Painlev\'e III′' and the Hankel Determinant Generated by a Singularly Perturbed Gaussian Weight

In this paper, we study the Hankel determinant generated by a singularly perturbed Gaussian weight $$w(x,t)=\mathrm{e}^{-x^{2}-\frac{t}{x^{2}}},\;\;x\in(-\infty, \infty),\;\;t>0.$$ By using the ladder operator approach associated with the orthogonal polynomials, we show that the logarithmic derivative of the Hankel determinant satisfies both a non-linear second order difference equation and a non-linear second order differential equation. The Hankel determinant also admits an integral representation involving a Painlev\'e III$'$. Furthermore, we consider the asymptotics of the Hankel determinant under a double scaling, i.e. $n\rightarrow\infty$ and $t\rightarrow 0$ such that $s=(2n+1)t$ is fixed. The asymptotic expansions of the scaled Hankel determinant for large $s$ and small $s$ are established, from which Dyson's constant appears.Comment: 22 page

Research on the Preparation and Performance of Binary Modified Maltodextrin Water-Reducing Agent

Using maltodextrin (MD) of different dextrose equivalent (DE) values, 1,3-propanesultone, and maleic anhydride as raw materials, a novel binary modified maltodextrin (BMMD) was synthesized and further applied as a water-reducing agent. Its structure was characterized by Fourier transform infrared (FT-IR) and UV. The rheological behavior of the sample solution and strengths for concrete were also determined and the adsorption was tested by TOC. The influence of the process parameters to degree of substitution (DS) and the dosage on the fluidity of cement paste were investigated. The results show that the optimal conditions of sulfonation were the MD of DE 15, m (sulfonated agent)/m (MD) of 1.4, the catalyst amount of 1% by mass MD, and the reaction time of 12 h; the optimal conditions of esterification were m (esterified agent)/m (SMD) of 0.6, the reaction temperature of 90°C, and the reaction time of 4 h. The optimal dosages of sulfonated maltodextrin (SMD) and BMMD were 0.475% and 0.45%, respectively. In this dosage, the main dispersion capacity of BMMD attributes to two kinds of anchoring groups (SO3-  &  COO-) and the appropriate molecular weight of MD

Z-ICL: Zero-Shot In-Context Learning with Pseudo-Demonstrations

Although large language models can be prompted for both zero- and few-shot learning, performance drops significantly when no demonstrations are available. In this paper, we introduce Z-ICL, a new zero-shot method that closes the gap by constructing pseudo-demonstrations for a given test input using a raw text corpus. Concretely, pseudo-demonstrations are constructed by (1) finding the nearest neighbors to the test input from the corpus and pairing them with random task labels, and (2) applying a set of techniques to reduce the amount of direct copying the model does from the resulting demonstrations. Evaluation on nine classification datasets shows that Z-ICL outperforms previous zero-shot methods by a significant margin, and is on par with in-context learning with labeled training data in the few-shot setting. Overall, Z-ICL provides a significantly higher estimate of the zero-shot performance levels of a model, and supports future efforts to develop better pseudo-demonstrations that further improve zero-shot results.Comment: 11 pages; 9 figure

Research on wear prediction of piston/cylinder pair in axial piston pumps

The piston/cylinder pair is the critical lubricating interface of axial piston pumps. It suffers from excessive wear, especially under high output pressure. The performance degradation of the piston/cylinder pair is significant to be clarified. In this paper, a wear prediction method of the piston/cylinder pair is established by coupling the load-bearing and lubrication parameters calculation model and the wear calculation model. The models are validated through experiments. The experimental and simulated results show that the wear of two ends of the cylinder bore is severe in the specific ranges of circumferential angle. The time-varying wear process of the piston/cylinder pair can be obtained by using this method; therefore, the maintenance time can be predicted

AN EXPLORATORY STUDY ON THE RELATIONSHIP BETWEEN EXECUTIVE-EMPLOYEE COMPENSATION GAP AND ENVIRONMENTAL PERFORMANCE: EVIDENCE FROM CHINESE LISTED MANUFACTURING COMPANIES

The paper explores the relationship between executive-employee compensation gap (EECG) and environmental performance, an ignored theoretical gap both in the field of consequences of executive compensation and the field of antecedents of environmental performance, by choosing the panel data consisting of 2320 firm-year observations in Chinese listed manufacturing companies during the period from 2011 to 2013 as the research sample. Empirical analysis based on multiple regression analysis adopting the method of OLS by applying SPSS19.0 provides a critical new finding: EECG has a negative effect on environmental performance, which holds robust with the change of the measures and the change of empirical models. Further investigation on EECG’s effect mechanism on environmental performance suggests that it is the short-termism and utilitarianism derived from extra EECG that can-do harm to environmental performance

Influence of Socioeconomic Factors, Gender and Indigenous Status on Smoking in Taiwan.

The indigenous Austronesian minority of Taiwan is heavily affected by health disparities which may include suffering from a greater burden of the tobacco epidemic. While a lack of representative data has historically precluded an investigation of the differences in smoking between Taiwanese ethnicities, these data have recently become available through an annual population-based telephone survey conducted by the Health Promotion Administration, Ministry of Health and Welfare (previously known as the Bureau of Health Promotion (BHP), Department of Health). We used the BHP monitoring data to observe the prevalence of smoking and environmental tobacco smoke exposure among indigenous and non-indigenous Taiwanese surrounding a tobacco welfare tax increase in 2006, investigate ethnic differences in smoking prevalence and environmental tobacco smoke exposure each year between 2005 and 2008, and perform multiple logistic regression to estimate measures of association between potential risk factors and smoking status. Despite significant ethnic and gender differences in smoking prevalence, smoking status was not found to be significantly associated with ethnicity after controlling for socioeconomic and demographic factors