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。     

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。     

Fuzzy Topological Representation Theory For D_(01)

In this paper, we shall introduce the concepts of fuzzy prime ideal, fuzzy Stone space, fuzzy fundamental set, etc. And the representations of a distributive lattice with 0, 1 (D_(01) denotes the equational class of such lattices) by fuzzy sets will be investigated and many useful results are obtained.     

The Priestley Separation Axiom for Scattered Spaces

Let R be a quasi-order on a compact Hausdorff topological space X. We prove that if X is scattered, then R satisfies the Priestley separation axiom if and only if R is closed in the product space X×X. Furthermore, if X is not scattered, then we show that there is a quasi-order on X that is closed in X×X but does not satisfy the Priestley separation axiom. As a result, we obtain a new characterization of scattered compact Hausdorff spaces.     

Effect of solvent type on polycondensation of TEOS catalyzed by DBTL as used for stone consolidation

We have investigated the effect of solvent in the sol–gel process of tetraethylorthosilicate (TEOS) when di-n-butyltin dilaurate (DBTL) is used as polycondensation catalyst. Two sets of materials similar to those employed in the field of stone consolidation were prepared in the laboratory by using either protic or aprotic solvents: (1) xerogels from TEOS/DBTL, and (2) composites from TEOS/colloidal silica particles/DBTL. The results have shown that the solvent directly influences the aggregation pathway of the condensates. For a mixture of methyl ethyl ketone/acetone (aprotic solvents), gels with a higher degree of condensation were obtained. In the case of TEOS xerogels, the materials are essentially non-porous. Additionally, the incorporation of colloidal silica particles induces an important increase in porosity, which is even more dramatic when ethanol is used as solvent, through the formation of micro and mesoporous materials as the concentration of particles is increased. A TEOS polymerization pathway is suggested depending on which system of solvents is used. Various analytical techniques were used to characterize the materials obtained.     

Study of titanium adsorption on perfect and defected BC3 nanotubes using density functional theory

Density functional theory calculations were used to study the titanium (Ti) adsorption on perfect and defected (4, 0) BC₃ nanotubes, considering Stone–Wales and vacancy defects. The binding energy values for these nanotubes were larger than the corresponding values for carbon nanotubes. The charge transfer from the Ti atom to nanotube was observed for all systems studied. The most exothermic binding process occurred for the Ti adsorption on a native V_B defect, which showed minimum structural deformation with respect to a perfect BC₃ tube. In the case of a nanotube with a reconstructed carbon vacancy, the adsorption of Ti generated a half-metallic anti-ferromagnet. The results obtained in this paper are relevant for spintronics and hydrogen adsorption applications.     

Weak‐quasi‐Stone algebras

In this paper we shall introduce the variety WQS of weak‐quasi‐Stone algebras as a generalization of the variety QS of quasi‐Stone algebras introduced in [9]. We shall apply the Priestley duality developed in [4] for the variety N of ¬‐lattices to give a duality for WQS. We prove that a weak‐quasi‐Stone algebra is characterized by a property of the set of its regular elements, as well by mean of some principal lattice congruences. We will also determine the simple and subdirectly irreducible algebras (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)