Search results for: singular differential equation.

Authors: Kaoutar Lamrini Uahabi, Mohamed Atounti

Abstract:

In the present work, we consider one category of curves denoted by L(p, k, r, n). These curves are continuous arcs which are trajectories of roots of the trinomial equation zn = αzk + (1 − α), where z is a complex number, n and k are two integers such that 1 ≤ k ≤ n − 1 and α is a real parameter greater than 1. Denoting by L the union of all trinomial curves L(p, k, r, n) and using the box counting dimension as fractal dimension, we will prove that the dimension of L is equal to 3/2.

Keywords: Feasible angles, fractal dimension, Minkowski sausage, trinomial curves, trinomial equation.

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Authors: Zhoucheng Bao, Haiyan Zhu, Tingting Pang, Zuling Wang

Abstract:

This paper presents a multi population Differential Evolution (DE) with adaptive mutation and local search for global optimization, named AMMADE in order to better coordinate the cooperation between the populations and the rational use of resources. In AMMADE, the population is divided based on the Euclidean distance sorting method at each generation to appropriately coordinate the cooperation between subpopulations and the usage of resources, such that the best-performed subpopulation will get more computing resources in the next generation. Further, an adaptive local search strategy is employed on the best-performed subpopulation to achieve a balanced search. The proposed algorithm has been tested by solving optimization problems taken from CEC2014 benchmark problems. Experimental results show that our algorithm can achieve a competitive or better result than related methods. The results also confirm the significance of devised strategies in the proposed algorithm.

Keywords: Differential evolution, multi-mutation strategies, memetic algorithm, adaptive local search.

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Authors: Nopparat Pochai

Abstract:

Smoke discharging is a main reason of air pollution problem from industrial plants. The obstacle of a building has an affect with the air pollutant discharge. In this research, a mathematical model of the smoke dispersion from two sources and one source with a structural obstacle is considered. The governing equation of the model is an isothermal mass transfer model in a viscous fluid. The finite element method is used to approximate the solutions of the model. The triangular linear elements have been used for discretising the domain, and time integration has been carried out by semi-implicit finite difference method. The simulations of smoke dispersion in cases of one chimney and two chimneys are presented. The maximum calculated smoke concentration of both cases are compared. It is then used to make the decision for smoke discharging and air pollutant control problems on industrial area.

Keywords: Air pollution, Smoke dispersion, Finite element method, Stream function, Vorticity equation, Convection-diffusion equation, Semi-implicit method

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Authors: S. Tupsie, A. Isaramongkolrak, P. Pao-la-or

Abstract:

This paper presents the mathematical model of electric field and magnetic field in transmission system, which performs in second-order partial differential equation. This research has conducted analyzing the electromagnetic field radiating to atmosphere around the transmission line, when there is the transmission line transposition in case of long distance distribution. The six types of 500 kV transposed HV transmission line with double circuit will be considered. The computer simulation is applied finite element method that is developed by MATLAB program. The problem is considered to two dimensions, which is time harmonic system with the graphical performance of electric field and magnetic field. The impact from simulation of six types long distance distributing transposition will not effect changing of electric field and magnetic field which surround the transmission line.

Keywords: Transposition, Electromagnetic Field, Finite Element Method (FEM), Transmission Line, Computer Simulation

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Authors: Fatemeh Panjeh Ali Beik

Abstract:

In the present work, we propose a new method for solving the matrix equation AXB=F . The new method can be considered as a generalized form of the well-known global full orthogonalization method (Gl-FOM) for solving multiple linear systems. Hence, the method will be called extended Gl-FOM (EGl- FOM). For implementing EGl-FOM, generalized forms of block Krylov subspace and global Arnoldi process are presented. Finally, some numerical experiments are given to illustrate the efficiency of our new method.

Keywords: Matrix equations, Iterative methods, Block Krylovsubspace methods.

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Authors: A. Junaid, M. A. Z. Raja, I. M. Qureshi

Abstract:

An evolutionary computing technique for solving initial value problems in Ordinary Differential Equations is proposed in this paper. Neural network is used as a universal approximator while the adaptive parameters of neural networks are optimized by genetic algorithm. The solution is achieved on the continuous grid of time instead of discrete as in other numerical techniques. The comparison is carried out with classical numerical techniques and the solution is found with a uniform accuracy of MSE ≈ 10-9 .

