An Analytical Technique,Based on Natural Transform to Solve Fractional-Order Parabolic Equations

This research article is dedicated to solving fractional-order parabolic equations using an innovative analytical technique. The Adomian decomposition method is well supported by natural transform to establish closed form solutions for targeted problems. The procedure is simple, attractive and is preferred over other methods because it provides a closed form solution for the given problems. The solution graphs are plotted for both integer and fractional-order, which shows that the obtained results are in good contact with the exact solution of the problems. It is also observed that the solution of fractional-order problems are convergent to the solution of integer-order problem. In conclusion, the current technique is an accurate and straightforward approximate method that can be applied to solve other fractional-order partial differential equations.     

基于分数阶傅里叶变换的模式测控一体化方法

提出了一种基于分数阶傅里叶变换的模式测控一体化方法。利用分数阶傅里叶变换光路对光纤模式耦合态进行空间调制和相位调制,以实现模式的有效分解。与双重傅里叶变换（F²）法以及空间和频谱成像（S²）法相比,采用的分数阶傅里叶变换法,通过改变分数阶参数,控制模式的空间分布以及模式间的叠加状态,更易于分解出高阶模式。基于分数阶傅里叶变换的模式测量方法可在更广泛空间,研究模式的空间和相位叠加以及模式分解,也可退化为F²法和S²法。     

离散式任意充磁角度Halbach永磁电机解析模型研究

Halbach电机因其自身优势在新型船舶推进、海洋洋流发电等方面受到广泛关注. 本文在假设铁磁材料线性和定子内表面光滑的条件下, 通过将任意充磁角度Halbach阵列等效为两组90° Halbach(或180° Halbach)阵列的矢量合成, 提出了一种分析离散式任意充磁角度Halbach永磁电机气隙磁场的解析方法; 通过对电机中磁标量势的傅里叶级数进行计算, 推导出了最简单的90° Halbach永磁电机在极坐标系下的气隙磁密表达式, 并在此基础上, 给出了任意充磁角度Halbach电机永磁体磁化强度在一个极下的表达式, 进而得出任意充磁角度Halbach电机气隙磁密的分布, 并分析了气隙磁密与电机极对数、永磁体厚度和充磁角度间的关系. 最后通过有限元和试验结果验证了本文方法的正确性. 关键词： 离散式Halbach电机 任意充磁角度 矢量等效 解析模型     

The equation-transform model for Dirac–Morse problem including Coulomb tensor interaction

The approximate solutions of Dirac equation with Morse potential in the presence of Coulomb-like tensor potential are obtained by using Laplace transform (LT) approach. The energy eigenvalue equation of the Dirac particles is found and some numerical results are obtained. By using convolution integral, the corresponding radial wave functions are presented in terms of confluent hypergeometric functions.     

Effect of Temperature and Comonomer Content on Thermal Behavior and Crystallization Property of the Propylene–Ethylene Random Copolymers

The effects of ethylene units content and crystallization temperature on the conformations, and the thermal and crystallization behavior were investigated by a combination of Fourier transform infrared (FTIR) spectroscopy, wide angle X-ray diffraction (WAXD), and differential scanning calorimetry (DSC). The characterization of FTIR spectroscopy proves that the longer helical conformation sequences of the propylene–ethylene random (PER) samples decrease, whereas the shorter helical conformation sequences increase with the increase in ethylene units content. The increase of the shorter helical conformation sequences is favorable for the formation of the γ-phase in the crystals. A group of broad endothermic peaks can be seen clearly in the DSC curves of PER copolymers, which may be associated with the melting of mixtures of the α- and γ-forms in the crystals. The melting point, crystallization temperature, and crystallinity degree of the PER copolymers decrease with the increase in ethylene units contents. Three typical melting peaks of the PER copolymers crystallized isothermally between 80°C and 130°C were observed. The two higher melting peaks result from melting of the α- and γ-phase in the crystals, whereas the materials crystallized on quenching give the lowest peak. The WAXD results confirm that the PER copolymers crystallize from the melt, as mixtures of α and γ forms, in a wide temperature range. The critical number ζ_lim of the crystallizable units for the α-form increases with the increase in crystallization temperature for PER copolymers, which is favorable for the formation of the γ phases. The amount of γ-form increases with the increase in crystallization temperature at the expense of its α component, then reaches a maximum value at the crystallization temperature of 115°C, and finally decreases with further increase in the crystallization temperature.     

