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Non-derivative solution to nonlinear dynamic optimal design of class two for deformation network monitoring

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中国有色金属学会会刊：英文版 2000年第4期10卷 551-554页

作者：陶华学郭金运山东科技大学山东泰安

Based on the nonlinear error equation of deformation network monitoring, the mathematical model of nonlinear dynamic optimal design of class two was put forward for the deformation network monitoring, in which the target function is the accuracy criterion and the constraint conditions are the network’s sensitivity, reliability and observing cost. Meanwhile a new non derivative solution to the nonlinear dynamic optimal design of class two was also put forward. The solving model uses the difference to stand for the first derivative of functions and solves the revised feasible direction to get the optimal solution to unknown parameters. It can not only make the solution to converge on the minimum point of the constraint problem, but decrease the calculating load.

关键词： deformation network monitoring nonlinear dynamic optimal design non derivative analytic method.

derivative of a Determinant with Respect to an Eigenvalue in the <i>LDU</i>Decomposition of a Non-Symmetric Matrix

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Applied Mathematics 2013年第3期4卷 464-468页

作者： Mitsuhiro Kashiwagi Tokai University Toroku Kumamoto Japan

We demonstrate that, when computing the LDU decomposition (a typical example of a direct solution method), it is possible to obtain the derivative of a determinant with respect to an eigenvalue of a non-symmetric matrix. Our proposed method augments an LDU decomposition program with an additional routine to obtain a program for easily evaluating the derivative of a determinant with respect to an eigenvalue. The proposed method follows simply from the process of solving simultaneous linear equations and is particularly effective for band matrices, for which memory requirements are significantly reduced compared to those for dense matrices. We discuss the theory underlying our proposed method and present detailed algorithms for implementing it.

关键词： derivative of Determinant Non-Symmetric Matrix Eigenvalue Band Matrix LDU Decomposition

Model-Following Designs Using Direct State derivative Measurement Feedback in Novel Reciprocal State Space Form

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Journal of Applied Mathematics and Physics 2019年第2期7卷 394-409页

作者： Yuan-Wei Tseng Rong-Ching Wu Department of Electrical Engineering I-Shou University Taiwan

The paper introduces effective and straightforward algorithms of both explicit and implicit model-following designs with state derivative measurement feedback in novel reciprocal state space form (RSS) to handle state derivative related performance output and state related performance output design cases. Applying proposed algorithms, no integrators are required. Consequently, implementation is simple and low-cost. Simulation has also been carried out to verify the proposed algorithms. Since acceleration can only be modeled as state derivative in state space form and micro-accelerometer which is the state derivative sensor is getting more and more attentions in many microelectromechanical and nanoelectromechanical systems (MEMS/NEMS) applications, the proposed algorithms are suitable for MEMS/NEMS systems installed with micro-accelerometers.

关键词： Reciprocal State Space Form State derivative Measurement Feedback Explicit Model-Following Design Implicit Model-Following Design

Non-Linear Phase Tomography Based on Fréchet derivative

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Advances in Computed Tomography 2014年第4期3卷 39-50页

作者： Valentina Davidoiu Bruno Sixou Max Langer Franoise Peyrin Centre de Recherche en Acquisition et Traitement de l’Image pour la Santé (CREATIS) Centre National de la Recherche Scientifique Unité Mixte de Recherche 5220—Institut National de la Santé et de la Recherche Médicale Unité 1044—Université Lyon 1—Institut National des Sciences Appliquées de Lyon Lyon France Centre de Recherche en Acquisition et Traitement de l’Image pour la Santé (CREATIS) Centre National de la Recherche Scientifique Unité Mixte de Recherche 5220—Institut National de la Santé et de la Recherche Médicale Unité 1044—Université Lyon 1—Institut National des Sciences Appliquées de Lyon Lyon France European Synchrotron Radiation Facility Grenoble France

