Search results for: optimal homotopy asymptotic method

Authors: M. Moradi Dalini, M. R. Talebi

Abstract:

This research revolves around a technical method according to combines econometric and multiobjective programming to select and obtain optimal solutions to management problems. It is taken for a generation that; it is important to analyze which combination of values of the explanatory variables -in an econometric method- would point to the simultaneous achievement of the best values of the response variables. In this case, if a certain degree of conflict is viewed among the response variables, we suggest a multiobjective method in order to the results obtained from a regression analysis. In fact, with the use of a multiobjective method, we will have the best decision about the conflicting relationship between the response variables and the optimal solution. The combined multiobjective programming and econometrics benefit is an assessment of a balanced “optimal” situation among them because a find of information can hardly be extracted just by econometric techniques.

Keywords: econometrics, multiobjective optimization, management problem, optimization

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Authors: Sagardeep Talukdar, Riki Dutta, Gautam Kumar Saharia, Sudipta Nandy

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In non-linear optics, the Fokas-Lenells equation (FLE) is a well-known integrable equation that describes how ultrashort pulses move across the optical fiber. It admits localized wave solutions, just like any other integrable equation. We apply the Hirota bilinearization method to obtain the soliton solution of FLE. The proposed bilinearization makes use of an auxiliary function. We apply the method to FLE with a vanishing boundary condition, that is, to obtain a bright soliton solution. We have obtained bright 1-soliton and 2-soliton solutions and propose a scheme for obtaining an N-soliton solution. We have used an additional parameter that is responsible for the shift in the position of the soliton. Further analysis of the 2-soliton solution is done by asymptotic analysis. In the non-vanishing boundary condition, we obtain the dark 1-soliton solution. We discover that the suggested bilinearization approach, which makes use of the auxiliary function, greatly simplifies the process while still producing the desired outcome. We think that the current analysis will be helpful in understanding how FLE is used in nonlinear optics and other areas of physics.

Keywords: asymptotic analysis, fokas-lenells equation, hirota bilinearization method, soliton

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Authors: Fernando Maass, Pablo Martin, Jorge Olivares

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The Bessel function J₀(x) is very important in Electrodynamics and Physics, as well as its zeros. In this work, a method to obtain high accuracy approximation is presented through an application to that function. In most of the applications of this function, the values of the zeros are very important. In this work, analytic approximations for this function have been obtained valid for all positive values of the variable x, which have high accuracy for the function as well as for the zeros. The approximation is determined by the simultaneous used of the power series and asymptotic expansion. The structure of the approximation is a combination of two rational functions with elementary functions as trigonometric and fractional powers. Here us in Pade method, rational functions are used, but now there combined with elementary functions us fractional powers hyperbolic or trigonometric functions, and others. The reason of this is that now power series of the exact function are used, but together with the asymptotic expansion, which usually includes fractional powers trigonometric functions and other type of elementary functions. The approximation must be a bridge between both expansions, and this can not be accomplished using only with rational functions. In the simplest approximation using 4 parameters the maximum absolute error is less than 0.006 at x ∼ 4.9. In this case also the maximum relative error for the zeros is less than 0.003 which is for the second zero, but that value decreases rapidly for the other zeros. The same kind of behaviour happens for the relative error of the maximum and minimum of the functions. Approximations with higher accuracy and more parameters will be also shown. All the approximations are valid for any positive value of x, and they can be calculated easily.

Keywords: analytic approximations, asymptotic approximations, Bessel functions, quasirational approximations

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Authors: Abbes Lounis, Kahina Louadj, Mohamed Aidene

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This paper presents an optimal control problem applied to a robot; the problem is to determine a command which makes it possible to reach a final state from a given initial state in record time. The approach followed to solve this optimization problem with constraints on the control starts by presenting the equations of motion of the dynamic system then by applying Pontryagin's maximum principle (PMP) to determine the optimal control, and Picard's successive approximation method combined with the shooting method to solve the resulting differential system.

