Search results for: discrete renewal equation

Authors: Fengxia Zheng

Abstract:

By using two new fixed point theorems for mixed monotone operators, the positive solution of nonlinear fractional differential equation boundary value problem is studied. Its existence and uniqueness is proved, and an iterative scheme is constructed to approximate it.

Keywords: Fractional differential equation, boundary value problem, positive solution, existence and uniqueness, fixed point theorem, mixed monotone operator.

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Authors: Soon-Mo Jung

Abstract:

The functional equation f(3x) = 4f(3x-3)+f(3x- 6) will be solved and its Hyers-Ulam stability will be also investigated in the class of functions f : R → X, where X is a real Banach space.

Keywords: Functional equation, Lucas sequence of the first kind, Hyers-Ulam stability.

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Authors: Shan Gao, Zaiming Liu

Abstract:

This paper treats a discrete-time batch arrival queue with single working vacation. The main purpose of this paper is to present a performance analysis of this system by using the supplementary variable technique. For this purpose, we first analyze the Markov chain underlying the queueing system and obtain its ergodicity condition. Next, we present the stationary distributions of the system length as well as some performance measures at random epochs by using the supplementary variable method. Thirdly, still based on the supplementary variable method we give the probability generating function (PGF) of the number of customers at the beginning of a busy period and give a stochastic decomposition formulae for the PGF of the stationary system length at the departure epochs. Additionally, we investigate the relation between our discretetime system and its continuous counterpart. Finally, some numerical examples show the influence of the parameters on some crucial performance characteristics of the system.

Keywords: Discrete-time queue, batch arrival, working vacation, supplementary variable technique, stochastic decomposition.

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Authors: Imad Chaddad, Andrei A. Kolyshkin

Abstract:

Linear and weakly nonlinear analysis of shallow wake flows is presented in the present paper. The evolution of the most unstable linear mode is described by the complex Ginzburg-Landau equation (CGLE). The coefficients of the CGLE are calculated numerically from the solution of the corresponding linear stability problem for a one-parametric family of shallow wake flows. It is shown that the coefficients of the CGLE are not so sensitive to the variation of the base flow profile.

Keywords: Ginzburg-Landau equation, shallow wake flow, weakly nonlinear theory.

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Authors: Jaipong Kasemsuwan

Abstract:

A numerical solution of the initial boundary value problem of the suspended string vibrating equation with the particular nonlinear damping term based on the finite difference scheme is presented in this paper. The investigation of how the second and third power terms of the nonlinear term affect the vibration characteristic. We compare the vibration amplitude as a result of the third power nonlinear damping with the second power obtained from previous report provided that the same initial shape and initial velocities are assumed. The comparison results show that the vibration amplitude is inversely proportional to the coefficient of the damping term for the third power nonlinear damping case, while the vibration amplitude is proportional to the coefficient of the damping term in the second power nonlinear damping case.

Keywords: Finite-difference method, the nonlinear damped equation, the numerical simulation, the suspended string equation

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Authors: D. H. Kim, Y. H. Kim, T. Kim

Abstract:

A new method identifies coupled fluid-structure system with a reduced set of state variables is presented. Assuming that the structural model is known a priori either from an analysis or a test and using linear transformations between structural and aeroelastic states, it is possible to deduce aerodynamic information from sampled time histories of the aeroelastic system. More specifically given a finite set of structural modes the method extracts generalized aerodynamic force matrix corresponding to these mode shapes. Once the aerodynamic forces are known, an aeroelastic reduced-order model can be constructed in discrete-time, state-space format by coupling the structural model and the aerodynamic system. The resulting reduced-order model is suitable for constant Mach, varying density analysis.

Keywords: ROM (Reduced-Order Model), aero elasticity, AGARD 445.6 wing.

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Authors: Tianxiu Lu, Peiyong Zhu

Abstract:

This paper is mainly concerned with a kind of coupled map lattices (CMLs). New definitions of dense δ-chaos and dense chaos (which is a special case of dense δ-chaos with δ = 0) in discrete spatiotemporal systems are given and sufficient conditions for these systems to be densely chaotic or densely δ-chaotic are derived.

Keywords: Discrete spatiotemporal systems, coupled map lattices, dense δ-chaos, Li-Yorke pairs.