Keywords: Neural networks, Unsupervised learning, Evolutionary computing, Numerical methods, Fitness evaluation function.

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Authors: Changqiao Wu, Guoqing Ding, Xin Chen

Abstract:

In this paper, ways of modeling dynamic measurement systems are discussed. Specially, for linear system with single-input single-output, it could be modeled with shallow neural network. Then, gradient based optimization algorithms are used for searching the proper coefficients. Besides, method with normal equation and second order gradient descent are proposed to accelerate the modeling process, and ways of better gradient estimation are discussed. It shows that the mathematical essence of the learning objective is maximum likelihood with noises under Gaussian distribution. For conventional gradient descent, the mini-batch learning and gradient with momentum contribute to faster convergence and enhance model ability. Lastly, experimental results proved the effectiveness of second order gradient descent algorithm, and indicated that optimization with normal equation was the most suitable for linear dynamic models.

Keywords: Dynamic system modeling, neural network, normal equation, second order gradient descent.

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Authors: N. M. A. Nik Long, Z. K. Eshkuvatov, M. Yaghobifar, M. Hasan

Abstract:

In this paper the exact solution of infinite boundary integral equation (IBIE) of the second kind with degenerate kernel is presented. Moreover Galerkin method with Laguerre polynomial is applied to get the approximate solution of IBIE. Numerical examples are given to show the validity of the method presented.

Keywords: Approximation, Galerkin method, Integral equations, Laguerre polynomial.

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Authors: Weerachi Sarakorn, I-Ming Tang

Abstract:

A mathematical model for the transmission of SARS is developed. In addition to dividing the population into susceptible (high and low risk), exposed, infected, quarantined, diagnosed and recovered classes, we have included a class called untraced. The model simulates the Gompertz curves which are the best representation of the cumulative numbers of probable SARS cases in Hong Kong and Singapore. The values of the parameters in the model which produces the best fit of the observed data for each city are obtained by using a differential evolution algorithm. It is seen that the values for the parameters needed to simulate the observed daily behaviors of the two epidemics are different.

Keywords: SARS, mathematical modelling, differential evolution algorithm.

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Authors: O. Hashemipour, S. G. Nabavi

Abstract:

A high-linearity and high-speed current-mode sampleand- hold circuit is designed and simulated using a 0.25μm CMOS technology. This circuit design is based on low voltage and it utilizes a fully differential circuit. Due to the use of only two switches the switch related noise has been reduced. Signal - dependent -error is completely eliminated by a new zero voltage switching technique. The circuit has a linearity error equal to ±0.05μa, i.e. 12-bit accuracy with a ±160 μa differential output - input signal frequency of 5MHZ, and sampling frequency of 100 MHZ. Third harmonic is equal to –78dB.

Keywords: Zero-voltage-technique, MOS-resistor, OTA, Feedback-resistor.

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Authors: Hsuan-Ku Liu

Abstract:

In this paper, the American exchange option (AEO) valuation problem is modelled as a free boundary problem. The critical stock price for an AEO is satisfied an integral equation implicitly. When the remaining time is large enough, an asymptotic formula is provided for pricing an AEO. The numerical results reveal that our asymptotic pricing formula is robust and accurate for the long-term AEO.

Keywords: Integral equation, asymptotic solution, free boundary problem, American exchange option.

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Authors: Katsunori Miura, Kiyoshi Akama, Hiroshi Mabuchi

Abstract:

In the Equivalent Transformation (ET) computation model, a program is constructed by the successive accumulation of ET rules. A method by meta-computation by which a correct ET rule is generated has been proposed. Although the method covers a broad range in the generation of ET rules, all important ET rules are not necessarily generated. Generation of more ET rules can be achieved by supplementing generation methods which are specialized for important ET rules. A Specialization-by-Equation (Speq) rule is one of those important rules. A Speq rule describes a procedure in which two variables included in an atom conjunction are equalized due to predicate constraints. In this paper, we propose an algorithm that systematically and recursively generate Speq rules and discuss its effectiveness in the synthesis of ET programs. A Speq rule is generated based on proof of a logical formula consisting of given atom set and dis-equality. The proof is carried out by utilizing some ET rules and the ultimately obtained rules in generating Speq rules.

