福建寿山溪蛋石的矿物学和谱学研究

溪蛋石是寿山石的著名品种之一,指散落在月洋溪中的一种山坑石,系寿山石中的芙蓉石品种的风化产物。残块经过雨水冲刷流入溪中,复受水流、河沙等长年冲击,形成浑圆卵石状外表,因其易于雕刻塑形,广受近代雕刻家好评。为了探究寿山溪蛋石的矿物学和谱学特征,运用常规的宝石学测试方法、X射线粉末衍射仪、傅里叶变换红外光谱仪、显微激光拉曼光谱仪和电子探针等测试方法,对几件黄色溪蛋石样品的矿物组成、红外及拉曼光谱特征、化学成分等展开了全面研究。常规宝石学测试结果表明,溪蛋石样品的相对密度约为2.8,摩式硬度小于3;为了避免层状硅酸盐矿物的择优取向性,XRD实验采用侧压法,测试结果表明,溪蛋石由较纯的叶蜡石组成,并以单斜晶系（2M型）叶蜡石的形式存在,以2θ=19°~22°之间4.44Å（020）,4.24Å（12）和4.17Å（111）三个衍射峰为特征,其中（12）和（111）两个衍射峰相距很近,在（12）衍射峰（2θ=21.06°）右侧出现了一个衍射肩;在2θ=28°~31°之间,以3.06Å（003）强峰（2θ=29.05°）为特征;采用红外光谱仪可以有效的确定溪蛋石基质和石皮部分的矿物成分。样品的红外光谱表明,溪蛋石的风化皮与基质部分矿物成分均为叶蜡石,指纹区的主要特征峰为1 122,1 068,1 052,949,853,835,812,541和484 cm-1,其中,1 122 cm-1归属于Si-O伸缩振动,1 068和1 052 cm-1附近强而尖锐的吸收峰由简并解除的Si-O-Si伸缩振动引起,949 cm-1左右的吸收窄带由Al-OH面内弯曲振动引起;853,835及812 cm-1处强度较弱的倒“山”字形吸收谱带属于Al-OH面外弯曲振动,541 cm-1处吸收峰为Si-O-Al伸缩振动引起,484 cm-1归属于Si-O弯曲振动;官能团区3 675 cm-1处尖锐的吸收峰由Al-OH伸缩振动所导致,指示了叶蜡石结构的高度有序化。采用显微激光拉曼光谱对溪蛋石中的包裹体进行测试,以确认其矿物成分。结果显示,点片状黑色包裹体为赤铁矿,拉曼特征峰为224,291,409,494以及1 315 cm-1,灰白色矿物为硬水铝石,拉曼特征峰出现在448,499和667 cm-1,还存在707,788和1 194 cm-1处弱峰,与硬水铝石的标准谱峰吻合。此外,基质部分在111,194和261 cm-1处的拉曼峰由Si-O键伸缩振动所致,706 cm-1处强而尖锐的拉曼峰以及3 670 cm-1处的峰是由O-H伸缩振动所致,与叶蜡石的拉曼光谱一致,也与红外光谱的测试结果对应。根据矿物单位分子中的电价平衡原则和正电荷总数,利用电子探针测试数据计算溪蛋石的平均晶体结构化学式为：(Al_1.98Na_0.02Cr_0.01)[(Si_3.98Al_0.02)O₁₀](OH)₂。溪蛋石化学成分稳定,主要含有Si（64.88%）,Al（27.55%）。寿山溪蛋石中含0.2%左右的Cr和0.02%左右的Fe和Cr元素含量远大于Fe元素,因此推测溪蛋石的浅黄色由Cr和Fe离子共同作用所致。     

应用XRF与ICP-MS研究陨石样品的元素分布

分别采用X射线荧光光谱无标样全定量分析法(XRF)和微波消解/电感耦合等离子体质谱法(ICP-MS)对铁陨石和石陨石样品进行了元素分析。XRF法检测陨石样品中的常量元素,ICP-MS检测陨石中的微量元素。实验结果表明：XRF法可以检测出陨石样品中含量在10 μg·g-1以上的所有金属和非金属元素,得出两类陨石中共同含有的6种常量元素是Fe,Mg,Si,Na,Al和Ca。不同地区的铁陨石中均含有大量的Fe,石陨石中含有大量的Si。ICP-MS法检测陨石中的24种元素,选出共同存在的9种元素V,Ni,Mo,Ag,Sn,La,Gd,Hg和Pb进行对比分析,得出铁陨石中的重金属元素和稀土元素的含量远高于石陨石。所有的铁陨石样品中Sn元素的含量大约是石陨石的10～25倍,铁陨石中稀土元素La和Gd的含量大约是石陨石的6倍,新疆的5A号和6A号铁陨石中Pb的含量比来自山东的铁陨石(1A, 2A, 3A, 4A)多5～13倍,来自内蒙古的石陨石(9B,10B)比来自新疆的石陨石(7B,8B)多了三种元素La,Mo和Gd。     

Nonstandard representations of locally compact groups

In the note, it is proved that, under natural conditions, any infinite-dimensional unitary representation T of a direct product of groups G = K × N, where K is a compact group and N is a locally compact Abelian group, is imaged by a representation of the nonstandard analog \(\tilde G\) of the group G in the group of nonstandard matrices of a fixed nonstandard size.     

