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perturbed circuits</title> <meta name="description" content="Search results for: singularly perturbed circuits"> <meta name="keywords" content="singularly perturbed circuits"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button 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action="https://publications.waset.org/abstracts/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="singularly perturbed circuits"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 373</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: singularly perturbed circuits</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">373</span> One Period Loops of Memristive Circuits with Mixed-Mode Oscillations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Wieslaw%20Marszalek">Wieslaw Marszalek</a>, <a href="https://publications.waset.org/abstracts/search?q=Zdzislaw%20Trzaska"> Zdzislaw Trzaska</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Interesting properties of various one-period loops of singularly perturbed memristive circuits with mixed-mode oscillations (MMOs) are analyzed in this paper. The analysis is mixed, both analytical and numerical and focused on the properties of pinched hysteresis of the memristive element and other one-period loops formed by pairs of time-series solutions for various circuits' variables. The memristive element is the only nonlinear element in the two circuits. A theorem on periods of mixed-mode oscillations of the circuits is formulated and proved. Replacements of memristors by parallel G-C or series R-L circuits for a MMO response with equivalent RMS values is also discussed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=mixed-mode%20oscillations" title="mixed-mode oscillations">mixed-mode oscillations</a>, <a href="https://publications.waset.org/abstracts/search?q=memristive%20circuits" title=" memristive circuits"> memristive circuits</a>, <a href="https://publications.waset.org/abstracts/search?q=pinched%20hysteresis" title=" pinched hysteresis"> pinched hysteresis</a>, <a href="https://publications.waset.org/abstracts/search?q=one-period%20loops" title=" one-period loops"> one-period loops</a>, <a href="https://publications.waset.org/abstracts/search?q=singularly%20perturbed%20circuits" title=" singularly perturbed circuits"> singularly perturbed circuits</a> </p> <a href="https://publications.waset.org/abstracts/20949/one-period-loops-of-memristive-circuits-with-mixed-mode-oscillations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/20949.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">470</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">372</span> Solution of Singularly Perturbed Differential Difference Equations Using Liouville Green Transformation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Y.%20N.%20Reddy">Y. N. Reddy</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The class of differential-difference equations which have characteristics of both classes, i.e., delay/advance and singularly perturbed behaviour is known as singularly perturbed differential-difference equations. The expression ‘positive shift’ and ‘negative shift’ are also used for ‘advance’ and ‘delay’ respectively. In general, an ordinary differential equation in which the highest order derivative is multiplied by a small positive parameter and containing at least one delay/advance is known as singularly perturbed differential-difference equation. Singularly perturbed differential-difference equations arise in the modelling of various practical phenomena in bioscience, engineering, control theory, specifically in variational problems, in describing the human pupil-light reflex, in a variety of models for physiological processes or diseases and first exit time problems in the modelling of the determination of expected time for the generation of action potential in nerve cells by random synaptic inputs in dendrites. In this paper, we envisage the use of Liouville Green Transformation to find the solution of singularly perturbed differential difference equations. First, using Taylor series, the given singularly perturbed differential difference equation is approximated by an asymptotically equivalent singularly perturbation problem. Then the Liouville Green Transformation is applied to get the solution. Several model examples are solved, and the results are compared with other methods. It is observed that the present method gives better approximate solutions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=difference%20equations" title="difference equations">difference equations</a>, <a href="https://publications.waset.org/abstracts/search?q=differential%20equations" title=" differential equations"> differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=singular%20perturbations" title=" singular perturbations"> singular perturbations</a>, <a href="https://publications.waset.org/abstracts/search?q=boundary%20layer" title=" boundary layer"> boundary layer</a> </p> <a href="https://publications.waset.org/abstracts/86176/solution-of-singularly-perturbed-differential-difference-equations-using-liouville-green-transformation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/86176.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">199</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">371</span> Spline Solution of Singularly Perturbed Boundary Value Problems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Reza%20Mohammadi">Reza Mohammadi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Using quartic spline, we develop a method for numerical solution of singularly perturbed two-point boundary-value problems. The purposed method is fourth-order accurate and applicable to problems both in singular and non-singular cases. The convergence analysis of the method is given. The resulting linear system of equations has been solved by using a tri-diagonal solver. We applied the presented method to test problems which have been solved by other existing methods in references, for comparison of presented method with the existing methods. Numerical results are given to illustrate the efficiency of our methods. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=second-order%20ordinary%20differential%20equation" title="second-order ordinary differential equation">second-order ordinary differential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=singularly-perturbed" title=" singularly-perturbed"> singularly-perturbed</a>, <a href="https://publications.waset.org/abstracts/search?q=quartic%20spline" title=" quartic spline"> quartic spline</a>, <a href="https://publications.waset.org/abstracts/search?q=convergence%20analysis" title=" convergence analysis"> convergence analysis</a> </p> <a href="https://publications.waset.org/abstracts/56960/spline-solution-of-singularly-perturbed-boundary-value-problems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/56960.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">295</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">370</span> Quartic Spline Method for Numerical Solution of Self-Adjoint Singularly Perturbed Boundary Value Problems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Reza%20Mohammadi">Reza Mohammadi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Using quartic spline, we develop a method for numerical solution of singularly perturbed two-point boundary-value problems. The purposed method is fourth-order accurate and applicable to problems both in singular and non-singular cases. The convergence analysis of the method is given. The resulting linear system of equations has been solved by using a tri-diagonal solver. We applied the presented method to test problems which have been solved by other existing methods in references, for comparison of presented method with the existing methods. Numerical results are given to illustrate the efficiency of our methods. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=second-order%20ordinary%20differential%20equation" title="second-order ordinary differential equation">second-order ordinary differential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=singularly-perturbed" title=" singularly-perturbed"> singularly-perturbed</a>, <a href="https://publications.waset.org/abstracts/search?q=quartic%20spline" title=" quartic spline"> quartic spline</a>, <a href="https://publications.waset.org/abstracts/search?q=convergence%20analysis" title=" convergence analysis"> convergence analysis</a> </p> <a href="https://publications.waset.org/abstracts/46459/quartic-spline-method-for-numerical-solution-of-self-adjoint-singularly-perturbed-boundary-value-problems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/46459.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">360</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">369</span> A Uniformly Convergent Numerical Scheme for a Singularly Perturbed Volterra Integrodifferential Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Nana%20Adjoah%20Mbroh">Nana Adjoah Mbroh</a>, <a href="https://publications.waset.org/abstracts/search?q=Suares%20Clovis%20Oukouomi%20Noutchie"> Suares Clovis Oukouomi Noutchie</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Singularly perturbed problems are parameter dependent problems, and they play major roles in the modelling of real-life situational problems in applied sciences. Thus, designing efficient numerical schemes to solve these problems is of much interest since the exact solutions of such problems may not even exist. Generally, singularly perturbed problems are identified by a small parameter multiplying at least the highest derivative in the equation. The presence of this parameter causes the solution of these problems to be characterized by rapid oscillations. This unique feature renders classical numerical schemes inefficient since they are unable to capture the behaviour of the exact solution in the part of the domain where the rapid oscillations are present. In this paper, a numerical scheme is proposed to solve a singularly perturbed Volterra Integro-differential equation. The scheme is based on the midpoint rule and employs the non-standard finite difference scheme to solve the differential part whilst the composite trapezoidal rule is used for the integral part. A fully fledged error estimate is performed, and Richardson extrapolation is applied to accelerate the convergence of the scheme. Numerical simulations are conducted to confirm the theoretical findings before and after extrapolation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=midpoint%20rule" title="midpoint rule">midpoint rule</a>, <a href="https://publications.waset.org/abstracts/search?q=non-standard%20finite%20difference%20schemes" title=" non-standard finite difference schemes"> non-standard finite difference schemes</a>, <a href="https://publications.waset.org/abstracts/search?q=Richardson%20extrapolation" title=" Richardson extrapolation"> Richardson extrapolation</a>, <a href="https://publications.waset.org/abstracts/search?q=singularly%20perturbed%20problems" title=" singularly perturbed problems"> singularly perturbed problems</a>, <a href="https://publications.waset.org/abstracts/search?q=trapezoidal%20rule" title=" trapezoidal rule"> trapezoidal rule</a>, <a href="https://publications.waset.org/abstracts/search?q=uniform%20convergence" title=" uniform convergence"> uniform convergence</a> </p> <a href="https://publications.waset.org/abstracts/151972/a-uniformly-convergent-numerical-scheme-for-a-singularly-perturbed-volterra-integrodifferential-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/151972.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">125</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">368</span> Singular Perturbed Vector Field Method Applied to the Problem of Thermal Explosion of Polydisperse Fuel Spray</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ophir%20Nave">Ophir Nave</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In our research, we present the concept of singularly perturbed vector field (SPVF) method, and its application to thermal explosion of diesel spray combustion. Given a system of governing equations, which consist of hidden Multi-scale variables, the SPVF method transfer and decompose such system to fast and slow singularly perturbed subsystems (SPS). The SPVF method enables us to understand the complex system, and simplify the calculations. Later powerful analytical, numerical and asymptotic methods (e.g method of integral (invariant) manifold (MIM), the homotopy analysis method (HAM) etc.) can be applied to each subsystem. We compare the results obtained by the methods of integral invariant manifold and SPVF apply to spray droplets combustion model. The research deals with the development of an innovative method for extracting fast and slow variables in physical mathematical models. The method that we developed called singular perturbed vector field. This method based on a numerical algorithm applied to global quasi linearization applied to given physical model. The SPVF method applied successfully to combustion processes. Our results were compared to experimentally results. The SPVF is a general numerical and asymptotical method that reveals the hierarchy (multi-scale system) of a given system. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=polydisperse%20spray" title="polydisperse spray">polydisperse spray</a>, <a href="https://publications.waset.org/abstracts/search?q=model%20reduction" title=" model reduction"> model reduction</a>, <a href="https://publications.waset.org/abstracts/search?q=asymptotic%20analysis" title=" asymptotic analysis"> asymptotic analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=multi-scale%20systems" title=" multi-scale systems"> multi-scale systems</a> </p> <a href="https://publications.waset.org/abstracts/71377/singular-perturbed-vector-field-method-applied-to-the-problem-of-thermal-explosion-of-polydisperse-fuel-spray" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/71377.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">219</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">367</span> Robust Numerical Method for Singularly Perturbed Semilinear Boundary Value Problem with Nonlocal Boundary Condition</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Habtamu%20Garoma%20Debela">Habtamu Garoma Debela</a>, <a href="https://publications.waset.org/abstracts/search?q=Gemechis%20File%20Duressa"> Gemechis File Duressa</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, our primary interest is to provide ε-uniformly convergent numerical techniques for solving singularly perturbed semilinear boundary value problems with non-local boundary condition. These singular perturbation problems are described by differential equations in which the highest-order derivative is multiplied by an arbitrarily small parameter ε (say) known as singular perturbation parameter. This leads to the existence of boundary layers, which are basically narrow regions in the neighborhood of the boundary of the domain, where the gradient of the solution becomes steep as the perturbation parameter tends to zero. Due to the appearance of the layer phenomena, it is a challenging task to provide ε-uniform numerical methods. The term 'ε-uniform' refers to identify those numerical methods in which the approximate solution converges to the corresponding exact solution (measured to the supremum norm) independently with respect to the perturbation parameter ε. Thus, the purpose of this work is to develop, analyze, and improve the ε-uniform numerical methods for solving singularly perturbed problems. These methods are based on nonstandard fitted finite difference method. The basic idea behind the fitted operator, finite difference method, is to replace the denominator functions of the classical derivatives with positive functions derived in such a way that they capture some notable properties of the governing differential equation. A uniformly convergent numerical method is constructed via nonstandard fitted operator numerical method and numerical integration methods to solve the problem. The non-local boundary condition is treated using numerical integration techniques. Additionally, Richardson extrapolation technique, which improves the first-order accuracy of the standard scheme to second-order convergence, is applied for singularly perturbed convection-diffusion problems using the proposed numerical method. Maximum absolute errors and rates of convergence for different values of perturbation parameter and mesh sizes are tabulated for the numerical example considered. The method is shown to be ε-uniformly convergent. Finally, extensive numerical experiments are conducted which support all of our theoretical findings. A concise conclusion is provided at the end of this work. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=nonlocal%20boundary%20condition" title="nonlocal boundary condition">nonlocal boundary condition</a>, <a href="https://publications.waset.org/abstracts/search?q=nonstandard%20fitted%20operator" title=" nonstandard fitted operator"> nonstandard fitted operator</a>, <a href="https://publications.waset.org/abstracts/search?q=semilinear%20problem" title=" semilinear problem"> semilinear problem</a>, <a href="https://publications.waset.org/abstracts/search?q=singular%20perturbation" title=" singular perturbation"> singular perturbation</a>, <a href="https://publications.waset.org/abstracts/search?q=uniformly%20convergent" title=" uniformly convergent"> uniformly convergent</a> </p> <a href="https://publications.waset.org/abstracts/130967/robust-numerical-method-for-singularly-perturbed-semilinear-boundary-value-problem-with-nonlocal-boundary-condition" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/130967.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">143</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">366</span> Polynomial Chaos Expansion Combined with Exponential Spline for Singularly Perturbed Boundary Value Problems with Random Parameter</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=W.%20K.%20Zahra">W. K. Zahra</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20A.%20El-Beltagy"> M. A. El-Beltagy</a>, <a href="https://publications.waset.org/abstracts/search?q=R.%20R.%20Elkhadrawy"> R. R. Elkhadrawy</a> </p> <p class="card-text"><strong>Abstract:</strong></p> So many practical problems in science and technology developed over the past decays. For instance, the mathematical boundary layer theory or the approximation of solution for different problems described by differential equations. When such problems consider large or small parameters, they become increasingly complex and therefore require the use of asymptotic methods. In this work, we consider the singularly perturbed boundary value problems which contain very small parameters. Moreover, we will consider these perturbation parameters as random variables. We propose a numerical method to solve this kind of problems. The proposed method is based on an exponential spline, Shishkin mesh discretization, and polynomial chaos expansion. The polynomial chaos expansion is used to handle the randomness exist in the perturbation parameter. Furthermore, the Monte Carlo Simulations (MCS) are used to validate the solution and the accuracy of the proposed method. Numerical results are provided to show the applicability and efficiency of the proposed method, which maintains a very remarkable high accuracy and it is ε-uniform convergence of almost second order. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=singular%20perturbation%20problem" title="singular perturbation problem">singular perturbation problem</a>, <a href="https://publications.waset.org/abstracts/search?q=polynomial%20chaos%20expansion" title=" polynomial chaos expansion"> polynomial chaos expansion</a>, <a href="https://publications.waset.org/abstracts/search?q=Shishkin%20mesh" title=" Shishkin mesh"> Shishkin mesh</a>, <a href="https://publications.waset.org/abstracts/search?q=two%20small%20parameters" title=" two small parameters"> two small parameters</a>, <a href="https://publications.waset.org/abstracts/search?q=exponential%20spline" title=" exponential spline"> exponential spline</a> </p> <a href="https://publications.waset.org/abstracts/100441/polynomial-chaos-expansion-combined-with-exponential-spline-for-singularly-perturbed-boundary-value-problems-with-random-parameter" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/100441.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">160</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">365</span> Probabilistic Modeling Laser Transmitter</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=H.%20S.%20Kang">H. S. Kang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Coupled electrical and optical model for conversion of electrical energy into coherent optical energy for transmitter-receiver link by solid state device is presented. Probability distribution for travelling laser beam switching time intervals and the number of switchings in the time interval is obtained. Selector function mapping is employed to regulate optical data transmission speed. It is established that regulated laser transmission from PhotoActive Laser transmitter follows principal of invariance. This considerably simplifies design of PhotoActive Laser Transmission networks. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=computational%20mathematics" title="computational mathematics">computational mathematics</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20difference%20Markov%20chain%20methods" title=" finite difference Markov chain methods"> finite difference Markov chain methods</a>, <a href="https://publications.waset.org/abstracts/search?q=sequence%20spaces" title=" sequence spaces"> sequence spaces</a>, <a href="https://publications.waset.org/abstracts/search?q=singularly%20perturbed%20differential%20equations" title=" singularly perturbed differential equations"> singularly perturbed differential equations</a> </p> <a href="https://publications.waset.org/abstracts/8445/probabilistic-modeling-laser-transmitter" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/8445.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">431</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">364</span> Exponential Spline Solution for Singularly Perturbed Boundary Value Problems with an Uncertain-But-Bounded Parameter </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Waheed%20Zahra">Waheed Zahra</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohamed%20El-Beltagy"> Mohamed El-Beltagy</a>, <a href="https://publications.waset.org/abstracts/search?q=Ashraf%20El%20Mhlawy"> Ashraf El Mhlawy</a>, <a href="https://publications.waset.org/abstracts/search?q=Reda%20Elkhadrawy"> Reda Elkhadrawy</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we consider singular perturbation reaction-diffusion boundary value problems, which contain a small uncertain perturbation parameter. To solve these problems, we propose a numerical method which is based on an exponential spline and Shishkin mesh discretization. While interval analysis principle is used to deal with the uncertain parameter, sensitivity analysis has been conducted using different methods. Numerical results are provided to show the applicability and efficiency of our method, which is ε-uniform convergence of almost second order. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=singular%20perturbation%20problem" title="singular perturbation problem">singular perturbation problem</a>, <a href="https://publications.waset.org/abstracts/search?q=shishkin%20mesh" title=" shishkin mesh"> shishkin mesh</a>, <a href="https://publications.waset.org/abstracts/search?q=two%20small%20parameters" title=" two small parameters"> two small parameters</a>, <a href="https://publications.waset.org/abstracts/search?q=exponential%20spline" title=" exponential spline"> exponential spline</a>, <a href="https://publications.waset.org/abstracts/search?q=interval%20analysis" title=" interval analysis"> interval analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=sensitivity%20analysis" title=" sensitivity analysis"> sensitivity analysis</a> </p> <a href="https://publications.waset.org/abstracts/91560/exponential-spline-solution-for-singularly-perturbed-boundary-value-problems-with-an-uncertain-but-bounded-parameter" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/91560.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">274</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">363</span> Stochastic Control of Decentralized Singularly Perturbed Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Walid%20S.%20Alfuhaid">Walid S. Alfuhaid</a>, <a href="https://publications.waset.org/abstracts/search?q=Saud%20A.