Ftir Studies on LB Film of Amphiphile with Schiff Base as Headgroup and Its Copper Complex

Two different ways to form monolayers and LB films (surface film and subphase film) of the complex have been used, where a novel amphiphile containing Schiff base as a headgroup was used as a ligand. the monolayer behavior at the air/water interface was characterized by π-A isotherms and two-dimensional molecular orientation of alkyl chains in LB films and thermal stability were measured by polarized and variable temperature FTIR transmission spectra, indicating that the LB film of the novel amphiphile and its copper(II) complex are very stable as well as stearic acid. Because incorporating the metal ion into the monolayer makes it more condensed, thermal stability of the LB film was enhanced. as can be compared from their structure and properties, subphase films are superior to surface films.     

Image denoising using trivariate prior model in nonsubsampled dual-tree complex contourlet transform domain and non-local means filter in spatial domain

Image denoising is always the basic problem of image processing, and the main challenge is how to effectively remove the noise and preserve the detailed information. This paper presents a new image denoising algorithm based on the combination of trivariate prior model in nonsubsampled dual-tree complex contourlet transformlet transform (NSDTCT) domain and non-local means filter (NLMF) in spatial domain. Firstly, NSDTCT is constructed by combining the dual-tree complex wavelet transform (DTCWT) and nonsubsampled directional filter banks (NSDFB). The noisy image is decomposed by using NSDTCT. Secondly, based on the correlation between the interscale and intrascale dependencies of NSDTCT coefficients, the distribution of the high frequency coefficients is modeled with the trivariate non-Gaussian distribution model. A nonlinear trivariate shrinkage function is derived in the framework of Bayesian theory, and then the denoised coefficients are obtained and inverse NSDTCT is performed to get the initial denoised image. Finally, NLMF is used to smooth the initial denoised image. Simulation experiment shows that our algorithm can obtain better performances than those outstanding denoising algorithms in terms of peak signal-to-noise ratio (PSNR), mean structural similarity (MSSIM) as well as visual quality.     

ANALYSIS OF MEBENDAZOLE POLYMORPHS BY FOURIER TRANSFORM INFRARED SPECTROMETRY USING CHEMOMETRIC METHODS

A Fourier transform infrared (FT-IR) spectrometric method diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) was developed for the rapid, direct measurement of mebendazole in drugs. Conventional KBr-spectra and DRIFTS-spectra were compared for best determination of active substance in drug formulations. Two chemometric approaches, partial least-squares (PLS2) and principal component regression (PCR+) methods were used in data procesing. The best results were obtained with the PLS2 method.     

Real‐Time Monitoring of Transport of Chlorinated Hydrocarbons from Industrial Areas Using Open‐Path FTIR Spectrometry with COL1SB

Abstract

Open‐path Fourier transform infrared (FTIR) spectrometry was used to continuously monitor 11 chlorinated hydrocarbon species in the region connecting two different industrial complexes for 24 hr. The single‐beam spectra obtained from open‐path FTIR were analyzed by newly developed software named COL1SB, which generates site‐specific background spectra as well as path‐averaged water vapor concentrations in addition to performing regression analyses. The path‐averaged water vapor concentrations calculated by the COL1SB agreed very well with those measured by a thermo‐hygrometer. In addition, site‐specific background spectra were generated by accounting for chemical absorption of 50 chemical species. The accurate estimation of path‐averaged water vapor concentrations, as well as the usage of site‐specific background spectra, enables chlorinated hydrocarbons to be measured by open‐path FTIR spectrometry at the ppb level. Among 11 chlorinated hydrocarbons considered here, trichlorofluoromethane, carbon tetrachloride, trichloroethylene, and tetrachloroethylene were identified as major chlorinated hydrocarbons having concentrations above 1 ppb. Wind affected the temporal variations of these chlorinated hydrocarbons, indicating the importance of local transport. However, the effect of wind differed from one species to another because of different source characteristics.     

Cramér theorem on symmetric spaces of noncompact type

We prove the Cramér theorem forK-invariant Gaussian measures on irreducible symmetric spacesX=G/K withG semisimple noncompact. To do this we use a kind of Abel transform ofK-invariant measures onX.This research is supported by KBN Grant.