Keywords: robotics, Pontryagin's Maximum Principle, PMP, Picard's method, shooting method, non-linear differential systems

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Authors: Eduard Marusic-Paloka

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The Darcy-Weisbach formula is used to compute the pressure drop of the fluid in the pipe, due to the friction against the wall. Because of its simplicity, the Darcy-Weisbach formula became widely accepted by engineers and is used for laminar as well as the turbulent flows through pipes, once the method to compute the mysterious friction coefficient was derived. Particularly in the second half of the 20th century. Formula is empiric, and our goal is to derive it from the basic conservation law, via rigorous asymptotic analysis. We consider the case of the laminar flow but with significant Reynolds number. In case of the perfectly smooth pipe, the situation is trivial, as the Navier-Stokes system can be solved explicitly via the Poiseuille formula leading to the friction coefficient in the form 64/Re. For the rough pipe, the situation is more complicated and some effects of the roughness appear in the friction coefficient. We start from the Navier-Stokes system in the pipe with periodically corrugated wall and derive an asymptotic expansion for the pressure and for the velocity. We use the homogenization techniques and the boundary layer analysis. The approximation derived by formal analysis is then justified by rigorous error estimate in the norm of the appropriate Sobolev space, using the energy formulation and classical a priori estimates for the Navier-Stokes system. Our method leads to the formula for the friction coefficient. The formula involves resolution of the appropriate boundary layer problems, namely the boundary value problems for the Stokes system in an infinite band, that needs to be done numerically. However, theoretical analysis characterising their nature can be done without solving them.

Keywords: Darcy-Weisbach law, pipe flow, rough boundary, Navier law

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Authors: Gubhinder Kundhi, Paul Rilstone

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Refined procedures for higher-order asymptotic theory for non-linear models are developed. These include a new method for deriving stochastic expansions of arbitrary order, new methods for evaluating the moments of polynomials of sample averages, a new method for deriving the approximate moments of the stochastic expansions; an application of these techniques to gather improved inferences with the weak instruments problem is considered. It is well established that Instrumental Variable (IV) estimators in the presence of weak instruments can be poorly behaved, in particular, be quite biased in finite samples. In our application, finite sample approximations to the distributions of these estimators are obtained using Edgeworth and Saddlepoint expansions. Departures from normality of the distributions of these estimators are analyzed using higher order analytical corrections in these expansions. In a Monte-Carlo experiment, the performance of these expansions is compared to the first order approximation and other methods commonly used in finite samples such as the bootstrap.

Keywords: edgeworth expansions, higher order asymptotics, saddlepoint expansions, weak instruments