%20Alghamdi"> Saud A. Alghamdi</a>, <a href="https://publications.waset.org/abstracts/search?q=John%20M.%20Watkins"> John M. Watkins</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Edwin%20Sawan"> M. Edwin Sawan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Designing a controller for stochastic decentralized interconnected large scale systems usually involves a high degree of complexity and computation ability. Noise, observability, and controllability of all system states, connectivity, and channel bandwidth are other constraints to design procedures for distributed large scale systems. The quasi-steady state model investigated in this paper is a reduced order model of the original system using singular perturbation techniques. This paper results in an optimal control synthesis to design an observer based feedback controller by standard stochastic control theory techniques using Linear Quadratic Gaussian (LQG) approach and Kalman filter design with less complexity and computation requirements. Numerical example is given at the end to demonstrate the efficiency of the proposed method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=decentralized" title="decentralized">decentralized</a>, <a href="https://publications.waset.org/abstracts/search?q=optimal%20control" title=" optimal control"> optimal control</a>, <a href="https://publications.waset.org/abstracts/search?q=output" title=" output"> output</a>, <a href="https://publications.waset.org/abstracts/search?q=singular%20perturb" title=" singular perturb"> singular perturb</a> </p> <a href="https://publications.waset.org/abstracts/45093/stochastic-control-of-decentralized-singularly-perturbed-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/45093.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">370</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">362</span> Modelling of Polymeric Fluid Flows between Two Coaxial Cylinders Taking into Account the Heat Dissipation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Alexander%20Blokhin">Alexander Blokhin</a>, <a href="https://publications.waset.org/abstracts/search?q=Ekaterina%20Kruglova"> Ekaterina Kruglova</a>, <a href="https://publications.waset.org/abstracts/search?q=Boris%20Semisalov"> Boris Semisalov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Mathematical model based on the mesoscopic theory of polymer dynamics is developed for numerical simulation of the flows of polymeric liquid between two coaxial cylinders. This model is a system of nonlinear partial differential equations written in the cylindrical coordinate system and coupled with the heat conduction equation including a specific dissipation term. The stationary flows similar to classical Poiseuille ones are considered, and the resolving equations for the velocity of flow and for the temperature are obtained. For solving them, a fast pseudospectral method is designed based on Chebyshev approximations, that enables one to simulate the flows through the channels with extremely small relative values of the radius of inner cylinder. The numerical analysis of the dependance of flow on this radius and on the values of dissipation constant is done. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=dynamics%20of%20polymeric%20liquid" title="dynamics of polymeric liquid">dynamics of polymeric liquid</a>, <a href="https://publications.waset.org/abstracts/search?q=heat%20dissipation" title=" heat dissipation"> heat dissipation</a>, <a href="https://publications.waset.org/abstracts/search?q=singularly%20perturbed%20problem" title=" singularly perturbed problem"> singularly perturbed problem</a>, <a href="https://publications.waset.org/abstracts/search?q=pseudospectral%20method" title=" pseudospectral method"> pseudospectral method</a>, <a href="https://publications.waset.org/abstracts/search?q=Chebyshev%20polynomials" title=" Chebyshev polynomials"> Chebyshev polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=stabilization%20technique" title=" stabilization technique"> stabilization technique</a> </p> <a href="https://publications.waset.org/abstracts/85108/modelling-of-polymeric-fluid-flows-between-two-coaxial-cylinders-taking-into-account-the-heat-dissipation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/85108.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">290</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">361</span> Synchronization of a Perturbed Satellite Attitude Motion</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sadaoui%20Djaouida">Sadaoui Djaouida</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the predictive control method is proposed to control the synchronization of two perturbed satellites attitude motion. Based on delayed feedback control of continuous-time systems combines with the prediction-based method of discrete-time systems, this approach only needs a single controller to realize synchronization, which has considerable significance in reducing the cost and complexity for controller implementation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=predictive%20control" title="predictive control">predictive control</a>, <a href="https://publications.waset.org/abstracts/search?q=synchronization" title=" synchronization"> synchronization</a>, <a href="https://publications.waset.org/abstracts/search?q=satellite%20attitude" title=" satellite attitude"> satellite attitude</a>, <a href="https://publications.waset.org/abstracts/search?q=control%20engineering" title=" control engineering"> control engineering</a> </p> <a href="https://publications.waset.org/abstracts/7615/synchronization-of-a-perturbed-satellite-attitude-motion" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/7615.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">555</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">360</span> Efficient Study of Substrate Integrated Waveguide Devices</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=J.%20Hajri">J. Hajri</a>, <a href="https://publications.waset.org/abstracts/search?q=H.%20Hrizi"> H. Hrizi</a>, <a href="https://publications.waset.org/abstracts/search?q=N.%20Sboui"> N. Sboui</a>, <a href="https://publications.waset.org/abstracts/search?q=H.%20Baudrand"> H. Baudrand</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents a study of SIW circuits (Substrate Integrated Waveguide) with a rigorous and fast original approach based on Iterative process (WCIP). The theoretical suggested study is validated by the simulation of two different examples of SIW circuits. The obtained results are in good agreement with those of measurement and with software HFSS. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=convergence%20study" title="convergence study">convergence study</a>, <a href="https://publications.waset.org/abstracts/search?q=HFSS" title=" HFSS"> HFSS</a>, <a href="https://publications.waset.org/abstracts/search?q=modal%20decomposition" title=" modal decomposition"> modal decomposition</a>, <a href="https://publications.waset.org/abstracts/search?q=SIW%20circuits" title=" SIW circuits"> SIW circuits</a>, <a href="https://publications.waset.org/abstracts/search?q=WCIP%20method" title=" WCIP method"> WCIP method</a> </p> <a href="https://publications.waset.org/abstracts/22247/efficient-study-of-substrate-integrated-waveguide-devices" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/22247.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">498</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">359</span> Two Kinds of Self-Oscillating Circuits Mechanically Demonstrated</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shiang-Hwua%20Yu">Shiang-Hwua Yu</a>, <a href="https://publications.waset.org/abstracts/search?q=Po-Hsun%20Wu"> Po-Hsun Wu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This study introduces two types of self-oscillating circuits that are frequently found in power electronics applications. Special effort is made to relate the circuits to the analogous mechanical systems of some important scientific inventions: Galileo’s pendulum clock and Coulomb’s friction model. A little touch of related history and philosophy of science will hopefully encourage curiosity, advance the understanding of self-oscillating systems and satisfy the aspiration of some students for scientific literacy. Finally, the two self-oscillating circuits are applied to design a simple class-D audio amplifier. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=self-oscillation" title="self-oscillation">self-oscillation</a>, <a href="https://publications.waset.org/abstracts/search?q=sigma-delta%20modulator" title=" sigma-delta modulator"> sigma-delta modulator</a>, <a href="https://publications.waset.org/abstracts/search?q=pendulum%20clock" title=" pendulum clock"> pendulum clock</a>, <a href="https://publications.waset.org/abstracts/search?q=Coulomb%20friction" title=" Coulomb friction"> Coulomb friction</a>, <a href="https://publications.waset.org/abstracts/search?q=class-D%20amplifier" title=" class-D amplifier"> class-D amplifier</a> </p> <a href="https://publications.waset.org/abstracts/9932/two-kinds-of-self-oscillating-circuits-mechanically-demonstrated" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/9932.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">356</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">358</span> Optimization and Design of Current-Mode Multiplier Circuits with Applications in Analog Signal Processing for Gas Industrial Package Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohamad%20Baqer%20Heidari">Mohamad Baqer Heidari</a>, <a href="https://publications.waset.org/abstracts/search?q=Hefzollah.Mohammadian"> Hefzollah.Mohammadian </a> </p> <p class="card-text"><strong>Abstract:</strong></p> This brief presents two original implementations of improved accuracy current-mode multiplier/divider circuits. Besides the advantage of their simplicity, these original multiplier/divider structures present the advantage of very small linearity errors that can be obtained as a result of the proposed design techniques (0.75% and 0.9%, respectively, for an extended range of the input currents). The original multiplier/divider circuits permit a facile reconfiguration, the presented structures representing the functional basis for implementing complex function synthesizer circuits. The proposed computational structures are designed for implementing in 0.18-µm CMOS technology, with a low-voltage operation (a supply voltage of 1.2 V). The circuits’ power consumptions are 60 and 75 µW, respectively, while their frequency bandwidths are 79.6 and 59.7 MHz, respectively. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=analog%20signal%20processing" title="analog signal processing">analog signal processing</a>, <a href="https://publications.waset.org/abstracts/search?q=current-mode%20%20operation" title=" current-mode operation"> current-mode operation</a>, <a href="https://publications.waset.org/abstracts/search?q=functional%20core" title=" functional core"> functional core</a>, <a href="https://publications.waset.org/abstracts/search?q=multiplier" title=" multiplier"> multiplier</a>, <a href="https://publications.waset.org/abstracts/search?q=reconfigurable%20circuits" title=" reconfigurable circuits"> reconfigurable circuits</a>, <a href="https://publications.waset.org/abstracts/search?q=industrial%20package%20systems" title=" industrial package systems"> industrial package systems</a> </p> <a href="https://publications.waset.org/abstracts/36406/optimization-and-design-of-current-mode-multiplier-circuits-with-applications-in-analog-signal-processing-for-gas-industrial-package-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/36406.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">374</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">357</span> Comparative Performance Analysis of Nonlinearity Cancellation Techniques for MOS-C Realization in Integrator Circuits</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hasan%20%C3%87i%C3%A7ekli">Hasan Çiçekli</a>, <a href="https://publications.waset.org/abstracts/search?q=Ahmet%20G%C3%B6k%C3%A7en"> Ahmet Gökçen</a>, <a href="https://publications.waset.org/abstracts/search?q=U%C4%9Fur%20%C3%87am"> Uğur Çam</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a comparative performance analysis of mostly used four nonlinearity cancellation techniques used to realize the passive resistor by MOS transistors is presented. The comparison is done by using an integrator circuit which is employing sequentially Op-amp, OTRA and ICCII as active element. All of the circuits are implemented by MOS-C realization and simulated by PSPICE program using 0.35 µm process TSMC MOSIS model parameters. With MOS-C realization, the circuits became electronically tunable and fully integrable which is very important in IC design. The output waveforms, frequency responses, THD analysis results and features of the nonlinearity cancellation techniques are also given. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=integrator%20circuits" title="integrator circuits">integrator circuits</a>, <a href="https://publications.waset.org/abstracts/search?q=MOS-C%20realization" title=" MOS-C realization"> MOS-C realization</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinearity%20cancellation" title=" nonlinearity cancellation"> nonlinearity cancellation</a>, <a href="https://publications.waset.org/abstracts/search?q=tuneable%20resistors" title=" tuneable resistors"> tuneable resistors</a> </p> <a href="https://publications.waset.org/abstracts/38167/comparative-performance-analysis-of-nonlinearity-cancellation-techniques-for-mos-c-realization-in-integrator-circuits" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/38167.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">533</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">356</span> Effect of the Structural Parameters on Subbands of Fibonacci AlxGa1-xAs/GaAs Superlattices</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Y.%20Sefir">Y. Sefir</a>, <a href="https://publications.waset.org/abstracts/search?q=Z.%20Aziz"> Z. Aziz</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Cherid"> S. Cherid</a>, <a href="https://publications.waset.org/abstracts/search?q=Z.%20F.%20Meghoufel"> Z. F. Meghoufel</a>, <a href="https://publications.waset.org/abstracts/search?q=F.%20Bendahama"> F. Bendahama</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Terkhi"> S. Terkhi</a>, <a href="https://publications.waset.org/abstracts/search?q=B.%20Bouadjemi.%20A.%20Zitouni%20S.%20Bentata"> B. Bouadjemi. A. Zitouni S. Bentata</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This work is to study the effect of the variation of structural parameters on the band structure in the quasiperiodic Fibonacci superlattices AlxGa1-xAs/GaAs using the formalism of the transfer matrix and Airy function. Our results show that increasing the width of Fibonacci’s wells of allows to the confinement of subminibands with a widening of minigaps, this causes a consistent and coherent fragmentation. The barrier thickness of Fibonacci bf acts on the width of subminibands by controlling the interaction force between neighboring eigenstates. Its increase gives rise to singularly extended states. The barrier height Fibonacci Vf permit to control the degree of structural disorder in these structures. The variation of these parameters permits the design of laser with modulated wavelength. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=transmission%20coefficient%20%E2%80%93%20Quasiperiodic%20superlattices-%20singularly%20localized%20and%20extended%20states-%20structural%20parameters-%20Laser%20with%20modulated%20wavelength" title="transmission coefficient – Quasiperiodic superlattices- singularly localized and extended states- structural parameters- Laser with modulated wavelength">transmission coefficient – Quasiperiodic superlattices- singularly localized and extended states- structural parameters- Laser with modulated wavelength</a> </p> <a href="https://publications.waset.org/abstracts/39812/effect-of-the-structural-parameters-on-subbands-of-fibonacci-alxga1-xasgaas-superlattices" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/39812.