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Maziar Salahi 《Journal of Applied Mathematics and Computing》2009,31(1-2):507-515
In this paper we consider solving ill-conditioned linear systems under nonnegativity constraints with noisy right hand sides. The classical approaches to solve such systems are constrained least square (quadratic programming) and barrier methods. First we present these classical methods. Then a modified version of the GMRES method (NGMRES) is presented. Since we assume that the coefficient matrices are ill-conditioned, then the Tikhonov regularization of the problem is considered. Our computational experiments show that the NGMRES provides us high quality solutions much faster than the other two approaches. 相似文献
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Maziar Salahi 《Central European Journal of Operations Research》2010,18(2):181-187
In this paper, first we show that for rank deficient matrices, the optimal solution of a single equality constrained quadratic
minimization problem can be found by relaxing the equality constraint to the inequality one, which makes the problem a convex
problem. Then we show that for full rank matrices, an optimal solution can be obtained using semidefinite optimization framework. 相似文献
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Heterodyne near-field scanning optical microscopy (H-NSOM) has proven useful as a tool for characterization of both amplitude and phase of on-chip photonic devices in air, but it has previously been unable to characterize devices with a dielectric overcladding, which is commonly used in practice for such devices. Here we demonstrate H-NSOM of a silicon waveguide with a liquid cladding emulating the solid dielectric. This technique allows characterization of practical devices with realistic refractive index profiles. Fourier analysis is used to estimate the effective refractive index of the mode from the measured data, showing an index shift of 0.08 from air to water cladding, which is seen to correspond well to simulations. 相似文献
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We propose a method for miniaturization of filters based on curved waveguide Bragg gratings, so that long structures can be packed into a small area on a chip. This eliminates the stitching errors introduced in the fabrication process, which compromise the performance of long Bragg gratings. Our approach relies on cascading curved waveguide Bragg gratings with the same radius of curvature. An analytical model for the analysis of these devices was developed, and a filter based on this model was designed and fabricated in a silicon on insulator platform. The filter had a total length of 920μm, occupied an area of 190μm×114μm, and exhibited a stop band of 1.7nm at 1.55μm and an extinction ratio larger than 23dB. 相似文献
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Maziar Salahi 《Applied Mathematics Letters》2010,23(5):605-608
Least squares solution of linear inequalities appears in many disciplines such as linear separability problems and inconsistency correction. In this paper we consider this problem with uncertainty in its data. Then we prove that its robust counterpart is equivalent to a second order conic linear optimization problem, which can be efficiently solved using interior point methods. 相似文献
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Diffuse reflectance spectroscopy (DRS) can be used as a rapid and sensitive method for the quantitative determination of low amounts of aluminum. In this analytical technique, the analyte in samples are extracted onto a solid sorbent matrix loaded with a colorimetric reagent and then quantified directly on the adsorbent surface. Alternatively, colored aluminum complexes formed in solution can also be immobilized onto adsorbent surface and be measured by DRS technique. Octadecyl silica disk, methyltrioctylammonium chloride–naphthalene and MCM-41 were examined as adsorbents. Eriochrome cyanine R and quinalizarin were used as coloring reagents. Optimal sorption conditions were found for each system of analyte–reagent–adsorbent. The concentration of analyte is determined using the appropriate form of the Kubelka–Munk function. We obtained for each of the aluminium–reagent–adsorbent system a calibration curve by plotting the absorbance versus the log 102[Al3+] μg ml−1. The linear dynamic range extends over two orders of magnitude within 0.01–15 μg ml−1 with little differences in the range and in the correlation coefficients among the adsorbents. We consider that for a rapid determination of aluminum a spot-test-DRS combination with a detection limit of 1.0 × 10−2 μg ml−1 is the more facile and preferred technique. 相似文献
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Behrooz Mirza Somayeh Soleimani‐Amiri Maziar Mirza 《Journal of Physical Organic Chemistry》2018,31(2)
Density functional theory (DFT) calculations introduced triplet ground states for [6]n SiC‐cyclacenes and ‐acenes with alternate silabenzene rings including silicon atoms in 2 opposite edges (n = 6, 8, 10, 12). The singlet‐triplet energy gap (ΔE(S‐T)), binding energy per atom (BE/n), and NBO calculation with very small band gap (ΔELUMO‐HOMO) confirmed the triplet ground states. In contrast to polyacenes, the singlet [6]n SiC‐cyclacenes displayed more stability improvement than triplets, through n increasing. This may open the way for synthesis of larger stable [6]n SiC‐cyclacenes. The ΔE(S‐T), BE/n, and the strain energy through homodesmic equations indicated more stability for larger [6]n SiC‐cyclacenes, which was more noticeable in singlet states. Cyclacenes and acenes with high conductivity and full point charge were introduced as suitable candidates for hydrogen storage. 相似文献
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