Procedia PDF Downloads 254

Authors: M. Pienaar, J. W. Odendaal, J. C. Smit, J. Joubert

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Simulations are commonly used to predict the bistatic radar cross section (RCS) of military targets since characterization measurements can be expensive and time consuming. It is thus important to accurately predict the bistatic RCS of targets. Computational electromagnetic (CEM) methods can be used for bistatic RCS prediction. CEM methods are divided into full-wave and asymptotic methods. Full-wave methods are numerical approximations to the exact solution of Maxwell’s equations. These methods are very accurate but are computationally very intensive and time consuming. Asymptotic techniques make simplifying assumptions in solving Maxwell's equations and are thus less accurate but require less computational resources and time. Asymptotic techniques can thus be very valuable for the prediction of bistatic RCS of electrically large targets, due to the decreased computational requirements. This study extends previous work by validating the accuracy of asymptotic techniques to predict bistatic RCS through comparison with full-wave simulations as well as measurements. Validation is done with canonical structures as well as complex realistic aircraft models instead of only looking at a complex slicy structure. The slicy structure is a combination of canonical structures, including cylinders, corner reflectors and cubes. Validation is done over large bistatic angles and at different polarizations. Bistatic RCS measurements were conducted in a compact range, at the University of Pretoria, South Africa. The measurements were performed at different polarizations from 2 GHz to 6 GHz. Fixed bistatic angles of β = 30.8°, 45° and 90° were used. The measurements were calibrated with an active calibration target. The EM simulation tool FEKO was used to generate simulated results. The full-wave multi-level fast multipole method (MLFMM) simulated results together with the measured data were used as reference for validation. The accuracy of physical optics (PO) and geometrical optics (GO) was investigated. Differences relating to amplitude, lobing structure and null positions were observed between the asymptotic, full-wave and measured data. PO and GO were more accurate at angles close to the specular scattering directions and the accuracy seemed to decrease as the bistatic angle increased. At large bistatic angles PO did not perform well due to the shadow regions not being treated appropriately. PO also did not perform well for canonical structures where multi-bounce was the main scattering mechanism. PO and GO do not account for diffraction but these inaccuracies tended to decrease as the electrical size of objects increased. It was evident that both asymptotic techniques do not properly account for bistatic structural shadowing. Specular scattering was calculated accurately even if targets did not meet the electrically large criteria. It was evident that the bistatic RCS prediction performance of PO and GO depends on incident angle, frequency, target shape and observation angle. The improved computational efficiency of the asymptotic solvers yields a major advantage over full-wave solvers and measurements; however, there is still much room for improvement of the accuracy of these asymptotic techniques.

Keywords: asymptotic techniques, bistatic RCS, geometrical optics, physical optics

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Authors: Hossein Kheiri, Bashir Naderi, Mohamad Reza Niknam

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In this paper we study the optimal synchronization of chaotic T-system with complete uncertain parameter. Optimal control laws and parameter estimation rules are obtained by using Hamilton-Jacobi-Bellman (HJB) technique and Lyapunov stability theorem. The derived control laws are optimal adaptive control and make the states of drive and response systems asymptotically synchronized. Numerical simulation shows the effectiveness and feasibility of the proposed method.

Keywords: Lyapunov stability, synchronization, chaos, optimal control, adaptive control

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Authors: Arcady Ponosov, Ramazan Kadiev

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Input-to-State Stability (ISS) is widely used in deterministic control theory but less known in the stochastic case. Roughly speaking, the theory explains when small perturbations of the right-hand sides of the system on the entire semiaxis cause only small changes in the solutions of the system, again on the entire semiaxis. This property is crucial in many applications. In the report, we explain how to define and study ISS for systems of linear stochastic differential equations with or without delays. The central result connects ISS with the property of Lyapunov stability. This relationship is well-known in the deterministic setting, but its stochastic version is new. As an application, a method of studying asymptotic Lyapunov stability for stochastic delay equations is described and justified. Several examples are provided that confirm the efficiency and simplicity of the framework.

Keywords: asymptotic stability, delay equations, operator methods, stochastic perturbations

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Authors: Amirreza Kosari, Hossein Maghsoudi, Malahat Givar

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In this study, the three-dimensional optimal path planning of a flying robot for Terrain Following / Terrain Avoidance (TF/TA) purposes using Direct Collocation has been investigated. To this purpose, firstly, the appropriate equations of motion representing the flying robot translational movement have been described. The three-dimensional optimal path planning of the flying vehicle in terrain following/terrain avoidance maneuver is formulated as an optimal control problem. The terrain profile, as the main allowable height constraint has been modeled using Fractal Generation Method. The resulting optimal control problem is discretized by applying Direct Collocation numerical technique, and then transformed into a Nonlinear Programming Problem (NLP). The efficacy of the proposed method is demonstrated by extensive simulations, and in particular, it is verified that this approach could produce a solution satisfying almost all performance and environmental constraints encountering a low-level flying maneuver

Keywords: path planning, terrain following, optimal control, nonlinear programming

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Authors: Hazem M. Al-Mofleh, John E. Daniels, Joseph W. McKean

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In this paper numerous robust fitting procedures are considered in estimating spatial variograms. In spatial statistics, the conventional variogram fitting procedure (non-linear weighted least squares) suffers from the same outlier problem that has plagued this method from its inception. Even a 3-parameter model, like the variogram, can be adversely affected by a single outlier. This paper uses the Hogg-Type adaptive procedures to select an optimal score function for a rank-based estimator for these non-linear models. Numeric examples and simulation studies will demonstrate the robustness, utility, efficiency, and validity of these estimates.