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">374</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">355</span> Tamper Resistance Evaluation Tests with Noise Resources</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Masaya%20Yoshikawa">Masaya Yoshikawa</a>, <a href="https://publications.waset.org/abstracts/search?q=Toshiya%20Asai"> Toshiya Asai</a>, <a href="https://publications.waset.org/abstracts/search?q=Ryoma%20Matsuhisa"> Ryoma Matsuhisa</a>, <a href="https://publications.waset.org/abstracts/search?q=Yusuke%20Nozaki"> Yusuke Nozaki</a>, <a href="https://publications.waset.org/abstracts/search?q=Kensaku%20Asahi"> Kensaku Asahi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Recently, side-channel attacks, which estimate secret keys using side-channel information such as power consumption and compromising emanations of cryptography circuits embedded in hardware, have become a serious problem. In particular, electromagnetic analysis attacks against cryptographic circuits between information processing and electromagnetic fields, which are related to secret keys in cryptography circuits, are the most threatening side-channel attacks. Therefore, it is important to evaluate tamper resistance against electromagnetic analysis attacks for cryptography circuits. The present study performs basic examination of the tamper resistance of cryptography circuits using electromagnetic analysis attacks with noise resources. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=tamper%20resistance" title="tamper resistance">tamper resistance</a>, <a href="https://publications.waset.org/abstracts/search?q=cryptographic%20circuit" title=" cryptographic circuit"> cryptographic circuit</a>, <a href="https://publications.waset.org/abstracts/search?q=hardware%20security%20evaluation" title=" hardware security evaluation"> hardware security evaluation</a>, <a href="https://publications.waset.org/abstracts/search?q=noise%20resources" title=" noise resources "> noise resources </a> </p> <a href="https://publications.waset.org/abstracts/25852/tamper-resistance-evaluation-tests-with-noise-resources" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/25852.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">504</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">354</span> Memristor-A Promising Candidate for Neural Circuits in Neuromorphic Computing Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Juhi%20Faridi">Juhi Faridi</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohd.%20Ajmal%20Kafeel"> Mohd. Ajmal Kafeel</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The advancements in the field of Artificial Intelligence (AI) and technology has led to an evolution of an intelligent era. Neural networks, having the computational power and learning ability similar to the brain is one of the key AI technologies. Neuromorphic computing system (NCS) consists of the synaptic device, neuronal circuit, and neuromorphic architecture. Memristor are a promising candidate for neuromorphic computing systems, but when it comes to neuromorphic computing, the conductance behavior of the synaptic memristor or neuronal memristor needs to be studied thoroughly in order to fathom the neuroscience or computer science. Furthermore, there is a need of more simulation work for utilizing the existing device properties and providing guidance to the development of future devices for different performance requirements. Hence, development of NCS needs more simulation work to make use of existing device properties. This work aims to provide an insight to build neuronal circuits using memristors to achieve a Memristor based NCS.  Here we throw a light on the research conducted in the field of memristors for building analog and digital circuits in order to motivate the research in the field of NCS by building memristor based neural circuits for advanced AI applications. This literature is a step in the direction where we describe the various Key findings about memristors and its analog and digital circuits implemented over the years which can be further utilized in implementing the neuronal circuits in the NCS. This work aims to help the electronic circuit designers to understand how the research progressed in memristors and how these findings can be used in implementing the neuronal circuits meant for the recent progress in the NCS. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=analog%20circuits" title="analog circuits">analog circuits</a>, <a href="https://publications.waset.org/abstracts/search?q=digital%20circuits" title=" digital circuits"> digital circuits</a>, <a href="https://publications.waset.org/abstracts/search?q=memristors" title=" memristors"> memristors</a>, <a href="https://publications.waset.org/abstracts/search?q=neuromorphic%20computing%20systems" title=" neuromorphic computing systems"> neuromorphic computing systems</a> </p> <a href="https://publications.waset.org/abstracts/100057/memristor-a-promising-candidate-for-neural-circuits-in-neuromorphic-computing-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/100057.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">174</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">353</span> A Sliding Mesh Technique and Compressibility Correction Effects of Two-Equation Turbulence Models for a Pintle-Perturbed Flow Analysis</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=J.%20Y.%20Heo">J. Y. Heo</a>, <a href="https://publications.waset.org/abstracts/search?q=H.%20G.%20Sung"> H. G. Sung</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Numerical simulations have been performed for assessment of compressibility correction of two-equation turbulence models suitable for large scale separation flows perturbed by pintle strokes. In order to take into account pintle movement, a sliding mesh method was applied. The chamber pressure, mass flow rate, and thrust have been analyzed, and the response lag and sensitivity at the chamber and nozzle were estimated for a movable pintle. The nozzle performance for pintle reciprocating as its insertion and extraction processes, were analyzed to better understand the dynamic performance of the pintle nozzle. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=pintle" title="pintle">pintle</a>, <a href="https://publications.waset.org/abstracts/search?q=sliding%20mesh" title=" sliding mesh"> sliding mesh</a>, <a href="https://publications.waset.org/abstracts/search?q=turbulent%20model" title=" turbulent model"> turbulent model</a>, <a href="https://publications.waset.org/abstracts/search?q=compressibility%20correction" title=" compressibility correction"> compressibility correction</a> </p> <a href="https://publications.waset.org/abstracts/3296/a-sliding-mesh-technique-and-compressibility-correction-effects-of-two-equation-turbulence-models-for-a-pintle-perturbed-flow-analysis" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/3296.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">489</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">352</span> Characteization and Optimization of S-Parameters of Microwave Circuits</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=N.%20Ourabia">N. Ourabia</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Boubaker%20Ourabia"> M. Boubaker Ourabia</a> </p> <p class="card-text"><strong>Abstract:</strong></p> An approach for modeling and numerical simulation of passive planar structures using the edge line concept is developed. With this method, we develop an efficient modeling technique for microstrip discontinuities. The technique obtains closed form expressions for the equivalent circuits which are used to model these discontinuities. Then, it would be easy to handle and to characterize complicated structures like T and Y junctions, truncated junctions, arbitrarily shaped junctions, cascading junctions and more generally planar multiport junctions. Another advantage of this method is that the edge line concept for arbitrary shape junctions operates with real parameters circuits. The validity of the method was further confirmed by comparing our results for various discontinuities (bend, filters) with those from HFSS as well as from other published sources. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=optimization" title="optimization">optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=CAD%20analysis" title=" CAD analysis"> CAD analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=microwave%20circuits" title=" microwave circuits"> microwave circuits</a>, <a href="https://publications.waset.org/abstracts/search?q=S-parameters" title=" S-parameters"> S-parameters</a> </p> <a href="https://publications.waset.org/abstracts/25946/characteization-and-optimization-of-s-parameters-of-microwave-circuits" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/25946.