Euler’s beta integral in Pietro Mengoli’s works

Beta integrals for several non-integer values of the exponents were calculated by Leonhard Euler in 1730, when he was trying to find the general term for the factorial function by means of an algebraic expression. Nevertheless, 70 years before, Pietro Mengoli (1626–1686) had computed such integrals for natural and half-integer exponents in his Geometriae Speciosae Elementa (1659) and Circolo(1672) and displayed the results in triangular tables. In particular, his new arithmetic–algebraic method allowed him to compute the quadrature of the circle. The aim of this article is to show how Mengoli calculated the values of these integrals as well as how he analysed the relation between these values and the exponents inside the integrals. This analysis provides new insights into Mengoli’s view of his algorithmic computation of quadratures.     

Atomic packing and short-to-medium range order evolution of Zr-Pd metallic glass

A larger-scale Zr₇₀Pd₃₀ alloy system has been simulated using molecular dynamics (MD) to investigate structure evolution in Zr₇₀Pd₃₀ metallic glass. The simulated pair distribution function of Zr₇₀Pd₃₀ metallic glass agrees well with the experimental results. Voronoi polyhedron analysis indicates that the icosahedra are not randomly distributed in space, but form characteristic intercrossed icosahedral clusters with medium-range order. Intercrossed icosahedral clusters are the dominant local configurations in Zr₇₀Pd₃₀ metallic glass and probably cause the quasicrystalline phase discovered in Zr₇₀Pd₃₀ metallic glass.     

Surface pollen assemblages of human-disturbed vegetation and their relationship with vegetation and climate in Northeast China

Pollen assemblages of 53 surface pollen samples from farmlands and wastelands in Northeast China were analyzed. Tree pollen percentages were usually higher than 30%, with Pinus (26.9%), Quercus (0.9%), Betula (0.9%) and Populus (0.7%) as the major types, and herb pollen percentages were usually higher than 50%, with weedy Poaceae (8.7%), Chenopodiaceae (7.1%), Artemisia (1.9%) and Compositae (3.5%) as the major taxa. Thus, the pollen assemblages were consistent with the regional vegetation compositions. However, there were differences in pollen assemblages among regions, especially among different geomorphological units. For example, in the mountains, there were more types of tree pollen and higher total percentages (average 42%) than in other areas, while cereal pollen percentages were lowest (11.2%). In the hills and high plains, herbs made up more than 60% of the pollens, with cereals (average 53.6%) the dominant type. In the low plains, pollen types were similar to those in the hills and high plains, but total pollen concentrations and the proportion of Concentricystes were much higher, while cereal pollen percentages were slightly lower (average 41.6%). Pollen assemblages in different land use types also differed. For example, in farmland, cereal pollen percentages were more than 40% and Chenopodiaceae was usually less than 2.5%, while in wasteland, weedy Poaceae was usually less than 10% and Chenopodiaceae was usually higher than 25%. Total pollen concentrations in farmland (average 3909 grains/g) were much lower than in wasteland (average 15074 grains/g). Redundancy analysis revealed that pollen assemblages were significantly negatively correlated with mean annual temperature (-0.73) and July mean temperature (-0.81) and significantly positively correlated with mean annual precipitation (0.48), indicating that pollen assemblages in the artificial or human-disturbed vegetation reflect regional climate well. Comparison of pollen assemblages in different areas of northern China showed that pollen concentrations reflect the intensities of human impact to some degree. For example, pollen concentrations decrease as human impacts increase in intensity. The cereal pollen proportions in farmland differed by area. In Northeast China, cereal pollen proportions were distinctly higher than in most other areas of northern China, suggesting differences in planting habits and climate.     

浅谈工程招标采用最低价中标法的可行和可控

最低价中标法是国际上通用的工程招投标评标方法,过去中国政府一直限制这种方法的应用.2000年1月1日开始实施的<中华人民共和国招标投标法>首次允许招标人可以选择最低报价者中标,从法律上为该方法在中国的应用带来转机.可这种评标办法在带来益处的同时也带来弊端,文章从可行和可控两个方面对最低价中标法进行剖析.     

Statistical inference for simple tree order in the means of stochastic order on stratified contingency tables

In this paper, we consider testing the hypothesis that all multinomial populations in the stratified contingency table are identically distributed against the alternative that all these popula-tions are in simple tree order. We provide an asymptotic represen-tation of the order-restricted maximum likelihood estimate of the unknown parameters. The resulting estimators are proven to be n-consistent and asymptotically normal under appropriate con-ditions. A chi-squared test method is used for this hypothesis t...     

Process capability analysis and estimation scheme for autocorrelated data

<正>Autocorrelation is prevalent in continuous production processes,such as the processes in the chemical and pharmaceutical industries.With the development of measurement technology and data acquisition technology,sampling frequency is getting higher and the existence of autocorrelation cannot be ignored.This paper analyzes five estimation schemes of process capability for autocorrelated data.Comparisons among these schemes are discussed for small sample and large sample.In conclusion,this paper gives a procedure of process capability analysis for autocorrelated data.     

New design and analysis of finite difference domain decomposition algorithm for the two-dimensional heat equation

<正> It is presented in this paper that the new design and its analysis of finite difference domaindecomposition algorithms for the two-dimensional heat equation,and the numerical results have shownthe stability and accuracy of the algorithms,where Saul'yev asymmetric schemes have been used atthe interface points.The Algorithm Ⅱ in this paper has further extended those developed by Dawsonand the others,Zhang and Shen.     

高层建筑施工管理应注意的事项及对策

经济发展对土地的利用率要求不断提高,高层建筑在城市建设中也越来越多,从写字间到居民住宅都可以看到高层建筑的身影。针对高层建筑的施工管理也随之成为建筑施工管理中的重点课题。本文试对高层建筑的施工管理进行分析,以资参考。     

And Yet It Moves: The Observability of the Rotation of the Earth

A central point of controversy in the time of the Copernican Revolution was the motion, or not, of the earth. We now take it for granted that Copernicus and Galileo were right; the earth really does move. But to what extent is this conclusion based on observation? This paper explores the meaning and observability of the rotation of the earth and shows that the phenomenon was not observable at the time of Galileo, and it is not observable now.