Central Sets Theorem along filters and some combinatorial consequences

The Central Sets Theorem was introduced by H. Furstenberg and then afterwards several mathematicians have provided various versions and extensions of this theorem. All of these theorems deal with central sets, and its origin from the algebra of Stone–?ech compactification of arbitrary semigroup, say $\beta S$. It can be proved that every closed subsemigroup of $\beta S$ is generated by a filter. We will show that, under some restrictions, one can derive the Central Sets Theorem for any closed subsemigroup of $\beta S$. We will derive this theorem using the corresponding filter and its algebra. Later we will also deal with how the notions of largeness along filters are preserved under some well behaved homomorphisms and give some consequences.     

MoS2/SnS异质结太阳能电池的模拟研究

硫化亚锡(SnS)是一种Ⅳ-Ⅵ族层状化合物半导体材料,其禁带宽度与太阳能电池最佳带隙1.5 eV非常接近,并且在可见光范围内光的吸收系数很大(α>10⁴ cm^-1),因此SnS是一种很有应用前景的材料。本文利用太阳能电池模拟软件wxAMPS模拟了MoS₂/SnS异质结太阳能电池,主要研究SnS吸收层的厚度、掺杂浓度和缺陷态等因素对太阳能电池性能的影响。研究发现:SnS吸收层最佳厚度为2 μm,最佳掺杂浓度为1.0×10¹⁵ cm^-3;同时高斯缺陷态浓度超过1.0×10¹⁵ cm^-3时,电池各项性能参数随着浓度的增加而减小,而带尾缺陷态超过1.0×10¹⁹ cm^-3·eV^-1时,电池性能才开始下降;其中界面缺陷态对太阳能电池影响比较严重,界面缺陷态浓度超过1.0×10¹² cm^-2时,开路电压、短路电流、填充因子和转换效率迅速下降。另外,通过模拟获得的转换效率高达24.87%,开路电压为0.88 V,短路电流为33.4 mA/cm²。由此可知,MoS₂/SnS异质结太阳能电池是一种很有发展潜力的光伏器件结构。     

单层2H-MoTe2光电效应的理论研究

材料的禁带宽度是影响光电探测器探测范围的重要因素。单层2H-MoTe₂因具有合适的禁带宽度引起了科研人员广泛的研究兴趣。本文基于非平衡态格林函数-密度泛函理论,采用第一性原理方法,研究了单层2H-MoTe₂的光电效应。结果表明:在线性偏振光照射下,MoTe₂产生的光电流函数与唯象理论相吻合;在光子能量范围1.6~1.8 eV (690~770 nm),对应于红光,能产生较大的光电流。利用能带结构和态密度分析了产生较大光电流的原因主要来自第一布里渊区S点的电子受激跃迁。同时发现在锯齿型方向偏压为0.8 V时,光电流达到峰值;然而在扶手椅型方向偏压为0.4 V时,光电流就达到峰值。这些计算结果可用于指导基于MoTe₂光电探测器的设计,尤其是红外光电探测器的设计。     

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.     

介观电路中量子纠缠的经典对应

从量子力学诞生日起,它的经典对应(或类比)一直是物理学家关心的话题.本文以介观电路量子化的框架中,带有互感的两个介观电容-电感(LC)电路为例,首次讨论了量子纠缠的经典类比(或对应)问题.先用有序算符内的积分理论证明其互感是产生量子纠缠的源头;再推导出求解特征频率的公式,就发现它与一个经典系统的小振动频率的表达式有相似之处,该经典系统组成如下:两个墙壁各连一个相同的弹簧,两个弹簧之间接着一个滑动小车可以在光滑的桌面上运动,小车挂有一根单摆.用分析力学求此系统的小振动频率,发现与上述介观电路的特征频率形式类似,单摆的摆动会造成小车来回振动,摆、小车和弹簧的互相牵制效应反映了小车和摆的"纠缠".     

