Search results for "Transform"
showing 10 items of 3975 documents
A generalized integration formula for indefinite integrals of special functions
2020
An integration formula for generating indefinite integrals which was presented in Conway JT [A Lagrangian method for deriving new indefinite integrals of special functions. Integral Transforms Spec...
Introducing randomness in the analysis of chemical reactions: An analysis based on random differential equations and probability density functions
2021
[EN] In this work we consider a particular randomized kinetic model for reaction-deactivation of hydrogen peroxide decomposition. We apply the Random Variable Transformation technique to obtain the first probability density function of the solution stochastic process under general conditions. From the rst probability density function, we can obtain fundamental statistical information, such as the mean and the variance of the solution, at every instant time. The transformation considered in the application of the Random Variable Transformation technique is not unique. Then, the first probability density function can take different expressions, although essentially equivalent in terms of comp…
Solving fully randomized higher-order linear control differential equations: Application to study the dynamics of an oscillator
2021
[EN] In this work, we consider control problems represented by a linear differential equation assuming that all the coefficients are random variables and with an additive control that is a stochastic process. Specifically, we will work with controllable problems in which the initial condition and the final target are random variables. The probability density function of the solution and the control has been calculated. The theoretical results have been applied to study, from a probabilistic standpoint, a damped oscillator.
A Unifying Framework for Perturbative Exponential Factorizations
2021
We propose a framework where Fer and Wilcox expansions for the solution of differential equations are derived from two particular choices for the initial transformation that seeds the product expansion. In this scheme, intermediate expansions can also be envisaged. Recurrence formulas are developed. A new lower bound for the convergence of theWilcox expansion is provided, as well as some applications of the results. In particular, two examples are worked out up to a high order of approximation to illustrate the behavior of the Wilcox expansion.
The contribution of geographical certification programs to farm income and rural economies: The case of Pecorino Siciliano PDO
2021
This study attempts to measure the capacity of the EU geographical certification scheme to positively influence the price of certified products and the incomes of their producers. A comparison of the economic results of two cheese-producing dairy farm enterprises with different business strategies and locations within the Sicilian hinterlands is performed in order to determine the transformation value of each dairy’s sheep milk into pecorino cheese (with and without the Protected Designation of Origin, or PDO, certification) and the related joint products (ricotta). The economic convenience of the total transformation of sheep milk into Pecorino Siciliano PDO and ricotta is also appraised. …
Structural characterization of Nigerian coals by X-ray diffraction, Raman and FTIR spectroscopy
2010
Abstract The structural parameters of six Nigerian coals were determined by X-ray diffraction, Raman and FTIR spectroscopy. This study reveals that the coals contain crystalline carbon of turbostratic structure with some amount of highly disordered amorphous carbon. The average lateral sizes ( L a ), stacking heights ( L c ) and interlayer spacing ( d 002 ) of the crystallite structures calculated from the X-ray intensities range from 16.47 to 25.70, 8.12 to 13.25 and 3.48 to 3.58 A, respectively. The L a values derived from the Raman spectra analyses using the classical linear relationship between 1/ L a and the D/G band ratio are higher (27.53–34.67 A) than values obtained from X-ray diff…
ATR-FTIR and XRD quantification of solid mixtures using the asymptotic constant ratio (ACR) methods. Application to geological samples of sodium and …
2019
Two asymptotic constant ratio methods applied to the quantification of individual components of solid samples using attenuated total reflectance-Fourier transform infrared spectroscopy (ATR-FTIR) and X-ray diffraction (XRD) are described. The methods involve the measurement of the peak current/peak areas of selected signals (diffraction peaks in XRD and absorption bands in ATR-FTIR) relative to the signal of standard added in constant proportion to the sample and the sample enriched with the analyte following the usual standard additions methodology. The proposed method compensates the absorption effects appearing in XRD and the presence of overlapping absorption bands of interferents by me…
Polarized Fourier transform infrared microscopy as a tool for structural analysis of adsorbates in molecular sieves
1992
Using FTIR microscopy with polarized IR radiation on silicalite I single crystals fully loaded with p-xylene, the existence of an ordered adsorbate could be proven for the first time by IR spectroscopy. By analyzing the polarized absorption bands the orientation of the p-xylene molecules relative to the host structure could be determined. The results agree well with structural data obtained from X-ray diffraction experiments. These first results suggest that polarized IR microscopy could develop into a powerful tool for the analysis of adsorbate structures, assisting in complete structure resolution by diffraction techniques
Water Sorption on Mesoporous Aluminosilicate MCM-41
1995
Characterization of the interaction of water with the highly ordered mesoporous solid MCM-41 (pore diameter ∼2.5 nm) is undertaken with the aid of several techniques (adsorption gravimetry, X-ray diffraction, Fourier transform infrared spectroscopy, and controlled rate-evolved gas analysis). The relatively complex water-MCM-41 interactions are characterized by a type V isotherm indicating an initial repulsive character followed by a capillary condensation step of the adsorbate. This highlights both hydrophobic and hydrophilic properties of this potential model mesoporous adsorbent.
Fast algorithms for free-space diffraction patterns calculation
1999
Here we present a fast algorithm for Fresnel integral calculation. Some fast algorithms using the fast Fourier transform are analysed and their performance has been checked. These methods are of easy implementation, but are only valid for a specific range of distances. Fast algorithms based on the Fractional Fourier transform allow accurate evaluation of the Fresnel integral from object to Fraunhofer domain in a single step.