Keywords: asymptotic relative efficiency, non-linear rank-based, rank estimates, variogram

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Authors: Andrey V. Timofeev, Dmitry V. Egorov

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The practical efficient approach is suggested for estimation of the seismoacoustic sources energy in C-OTDR monitoring systems. This approach represents the sequential plan for confidence estimation both the seismoacoustic sources energy, as well the absorption coefficient of the soil. The sequential plan delivers the non-asymptotic guaranteed accuracy of obtained estimates in the form of non-asymptotic confidence regions with prescribed sizes. These confidence regions are valid for a finite sample size when the distributions of the observations are unknown. Thus, suggested estimates are non-asymptotic and nonparametric, and also these estimates guarantee the prescribed estimation accuracy in the form of the prior prescribed size of confidence regions, and prescribed confidence coefficient value.

Keywords: nonparametric estimation, sequential confidence estimation, multichannel monitoring systems, C-OTDR-system, non-lineary regression

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Authors: Mahmoud Lot

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In this article, we will discuss the solution of elliptic optimal control problem. First, by using the nite element method, we obtain the discrete form of the problem. The obtained discrete problem is actually a large scale constrained optimization problem. Solving this optimization problem with traditional methods is difficult and requires a lot of CPU time and memory. But split Bergman method converts the constrained problem to an unconstrained, and hence it saves time and memory requirement. Then we use the split Bregman method for solving this problem, and examples show the speed and accuracy of split Bregman methods for solving these types of problems. We also use the SQP method for solving the examples and compare with the split Bregman method.

Keywords: Split Bregman Method, optimal control with elliptic partial differential equation constraint, finite element method

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Authors: Arcady Ponosov., Ramazan Kadiev

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The work studies the global moment stability of solutions of systems of nonlinear differential Itô equations with delays. A modified regularization method (W-method) for the analysis of various types of stability of such systems, based on the choice of the auxiliaryequations and applications of the theory of positive invertible matrices, is proposed and justified. Development of this method for deterministic functional differential equations is due to N.V. Azbelev and his students. Sufficient conditions for the moment stability of solutions in terms of the coefficients for sufficiently general as well as specific classes of Itô equations are given.

Keywords: asymptotic stability, delay equations, operator methods, stochastic noise

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Authors: Taehan Bae

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In this paper, a class of length-biased Weibull mixtures is presented to model loss severity data. The proposed model generalizes the Erlang mixtures with the common scale parameter, and it shares many important modelling features, such as flexibility to fit various data distribution shapes and weak-denseness in the class of positive continuous distributions, with the Erlang mixtures. We show that the asymptotic tail estimate of the length-biased Weibull mixture is Weibull-type, which makes the model effective to fit loss severity data with heavy-tailed observations. A method of statistical estimation is discussed with applications on real catastrophic loss data sets.

Keywords: Erlang mixture, length-biased distribution, transformed gamma distribution, asymptotic tail estimate, EM algorithm, expectation-maximization algorithm

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Authors: Yingyi Zhou, Tohru Kawabe

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With the spread of EVs (electric Vehicles), the ride comfort has been gaining a lot of attention. The influence of the lateral acceleration is important for the improvement of ride comfort of EVs as well as the longitudinal acceleration, especially upon turning of the vehicle. Therefore, this paper proposes a practical optimal speed control method to greatly improve the ride comfort in the vehicle turning situation. For consturcting this method, effective criteria that can appropriately evaluate deterioration of ride comfort is derived. The method can reduce the influence of both the longitudinal and the lateral speed changes for providing a confortable ride. From several simulation results, we can see the fact that the method can prevent aggravation of the ride comfort by suppressing the influence of longitudinal speed change in the turning situation. Hence, the effectiveness of the method is recognized.