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Authors: M. Zamani, O. Kahar

Abstract:

Solution to unsteady Navier-Stokes equation by Splitting method in physical orthogonal algebraic curvilinear coordinate system, also termed 'Non-linear grid system' is presented. The linear terms in Navier-Stokes equation are solved by Crank- Nicholson method while the non-linear term is solved by the second order Adams-Bashforth method. This work is meant to bring together the advantage of Splitting method as pressure-velocity solver of higher efficiency with the advantage of consuming Non-linear grid system which produce more accurate results in relatively equal number of grid points as compared to Cartesian grid. The validation of Splitting method as a solution of Navier-Stokes equation in Nonlinear grid system is done by comparison with the benchmark results for lid driven cavity flow by Ghia and some case studies including Backward Facing Step Flow Problem.

Keywords: Navier-Stokes, 'Non-linear grid system', Splitting method.

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Authors: M. Ghalambaz, A.R. Noghrehabadi, M.A. Behrang, E. Assareh, A. Ghanbarzadeh, N.Hedayat

Abstract:

This study presents a hybrid neural network and Gravitational Search Algorithm (HNGSA) method to solve well known Wessinger's equation. To aim this purpose, gravitational search algorithm (GSA) technique is applied to train a multi-layer perceptron neural network, which is used as approximation solution of the Wessinger's equation. A trial solution of the differential equation is written as sum of two parts. The first part satisfies the initial/ boundary conditions and does not contain any adjustable parameters and the second part which is constructed so as not to affect the initial/boundary conditions. The second part involves adjustable parameters (the weights and biases) for a multi-layer perceptron neural network. In order to demonstrate the presented method, the obtained results of the proposed method are compared with some known numerical methods. The given results show that presented method can introduce a closer form to the analytic solution than other numerical methods. Present method can be easily extended to solve a wide range of problems.

Keywords: Neural Networks, Gravitational Search Algorithm (GSR), Wessinger's Equation.

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Authors: Makhlouf Mourad, Medkour Mihoub, Bouchher Omar, Messabih Sidi Mohamed, Benrachedi Khaled

Abstract:

This work is the modeling and simulation of fluid flow (liquid) through porous media. This type of flow occurs in many situations of interest in applied sciences and engineering, fluid (oil) consists of several individual substances in pure, single-phase flow is incompressible and isothermal. The porous medium is isotropic, homogeneous optionally, with the rectangular format and the flow is two-dimensional. Modeling of hydrodynamic phenomena incorporates Darcy's law and the equation of mass conservation. Correlations are used to model the density and viscosity of the fluid. A finite volume code is used in the discretization of differential equations. The nonlinearity is treated by Newton's method with relaxation coefficient. The results of the simulation of the pressure and the mobility of liquid flowing through porous media are presented, analyzed, and illustrated.

Keywords: Darcy equation, middle porous, continuity equation, Peng Robinson equation, mobility.

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Authors: António L. Topa

Abstract:

A complete spectral representation for the electromagnetic field of planar multilayered waveguides inhomogeneously filled with omega media is presented. The problem of guided electromagnetic propagation is reduced to an eigenvalue equation related to a 2 ´ 2 matrix differential operator. Using the concept of adjoint waveguide, general bi-orthogonality relations for the hybrid modes (either from the discrete or from the continuous spectrum) are derived. For the special case of homogeneous layers the linear operator formalism is reduced to a simple 2 ´ 2 coupling matrix eigenvalue problem. Finally, as an example of application, the surface and the radiation modes of a grounded omega slab waveguide are analyzed.

Keywords: Metamaterials, linear operators, omega media, layered waveguide, orthogonality relations

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Authors: Ju H. Park, S.M. Lee

Abstract:

In this paper, we propose a robust controller design method for discrete-time systems with sector-bounded nonlinearities and time-varying delay. Based on the Lyapunov theory, delaydependent stabilization criteria are obtained in terms of linear matrix inequalities (LMIs) by constructing the new Lyapunov-Krasovskii functional and using some inequalities. A robust state feedback controller is designed by LMI framework and a reciprocally convex combination technique. The effectiveness of the proposed method is verified throughout a numerical example.

Keywords: Lur'e systems, Time-delay, Stabilization, LMIs.