中国出境旅游的外交效应

2000年以来，中国出境旅游高增长、高消费，影响力不断增大，成为国家外交战略的重要内容，外交效应逐渐显现。通过辨析中国出境旅游外交效应的概念、表现形式和结果，基于10个中国主要出境目的国的旅游互动数据，采用DIF-GMM计量经济模型，实证检验了中国出境旅游外交效应。结果表明，中国通过有序推进ADS协议、加强经济援助、举办“旅游年”活动、实施旅游“制裁”，并积极参与国际制度建设等旅游外交行为，促进了与世界各国的友好交往，维护了自身核心利益，提升了外交软实力和国际影响力。国际旅游反作用于国际关系，对国际关系具有显著的正向促进作用，不仅是国际关系的结果，而且是其重要动因之一。中国出境旅游与政治、经济、社会、文化等联动，多方面提升了中国的国际影响力。     

Nonmetal-to-metal transition in dense fluid helium

The nonmetal-to-metal transition in dense fluid helium is discussed, which has been, in analogy to metallization of hydrogen, predicted as first-order plasma phase transition using chemical models for the equation of state and plasma composition. However, recent ab initio simulations performed for dense fluid helium indicate that this transition is continuous in the considered regime, without a density jump and latent heat as characteristic of a first-order phase transition. Implications for some astrophysical plasmas are discussed.     

Projective well orders and coanalytic witnesses

We further develop a forcing notion known as Coding with Perfect Trees and show that this poset preserves, in a strong sense, definable P-points, definable tight MAD families and definable selective independent families. As a result, we obtain a model in which $\mathfrak{a}=\mathfrak{u}=\mathfrak{i}={\mathrm{?}}_1<2^{{\mathrm{?}}_0}={\mathrm{?}}_2$, each of $\mathfrak{a}$, $\mathfrak{u}$, $\mathfrak{i}$ has a ${\mathrm{\Pi }}_1^1$ witness and there is a ${\mathrm{\Delta }}_3^1$ well-order of the reals. Note that both the complexity of the witnesses of the above combinatorial cardinal characteristics, as well as the complexity of the well-order are optimal. In addition, we show that the existence of a ${\mathrm{\Delta }}_3^1$ well-order of the reals is consistent with $\mathfrak{c}={\mathrm{?}}_2$ and each of the following: $\mathfrak{a}=\mathfrak{u}<\mathfrak{i}$, $\mathfrak{a}=\mathfrak{i}<\mathfrak{u}$, $\mathfrak{a}<\mathfrak{u}=\mathfrak{i}$, where the smaller cardinal characteristics have co-analytic witnesses.Our methods allow the preservation of only sufficiently definable witnesses, which significantly differs from other preservation results of this type.     

UPLC-Q/TOF-MS coupled with multivariate analysis for comparative analysis of metabolomic in Dendrobium nobile from different growth altitudes

Dendrobium nobile alkaloids (DNLA) and glycosides are the main active components extracted from Dendrobium nobile Lindl. (D. nobile) used for thousands of years in China. The pharmacological effects of the above chemical components are significantly different. D. nobile is mainly grown at an altitude ranging from 230 to 800 m in Chishui City, Northwest Guizhou Province. However, it is unclear whether the metabolite in D. nobile is influenced by the planting altitude. Hence, to reveal the different metabolite in D. nobile cultivated at the altitude of 336 m, 528 m, and 692 m, ultra-high performance liquid chromatography with Q/TOF-MS couple with multivariate analysis were developed. Using the orthogonal partial least squares-discriminant analysis, 19 different metabolites were discovered and then tentatively assigned their structures as alkaloids and glycosides by comparing mass spectrometry data with in-house database and literature. Moreover, the result of semiquantitative analysis showed the content of dendrobine that was belonged to alkaloids significantly increased at the altitude of 692 m, whereas the content of glycosides demonstrated an accumulation trend at the altitude of 528 m. The results could provide valuable information for the optimal clinical drug therapeutics and provide a reference for quality control.