Y3+/Li+和Y3+/Na+双掺杂氟化钡快响应闪烁晶体

氟化钡(BaF₂)晶体是已知响应最快的闪烁晶体,在高能物理、核物理及核医学等领域有着广泛的应用前景。抑制BaF₂晶体的慢发光成分对其工程应用至关重要。本文利用坩埚下降法制备了高Y³⁺掺杂浓度5%、8%、10%(摩尔分数)的BaF₂晶体,并采用Y³⁺与碱金属离子(Li⁺、Na⁺)共掺杂的方法形成电荷补偿阻止间隙F^-的产生,制备了双掺杂型BaF₂快响应闪烁晶体,进而基于优化的5 ns和2 500 ns时间门宽测试方法,研究了Y³⁺掺杂浓度以及Y³⁺与碱金属离子(Li⁺、Na⁺)共掺杂浓度对BaF₂闪烁晶体快/慢成分比的影响规律。结果表明,生长的高浓度Y³⁺掺杂BaF₂晶体的光学质量优异,在220 nm和300 nm处透过率分别高于90%和92%;随着Y³⁺掺杂浓度由0提高至10%,BaF₂晶体的慢发光成分显著降低,快/慢成分比由0.15提高至1.21;生长的Y³⁺/Li⁺及Y³⁺/Na⁺共掺杂BaF₂晶体的慢发光成分较Y³⁺掺杂BaF₂晶体进一步降低,快/慢成分比最高分别可达1.63和1.61。研制的双掺杂BaF₂快响应闪烁晶体有望应用于高能物理、核物理前沿实验等重要领域。     

Optimal deterministic algorithms for some variants of Online Quota Traveling Salesman Problem

This paper is concerned with the Online Quota Traveling Salesman Problem. Depending on the symmetry of the metric and the requirement for the salesman to return to the origin, four variants are analyzed. We present optimal deterministic algorithms for each variant defined on a general space, a real line, or a half-line. As a byproduct, an improved lower bound for a variant of Online TSP on a half-line is also obtained.     

The Economics of Social Stratification in Premodern Societies

We present a microeconomic model of social stratification, which includes an endogenous fertility component. In the model, egalitarian and stratified societies coexist. The latter are divided into 2 hereditary classes: a warrior elite and a productive class. The model entails that the extra cost warriors must incur to train and equip their children for war determines the relative sizes of both classes and the degree of economic inequality. Higher costs of warrior children imply a greater economic advantage for warriors and a smaller ratio of warriors to producers. These results are consistent with the historical evidence. Finally, we explore conditions under which the social contributions of the warrior elite could discourage a revolution.     

Monitoring the quality consistency of Weibizhi tablets by micellar electrokinetic chromatography fingerprints combined with multivariate statistical analyses,the simple quantified ratio fingerprint method,and the fingerprint–efficacy relationship

Micellar electrokinetic chromatography fingerprinting combined with quantification was successfully developed and applied to monitor the quality consistency of Weibizhi tablets, which is a classical compound preparation used to treat gastric ulcers. A background electrolyte composed of 57 mmol/L sodium borate, 21 mmol/L sodium dodecylsulfate and 100 mmol/L sodium hydroxide was used to separate compounds. To optimize capillary electrophoresis conditions, multivariate statistical analyses were applied. First, the most important factors influencing sample electrophoretic behavior were identified as background electrolyte concentrations. Then, a Box–Benhnken design response surface strategy using resolution index RF as an integrated response was set up to correlate factors with response. RF reflects the effective signal amount, resolution, and signal homogenization in an electropherogram, thus, it was regarded as an excellent indicator. In fingerprint assessments, simple quantified ratio fingerprint method was established for comprehensive quality discrimination of traditional Chinese medicines/herbal medicines from qualitative and quantitative perspectives, by which the quality of 27 samples from the same manufacturer were well differentiated. In addition, the fingerprint–efficacy relationship between fingerprints and antioxidant activities was established using partial least squares regression, which provided important medicinal efficacy information for quality control. The present study offered an efficient means for monitoring Weibizhi tablet quality consistency.     

