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Abstract: The aim of this paper is to design a neural network based adaptive control scheme for redundant manipulators in the presence of model uncertainties and external disturbances together with multiple self-motion criteria. With reference to the paper (N. Kumar, V. Panwar, N. Sukavanam, S.P. Sharma, J.H. Borm, Neural network based nonlinear tracking control of kinematically redundant robot manipulators, Mathematical and Computer Modelling 53 (2011) 1889–1901), an adaptive mechanism is also developed to estimate the uncertain bound of external disturbances and neural network approximation error etc. without requirement of known bounds. By Lyapunov method asymptotic error convergence can be guaranteed for both task-space and sub-task tracking errors. A comparative simulation study with a robust controller and the proposed controller are included for a 3 link planar robot manipulator. [Copyright &y& Elsevier]

Abstract: Part 1 of this paper proposed a methodology for the efficient determination of gradient information, when optimising a vehicle’s suspension characteristics for ride comfort and handling. The non-linear full vehicle model, and simplified models for gradient information has been discussed, and validated. In this paper, the simplified models presented in Part 1 are used for gradient information simulations. The convergence histories of the optimisation are compared to those obtained when only the full, computationally expensive, vehicle model is used. For illustration of the proposed gradient-based optimisation methodology, up to four design variables are considered in modelling the suspension characteristics. The proposed methodology is found to be an efficient alternative for the optimisation of the vehicle’s suspension characteristics. The undesirable effects associated with noise in the gradient information is effectively reduced, using the simplified models. Substantial benefits are achieved in terms of computational time needed to reach a solution. [Copyright &y& Elsevier]

Abstract: In this paper we study the transport of a reactive solute through a thin (or long) cylindrical pipe filled with micropolar fluid. We suppose that the solute particles undergo a first-order chemical reaction at the lateral boundary of the pipe. The effective model for solute concentration is derived by means of a formal asymptotic analysis with respect to the pipe’s thickness. The asymptotic approximation is built, showing explicitly the effects of fluid microstructure and chemical reaction on the solute dispersion. [Copyright &y& Elsevier]

Abstract: Conductivity of non-overlapping disks embedded in a two-dimensional background can be investigated by the method of images which is based on the successive application of the inversions with respect to circles. For closely placed disks, the classical method of images yields slowly convergent series. The method of images can be treated as an application of successive approximations to a system of functional equations. In this paper, modified functional equations are deduced to essentially accelerate the convergence. [Copyright &y& Elsevier]

Abstract: In this paper, with the compounded rate of removed errors, a new software reliability model is proposed. By the least squares and first-order differential methods, the approximate parameters of the model are obtained. The applicability of proposed model is demonstrated on three well-known real software data sets. The results show that our model has a good capability of fitting and predicting. Moreover, when we own enough history failure data of software, predicting results will be fairly accurate. [Copyright &y& Elsevier]

Abstract: In this paper, a multi-step differential transform method (MsDTM) is performed to give approximate and analytical solutions of nonlinear fractional order ordinary differential equation systems such as a model for HIV infection of CD4+ T cells. The numerical solutions obtained from the proposed method indicate that the approach is easy to implement and accurate when applied to systems of fractional differential equations. Some figures are presented to show the reliability and simplicity of the methods. [Copyright &y& Elsevier]

Abstract: Geometric modelling using Partial Differential Equations (PDEs) has been gradually recognised due to its smooth instinct, as well as the ability to generate a variety of geometric shapes by intuitively manipulating a relatively small set of PDE boundary curves. In this paper we explore and demonstrate the feasibility of the PDE method in facial geometry parameterisation. The geometry of a generic face is approximated by evaluating spectral solutions to a group of fourth order elliptic PDEs. Our PDE-based parameterisation scheme can produce and animate a high-resolution 3D face with a relatively small number of parameters. By taking advantage of parametric representation, the PDE method can use one fixed animation scheme to manipulate the facial geometry in varying Levels of Detail (LODs), without any further process. [Copyright &y& Elsevier]

Abstract: In this paper we propose the numerical solutions of stochastic initial value problems via random Runge–Kutta methods of the second order and mean square convergence of these methods is proved. A random mean value theorem is required and established. The concept of mean square modulus of continuity is also introduced. Expectation and variance of the approximating process are computed. Numerical examples show that the approximate solutions have a good degree of accuracy. [Copyright &y& Elsevier]

Abstract: In this paper, the Laplace Adomian Decomposition Method is implemented to give an approximate solution of nonlinear ordinary differential equation systems, such as a model for HIV infection of cells. The technique is described and illustrated with numerical example. Some plots are presented to show the reliability and simplicity of the methods. [ABSTRACT FROM AUTHOR]

Abstract: One important issue in DEA which has been studied by many DEA researchers is the sensitivity of the results of an analysis to perturbations in the data. This paper develops a procedure for performing a sensitivity analysis of the inefficient decision making units (DMUs). The procedure yields an exact “Necessary Change Region” in which the efficiency score of a specific inefficient DMU changes to a defined efficiency score. In what follows, we identify a new frontier, and prove the efficiency score of each arbitrary unit on it which is defined as the efficiency score. [ABSTRACT FROM AUTHOR]

Abstract: The subject of this paper are analytic approximate methods for pantograph stochastic differential equations with Markovian switching, as well as their counterparts without Markovian switching. Approximate equations are defined on equidistant partitions of the time interval, and their coefficients are Taylor approximations of the coefficients of the initial equation. In the case with Markovian switching we will present the approximate method based on Taylor approximation of coefficients in two arguments and show that the appropriate approximate solutions converge in the -norm to the solution of the initial equation. Then we will present the other approximate method which deals with Taylor approximation in the first argument. In both cases the closeness between the approximate solution and the solution of the initial equation depends on the number of degrees in Taylor approximations of coefficients, although the presence of the Markov chain affects it. These approximate methods are then adapted to the case without Markovian switching. The first method gives the possibility of proving convergence as well as a.s. convergence of the appropriate sequence of approximate solutions to the solution of the initial equation. [ABSTRACT FROM AUTHOR]

Abstract: A methodology is proposed for the efficient determination of gradient information, when performing gradient based optimisation of an off-road vehicle’s suspension system. The methodology is applied to a computationally expensive, non-linear vehicle model, that exhibits severe numerical noise. A recreational off-road vehicle is modelled in MSC.ADAMS, and coupled to MATLAB for the execution of the optimisation. The successive approximation method, Dynamic-Q, is used for the optimisation of the spring and damper characteristics. Optimisation is performed for both ride comfort and handling. The determination of the objective function value is performed using computationally expensive numerical simulations. This paper proposes a non-linear pitch-plane model, to be used for the gradient information, when optimising ride comfort. When optimising for handling, a non-linear four wheel model, that includes roll, is used. The gradients of the objective function and constraint functions are obtained through the use of central finite differences, within Dynamic-Q, via numerical simulation using the proposed simplified models. The importance of correctly scaling these simplified models is emphasised. The models are validated against experimental results. The simplified vehicle models exhibit significantly less numerical noise than the full vehicle simulation model, and solve in significantly less computational time. [Copyright &y& Elsevier]