Keywords: electric vehicle, speed control, ride comfort, optimal control theory, driving support system

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Authors: M. Y. Malik, Farzana Khan

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In this article, we discuss the behavior of viscous fluid near stagnation point over a stretching cylinder with variable thermal conductivity. The effects of slip conditions are also encountered. Thermal conductivity is considered as a linear function of temperature. By using homotopy analysis method and Fehlberg method we compare the graphical results for both momentum and energy equations. The effect of different parameters on velocity and temperature fields are shown graphically.

Keywords: slip conditions, stretching cylinder, heat generation/absorption, stagnation point flow, variable thermal conductivity

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Authors: Saba Riaz, Syed A. Hussain

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This paper is addressing the estimation method of the unknown population variance of the variable of interest. A new generalized class of estimators of the finite population variance has been suggested using the auxiliary information. To improve the precision of the proposed class, known population variance of the auxiliary variable has been used. Mathematical expressions for the biases and the asymptotic variances of the suggested class are derived under large sample approximation. Theoretical and numerical comparisons are made to investigate the performances of the proposed class of estimators. The empirical study reveals that the suggested class of estimators performs better than the usual estimator, classical ratio estimator, classical product estimator and classical linear regression estimator. It has also been found that the suggested class of estimators is also more efficient than some recently published estimators.

Keywords: study variable, auxiliary variable, finite population variance, bias, asymptotic variance, percent relative efficiency

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Authors: A. Khernane, N. Khelil, L. Djerou

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The aim of this work is to study the numerical implementation of the Hilbert uniqueness method for the exact boundary controllability of Euler-Bernoulli beam equation. This study may be difficult. This will depend on the problem under consideration (geometry, control, and dimension) and the numerical method used. Knowledge of the asymptotic behaviour of the control governing the system at time T may be useful for its calculation. This idea will be developed in this study. We have characterized as a first step the solution by a minimization principle and proposed secondly a method for its resolution to approximate the control steering the considered system to rest at time T.

Keywords: boundary control, exact controllability, finite difference methods, functional optimization

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Authors: Jie Bai, Yongsheng Gao, Shengxin Wang, Jie Zhao

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Through the establishment of the elbow biomechanical model, it can provide theoretical guide for rehabilitation therapy on the upper limb of the human body. A biomechanical model of the elbow joint can be built by the connection of muscle force model and elbow dynamics. But there are many undetermined coefficients in the model like the optimal joint angle and optimal muscle force which are usually specified as the experimental parameters of other workers. Because of the individual differences, there is a certain deviation of the final result. To this end, the RMS value of the deviation between the actual angle and calculated angle is considered. A set of coefficients which lead to the minimum RMS value will be chosen to be the optimal parameters. The direct search method and the conjugacy search method are used to get the optimal parameters, thus the model can be more accurate and mode adaptability.

Keywords: elbow biomechanical model, RMS, direct search, conjugacy search

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Authors: Eddegdag Nasser, Naamane Azzeddine, Radouani Mohammed, Ensam Meknes

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In this study, we are interested in the asymptotic modeling of the two-dimensional stationary supersonic flow of a viscous compressible fluid around wing airfoil. The aim of this article is to solve the partial differential equations of the flow far from the leading edge and near the wall using the triple-deck technique is what brought again in precision according to the principle of least degeneration. In order to validate our theoretical model, these obtained results will be compared with the experimental results. The comparison of the results of our model with experimentation has shown that they are quantitatively acceptable compared to the obtained experimental results. The experimental study was conducted using the AF300 supersonic wind tunnel and a NACA Reduced airfoil model with two pressure Taps on extrados. In this experiment, we have considered the incident upstream supersonic Mach number over a dissymmetric NACA airfoil wing. The validation and the accuracy of the results support our model.

