Gödel’s proof

In 1931, the great Austrian mathematician Kurt Gödel proved “all consistent axiomatic formulations of number theory include undecidable propositions”. This discovery of Gödel and its proof had enormous repercussions in mathematics and computer science. The proof hinged upon the writing of a self-referential mathematical statement, in the same way as the liar’s paradox — I am lying — is a self-referential statement. In this three-part article, we describe Gödel’s discovery and his famous proof.     

Computed tomography using level set method and algebraic reconstruction technique

In this paper, a novel reconstruction technique based on level set method and algebraic reconstruction technique is proposed for multiphase flow computed tomography (CT) system. The curvature-driven noise reduction method is inserted into the conventional iteration procedure of algebraic reconstruction technique to improve the image quality and convergence speed with limited projection data. By evolving the image as a set of iso-intensity contours after each updation, the sufficient number of iterations for acceptable results is reduced by 80%-90%, while the image quality is enhanced obviously. Quantitative evaluation of image quality is given by using both relative image error and correlation coefficient. The resultant images can be utilized to detect flow regimes for monitoring industrial multiphase flow. Laboratory results demonstrate the feasibility of the proposed method. Phantoms of four typical flow regimes can be reconstructed from few-view projection data efficiently, and the corresponding image errors and correlation coefficients are acceptable for the cases tested in this paper.     

Resistance partial factor and reliability of cast ball-and-socket support joint

Considering the uncertainty of material performance, geometric characteristic and analysis method, the analysis of statistical parameters of the resistance of cast ball-and-socket support joints and the reliability analysis are carried out by JC method (improved first-order second-moment method) based on the relevant experimental data. Results show that the resistance partial factor of the joint increases with the increase of the reliability index. The resistance partial factors are suggested corresponding to the reliability index under different load combinations. Moreover, the suggested resistance partial factor is adopted in reliability design, and it is found that the reliability index of the joint is larger than the target reliability index. The optimal load combination is the one in which live load plays an important control role. Finally, based on the suggested resistance partial factors, the reliability analysis of cast ball-and-socket support joints of a project is conducted.     

非形式逻辑及其早期历史发展

"非形式逻辑"作为逻辑的子领域,最初出现于1970至1980年代的美国和加拿大,本文意在回顾非形式逻辑发展的早期历史进程.本文假定,当我们从历史的角度来考察时,非形式逻辑的本质能够得以阐明.因此,我将以观念史领域的评论作为出发点.之所以不从理论的要素谈起并把历史留给历史学家,其中一个理由在于"非形式逻辑"这个词并不指示一个理论.非形式逻辑部分地可看作是某个思潮,部分地可当作一种论证研究进路,部分地涉及到对逻辑之本质的看法,这些都可以通过考察非形式逻辑的发展史来加以理解.本文的第一部分追溯了非形式逻辑的兴起,概括了其思想史和社会史,并评述了其早期发展中的主要人物、教科书,以及主要的论旨及其社会化.第二部分简要描述了<逻辑的自我辩护>这本教科书中的一些革新.第三部分简要涉及非形式逻辑与其它领域的早期互动.     

Discrimination and Ethnic–Racial Identity: Understanding Direction of Effects Using Within- and Between-Person Analyses

Ethnic–racial identity (ERI) development and ethnic–racial discrimination are two salient experiences among adolescents in the United States. Despite growing awareness of the costs and benefits of these experiences individually, we know little about how they may influence one another. The current study examined competing hypotheses relating discrimination and components of ERI (i.e., exploration, resolution, affirmation) among a sample of Mexican-origin adolescent mothers (N = 181; M_age at Wave 1 = 16.83, SD = 1.01) across six waves of data. Findings revealed that within-person changes in discrimination predicted subsequent ERI resolution and affirmation; however, ERI did not predict subsequent discrimination. Between-person effects of discrimination on affirmation were significant. Our findings underscore the importance of discrimination experiences in shaping Mexican-origin adolescent mothers’ normative developmental competencies.     

Smart Conformists: Children and Adolescents Associate Conformity With Intelligence Across Cultures

The current study used a novel methodology based on multivocal ethnography to assess the relations between conformity and evaluations of intelligence and good behavior among Western (U.S.) and non-Western (Ni-Vanuatu) children (6- to 11-year-olds) and adolescents (13- to 17-year-olds; N = 256). Previous research has shown that U.S. adults were less likely to endorse high-conformity children as intelligent than Ni-Vanuatu adults. The current data demonstrate that in contrast to prior studies documenting cultural differences between adults' evaluations of conformity, children and adolescents in the United States and Vanuatu have a conformity bias when evaluating peers' intelligence and behavior. Conformity bias for good behavior increases with age. The results have implications for understanding the interplay of conformity bias and trait psychology across cultures and development.