An adaptive strategy for selecting representative calibration samples in the continuous wavelet domain for near-infrared spectral analysis

Sample selection is often used to improve the cost-effectiveness of near-infrared (NIR) spectral analysis. When raw NIR spectra are used, however, it is not easy to select appropriate samples, because of background interference and noise. In this paper, a novel adaptive strategy based on selection of representative NIR spectra in the continuous wavelet transform (CWT) domain is described. After pretreatment with the CWT, an extension of the Kennard–Stone (EKS) algorithm was used to adaptively select the most representative NIR spectra, which were then submitted to expensive chemical measurement and multivariate calibration. With the samples selected, a PLS model was finally built for prediction. It is of great interest to find that selection of representative samples in the CWT domain, rather than raw spectra, not only effectively eliminates background interference and noise but also further reduces the number of samples required for a good calibration, resulting in a high-quality regression model that is similar to the model obtained by use of all the samples. The results indicate that the proposed method can effectively enhance the cost-effectiveness of NIR spectral analysis. The strategy proposed here can also be applied to different analytical data for multivariate calibration.     

伪补分配格上的主同余关系

本文研究了伪补分配格Ｌ的＊－同余关系的基本性质。主要给出了：⑴主同余θ＊（ａ,ｂ）的一个具体刻划;⑵理想Ⅰ成为同余理想的一个充要条件的以Ⅰ为核心的最小＊－同余θ＊（Ｉ）;⑶Ｌ上的格同余θＬ（ａ,ｂ）成为＊－同余的干充要条件。其中的大部分结果必进或包含了已有的结论。     

用若丹明B光度法测定石煤渣中微量钒

研究了痕量V(Ⅴ)催化KBrO3 氧化还原型若丹明B(RRhB)的显色反应 ,建立了光度法测定石煤渣中痕量V(Ⅴ)的新方法。结果表明在抗坏血酸存在下具有高灵敏的显色反应 ,摩尔吸光系数为3.8×105 L·mol-1·cm-1,显色程度与V(Ⅴ)量在0～100μg/L范围内符合比耳定律。该法用于测定石煤渣中的微量V时 ,结果令人满意。     

A dispersion-corrected density functional theory study of the noncovalent interactions between nucleobases and carbon nanotube models containing stone–wales defects

The noncovalent bonding between nucleobases (NBs) and Stone–Wales (SW) defect-containing closed-end single-walled carbon nanotubes (SWNTs) was theoretically studied in the framework of density function theory using a dispersion-corrected functional PBE-G06/DNP. The models employed in this study were armchair nanotube (ANT) (5,5) and zigzag nanotube (ZNT) (10,0), which incorporated SW defects in different orientations. In one of them, the (7,7) junction is tilted with respect to SWNT axis (ANT-t and ZNT-t), whereas in ANT-p and ZNT-p models the (7,7) junction is parallel and perpendicular to the axis, respectively. The binding energies for uracil, thymine, cytosine, 5-methylcytosine, adenine, and guanine interacting with the defect-containing nanotube models were compared to the values previously obtained with the same calculation technique for the case of defect-free SWNTs, both in the gas phase (vacuum) and in aqueous medium. For most models, the interaction strength tends to be higher for purine than for pyrimidine complexes, with a clear exception of the systems including ZNT-p, both in vacuum and in aqueous medium. As it could be expected, the binding strength in the latter case is lower as compared to that in vacuum, roughly by 2–4 kcal/mol, due to the implicit inclusion of a medium (i.e., water) via the conductor-like screening model model. The closest contacts between NBs and SWNT models, frontier orbital distribution, and highest-occupied molecular orbital–lowest-unoccupied molecular orbital gap energies are analyzed as well. © 2019 Wiley Periodicals, Inc.     

Isometries of Lipschitz type function spaces

In this article, we describe isometries over the Lipschitz spaces under certain conditions. Indeed, we provide a unified proof for the main results of 3 and 5 in a more general setting. Finally, we extend our results for some other functions spaces like the space of vector‐valued little Lipschitz maps and pointwise Lipschitz maps.     

On modal logics arising from scattered locally compact Hausdorff spaces

For a topological space X, let $\mathsf{L}(X)$ be the modal logic of X where □ is interpreted as interior (and hence ◇ as closure) in X. It was shown in [3] that the modal logics S4, S4.1, S4.2, S4.1.2, S4.Grz, ${\mathsf{S4}.\mathsf{Grz}}_n$ ($n\ge 1$), and their intersections arise as $\mathsf{L}(X)$ for some Stone space X. We give an example of a scattered Stone space whose logic is not such an intersection. This gives an affirmative answer to [3, Question 6.2]. On the other hand, we show that a scattered Stone space that is in addition hereditarily paracompact does not give rise to a new logic; namely we show that the logic of such a space is either S4.Grz or ${\mathsf{S4}.\mathsf{Grz}}_n$ for some $n\ge 1$. In fact, we prove this result for any scattered locally compact open hereditarily collectionwise normal and open hereditarily strongly zero-dimensional space.     

Effect of electric field on the electrical conductivity of defected carbon nanotube: Multifractal properties of the wavefunctions

A theoretical analysis of controllable metal–insulator transition is performed by carrying out a quantum chaos analysis for a single-walled carbon nanotube which is affected by topological Stone–Wales defect. Nanotubes have recently attracted attention as promising materials for flexible nanoelectronic devices. Individual topological Stone–Wales defects have been identified experimentally in carbon nanotubes (CNTs) and graphene. The findings reveal that defected CNT displays a gradual crossover from metal to insulator phase in a longitudinal electric field. By determining the threshold value of the electric field for metal–insulator transition, CNT may be used as a switch in electronic devices. Our results are obtained by calculating the singularity spectrum of a nearest-neighbor tight-binding model. Also, quantum chaos theory is used for obtaining a detailed understanding of a dynamic phase transition from delocalized states (chaotic) to localized states (Poisson). More interestingly, the appearance of negative differential resistance for pure CNT suggests potential applications in nanoelectronic devices.