Keywords: supersonic, viscous, triple deck technique, asymptotic methods, AF300 supersonic wind tunnel, reduced airfoil model

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Authors: Yuanhao Gao, Ping Lin, Kees Weijer

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An optimal control system model is proposed for the cell flow in the process of chick embryo gastrulation in this paper. The target is to determine the cellular interaction forces which are hard to measure. This paper will take an approach to investigate the forces with the idea of the inverse problem. By choosing the forces as the control variable and regarding the cell flow as Stokes fluid, an objective functional will be established to match the numerical result of cell velocity with the experimental data. So that the forces could be determined by minimizing the objective functional. The Lagrange multiplier method is utilized to derive the state and adjoint equations consisting the optimal control system, which specifies the first-order necessary conditions. Finite element method is used to discretize and approximate equations. A conjugate gradient algorithm is given for solving the minimum solution of the system and determine the forces.

Keywords: optimal control model, Stokes equation, conjugate gradient method, finite element method, chick embryo gastrulation

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Authors: Yuanhao Gao, Pin Lin, Kees Weijer

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In this paper, we will determine the external body force distribution with analysis of stokes fluid motion using mathematical modelling and numerical approaching. The body force distribution is regarded as the unknown variable and could be determined by the idea of optimal control theory. The Stokes flow motion and its velocity are generated by given forces in a unit square domain. A regularized objective functional is built to match the numerical result of flow velocity with the generated velocity data. So that the force distribution could be determined by minimizing the value of objective functional, which is also the difference between the numerical and experimental velocity. Then after utilizing the Lagrange multiplier method, some partial differential equations are formulated consisting the optimal control system to solve. Finite element method and conjugate gradient method are used to discretize equations and deduce the iterative expression of target body force to compute the velocity numerically and body force distribution. Programming environment FreeFEM++ supports the implementation of this model.

Keywords: optimal control model, Stokes equation, finite element method, conjugate gradient method

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Authors: Ayman Baklizi

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Based on type II censored data, we consider interval estimation of the quantiles of the two-parameter exponential distribution and the difference between the quantiles of two independent two-parameter exponential distributions. We derive asymptotic intervals, Bayesian, as well as intervals based on the generalized pivot variable. We also include some bootstrap intervals in our comparisons. The performance of these intervals is investigated in terms of their coverage probabilities and expected lengths.

Keywords: asymptotic intervals, Bayes intervals, bootstrap, generalized pivot variables, two-parameter exponential distribution, quantiles

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Authors: Li-Ching Chen

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The case-control design has been widely applied in clinical and epidemiological studies to investigate the association between risk factors and a given disease. The retrospective design can be easily implemented and is more economical over prospective studies. To adjust effects for confounding factors, methods such as stratification at the design stage and may be adopted. When some major confounding factors are difficult to be quantified, a matching design provides an opportunity for researchers to control the confounding effects. The matching effects can be parameterized by the intercepts of logistic models and the conditional logistic regression analysis is then adopted. This study demonstrates an information-matrix-based goodness-of-fit statistic to test the validity of the logistic regression model for matched case-control data. The asymptotic null distribution of this proposed test statistic is inferred. It needs neither to employ a simulation to evaluate its critical values nor to partition covariate space. The asymptotic power of this test statistic is also derived. The performance of the proposed method is assessed through simulation studies. An example of the real data set is applied to illustrate the implementation of the proposed method as well.

Keywords: conditional logistic model, goodness-of-fit, information matrix, matched case-control studies

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Authors: Tomoaki Hashimoto

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Recently, optimal control problems subject to probabilistic constraints have attracted much attention in many research field. Although probabilistic constraints are generally intractable in optimization problems, several methods haven been proposed to deal with probabilistic constraints. In most methods, probabilistic constraints are transformed to deterministic constraints that are tractable in optimization problems. This paper examines a method for transforming probabilistic constraints into deterministic constraints for a class of probabilistic constrained optimal control problems.