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Authors: Tong Liu, Xuan Xu, Xiaodi Wang

Abstract:

Computational techniques derived from digital image processing are playing a significant role in the security and digital copyrights of multimedia and visual arts. This technology has the effect within the domain of computers. This research presents discrete M-band wavelet transform (MWT) and cosine transform (DCT) based watermarking algorithm by incorporating the principal component analysis (PCA). The proposed algorithm is expected to achieve higher perceptual transparency. Specifically, the developed watermarking scheme can successfully resist common signal processing, such as geometric distortions, and Gaussian noise. In addition, the proposed algorithm can be parameterized, thus resulting in more security. To meet these requirements, the image is transformed by a combination of MWT & DCT. In order to improve the security further, we randomize the watermark image to create three code books. During the watermark embedding, PCA is applied to the coefficients in approximation sub-band. Finally, first few component bands represent an excellent domain for inserting the watermark.

Keywords: discrete M-band wavelet transform , discrete M-band wavelet transform, randomized watermark, principal component analysis

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Authors: R. M. Farouk

Abstract:

In this paper, we present an analytical analysis of the representation of images as the magnitudes of their transform with the discrete wavelets. Such a representation plays as a model for complex cells in the early stage of visual processing and of high technical usefulness for image understanding, because it makes the representation insensitive to small local shifts. We found that if the signals are band limited and of zero mean, then reconstruction from the magnitudes is unique up to the sign for almost all signals. We also present an iterative reconstruction algorithm which yields very good reconstruction up to the sign minor numerical errors in the very low frequencies.

Keywords: Wavelets, Image processing signal processing, Image reconstruction

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Authors: S. E. Oraby, A.M. Alaskari

Abstract:

The stochastic nature of tool life using conventional discrete-wear data from experimental tests usually exists due to many individual and interacting parameters. It is a common practice in batch production to continually use the same tool to machine different parts, using disparate machining parameters. In such an environment, the optimal points at which tools have to be changed, while achieving minimum production cost and maximum production rate within the surface roughness specifications, have not been adequately studied. In the current study, two relevant aspects are investigated using coated and uncoated inserts in turning operations: (i) the accuracy of using machinability information, from fixed parameters testing procedures, when variable parameters situations are emerged, and (ii) the credibility of tool life machinability data from prior discrete testing procedures in a non-stop machining. A novel technique is proposed and verified to normalize the conventional fixed parameters machinability data to suit the cases when parameters have to be changed for the same tool. Also, an experimental investigation has been established to evaluate the error in the tool life assessment when machinability from discrete testing procedures is employed in uninterrupted practical machining.

Keywords: Machinability, tool life, tool wear, wear variability

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Authors: Eldin Wee Chuan Lim

Abstract:

The mixing behaviors of dry and wet granular materials in gas fluidized bed systems were investigated computationally using the combined Computational Fluid Dynamics and Discrete Element Method (CFD-DEM). Dry particles were observed to mix fairly rapidly during the fluidization process due to vigorous relative motions between particles induced by the flow of gas. In contrast, due to the presence of strong cohesive forces arising from capillary liquid bridges between wet particles, the mixing efficiencies of wet granular materials under similar operating conditions were observed to be reduced significantly.

Keywords: Computational Fluid Dynamics, Discrete Element Method, Gas Fluidization, Mixing, Wet particles

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Authors: M. Zarebnia, R. Parvaz

Abstract:

In this paper the Kuramoto-Sivashinsky equation is solved numerically by collocation method. The solution is approximated as a linear combination of septic B-spline functions. Applying the Von-Neumann stability analysis technique, we show that the method is unconditionally stable. The method is applied on some test examples, and the numerical results have been compared with the exact solutions. The global relative error and L∞ in the solutions show the efficiency of the method computationally.

Keywords: Kuramoto-Sivashinsky equation, Septic B-spline, Collocation method, Finite difference.

