Pure Weierstrass gaps from a quotient of the Hermitian curve

In this paper, by employing some results on Kummer extensions, we give an arithmetic characterization of pure Weierstrass gaps at many totally ramified places on a quotient of the Hermitian curve, including the well-studied Hermitian curve as a special case. The cardinality of these pure gaps is explicitly investigated. In particular, the numbers of gaps and pure gaps at a pair of distinct places are determined precisely, which can be regarded as an extension of the previous work by Matthews (2001) considered Hermitian curves. Additionally, some concrete examples are provided to illustrate our results.     

Pure strategy Nash equilibria and the probabilistic prospects of Stackelberg players

We consider the set of all m×n bimatrix games with ordinal payoffs. We show that on the subset E of such games possessing at least one pure strategy Nash equilibrium, both players prefer the role of leader to that of follower in the corresponding Stackelberg games. This preference is in the sense of first-degree stochastic dominance by leader payoffs of follower payoffs. It follows easily that on the complement of E, the follower’s role is preferred in the same sense. Thus we see a tendency for leadership preference to obtain in the presence of multiple pure strategy Nash equilibria in the underlying game.     

A Categorical Structure for the Virtual Braid Group

This article gives a new interpretation of the virtual braid group in terms of a strict monoidal category SC that is freely generated by one object and three morphisms, two of the morphisms corresponding to basic pure virtual braids and one morphism corresponding to a transposition in the symmetric group. This point of view makes many relationships between the virtual braid group and the pure virtual braid group apparent, and makes representations of the virtual braid groups and pure virtual braid groups via solutions to the algebraic Yang–Baxter Equation equally transparent. In this categorical framework, the virtual braid group has nothing to do with the plane and nothing to do with virtual crossings. It is a natural group associated with the structure of algebraic braiding.     

Pure ℓ-Ideals in Lattice-Ordered Rings#

An ?-ideal I of a commutative lattice-ordered ring R with positive identity element is called a pure ?-ideal if R  =  I  + ?( x ) for each x  ∈  I , where ?(x) is the ?-annihilator of x in R . In this article, we give some results on pure ?-ideals and study the ?-ideal structure of a commutative lattice-ordered ring with positive identity element by using pure ?-ideals.     

Recent progress on pure organic room temperature phosphorescence materials based on host-guest interactions

Pure organic room temperature phosphorescence (RTP) has been attracting a lot interest recently. So far, many strategies have succeeded in achieving efficient organic RTP materials by increasing the rate of intersystem crossing (ISC) and suppressing non-radiative transitions. In supramolecular chemistry, the control and regulation of molecular recognition based on the role of the host and guest in supramolecular polymers matrix, has attracted much attention. Recently, researchers have successfully achieved room temperature phosphorescence of pure organic complexes through host-guest interactions. The host molecule specifically includes the phosphorescent guest to reduce non-radiative transitions and enhance room temperature phosphorescence emission. This review aims to describe the developments and achievements of pure organic room temperature phosphorescence systems through the mechanism of host-guest interactions in recent years, and demonstrates the exploration and pursuit of phosphorescent materials of researchers in different fields.     

全息光盘存储器的数据存取与像素匹配

全息光盘存储(HDS)技术作为一种非常具有潜力的新型信息存储技术, 是下一代光盘发展的目标。在全息光盘存储系统中, 为了实现数据精确快速地写入和读出, 降低误码率, 需要在整个高分辨率页面上实现空间光调制器(SLM)与光电阵列耦合器(CCD)之间1∶1像素匹配。在体全息存储理论和光学设计理论基础上, 研究实现SLM和CCD像素1∶1匹配的方法, 提出了实现像素匹配的要求和条件, 并且按照此要求完成该全息光盘存储器的光学系统。实验中, 分别使用随机数据掩膜版和SLM实现了对CCD的512×512精确像素匹配, 在光学系统中引入存储介质条件下, 图像质量良好, 掩膜版和SLM原始误码率分别为2.5×10-4和1.5×10-4。     

Multivariate optimization and comparison between conventional extraction (CE) and ultrasonic-assisted extraction (UAE) of carotenoid extraction from cashew apple

Carotenoids are an essential component of cashew and can be used in pharmaceuticals, cosmetics, natural pigment, food additives, among other applications. The present work focuses on optimizing and comparing conventional and ultrasound-assisted extraction methods. Every optimization step took place with a 1:1 (w:w) mixture of yellow and red cashew apples lyophilized and ground in a cryogenic mill. A Simplex-centroid design was applied for both methods, and the solvents acetone, methanol, ethanol, and petroleum ether were evaluated. After choosing the extractor solvent, a central composite design was applied to optimize the sample mass (59–201 mg) and extraction time (6–34 min). The optimum conditions for the extractor solvent were 38% acetone, 30% ethanol, and 32% petroleum ether for CE and a mixture of 44% acetone and 56% methanol for UAE. The best experimental conditions for UAE were a sonication time of 19 min and a sample mass of 153 mg, while the CE was 23 min and 136 mg. Comparing red and yellow cashews, red cashews showed a higher carotenoid content in both methodologies. The UAE methodology was ca. 21% faster, presented a more straightforward composition of extracting solution, showed an average yield of superior carotenoid content in all samples compared to CE. Therefore, UAE has demonstrated a simple, efficient, fast, low-cost adjustment methodology and a reliable alternative for other applications involving these bioactive compounds in the studied or similar matrix.     

Tutorial review on validation of liquid chromatography–mass spectrometry methods: Part II

This is the part II of a tutorial review intending to give an overview of the state of the art of method validation in liquid chromatography mass spectrometry (LC–MS) and discuss specific issues that arise with MS (and MS–MS) detection in LC (as opposed to the “conventional” detectors). The Part II starts with briefly introducing the main quantitation methods and then addresses the performance related to quantification: linearity of signal, sensitivity, precision, trueness, accuracy, stability and measurement uncertainty. The last section is devoted to practical considerations in validation. With every performance characteristic its essence and terminology are addressed, the current status of treating it is reviewed and recommendations are given, how to handle it, specifically in the case of LC–MS methods.     

Robust regression credibility: The influence function approach

In classical credibility theory we assume that the vector of claims conditionally on has independent components with identical means. However, this assumption is sometimes unrealistic. To relax this condition Hachemeister (Hachemeister, C.A., 1975. Credibility for regression models with application to trend. In: Kahn, P. (Ed.), Credibility, Theory and Applications. Academic Press, New York) introduced regressors. The presence of large claims can perturb the credibility premium estimation. The lack of robustness of regression credibility estimators, as well as the fairness of tariff evaluation, led to the development of this paper. Our proposal is to apply robust statistics to the regression credibility estimation by using the robust influence function approach of M-estimators.