Keywords: Equivalent transformation, ET rule, Equation of two variables, Rule generation, Specialization-by-Equation rule

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Authors: Dezhi Liu

Abstract:

In the paper, based on stochastic analysis theory and Lyapunov functional method, we discuss the mean square stability of impulsive stochastic delay differential equations with markovian switching and poisson jumps, and the sufficient conditions of mean square stability have been obtained. One example illustrates the main results. Furthermore, some well-known results are improved and generalized in the remarks.

Keywords: Impulsive, stochastic, delay, Markovian switching, Poisson jumps, mean square stability.

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Authors: M. Dachyar, Fatkhurrohman

Abstract:

Innovation is being view from four areas of innovation, product, service, technology, and marketing. Whereas customer loyalty is composed of customer expectation, perceived quality, perceived value, corporate image, customer satisfaction, customer trust/confidence, customer commitment, customer complaint, and customer loyalty. This study aimed to investigate the influence of innovation factors to customer loyalty to GSM in the telecom companies where use of products and services. Structural Equation Modeling (SEM) using to analyze innovation factors. It was found the factor of innovation have significant influence on customer loyalty.

Keywords: Innovation, telecommunication, customer loyalty, SEM

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Authors: Saidu Ibrahim, Winston M. W. Shakantu

Abstract:

The problem of construction material waste remains unresolved, as a significant percentage of the materials delivered to some project sites end up as waste which might result in additional project cost. Cost overrun is a problem which affects 90% of the completed projects in the world. The argument on how to eliminate it has been on-going for the past 70 years, but there is neither substantial improvement nor significant solution for mitigating its detrimental effects. Research evidence has proposed various construction cost overruns and material-waste management approaches; nonetheless, these studies failed to give a clear indication on the framework and the equation for managing construction material waste and cost overruns. Hence, this research aims to develop a conceptual framework and a mathematical equation for managing material waste and cost overrun in the construction industry. The paper adopts the desktop methodological approach. This involves comparing the causes of material waste and those of cost overruns from the literature to determine the possible relationship. The review revealed a relationship between material waste and cost overrun that; increase in material waste would result to a corresponding increase in the amount of cost overrun at both the pre-contract and the post contract stages of a project. It was found from the equation that achieving an effective construction material waste management must ensure a “Good Quality-of-Planning, Estimating, and Design Management” and a “Good Quality- of-Construction, Procurement and Site Management”; a decrease in “Design Complexity” which would reduce “Material Waste” and subsequently reduce the amount of cost overrun by 86.74%. The conceptual framework and the mathematical equation developed in this study are recommended to the professionals of the construction industry.

Keywords: Conceptual framework, cost overrun, material waste, project stags.

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Authors: S. Homrossukon, D. Aromstain

Abstract:

The simple methods used to plan and measure non patterned production system are developed from the basic definition of working efficiency. Processing time is assigned as the variable and used to write the equation of production efficiency. Consequently, such equation is extensively used to develop the planning method for production of interest using one-dimensional stock cutting problem. The application of the developed method shows that production efficiency and production planning can be determined effectively.

Keywords: Production Planning, Parallel Machine, Production Measurement, Cutting and Packing.

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Authors: N. Senu, I. A. Kasim, F. Ismail, N. Bachok

Abstract:

In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing method when solving the second-order differential equations with periodic solutions using constant step size.

Keywords: Dissipation, Oscillatory solutions, Phase-lag, Runge- Kutta methods.

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Authors: Kayvan Ahmadi, Hossein Shamsi

Abstract:

This paper proposes a low-voltage and low-power fully integrated digitally tuned continuous-time channel selection filter for WiMAX applications. A 5th-order elliptic low-pass filter is realized in a Gm-C topology. The bandwidth of the fully differential filter is reconfigurable from 2.5MHz to 20MHz (8x) for different requirements in WiMAX applications. The filter is simulated in a standard 90nm CMOS process. Simulation results show the THD (@Vout =100mVpp) is less than -66dB. The in-band ripple of the filter is about 0.15dB. The filter consumes 1.5mW from a supply voltage of 0.9V.