Phase imaging coupled to micro-tomography acquisition has emerged as a powerful tool to investigate specimens in a non-destructive manner. While the intensity data can be acquired and recorded, the phase information of the signal has to be “retrieved” from the data modulus only. Phase retrieval is an ill-posed non-linear problem and regularization techniques including a priori knowledge are necessary to obtain stable solutions. Several linear phase recovery methods have been proposed and it is expected that some limitations resulting from the linearization of the direct problem will be overcome by taking into account the non-linearity of the phase problem. To achieve this goal, we propose and evaluate a non-linear algorithm for in-line phase micro-tomography based on an iterative Landweber method with an analytic calculation of the Fréchet derivative of the phase-intensity relationship and of its adjoint. The algorithm was applied in the projection space using as initialization the linear mixed solution. The efficacy of the regularization scheme was evaluated on simulated objects with a slowly and a strongly varying phase. Experimental data were also acquired at ESRF using a propagation-based X-ray imaging technique for the given pixel size 0.68 μm. Two regularization scheme were considered: first the initialization was obtained without any prior on the ratio of the real and imaginary parts of the complex refractive index and secondly a constant a priori value was assumed on ?. The tomographic central slices of the refractive index decrement were compared and numerical evaluation was performed. The non-linear method globally decreases the reconstruction errors compared to the linear algorithm and is achieving better reconstruction results if no prior is introduced in the initialization solution. For in-line phase micro-tomography, this non-linear approach is a new and interesting method in biomedical studies where the exact value of the a priori ratio is not known.

关键词： Phase Retrieval In-Line Phase Tomography Inverse Problems Non-Linear Problem Non-Linear Optimization Fréchet derivative Coherent Imaging Fresnel Diffraction Phase Contrast X-Ray Imaging

Synthesis and Characterization of Benzothiazol derivative as a Corrosion Inhibitor for Carbon Steel in Seawater

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Materials Sciences and Applications 2015年第7期6卷 681-693页

作者： Abdulkareem Mohammed Ali Al-Sammarraie Khulood Abid Al-Saade Mohammed H. A. Al-Amery Department of Chemistry College of Science Baghdad University Baghdad Iraq

2(Benzo[d]thiazol-2-ylamino)-2-(2-hydroxy-phenyl) acetonitrile derivative was prepared and characterized using thin liquid chromatography, FTIR, 1H NMR and 13C NMR. The corrosion protectiveness, kinetics, and thermodynamics of the prepared derivative as inhibitor in artificial sea water/carbon steel (CK45) system were studied. Three concentrations of the prepared inhibitor were examined, namely, 10, 100, and 1000 ppm;protection efficiencies of 23% to 73% were recorded. It was found that the experimental data obtained from polarization reading could be fitted by Langmuir isotherm and Frumkin’s isotherm;the best fit adsorption isotherm was the Frumkin adsorption isotherm. The small negative value of ΔGads indicates the spontaneity of a physical adsorption process and the stability of the adsorbed layer on the carbon steel surface. Analysis of the temperature dependence of inhibition efficiency as well as comparison of corrosion activation in absence and in presence of the inhibitors gives some insight into the possible inhibition mechanism.

关键词： Corrosion Inhibition Benzothiazole derivative Corrosion Kinetics

Synthesis and Spectroscopic Properties of Ferrocenyl derivative Containing Donor and Acceptor Groups

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International Journal of Organic Chemistry 2017年第3期7卷 284-294页

作者： Makoto Minato Chiharu Sorai Takashi Ito Masashi Kiguchi Midori Kato Department of Materials Chemistry Faculty of Engineering Yokohama National University Yokohama Japan Advanced Research Laboratory Hitachi Ltd. Hatoyama Japan

Much interest has been devoted to organometallic NLO materials. We have become interested in exploring the utility of ferrocenyl group as the conjugating bridge. Thus, we synthesized 1-{{[1,3-(5-methylbenzo)dithiol]-2-yli- dene}methyl}-1’-[2-(p-nitrophenyl)-(E)-ethenyl]ferrocene (1). This new ferrocenyl compound has a donor and an acceptor group in 1,1’-positions. Investigations of the solvatochromic property of the compound revealed that it has polarized structure in a polar solvent, such as DMF. SHG efficiency of the compound was estimated by an SHEW (second-harmonic generation with the evanescent wave) method.

