Transcendental values of the digamma function

Let ψ(x) denote the digamma function, that is, the logarithmic derivative of Euler's Γ-function. Let q be a positive integer greater than 1 and γ denote Euler's constant. We show that all the numbers

     

基于神经网络的间隙机构运动副磨损预测

应用BP神经网络建立了磨损率与接触应力、滑动速度和材料硬度之间的非线性关系模型,并对该网络模型进行了验证和测试,结果表明,训练良好的神经网络模型能够准确反映样本所蕴含的内在磨损规律,且具有较好的预测效果。基于非线性弹簧阻尼模型和修正的Coulomb摩擦力模型对含间隙曲柄滑块机构进行数值仿真分析,获得间隙机构运动副的接触应力和相对滑动速度,利用训练好的神经网络磨损模型对轴套的磨损进行迭代磨损预测分析,发现随着曲柄转数的增加,轴套表面一些特定位置处的磨损越来越严重,最终导致轴套表面出现非均匀磨损现象,其原因是间隙机构运转过程在一些特定位置处产生了较大接触应力和碰撞力。     

Specificity and Origin of the Stability of the Sr Isotopic Ratio in Champagne Wines

The ⁸⁷Sr/⁸⁶Sr ratio of 39 Champagnes from six different brands, originating from the whole “Appellation d’Origine Contrôlée” (AOC) Champagne was analyzed to establish a possible relation with the geographical origin. Musts (i.e., grape juice) and base wines were also analyzed to study the evolution of the Sr isotopic ratio during the elaboration process of sparkling wine. The results demonstrate that there is a very homogeneous Sr isotopic ratio (⁸⁷Sr/⁸⁶Sr = 0.70812, n = 37) and a narrow span of variability (2σ = 0.00007, n = 37). Moreover, the Sr concentrations in Champagnes have also low variability, which can be in part explained by the homogeneity of the bedrock in the AOC Champagne. Measurements of the ⁸⁷Sr/⁸⁶Sr ratio from musts and base wines show that blending during Champagne production plays a major role in the limited variability observed. Further, the ⁸⁷Sr/⁸⁶Sr of the musts were closely linked to the ⁸⁷Sr/⁸⁶Sr ratio of the vineyard soil. It appears that the ⁸⁷Sr/⁸⁶Sr of the product does not change during the elaboration process, but its variability decreases throughout the process due to blending. Both the homogeneity of the soil composition in the Champagne AOC and the blending process during the wine making process with several blending steps at different stages account for the unique and stable Sr isotopic signature of the Champagne wines.     

Structural modifications of diamond like carbon films induced by MeV nitrogen ion irradiation

Diamond-like carbon (DLC) films were deposited on Si(1 0 0) substrates using plasma deposition technique. The deposited films were irradiated using 2 MeV N⁺ ions at fluences of 1×10¹⁴, 1×10¹⁵ and 5×10¹⁵ ions/cm². Samples have been characterized by using Raman spectroscopy, X-ray photoelectron spectroscopy (XPS) and high-resolution transmission electron microscopy (HRTEM). Analysis of Raman spectra shows a gradual shift of both D and G band peaks towards higher frequencies along with an increase of the intensity ratio, I(D)/I(G), with increasing ion fluence in irradiation. These results are consistent with an increase of sp² bonding. XPS results also show a monotonic increase of sp²/sp³ hybridization ratio with increasing ion fluence. Plan view TEM images show the formation of clusters in the irradiated DLC films. HRTEM micrographs from the samples irradiated at a fluence of 5×10¹⁵ ions/cm² show the lattice image with an average interplanar spacing of 0.34 nm, revealing that the clusters are graphite clusters. The crystallographic planes in these clusters are somewhat distorted compared to the perfect graphite structure.     