Keywords: Common-mode feedback, continuous-time, fully differential transconductor, Gm-C topology, low-voltage

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Authors: Shiping Zhou, Minggen Cui

Abstract:

This paper investigates the inverse problem of determining the unknown time-dependent leading coefficient in the parabolic equation using the usual conditions of the direct problem and an additional condition. An algorithm is developed for solving numerically the inverse problem using the technique of space decomposition in a reproducing kernel space. The leading coefficients can be solved by a lower triangular linear system. Numerical experiments are presented to show the efficiency of the proposed methods.

Keywords: parabolic equations, coefficient inverse problem, reproducing kernel.

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Authors: J.S.C. Prentice

Abstract:

The RK1GL2X3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on the RK1GL2 method which, in turn, is a particular case of the general RKrGLm method. The RK1GL2X3 method is a fourth-order method, even though its underlying Runge-Kutta method RK1 is the first-order Euler method, and hence, RK1GL2X3 is considerably more efficient than RK1. This enhancement is achieved through an implementation involving triple-nested two-point Gauss- Legendre quadrature.

Keywords: RK1GL2X3, RK1GL2, RKrGLm, Runge-Kutta, Gauss-Legendre, initial value problem, local error, global error.

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Authors: Alexander Breitholz, Wolfgang Arlt, Ki-Pung Yoo

Abstract:

Group contribution based models are widely used in industrial applications for its convenience and flexibility. Although a number of group contribution models have been proposed, there were certain limitations inherent to those models. Models based on group contribution excess Gibbs free energy are limited to low pressures and models based on equation of state (EOS) cannot properly describe highly nonideal mixtures including acids without introducing additional modification such as chemical theory. In the present study new a new approach derived from quantum chemistry have been used to calculate necessary EOS group interaction parameters. The COSMO-RS method, based on quantum mechanics, provides a reliable tool for fluid phase thermodynamics. Benefits of the group contribution EOS are the consistent extension to hydrogen-bonded mixtures and the capability to predict polymer-solvent equilibria up to high pressures. The authors are confident that with a sufficient parameter matrix the performance of the lattice EOS can be improved significantly.

Keywords: COSMO-RS, Equation of State, Group contribution, Lattice Fluid, Phase equilibria.

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Authors: Wan-Hyun Cho, In-Seop Na, Seong-ChaeSeo, Sang-Kyoon Kim, Soon-Young Park

Abstract:

In this paper, we propose the variational approach to solve single image defogging problem. In the inference process of the atmospheric veil, we defined new functional for atmospheric veil that satisfy edge-preserving regularization property. By using the fundamental lemma of calculus of variations, we derive the Euler-Lagrange equation foratmospheric veil that can find the maxima of a given functional. This equation can be solved by using a gradient decent method and time parameter. Then, we can have obtained the estimated atmospheric veil, and then have conducted the image restoration by using inferred atmospheric veil. Finally we have improved the contrast of restoration image by various histogram equalization methods. The experimental results show that the proposed method achieves rather good defogging results.

Keywords: Image defogging, Image restoration, Atmospheric veil, Transmission, Variational approach, Euler-Lagrange equation, Image enhancement.

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Authors: Qiuling Xie, Shanliang Zhu, Zongdi Sun

Abstract:

In this paper, we analyzed the correlation relationship among PM2.5 from other five Air Quality Indices (AQIs) based on the grey relational degree, and built a multivariate nonlinear regression equation model of PM2.5 and the five monitoring indexes. For the optimal control problem of PM2.5, we took the partial large Cauchy distribution of membership equation as satisfaction function. We established a nonlinear programming model with the goal of maximum performance to price ratio. And the optimal control scheme is given.

Keywords: Grey relational degree, multiple linear regression, membership function, nonlinear programming.

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Authors: Mahmoud Zarrini, R.N. Pralhad

Abstract:

In this chapter, we have studied Variation of velocity in incompressible fluid over a moving surface. The boundary layer equations are on a fixed or continuously moving flat plate in the same or opposite direction to the free stream with suction and injection. The boundary layer equations are transferred from partial differential equations to ordinary differential equations. Numerical solutions are obtained by using Runge-Kutta and Shooting methods. We have found numerical solution to velocity and skin friction coefficient.

Keywords: Boundary layer, continuously moving surface, shooting method, skin friction coefficient.

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Authors: Hassan Manouzi

Abstract:

We present in this paper a useful strategy to solve stochastic partial differential equations (SPDEs) involving stochastic coefficients. Using the Wick-product of higher order and the Wiener-Itˆo chaos expansion, the SPDEs is reformulated as a large system of deterministic partial differential equations. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. To obtain the chaos coefficients in the corresponding deterministic equations, we use a least square formulation. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.

