Accurate Geometry and Non-Covalent Interactions in 1-Phenylethanol and its Monohydrate: A Rotational Study

The pure rotational spectra of 1-phenylethanol and its monohydrate were measured by using a pulsed jet Fourier transform microwave spectrometer. One conformer of the 1-phenylethanol monomer with the trans form was observed in the pulsed jet. The experimental values of rotational constants of ten isotopologues, including eight mono-substituted ¹³C and one D isotopologues, allow an accurate structure determination of the skeleton of 1-phenylethanol. For its monohydrate, only one isomer has been observed, of which 1-phenylethanol adopts the trans form and binds with water through an O−H⋅⋅⋅O_w and an O_w−H⋅⋅⋅π hydrogen bond. Each rotational transition displays a doublet with a relative intensity ratio of 1 : 3, due to a hindered internal rotation of water around its C₂ axis. This study provides the information on accurate geometry of 1-phenylethanol (PE) and large amplitude motion of water in the PE monohydrate.     

Roller bearing acoustic signature extraction by wavelet packet transform,applications in fault detection and size estimation

Continuous online monitoring of rotating machines is necessary to assess real-time health conditions so as to enable early detection of operation problems and thus reduce the possibility of downtime. Rolling element bearings are crucial parts of many machines and there has been an increasing demand to find effective and reliable health monitoring technique and advanced signal processing to detect and diagnose the size and location of incipient defects. Condition monitoring of rolling element bearings, comprises four main stages which are, statistical analysis, fault diagnostics, defect size calculation, and prognostics. In this paper the effect of defect size, operating speed, and loading conditions on statistical parameters of acoustic emission (AE) signals, using design of experiment method (DOE), have been investigated to select the most sensitive parameters for diagnosing incipient faults and defect growth on rolling element bearings. A modified and effective signal processing algorithm is designed to diagnose localized defects on rolling element bearings components under different operating speeds, loadings, and defect sizes. The algorithm is based on optimizing the ratio of Kurtosis and Shannon entropy to obtain the optimal band pass filter utilizing wavelet packet transform (WPT) and envelope detection. Results show the superiority of the developed algorithm and its effectiveness in extracting bearing characteristic frequencies from the raw acoustic emission signals masked by background noise under different operating conditions. To experimentally measure the defect size on rolling element bearings using acoustic emission technique, the proposed method along with spectrum of squared Hilbert transform are performed under different rotating speeds, loading conditions, and defect sizes to measure the time difference between the double AE impulses. Measurement results show the power of the proposed method for experimentally measuring size of different fault shapes using acoustic emission signals.     

New index transforms of the Lebedev–Skalskaya type

New index transforms, involving the real part of the modified Bessel function of the first kind as the kernel are considered. Mapping properties such as the boundedness and invertibility are investigated for these operators in the Lebesgue spaces. Inversion theorems are proved. As an interesting application, a solution of the initial value problem for the second-order partial differential equation, involving the Laplacian, is obtained. It is noted that the corresponding operators with the imaginary part of the modified Bessel function of the first kind lead to the familiar Kontorovich–Lebedev transform and its inverse.     

Mexican hat wavelet transform of distributions

Theory of Weierstrass transform is exploited to derive many interesting new properties of the Mexican hat wavelet transform. A real inversion formula in the differential operator form for the Mexican hat wavelet transform is established. Mexican hat wavelet transform of distributions is defined and its properties are studied. An approximation property of the distributional wavelet transform is investigated which is supported by a nice example.     

Computation of Greeks in LIBOR models driven by time–inhomogeneous Lévy processes

The aim of this article is to compute Greeks, i.e. price sensitivities in the framework of the Lévy LIBOR model. Two approaches are discussed. The first approach is based on the integration-by-parts formula, which lies at the core of the application of the Malliavin calculus to finance. The second approach consists of using Fourier-based methods for pricing derivatives. We illustrate the result by applying the formula to a caplet price where the jump part of the driving process of the underlying model is given by a time–inhomogeneous Gamma process and alternatively by a Variance Gamma process.     

