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61.
《Analytical letters》2012,45(2):239-252
Abstract Two mixtures (caffeine mixture (I) and codeine mixture (II)) of 3-components, containing acetaminophen and salicylamide as majors, have been assayed using different computer-assisted spectrophotometric methods. These methods are the Unique Absorbance Method (UAM), the Unique Orthogonal Function Method (UOFM), and Unique Fourier Function Method (UFFM), and also their correspondences under the least squares approach. The parameters have been optimized for the accurate determination of the minor component caffeine in mixture (I). In mixture (II), however. codeine has been extracted - in two steps-prior to the correction of interferences from the major components acetaminophen and salicylamide. 相似文献
62.
The V-system is a complete orthogonal system of functions defined on the interval [0, 1], generated by finite Legendre polynomials
and the dilation and translation of a function generator, which consists of a finite number of continuous and discontinuous
functions. The V-system has interesting properties, such as orthogonality, symmetry, completeness and short compact support.
It is shown in this paper that the V-system is essentially a special multi-wavelet basis. As a result, some basic properties
of the V-system are established through the well-developed theory of multi-wavelets. From this point of view, more other V-systems
are constructed. 相似文献
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64.
Matti Schneider 《Mathematical Methods in the Applied Sciences》2015,38(13):2761-2778
The FFT‐based homogenization method of Moulinec–Suquet has recently attracted attention because of its wide range of applicability and short computational time. In this article, we deduce an optimal a priori error estimate for the homogenization method of Moulinec–Suquet, which can be interpreted as a spectral collocation method. Such methods are well‐known to converge for sufficiently smooth coefficients. We extend this result to rough coefficients. More precisely, we prove convergence of the fields involved for Riemann‐integrable coercive coefficients without the need for an a priori regularization. We show that our L2 estimates are optimal and extend to mildly nonlinear situations and Lp estimates for p in the vicinity of 2. The results carry over to the case of scalar elliptic and curl ? curl‐type equations, encountered, for instance, in stationary electromagnetism. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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67.
An efficient meshfree point collocation moving least squares method to solve the interface problems with nonhomogeneous jump conditions
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Ameneh Taleei Mehdi Dehghan 《Numerical Methods for Partial Differential Equations》2015,31(4):1031-1053
We are going to study a simple and effective method for the numerical solution of the closed interface boundary value problem with both discontinuities in the solution and its derivatives. It uses a strong‐form meshfree method based on the moving least squares (MLS) approximation. In this method, for the solution of elliptic equation, the second‐order derivatives of the shape functions are needed in constructing the global stiffness matrix. It is well‐known that the calculation of full derivatives of the MLS approximation, especially in high dimensions, is quite costly. In the current work, we apply the diffuse derivatives using an efficient technique. In this technique, we calculate the higher‐order derivatives using the approximation of lower‐order derivatives, instead of calculating directly derivatives. This technique can improve the accuracy of meshfree point collocation method for interface problems with nonhomogeneous jump conditions and can efficiently estimate diffuse derivatives of second‐ and higher‐orders using only linear basis functions. To introduce the appropriate discontinuous shape functions in the vicinity of interface, we choose the visibility criterion method that modifies the support of weight function in MLS approximation and leads to an efficient computational procedure for the solution of closed interface problems. The proposed method is applied for elliptic and biharmonic interface problems. For the biharmonic equation, we use a mixed scheme, which replaces this equation by a coupled elliptic system. Also the application of the present method to elasticity equation with discontinuities in the coefficients across a closed interface has been provided. Representative numerical examples demonstrate the accuracy and robustness of the proposed methodology for the closed interface problems. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1031–1053, 2015 相似文献
68.
It is well known that mutually orthogonal latin squares, or MOLS, admit a (Kronecker) product construction. We show that, under mild conditions, “triple products” of MOLS can result in a gain of one square. In terms of transversal designs, the technique is to use a construction of Rolf Rees twice: once to obtain a coarse resolution of the blocks after one product, and next to reorganize classes and resolve the blocks of the second product. As consequences, we report a few improvements to the MOLS table and obtain a slight strengthening of the famous theorem of MacNeish. 相似文献
69.
To optimize the accuracy of near-infrared non-invasive hemoglobin (Hb) clinical detection, high-performance instrument and prepossessing algorithm have been investigated. A near-infrared spectrophotometric system was constructed adopting InGaAs detector array with 16 pixels and plane grating spectrometer to obtain high signal noise ratio (SNR) spectral data. In our experiment, we applied the device independently to collect spectra data from 91 volunteers’ fingertips non-invasively. Two prediction tests were conducted to verify the effects of preprocessing algorithms improving the accuracy of near-infrared Hb detection and exclude the occasionality of satisfactory results in a single trial. Our non-invasive Hb detection methods were based on partial least squares (PLS). In each test, PLS, MSC coupled with PLS, DOSC coupled with PLS, three methods for non-invasive Hb detection, were analyzed respectively. The results of two trials showed that only DOSC & PLS performed excellently in both predictive ability and stability, obviously better than other two methods. Relative RMSEP was 6.16% in predicting test 1, 6.08% in predicting test 2, almost reaching the requirements of clinical application. It indicates that our independent-developed high-performance instrument and the method DOSC coupled with PLS are promising in non-invasive Hb detection clinical application. 相似文献
70.
In this article, boundary characteristic orthogonal polynomials have been implemented in the Rayleigh–Ritz method to investigate free vibration of non-uniform Euler–Bernoulli nanobeams based on nonlocal elasticity theory. Non-uniform cross section of nanobeams has been considered by taking linear as well as quadratic variations of Young's modulus and density along the space coordinate. Detailed analysis has been reported for all the possible cases of such variations. The objective of the present study is to analyze the effects of nonlocal parameter, boundary condition, length-to-diameter ratio and non-uniform parameter on the frequency parameters. It is found that clamped nanobeams are having highest frequency parameters than other types of boundary conditions for a particular set of parameters. It is also observed that frequency parameters decrease with increase in scaling effect parameter. First four deflection shapes of non-uniform nanobeams have also been incorporated. In this analysis, some of the new results in terms of boundary conditions have also been included. 相似文献