Structural studies of cyclic ureas: 3. Enthalpy of formation of barbital

A thermochemical and thermophysical study has been carried out for crystalline barbital [5,5′-diethylbarbituric acid]. The thermochemical study was made by static bomb combustion calorimetry, from which the standard () molar enthalpy of formation of the crystalline barbital, at T = 298.15 K, was derived as −(753.0 ± 1.8) kJ · mol⁻¹. The thermophysical study was made by differential scanning calorimetry over the temperature interval (265 to 470) K. A solid–solid phase transition was found at T = 413.3 K. The vapour pressures of the crystalline barbital were measured at several temperatures between T = (355 and 377) K, by the Knudsen mass-loss effusion technique, from which the standard molar enthalpy of sublimation, at T = 298.15 K was derived as (117.3 ± 0.6) kJ · mol⁻¹. The combination of the experimental results yielded the standard molar enthalpy of formation of barbital in the gaseous phase, at T = 298.15 K, as −(635.8 ± 1.9) kJ · mol⁻¹. This value is compared and discussed with our theoretical calculations by several methods (Gaussian-n theories G2 and G3, complete basis set CBS-QB3, density functional B3P86 and B3LYP) by means of atomization and isodesmic reaction schemes.     

Semi-Lagrangian semi-implicit time-splitting scheme for a regional model of the atmosphere

Semi-Lagrangian semi-implicit (SLSI) method is currently one of the most efficient approaches for numerical solution of the atmosphere dynamics equations. In this research we apply splitting techniques in the context of a two-time-level SLSI scheme in order to simplify the treatment of the slow physical modes and optimize the solution of the elliptic equations related to implicit part of the scheme. The performed numerical experiments show the accuracy and computational efficiency of the scheme.     

Comparison of different spatial grids for numerical schemes of geophysical fluid dynamics

The generation of computational grids is an important component contributing to the efficiency of numerical schemes of atmosphere/ocean dynamics. In this study the problem of construction of the most uniform grids based on conformal mappings of spherical domains is considered. Stereographic, cylindrical and conic grids for computational rectangles are developed and their uniformity is compared. Numerical experiments with two schemes approximating shallow water equations are performed in order to assess the practical efficiency of the constructed grids and to compare the numerical results with analytical evaluations.     

蛋白质结构的主成分分析及氧链糖基化位点的人工神经网络预测

糖基化是蛋白质翻译后修饰的重要形式之一,氧链糖基化是糖基化的一种主要类型,对蛋白质氧链糖基化位点进行预测具有重要的意义.以窗口长度为41的蛋白质序列为研究对象,采用稀疏编码,利用主成分分析法研究了氧链糖基化蛋白质序列的结构特点;在提取主成分的基础上,设计了一个含单隐层的BP神经网络(256—8—4),对蛋白质氧链糖基化位点进行预测,把蛋白质序列分为4类;并同直接用BP神经网络分类的结果相比较,实验结果证明提出的方法省时,准确,预测的准确率达80~90%.     

Probability density in the complex plane

The correspondence principle asserts that quantum mechanics resembles classical mechanics in the high-quantum-number limit. In the past few years, many papers have been published on the extension of both quantum mechanics and classical mechanics into the complex domain. However, the question of whether complex quantum mechanics resembles complex classical mechanics at high energy has not yet been studied. This paper introduces the concept of a local quantum probability density ρ(z) in the complex plane. It is shown that there exist infinitely many complex contours C of infinite length on which ρ(z) dz is real and positive. Furthermore, the probability integral is finite. Demonstrating the existence of such contours is the essential element in establishing the correspondence between complex quantum and classical mechanics. The mathematics needed to analyze these contours is subtle and involves the use of asymptotics beyond all orders.     

近红外光谱技术快速鉴别地沟油与食用植物油的研究

地沟油检测是我国食品安全最为关注的话题之一,它给人们的生活健康带来了极大的危害。国内现有的检测手段也仅停留在定性检测水平上,只能确定地沟油的有无,还难以进行定量检测。本实验利用近红外光谱技术与光纤传感技术相结合的新方法对勾兑混合油中地沟油的含量进行了定量分析。将煎炸老油与九三大豆油按照一定的体积比进行勾兑,共计50个样本,采集其近红外透射光谱,分别采用偏最小二乘法(PLS)和BP人工神经网络建立了煎炸老油含量的定量分析模型,校正集决定系数分别为0.908和0.934,验证集决定系数分别为0.961和0.952,均方估计残差(RMSEC)为0.184和0.136,预测均方根误差(RMSEP)都为0.111 6,符合应用要求,同时还结合主成分分析法(PCA)对煎炸老油与食用植物油进行了鉴别,识别准确率为100%。实验研究证明近红外光谱技术不仅可以准确快速的定性分析地沟油, 还能定量的检测地沟油的含量,在油脂的检测方面具有很大的应用前景。