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Authors: Xin Zhao, Yin-fan Zhu, Wei-ping Wang, Qun Li

Abstract:

The Influence Diagrams (IDs) is a kind of Probabilistic Belief Networks for graphic modeling. The usage of IDs can improve the communication among field experts, modelers, and decision makers, by showing the issue frame discussed from a high-level point of view. This paper enhances the Time-Sliced Influence Diagrams (TSIDs, or called Dynamic IDs) based formalism from a Discrete Event Systems Modeling and Simulation (DES M&S) perspective, for Exploring Analysis (EA) modeling. The enhancements enable a modeler to specify times occurred of endogenous events dynamically with stochastic sampling as model running and to describe the inter- influences among them with variable nodes in a dynamic situation that the existing TSIDs fails to capture. The new class of model is named Dynamic-Stochastic Influence Diagrams (DSIDs). The paper includes a description of the modeling formalism and the hiberarchy simulators implementing its simulation algorithm, and shows a case study to illustrate its enhancements.

Keywords: Time-sliced influence diagrams, discrete event systems, dynamic-stochastic influence diagrams, modeling formalism, simulation algorithm.

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Authors: Qingqing Wang, Baocheng Chen, Shouming Zhong

Abstract:

This paper deals with the problem of stability of neural networks with leakage, discrete and distributed delays. A new Lyapunov functional which contains some new double integral terms are introduced. By using appropriate model transformation that shifts the considered systems into the neutral-type time-delay system, and by making use of some inequality techniques, delay-dependent criteria are developed to guarantee the stability of the considered system. Finally, numerical examples are provided to illustrate the usefulness of the proposed main results.

Keywords: Neural networks, Stability, Time-varying delays, Linear matrix inequality.

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Authors: Alpesh Adeshara, Rajendrasinh Jadeja, Praghnesh Bhatt

Abstract:

Implementation of advanced technologies requires sophisticated instruments that deal with the operation, control, restoration and protection of rapidly growing power system network under normal and abnormal conditions. Presently, the applications of Phasor Measurement Unit (PMU) are widely found in real time operation, monitoring, controlling and analysis of power system network as it eliminates the various limitations of supervisory control and data acquisition system (SCADA) conventionally used in power system. The use of PMU data is very rapidly increasing its importance for online and offline analysis. Wide area measurement system (WAMS) is developed as new technology by use of multiple PMUs in power system. The present paper proposes a model of Matlab based PMU using Discrete Fourier Transform (DFT) algorithm and evaluation of its operation under different contingencies. In this paper, PMU based two bus system having WAMS network is presented as a case study.

Keywords: DFT-Discrete Fourier Transform, GPS-Global Positioning System, PMU-Phasor Measurement System, WAMS-Wide Area Monitoring System.

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Authors: Pushpa N. Rathie, Prabhata K. Swamee, André L. B. Cavalcante, Luan Carlos de S. M. Ozelim

Abstract:

Implicit equations play a crucial role in Engineering. Based on this importance, several techniques have been applied to solve this particular class of equations. When it comes to practical applications, in general, iterative procedures are taken into account. On the other hand, with the improvement of computers, other numerical methods have been developed to provide a more straightforward methodology of solution. Analytical exact approaches seem to have been continuously neglected due to the difficulty inherent in their application; notwithstanding, they are indispensable to validate numerical routines. Lagrange-s Inversion Theorem is a simple mathematical tool which has proved to be widely applicable to engineering problems. In short, it provides the solution to implicit equations by means of an infinite series. To show the validity of this method, the tree-parameter infiltration equation is, for the first time, analytically and exactly solved. After manipulating these series, closed-form solutions are presented as H-functions.

Keywords: Green-Ampt Equation, Lagrange's Inversion Theorem, Talsma-Parlange Equation, Three-Parameter Infiltration Equation

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Authors: Fengxia Zheng, Chuanyun Gu

Abstract:

By using a fixed point theorem of a sum operator, the existence and uniqueness of positive solution for a class of boundary value problem of nonlinear fractional differential equation is studied. An iterative scheme is constructed to approximate it. Finally, an example is given to illustrate the main result.

Keywords: Fractional differential equation, Boundary value problem, Positive solution, Existence and uniqueness, Fixed point theorem of a sum operator.

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Authors: Khosrow Maleknejad, Reza Mollapourasl, Parvin Torabi, Mahdiyeh Alizadeh,

Abstract:

Sinc-collocation scheme is one of the new techniques used in solving numerical problems involving integral equations. This method has been shown to be a powerful numerical tool for finding fast and accurate solutions. So, in this paper, some properties of the Sinc-collocation method required for our subsequent development are given and are utilized to reduce integral equation of the first kind to some algebraic equations. Then convergence with exponential rate is proved by a theorem to guarantee applicability of numerical technique. Finally, numerical examples are included to demonstrate the validity and applicability of the technique.