Keywords: Least squares, Wick product, SPDEs, finite element, Wiener chaos expansion, gradient method.

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Authors: Watcharakorn Thongchuay, Puntip Toghaw, Montri Maleewong

Abstract:

The Wavelet-Galerkin finite element method for solving the one-dimensional heat equation is presented in this work. Two types of basis functions which are the Lagrange and multi-level wavelet bases are employed to derive the full form of matrix system. We consider both linear and quadratic bases in the Galerkin method. Time derivative is approximated by polynomial time basis that provides easily extend the order of approximation in time space. Our numerical results show that the rate of convergences for the linear Lagrange and the linear wavelet bases are the same and in order 2 while the rate of convergences for the quadratic Lagrange and the quadratic wavelet bases are approximately in order 4. It also reveals that the wavelet basis provides an easy treatment to improve numerical resolutions that can be done by increasing just its desired levels in the multilevel construction process.

Keywords: Galerkin finite element method, Heat equation , Lagrange basis function, Wavelet basis function.

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Authors: M. A. Ghorbani, M. Pasbani Khiavi

Abstract:

In this paper, the dam-reservoir interaction is analyzed using a finite element approach. The fluid is assumed to be incompressible, irrotational and inviscid. The assumed boundary conditions are that the interface of the dam and reservoir is vertical and the bottom of reservoir is rigid and horizontal. The governing equation for these boundary conditions is implemented in the developed finite element code considering the horizontal and vertical earthquake components. The weighted residual standard Galerkin finite element technique with 8-node elements is used to discretize the equation that produces a symmetric matrix equation for the damreservoir system. A new boundary condition is proposed for truncating surface of unbounded fluid domain to show the energy dissipation in the reservoir, through radiation in the infinite upstream direction. The Sommerfeld-s and perfect damping boundary conditions are also implemented for a truncated boundary to compare with the proposed far end boundary. The results are compared with an analytical solution to demonstrate the accuracy of the proposed formulation and other truncated boundary conditions in modeling the hydrodynamic response of an infinite reservoir.

Keywords: Reservoir, finite element, truncated boundary, hydrodynamic pressure

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Authors: J. Ranjbarn, A. Alibeigloo

Abstract:

In this paper, we present an analytical method for analysis of nano-scale spherical shell subjected to thermo-mechanical shocks based on nonlocal elasticity theory. Thermo-mechanical properties of nano shpere is assumed to be temperature dependent. Governing partial differential equation of motion is solved analytically by using Laplace transform for time domain and power series for spacial domain. The results in Laplace domain is transferred to time domain by employing the fast inverse Laplace transform (FLIT) method. Accuracy of present approach is assessed by comparing the the numerical results with the results of published work in literature. Furtheremore, the effects of non-local parameter and wall thickness on the dynamic characteristics of the nano-sphere are studied.

Keywords: Nano-scale spherical shell, nonlocal elasticity theory, thermomechanical shock.

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Authors: A. Brener, B. Balabekov, N. Zhumataev

Abstract:

In the paper we submit the non-local modification of kinetic Smoluchowski equation for binary aggregation applying to dispersed media having memory. Our supposition consists in that that intensity of evolution of clusters is supposed to be a function of the product of concentrations of the lowest orders clusters at different moments. The new form of kinetic equation for aggregation is derived on the base of the transfer kernels approach. This approach allows considering the influence of relaxation times hierarchy on kinetics of aggregation process in media with memory.

Keywords: Binary aggregation, Media with memory, Non-local model, Relaxation times

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Authors: Wei-Der Chang, Dai-Ming Chang, Eri-Wei Chiang, Chia-Hung Lin, Jian-Liung Chen

Abstract:

In this paper, a fractional-order FIR differentiator design method using the differential evolution (DE) algorithm is presented. In the proposed method, the FIR digital filter is designed to meet the frequency response of a desired fractal-order differentiator, which is evaluated in the frequency domain. To verify the design performance, another design method considered in the time-domain is also provided. Simulation results reveal the efficiency of the proposed method.

Keywords: Fractional-order differentiator, FIR digital filter, Differential evolution algorithm.

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