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">454</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">351</span> Paper-Based Detection Using Synthetic Gene Circuits</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Vanessa%20Funk">Vanessa Funk</a>, <a href="https://publications.waset.org/abstracts/search?q=Steven%20Blum"> Steven Blum</a>, <a href="https://publications.waset.org/abstracts/search?q=Stephanie%20Cole"> Stephanie Cole</a>, <a href="https://publications.waset.org/abstracts/search?q=Jorge%20Maciel"> Jorge Maciel</a>, <a href="https://publications.waset.org/abstracts/search?q=Matthew%20Lux"> Matthew Lux</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Paper-based synthetic gene circuits offer a new paradigm for programmable, fieldable biodetection. We demonstrate that by freeze-drying gene circuits with in vitro expression machinery, we can use complimentary RNA sequences to trigger colorimetric changes upon rehydration. We have successfully utilized both green fluorescent protein and luciferase-based reporters for easy visualization purposes in solution. Through several efforts, we are aiming to use this new platform technology to address a variety of needs in portable detection by demonstrating several more expression and reporter systems for detection functions on paper. In addition to RNA-based biodetection, we are exploring the use of various mechanisms that cells use to respond to environmental conditions to move towards all-hazards detection. Examples include explosives, heavy metals for water quality, and toxic chemicals. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=cell-free%20lysates" title="cell-free lysates">cell-free lysates</a>, <a href="https://publications.waset.org/abstracts/search?q=detection" title=" detection"> detection</a>, <a href="https://publications.waset.org/abstracts/search?q=gene%20circuits" title=" gene circuits"> gene circuits</a>, <a href="https://publications.waset.org/abstracts/search?q=in%20vitro" title=" in vitro"> in vitro</a> </p> <a href="https://publications.waset.org/abstracts/71047/paper-based-detection-using-synthetic-gene-circuits" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/71047.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">394</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">350</span> First Order Filter Based Current-Mode Sinusoidal Oscillators Using Current Differencing Transconductance Amplifiers (CDTAs)</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=S.%20Summart">S. Summart</a>, <a href="https://publications.waset.org/abstracts/search?q=C.%20Saetiaw"> C. Saetiaw</a>, <a href="https://publications.waset.org/abstracts/search?q=T.%20Thosdeekoraphat"> T. Thosdeekoraphat</a>, <a href="https://publications.waset.org/abstracts/search?q=C.%20Thongsopa"> C. Thongsopa</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This article presents new current-mode oscillator circuits using CDTAs which is designed from block diagram. The proposed circuits consist of two CDTAs and two grounded capacitors. The condition of oscillation and the frequency of oscillation can be adjusted by electronic method. The circuits have high output impedance and use only grounded capacitors without any external resistor which is very appropriate to future development into an integrated circuit. The results of PSPICE simulation program are corresponding to the theoretical analysis. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=current-mode" title="current-mode">current-mode</a>, <a href="https://publications.waset.org/abstracts/search?q=quadrature%20oscillator" title=" quadrature oscillator"> quadrature oscillator</a>, <a href="https://publications.waset.org/abstracts/search?q=block%20diagram" title=" block diagram"> block diagram</a>, <a href="https://publications.waset.org/abstracts/search?q=CDTA" title=" CDTA"> CDTA</a> </p> <a href="https://publications.waset.org/abstracts/8914/first-order-filter-based-current-mode-sinusoidal-oscillators-using-current-differencing-transconductance-amplifiers-cdtas" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/8914.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">453</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">349</span> Propagation of W Shaped of Solitons in Fiber Bragg Gratings</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mezghiche%20Kamel">Mezghiche Kamel</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We present solitary wave solutions for the perturbed nonlinear Schrodinger (PNLS) equation describing propagation of femtosecond light pulses through the ﬁber Bragg grating structure where the pulse dynamics is governed by the nonlinear-coupled mode (NLCM) equations. Using the multiple scale analysis, we reduce the NLCM equations into the perturbed nonlinear Schrodinger (PNLS) type equation. Unlike the reported solitary wave solutions of the PNLS equation, the novel ones can describe W shaped of solitons and their properties. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=%EF%AC%81ber%20bragg%20grating" title="ﬁber bragg grating">ﬁber bragg grating</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear-coupled%20mode%20equations" title=" nonlinear-coupled mode equations"> nonlinear-coupled mode equations</a>, <a href="https://publications.waset.org/abstracts/search?q=w%20shaped%20of%20solitons" title=" w shaped of solitons"> w shaped of solitons</a>, <a href="https://publications.waset.org/abstracts/search?q=PNLS" title=" PNLS"> PNLS</a> </p> <a href="https://publications.waset.org/abstracts/12669/propagation-of-w-shaped-of-solitons-in-fiber-bragg-gratings" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/12669.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">769</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">348</span> Importance of Hardware Systems and Circuits in Secure Software Development Life Cycle</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mir%20Shahriar%20Emami">Mir Shahriar Emami</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Although it is fully impossible to ensure that a software system is quite secure, developing an acceptable secure software system in a convenient platform is not unreachable. In this paper, we attempt to analyze software development life cycle (SDLC) models from the hardware systems and circuits point of view. To date, the SDLC models pay merely attention to the software security from the software perspectives. In this paper, we present new features for SDLC stages to emphasize the role of systems and circuits in developing secure software system through the software development stages, the point that has not been considered previously in the SDLC models. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=SDLC" title="SDLC">SDLC</a>, <a href="https://publications.waset.org/abstracts/search?q=SSDLC" title=" SSDLC"> SSDLC</a>, <a href="https://publications.waset.org/abstracts/search?q=software%20security" title=" software security"> software security</a>, <a href="https://publications.waset.org/abstracts/search?q=software%20process%20engineering" title=" software process engineering"> software process engineering</a>, <a href="https://publications.waset.org/abstracts/search?q=hardware%20systems%20and%20circuits%20security" title=" hardware systems and circuits security"> hardware systems and circuits security</a> </p> <a href="https://publications.waset.org/abstracts/55558/importance-of-hardware-systems-and-circuits-in-secure-software-development-life-cycle" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/55558.