Keywords: Integral equation, Fredholm type, Collocation method, Sinc approximation.

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Authors: Mamta Patel, R. N. Patel

Abstract:

Transmission and distribution lines are vital links between the generating unit and consumers. They are exposed to atmosphere, hence chances of occurrence of fault in transmission line is very high which has to be immediately taken care of in order to minimize damage caused by it. In this paper Discrete wavelet transform of voltage signals at the two ends of transmission lines have been analyzed. The transient energy of the detail information of level five is calculated for different fault conditions. It is observed that the variation of transient energy of healthy and faulted line can give important information which can be very useful in classifying and locating the fault.

Keywords: Wavelet, Discrete wavelet transform, Multiresolution analysis, Transient energy

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Authors: Swarniv Chandra, Sibarjun Das, Agniv Chandra, Basudev Ghosh, Apratim Jash

Abstract:

Using the quantum hydrodynamic (QHD) model the nonlinear properties of ion-acoustic waves in are lativistically degenerate quantum plasma is investigated by deriving a nonlinear Spherical Kadomtsev–Petviashvili (SKP) equation using the standard reductive perturbation method equation. It was found that the electron degeneracy parameter significantly affects the linear and nonlinear properties of ion-acoustic waves in quantum plasma.

Keywords: Kadomtsev-Petviashvili equation, Ion-acoustic Waves, Relativistic Degeneracy, Quantum Plasma, Quantum Hydrodynamic Model.

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Authors: Omid Sojodishijani, Saeed Ebrahimijam, Vahid Rostami

Abstract:

This paper presents an optimized algorithm for robot localization which increases the correctness and accuracy of the estimating position of mobile robot to more than 150% of the past methods [1] in the uncertain and noisy environment. In this method the odometry and vision sensors are combined by an adapted well-known discrete kalman filter [2]. This technique also decreased the computation process of the algorithm by DKF simple implementation. The experimental trial of the algorithm is performed on the robocup middle size soccer robot; the system can be used in more general environments.

Keywords: Discrete Kalman filter, odometry sensor, omnidirectional vision sensor, Robot Localization.

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Authors: Qingqing Wang, Baocheng Chen, Shouming Zhong

Abstract:

In this paper, the problem of stability criteria for Markovian jumping BAM neural networks with leakage and discrete delays has been investigated. Some new sufficient condition are derived based on a novel Lyapunov-Krasovskii functional approach. These new criteria based on delay partitioning idea are proved to be less conservative because free-weighting matrices method and a convex optimization approach are considered. Finally, one numerical example is given to illustrate the the usefulness and feasibility of the proposed main results.

Keywords: Stability, Markovian jumping neural networks, Timevarying delays, Linear matrix inequality.

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Authors: Changqing Yang, Jianhua Hou, Beibo Qin

Abstract:

A numerical method for Riccati equation is presented in this work. The method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The operational matrices of derivative and product of hybrid functions are presented. These matrices together with the tau method are then utilized to transform the differential equation into a system of algebraic equations. Corresponding numerical examples are presented to demonstrate the accuracy of the proposed method.

Keywords: Hybrid functions, Riccati differential equation, Blockpulse, Chebyshev polynomials, Tau method, operational matrix.

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Authors: H. N. Agiza, M. A. Sohaly, M. A. Elfouly

Abstract:

Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.

Keywords: Parkinson's disease, Step method, delay differential equation, simulation.

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Authors: Meng Hu, Lili Wang

Abstract:

This paper deals with a nonlinear fractional differential equation with integral boundary condition of the following form:  Dαt x(t) = f(t, x(t),Dβ t x(t)), t ∈ (0, 1), x(0) = 0, x(1) = 1 0 g(s)x(s)ds, where 1 < α ≤ 2, 0 < β < 1. Our results are based on the Schauder fixed point theorem and the Banach contraction principle.

Keywords: Fractional differential equation, Integral boundary condition, Schauder fixed point theorem, Banach contraction principle.

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