Small-Maturity Asymptotics for the At-The-Money Implied Volatility Slope in Lévy Models

We consider the at-the-money (ATM) strike derivative of implied volatility as the maturity tends to zero. Our main results quantify the behaviour of the slope for infinite activity exponential Lévy models including a Brownian component. As auxiliary results, we obtain asymptotic expansions of short maturity ATM digital call options, using Mellin transform asymptotics. Finally, we discuss when the ATM slope is consistent with the steepness of the smile wings, as given by Lee’s moment formula.     

Microlocal analysis of quasianalytic Gelfand-Shilov type ultradistributions

We introduce a global wave front set suitable for the analysis of tempered ultradistributions of quasi-analytic Gelfand–Shilov type. We study the transformation properties of the wave front set and use them to give microlocal existence results for pullbacks and products. We further study quasi-analytic microlocality for classes of localization and ultradifferential operators, and prove microellipticity for differential operators with polynomial coefficients.     

黄土区金盏菊幼苗根部细胞壁对Pb/Cd复合胁迫响应的FTIR和Raman光谱

植物修复法是新兴的重金属污染土壤修复手段,也是未来极富应用潜力的主流技术之一。植物根部细胞壁作为重金属/土壤/植物相的交界面,天然地成为修复效能调控过程的关键部位和信号通道。植物细胞壁与重金属离子的作用行为具有物理化学和生理生化的双重属性,但以光谱技术为切入点,原位解析植物根部细胞壁对土壤重金属离子的响应关系还不多见。以黄土区修复植物金盏菊幼苗为研究对象,分析Pb/Cd复合胁迫对其根部细胞壁形貌的影响,借助X射线荧光光谱(XRF)、X射线衍射(XRD)、傅里叶变换红外光谱(FTIR)和拉曼光谱(Raman)揭示细胞壁对Pb/Cd胁迫的响应信号。结果发现:Pb/Cd胁迫导致金盏菊根部细胞壁弯曲萎缩,表面分布若干点状深色沉积物颗粒;XRF证实细胞壁Pb/Xd含量增加,但XRD图谱没有发现典型Pb/Xd结晶峰。FTIP图谱中—OH振动峰定位于3 416 cm~(-1)处,表明Pb/Cd离子与—OH间可能存在配位键合;1 701和1 593 cm~(-1)处的特征峰分别移动到1 736和1 618 cm~(-1),说明Pb/Cd胁迫改变了金盏菊根部细胞壁蛋白质结构属性。Raman光谱中2 960 cm~(-1)附近峰强增加,暗示Pb/Cd胁迫影响了细胞壁纤维素分子排列方向。可以认为,细胞壁组分(果胶、蛋白质、纤维素等)和典型官能团(—OH,N—H,C=O等)对于减缓Pb/Cd胁迫引起的金盏菊根部细胞壁毒害效应贡献较大。     

不同产地中国沙棘的傅里叶变换红外光谱识别研究

采用傅里叶变换红外光谱结合二阶导数光谱对不同产地的中国沙棘进行识别研究。结果表明,不同产地中国沙棘的一维红外光谱在2 925,2 854,1 743,1 541和1 173cm~(-1)等处都有表征脂类、黄酮类和糖类成分的特征吸收峰。但因产地不同,各样本吸收峰的位置和强度均存在一定差异。此外,3 429~3 336cm~(-1)范围处以及1 744cm~(-1)附近处的吸收峰是识别不同产地中国沙棘主要特征峰;比较各产地中国沙棘的二阶导数红外图谱发现,1 030和1 516cm~(-1)的吸收峰能够进一步确认样本中的黄酮类化合物的存在。此外,各样本在1 711和1 476cm~(-1)附近的吸收峰以及1 689~1 515和1 400~1 175cm~(-1)处吸收峰的强度和位置均具有显著差异。一维红外光谱和二阶导数光谱的结合,可以为不同产地中国沙棘的识别分析提供科学数据。该方法快速、直观、简便,能够为不同产地中国沙棘的整体化学成分提供大量信息,有助于中国沙棘的整体质量控制以及有效成分定性分析研究。