基于改进的GM(1,1)-Markov链组合模型广东省单位GDP能耗预测

本文以灰色系统理论的GM(1,1)模型和随机过程理论的Markov链模型为基础构建了一个动态GM(1,1)-Markov链组合预测模型。该模型同时利用了GM(1,1)模型对序列趋势因素良好的拟合能力和Markov链模型对残差序列信息的提取能力。为进一步提高该模型的预测精度,用泰勒(Taylor)近似方法和新信息优先的思想对该模型进行了改进。最后,以1991-2014年广东省单位GDP能耗数据实证了该模型的预测效果。     

Theoretical investigation of the weak interactions of rare gas atoms with silver clusters by resonance Raman spectroscopy modeling

The interactions of rare gas atoms (Rg = Ar, Kr, and Xe) with small neutral and cationic silver clusters have been investigated by density functional methods and the effect of these weak interactions on the resonance Raman spectra of the complexes has been evaluated. The resonance Raman technique that depends on the properties of ground and excited state, seems deeply sensitive to the weak rare gas–metal cluster interactions, and the use of inert gases has been proven to be an excellent approach to recognize the ability of this technique to detect extremely weak interactions. In this work, for , and complexes the IR, normal and resonance Raman spectra have been calculated and the effect of rare gas–cluster stretching vibration ( ) on the pattern and the relative intensities of different spectra have been investigated. The resonance Raman spectra for the weakly interacted complexes (with the interaction energies less than ?2.0 kcal/mol) exhibit the vibration with the detectable intensity that its intensity increases by going from Ag₆–Ar to Ag₆–Xe complex. Moreover, the resonance Raman spectra (based on the excited state gradient approximation) for high intensity nearly degenerate excited states, proved the effect of accumulation of the excited state charge density on the relative intensity of vibration.     

About the compatibility between ansatzes and constraints for a local formulation of orbital‐free density functional theory

Functional properties that are exact for the Hohenberg–Kohn functional may turn into mutually exclusive constraints at a given level of ansatz. This is exemplarily shown for the local density approximation. Nevertheless, it is possible to reach exactly the Kohn–Sham data from an orbital‐free density functional framework based on simple one‐point functionals by starting from the Levy–Perdew–Sahni formulation. The energy value is obtained from the density‐potential pair, and therefore does not refer to the functional dependence of the potential expression. Consequently, the potential expression can be obtained from any suitable model and is not required to follow proper scaling behavior.     

Characterization of Chickpea Flour by Near Infrared Spectroscopy and Chemometrics

Near infrared (NIR) spectrometry was used for the rapid characterization of quality parameters in desi chickpea flour (besan). Partial least square regression, principal component regression (PCR), interval partial least squares (iPLS), and synergy interval partial least squares (siPLS) were used to determine the protein, carbohydrate, fat, and moisture concentrations of besan. Spectra were collected in reflectance mode using a lab-built predispersive filter-based instrument from 700 to 2500?nm. The quality parameters were also determined by standard methods. The root mean square error (RMSE) for the calibration and validation sets was used to evaluate the performance of the models. The correlation coefficients for moisture, fat, protein, and carbohydrates in chickpea flour exceeded 0.96 using PLS and PCR models using the full spectral range. Wavelengths from 2100 to 2345?nm had the lowest RMSE for quality parameters by iPLS. The error was further decreased by 0.41, 0.1, and 1.1% for carbohydrates, fats, and proteins by siPLS. The NIR spectral regions yielding the lowest RMSE of prediction were 1620–2345?nm for carbohydrates, 1180–1590?nm and 1860–2094?nm for fat, and 1700–2345?nm for proteins. The study shows that chickpea flour quality parameters were accurately determined using the optimized wavelengths.     

Characterization of Gasoline by 1H Nuclear Magnetic Resonance and Chemometrics

Automotive fuel adulteration is an old and significant problem. One common type of fuel adulteration is the addition of diesel to gasoline. Unsupervised models were developed through hierarchical cluster and principal component analysis models. Supervised models through partial least square discriminant analysis using ¹H nuclear magnetic resonance spectra as the input were used to classify samples as adulterated or unadulterated. Quantitative models were developed using partial least squares to determine the gasoline and diesel concentrations in the samples. This set contained samples composed of pure gasoline and anhydrous ethanol reproducing commercial gasoline and other samples treated with diesel. Hierarchical cluster and principal component analysis did not distinguish between adulterated and unadulterated samples except for the most adulterated materials. However, partial least square discriminant analysis classified 100% of the samples correctly. The partial least square algorithm provided excellent regression models for the gasoline and diesel content. The determination coefficient was 0.9920 for both models, whereas the root mean square error of cross-validation and root mean square error of prediction for the diesel model were 2.32 and 1.42%, respectively, and 2.40 and 1.38% for the gasoline model.     

Reconstruction of the Linear Ordinary Differential System Based on Discrete Points

In this paper, we discuss an inverse problem, i.e., the reconstruction of a linear differential dynamic system from the given discrete data of the solution. We propose a model and a corresponding algorithm to recover the coefficient matrix of the differential system based on the normal vectors from the given discrete points, in order to avoid the problem of parameterization in curve fitting and approximation. We also give some theoretical analysis on our algorithm. When the data points are taken from the solution curve and the set composed of these data points is not degenerate, the coefficient matrix $A$ reconstructed by our algorithm is unique from the given discrete and noisefree data. We discuss the error bounds for the approximate coefficient matrix and the solution which are reconstructed by our algorithm. Numerical examples demonstrate the effectiveness of the algorithm.     

Combining field‐amplified sample stacking with moving reaction boundary electrophoresis on a paper chip for the preconcentration and separation of metal ions

A common drawback of paper‐based separation devices is their poor detection limit. In this study, we combined field‐amplified sample stacking with moving reaction boundary electrophoresis on a paper chip with six array channels for the parallel separation and concentration of multiple samples. With a new hyphenated technique, the brown I₂ from the Fe³⁺/I⁻ oxidation–reduction reaction emerged near the boundary between the dilute ethylene diamine tetraacetic acid and potassium iodide and highly concentrated KCl solutions. For the separation and concentration of three components, Cr³⁺, Cu²⁺, and Fe³⁺, the Fe³⁺ detection limit was improved at least 266‐fold by comparing the hyphenated technique with moving reaction boundary electrophoresis. The detection limit of Fe³⁺ was found to be as low as 0.34 ng (20 μM) on the paper chip. We also demonstrated the analysis of a real sample of four metal ions, with detection limits as follows: 0.16 μg Cr³⁺, 1.5 μg Ni²⁺, 0.64 μg Cu²⁺, and 1.5 μg Co²⁺. The synergy of field‐amplified sample stacking and moving reaction boundary electrophoresis in the micron paper‐based array channels dramatically improved the detection limit and throughput of paper‐based electrophoresis.     

Remarks on the Born approximation and the Factorization Method

In this paper, we compare the far-field operators for the full nonlinear inverse scattering problem with the Born approximation as its linearization. The Factorization Method shows that both operators share the same behavior with respect to illposedness of the inverse problem. The results are derived for acoustic and electromagnetic scattering problems and the corresponding problem in electrical impedance tomography.