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">261</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">347</span> Stochastic Age-Structured Population Models</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Arcady%20Ponosov">Arcady Ponosov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Many well-known age-structured population models are derived from the celebrated McKendrick-von Foerster equation (MFE), also called the biological conservation law. A similar technique is suggested for the stochastically perturbed MFE. This technique is shown to produce stochastic versions of the deterministic population models, which appear to be very different from those one can construct by simply appending additive stochasticity to deterministic equations. In particular, it is shown that stochastic Nicholson’s blowflies model should contain both additive and multiplicative stochastic noises. The suggested transformation technique is similar to that used in the deterministic case. The difference is hidden in the formulas for the exact solutions of the simplified boundary value problem for the stochastically perturbed MFE. The analysis is also based on the theory of stochastic delay differential equations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=boundary%20value%20problems" title="boundary value problems">boundary value problems</a>, <a href="https://publications.waset.org/abstracts/search?q=population%20models" title=" population models"> population models</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20delay%20differential%20equations" title=" stochastic delay differential equations"> stochastic delay differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20partial%20differential%20equation" title=" stochastic partial differential equation"> stochastic partial differential equation</a> </p> <a href="https://publications.waset.org/abstracts/138398/stochastic-age-structured-population-models" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/138398.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">254</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">346</span> Efficient Modeling Technique for Microstrip Discontinuities</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Nassim%20Ourabia">Nassim Ourabia</a>, <a href="https://publications.waset.org/abstracts/search?q=Malika%20Ourabia"> Malika Ourabia</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A new and efficient method is presented for the analysis of arbitrarily shaped discontinuities. The technique obtains closed form expressions for the equivalent circuits which are used to model these discontinuities. Then it would be easy to handle and to characterize complicated structures like T and Y junctions, truncated junctions, arbitrarily shaped junctions, cascading junctions, and more generally planar multiport junctions. Another advantage of this method is that the edge line concept for arbitrary shape junctions operates with real parameters circuits. The validity of the method was further confirmed by comparing our results for various discontinuities (bend, filters) with those from HFSS as well as from other published sources. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=CAD%20analysis" title="CAD analysis">CAD analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=contour%20integral%20approach" title=" contour integral approach"> contour integral approach</a>, <a href="https://publications.waset.org/abstracts/search?q=microwave%20circuits" title=" microwave circuits"> microwave circuits</a>, <a href="https://publications.waset.org/abstracts/search?q=s-parameters" title=" s-parameters"> s-parameters</a> </p> <a href="https://publications.waset.org/abstracts/25945/efficient-modeling-technique-for-microstrip-discontinuities" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/25945.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">516</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">345</span> Design and Implementation of Testable Reversible Sequential Circuits Optimized Power</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=B.%20Manikandan">B. Manikandan</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Vijayaprabhu"> A. Vijayaprabhu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The conservative reversible gates are used to designed reversible sequential circuits. The sequential circuits are flip-flops and latches. The conservative logic gates are Feynman, Toffoli, and Fredkin. The design of two vectors testable sequential circuits based on conservative logic gates. All sequential circuit based on conservative logic gates can be tested for classical unidirectional stuck-at faults using only two test vectors. The two test vectors are all 1s, and all 0s. The designs of two vectors testable latches, master-slave flip-flops and double edge triggered (DET) flip-flops are presented. We also showed the application of the proposed approach toward 100% fault coverage for single missing/additional cell defect in the quantum- dot cellular automata (QCA) layout of the Fredkin gate. The conservative logic gates are in terms of complexity, speed, and area. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=DET" title="DET">DET</a>, <a href="https://publications.waset.org/abstracts/search?q=QCA" title=" QCA"> QCA</a>, <a href="https://publications.waset.org/abstracts/search?q=reversible%20logic%20gates" title=" reversible logic gates"> reversible logic gates</a>, <a href="https://publications.waset.org/abstracts/search?q=POS" title=" POS"> POS</a>, <a href="https://publications.waset.org/abstracts/search?q=SOP" title=" SOP"> SOP</a>, <a href="https://publications.waset.org/abstracts/search?q=latches" title=" latches"> latches</a>, <a href="https://publications.waset.org/abstracts/search?q=flip%20flops" title=" flip flops"> flip flops</a> </p> <a href="https://publications.waset.org/abstracts/42418/design-and-implementation-of-testable-reversible-sequential-circuits-optimized-power" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/42418.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">304</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">344</span> SPICE Modeling for Evaluation of Distribution System Reliability Indices</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=G.%20N.%20Srinivas">G. N. Srinivas</a>, <a href="https://publications.waset.org/abstracts/search?q=K.%20Raju"> K. Raju</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents Markov processes for determining the reliability indices of distribution system. The continuous Markov modeling is applied to a complex radial distribution system and electrical equivalent circuits are developed for the modeling. In general PSPICE is being used for electrical and electronic circuits and various applications of power system like fault analysis, transient analysis etc. In this paper, the SPICE modeling equivalent circuits which are developed are applied in a novel way to Distribution System reliability analysis. These circuits are simulated using PSPICE software to obtain the state probabilities, the basic and performance indices. Thus the basic indices and the performance indices obtained by this method are compared with those obtained by FMEA technique. The application of the concepts presented in this paper are illustrated and analyzed for IEEE-Roy Billinton Test System (RBTS). <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=distribution%20system" title="distribution system">distribution system</a>, <a href="https://publications.waset.org/abstracts/search?q=Markov%20Model" title=" Markov Model"> Markov Model</a>, <a href="https://publications.waset.org/abstracts/search?q=reliability%20indices" title=" reliability indices"> reliability indices</a>, <a href="https://publications.waset.org/abstracts/search?q=spice%20simulation" title=" spice simulation "> spice simulation </a> </p> <a href="https://publications.waset.org/abstracts/2903/spice-modeling-for-evaluation-of-distribution-system-reliability-indices" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/2903.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">539</span> </span> </div> </div> <ul class="pagination"> <li class="page-item disabled"><span class="page-link">&lsaquo;</span></li> <li class="page-item active"><span class="page-link">1</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=singularly%20perturbed%20circuits&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=singularly%20perturbed%20circuits&page=3">3</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=singularly%20perturbed%20circuits&page=4">4</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=singularly%20perturbed%20circuits&page=5">5</a></li> <li class="page-item"><a class="page-link" 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