Keywords: optimal control, stochastic systems, discrete-time systems, probabilistic constraints

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Authors: Pius W. Molo Chin

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Real life problems such as the Huxley equation are always modeled as nonlinear differential equations. These problems need accurate and reliable methods for their solutions. In this paper, we propose a nonstandard finite difference method in time and the Galerkin combined with the compactness method in the space variables. This coupled method, is used to analyze a two dimensional Huxley equation for the existence and uniqueness of the continuous solution of the problem in appropriate spaces to be defined. We proceed to design a numerical scheme consisting of the aforementioned method and show that the scheme is stable. We further show that the stable scheme converges with the rate which is optimal in both the L2 as well as the H1-norms. Furthermore, we show that the scheme replicates the decaying qualities of the exact solution. Numerical experiments are presented with the help of an example to justify the validity of the designed scheme.

Keywords: Huxley equations, non-standard finite difference method, Galerkin method, optimal rate of convergence

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Authors: Mohammad Reza Shahnazari, Reza Kazemi, Ali Saberi

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Most of the engineering problems are in nonlinear forms. Nonlinear boundary layer problems defined in infinite intervals contain specific complexities, especially in boundary layer condition conformance. As an example of these nonlinear complex problems, the well-known Blasius equation can be mentioned, which itself is one of the classic boundary layer problems. No analytical solution has been proposed yet for the Blasius equation due to its complexity. In this paper, an analytical method, namely the Kourosh method, based on the singularity perturbation method and the Liao homotopy analysis is utilized to solve the Blasius problem. In this method, an inner solution is developed in the [0,1] interval to expedite the solution convergence. The magnitude of the f ˝(0), as an essential quantity for determining the physical parameters, is directly calculated from the solution of the boundary condition problem. The advantages of this solution are that it does not need any numerical solution, it has a closed form and that its validation is shown in the entire [0,∞] interval. Furthermore, all of the desirable parameters could be extracted through a series of simple analytical operations from the final solution. This solution also satisfies the continuity conditions, which is one of the main contributions of this paper in comparison with most of the other proposed analytical solutions available in the literature. Comparison with numerical solutions reveals that the proposed method is highly accurate and convenient for application.

Keywords: Blasius equation, boundary layer, Kourosh method, analytical solution

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Authors: Shilan Rahmani Azr, Siavash Emtiyaz

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Recent development in computing and communicative technologies leads to much easier mobile accessibility to the information. Users can access to the information in different places using various deceives in which the care variety of abilities. Meanwhile, the format and details of electronic documents are changing each day. In these cases, a mismatch is created between content and client’s abilities. Recently the service-oriented content adaption has been developed which the adapting tasks are dedicated to some extended services. In this method, the main problem is to choose the best appropriate service among accessible and distributed services. In this paper, a method for determining the optimal path to the best services, based on the quality control parameters and user preferences, is proposed using max heap tree. The efficiency of this method in contrast to the other previous methods of the content adaptation is related to the determining the optimal path of the best services which are measured. The results show the advantages and progresses of this method in compare of the others.

Keywords: service-oriented content adaption, QoS, max heap tree, web services

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Authors: Satyanarayana Engu, Ahmed Mohd, V. Murugan

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We study the large time asymptotics of solutions to the Cauchy problem for a forced Burgers equation (FBE) with the initial data, which is continuous and summable on R. For which, we first derive explicit solutions of FBE assuming a different class of initial data in terms of Hermite polynomials. Later, by violating this assumption we prove the existence of a solution to the considered Cauchy problem. Finally, we give an asymptotic approximate solution and establish that the error will be of order O(t^(-1/2)) with respect to L^p -norm, where 1≤p≤∞, for large time.

Keywords: Burgers equation, Cole-Hopf transformation, Hermite polynomials, large time asymptotics

Procedia PDF Downloads 295