confounding their efforts, the medical community has witnessed high rates of burnout and post-traumatic stress amongst themselves. Whilst the prevailing literature has offered glimpses into their professional war, no review thus far has collated the deeply personal reflections of physicians and ascertained how their self-concept, self-esteem and perceived self-worth has altered during this crisis. Without adequate intervention, this may (...) have profound effects on their mental and physical health, personal relationships and professional efficacy.MethodsWith mentions of the coronavirus pervading social media by the millions, this paper set out to collate and thematically analyse social media posts containing first-person physician reflections on how COVID-19 affected their lives and their coping mechanisms. A consistent search strategy was employed and a PRISMA flowchart was used to map out the inclusion/exclusion criteria.ResultsA total of 590 social media posts were screened, 511 evaluated, and 108 included for analysis. Salient themes identified include Disruptions to Personal Psycho-Emotional State, Disruptions to Professional Care Delivery, Concern for Family, Response from Institution, Response from Society and Coping Mechanisms.ConclusionIt is evident that the distress experienced by physicians during this time has been manifold, multi-faceted and dominantly negative. Self-concepts were distorted with weakened self-esteem and perceived self-worth observed. The Ring Theory of Personhood (RToP) was adopted to explain COVID-19’s impact on physician personhood as it considers existential, individual, relational and social concepts of the self. These entwined self-concepts serve as ‘compensatory’ to one another, with coping mechanisms buffering and fortifying the physician’s overall personhood. With healthcare institutions playing a vital role in providing timely and targeted support, it was further proposed that a comprehensive assessment tool based on the RToP could be developed to detect at-risk physicians and evaluate the presence and effectiveness of established support structures. (shrink)