Symmetry and the golden ratio in the analysis of a regular pentagon

The regular pentagon had a symbolic meaning in the Pythagorean and Platonic philosophies and a subsequent important role in Western thought, appearing also in arts and architecture. A property of regular pentagons, which was probably discovered by the Pythagoreans, is that the ratio between the diagonal and the side of these pentagons is equal to the golden ratio. Here, we will study some relations existing between a regular pentagon and this ratio. First, we will focus on the group of fivefold rotational symmetry, to find the position in the complex plane of the vertices of this geometric figure. Then, we will propose an analytic method to solve the same problem based on the Cartesian coordinates, a method where we find the golden ratio without any specific geometric consideration. This study shows a comparison of the use of complex numbers, symmetries and analytic methods, applied to a subject which can be interesting for general education in mathematics. In fact, the proposed approach can convey and link several concepts, requiring only a general pre-college education, showing at the same time the richness that mathematics can offer in solving geometric problems.     

Stability and Neimark–Sacker bifurcation of a ratio‐dependence predator–prey model

In this paper, stability and bifurcation of a two‐dimensional ratio‐dependence predator–prey model has been studied in the close first quadrant . It is proved that the model undergoes a period‐doubling bifurcation in a small neighborhood of a boundary equilibrium and moreover, Neimark–Sacker bifurcation occurs at a unique positive equilibrium. We study the Neimark–Sacker bifurcation at unique positive equilibrium by choosing b as a bifurcation parameter. Some numerical simulations are presented to illustrate theocratical results. Copyright © 2017 John Wiley & Sons, Ltd.     

Limit theorems for random walks

We consider a random walk $S_{\tau }$ which is obtained from the simple random walk $S$ by a discrete time version of Bochner’s subordination. We prove that under certain conditions on the subordinator $\tau$ appropriately scaled random walk $S_{\tau }$ converges in the Skorohod space to the symmetric $\alpha$-stable process $B^{\alpha }$. We also prove asymptotic formula for the transition function of $S_{\tau }$ similar to the Pólya’s asymptotic formula for $B^{\alpha }$.     

基于在线HHT和SVM的汽油机轻微漏气故障识别方法

针对汽油机轻微漏气故障会被闭环反馈控制所掩盖,提出了一种基于在线希尔伯特变换(Hilbert-Huang Transform,HHT)和支持向量机(Support vector machine,SVM)的两阶段微小故障识别方法(Online HHT-SVM,OHS).第一阶段在嵌入式两滑动时间窗内通过HHT对发动机空燃比数据流进行在线时频分析,以实时获取空燃比发生异常的时刻;第二阶段通过SVM对异常时刻的数据流故障模式进行离线识别.根据氧传感器信号特征,对经验模态分解(Empirical mode decomposition,EMD)算法进行了改进,并从理论上进行了证明.基于两款发动机的实际运行数据验证了该方法的有效性.     

具有缺失数据的Eichhorn模型

为了解决在Eichhorn乘法扰动模型中存在的项目无回答问题,对敏感变量总体均值在辅助变量总体均值已知与未知条件下提出了比率插补方法.理论比较和数值模拟得出的结果表明提出的插补方法比传统的方法效率更高.     

Indefinite integrals involving complete elliptic integrals of the third kind

A method developed recently for obtaining indefinite integrals of functions obeying inhomogeneous second-order linear differential equations has been applied to obtain integrals with respect to the modulus of the complete elliptic integral of the third kind. A formula is derived which gives an integral involving the complete integral of the third kind for every known integral for the complete elliptic integral of the second kind. The formula requires only differentiation and can therefore be applied for any such integral, and it is applied here to almost all such integrals given in the literature. Some additional integrals are derived using the recurrence relations for the complete elliptic integrals. This gives a total of 27 integrals for the complete integral of the third kind, including the single integral given in the literature. Some typographical errors in a previous related paper are corrected.