关键词： Nonlinear Optical Material Ferrocenyl derivative Solvatochromic Property SHG Efficiency

<i>L</i>-Stable Block Hybrid Second derivative Algorithm for Parabolic Partial Differential Equations

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American Journal of Computational Mathematics 2014年第2期4卷 87-92页

作者： Fidele Fouogang Ngwane Samuel Nemsefor Jator Department of Mathematics and Statistics Austin Peay State University Clarksville USA Department of Mathematics USC Salkehatchie Allendale USA

An L-stable block method based on hybrid second derivative algorithm (BHSDA) is provided by a continuous second derivative method that is defined for all values of the independent variable and applied to parabolic partial differential equations (PDEs). The use of the BHSDA to solve PDEs is facilitated by the method of lines which involves making an approximation to the space derivatives, and hence reducing the problem to that of solving a time-dependent system of first order initial value ordinary differential equations. The stability properties of the method is examined and some numerical results presented.

关键词： Hybrid Second derivative Method Off-Step Point Parabolic Partial Differential Equations

A New Definition for Generalized First derivative of Nonsmooth Functions

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Applied Mathematics 2011年第10期2卷 1252-1257页

作者： Ali Vahidian Kamyad Mohammad Hadi Noori Skandari Hamid Reza Erfanian 不详

In this paper, we define a functional optimization problem corresponding to smooth functions which its optimal solution is first derivative of these functions in a domain. These functional optimization problems are applied for non-smooth functions which by solving these problems we obtain a kind of generalized first derivatives. For this purpose, a linear programming problem corresponding functional optimization problem is obtained which their optimal solutions give the approximate generalized first derivative. We show the efficiency of our approach by obtaining derivative and generalized derivative of some smooth and nonsmooth functions respectively in some illustrative examples.

关键词： Generalized derivative Smooth and Nonsmooth Functions Fourier analysis Linear Programming Functional Optimization

Determination of Fenofibrate and the Degradation Product Using Simultaneous UV-derivative Spectrometric Method and HPLC

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American Journal of Analytical Chemistry 2011年第3期2卷 332-343页

作者： Fathy M. M. Salamaa Mohamed W. I. Nassar Mohie M. K. Sharaf El-Din Khalid A. M. Attia Mohamed Yousri Kaddah Department of Pharmaceutical Chemistry College of Pharmacy King Khalid University Abha 1882 Saudi Arabia

Two new selective, precise, and accurate methods were developed for the determination of fenofibrate in the presence of its basic degradation product. In the first method fenofibrate was determined using an algorithm bivariate calibration derivative method, in which an optimum pair of wavelengths was chosen for the determination of different binary mixtures. In the second method (HPLC), separation was achieved on RESTEK Pinnacle II phenyl column (5 μm, 250 × 4.6 mm) and Pinnacle II phenyl (5 μm, 10 × 4 mm) guard cartridge using a mobile phase consisting of methanol –0.1% phosphoric acid (60:40, v/v) at a flow rate 2 mL●min–1, and the column oven temperature was set at 50°C. The UV detector was time programmed at 302 nm and 289 nm for the internal standard (I.S.) and fenofibrate, respectively. The proposed methods were successfully applied for the determination of fenofibrate and its degradation product in the laboratory-prepared mixture and in pharmaceutical formulation. The assay results obtained using the bivariate method were statistically compared to those of the HPLC method and good agreement was observed.

关键词： Fenofibrate Stability Degradation Product UV derivative Spectrometric Method HPLC