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This paper re-examines the long-run causal relationship between military expenditure and economic growth in China over the period 1952–2010. An empirical econometric analysis based on a Barro-style growth model is conducted. By employing the Bartlett corrected trace test, which provides better approximations of the finite sample distribution to determine the rank of cointegration, the results support the existence of a single long-run equilibrium relationship between the variables. Furthermore, it is confirmed that the cumulated shocks of military expenditure primarily originate from different components of shocks that relate to economic development rather than the other way round. [ABSTRACT FROM AUTHOR]

Interval-censored data arise when a failure time say,Tcannot be observed directly but can only be determined to lie in an interval obtained from a series of inspection times. The frequentist approach for analysing interval-censored data has been developed for some time now. It is very common due to unavailability of software in the field of biological, medical and reliability studies to simplify the interval censoring structure of the data into that of a more standard right censoring situation by imputing the midpoints of the censoring intervals. In this research paper, we apply the Bayesian approach by employing Lindley's 1980, and Tierney and Kadane 1986 numerical approximation procedures when the survival data under consideration are interval-censored. The Bayesian approach to interval-censored data has barely been discussed in literature. The essence of this study is to explore and promote the Bayesian methods when the survival data been analysed are is interval-censored. We have considered only a parametric approach by assuming that the survival data follow a loglogistic distribution model. We illustrate the proposed methods with two real data sets. A simulation study is also carried out to compare the performances of the methods. [ABSTRACT FROM AUTHOR]

This paper presents a study on lookahead hierarchies for restarting automata with auxiliary symbols. We show that the class of languages for deterministic monotone or monotone restarting automaton, whose restart step and rewrite step are separated, coincides with that of the same type of restarting automaton whose restart and rewrite steps are not separated, for any fixed lookahead size. For the non-monotone deterministic case, the lookahead length must be approximately doubled. We then turn our attention to restarting automata with small lookahead. For the general restarting automaton model, we show that there are just two different classes of languages recognized, through the restriction of lookahead size: those with lookahead size 1 and those with lookahead size 2. We also show that the respective (left-) monotone restarting automaton models characterize the context-free languages and that the respective right–left-monotone restarting automata characterize the linear languages both with just lookahead length 2. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a generalized Laguerre spectral method for Fisher's-type equation with inhomogeneous boundary conditions on a semi-infinite interval. By reformulating the equation with suitable functional transform, it is shown that the generalized Laguerre approximations are convergent on a semi-infinite interval with spectral accuracy. An efficient and accurate algorithm based on the generalized Laguerre approximations to the transformed equation is developed and implemented. Numerical results show the efficiency of this approach and coincide well with theoretical analysis. [ABSTRACT FROM PUBLISHER]

In this paper, we study the conductivity coefficient determination in the heat equation from observation of the lateral Dirichlet-to-Neumann map. We define a bilinear form functionQγassociated to the boundary condition and the Dirichlet-to-Neumann map, and prove that the linearized problemd Qγis injective. Based on the idea of complex geometrical optics solutions, we give two approximations to the conductivity coefficient by using the Fourier truncation method and the mollification method. Under the a priori assumption of the conductivity, we estimate the errors between the conductivity coefficient and its approximations by setting a suitable bound of the frequency. [ABSTRACT FROM PUBLISHER]

In this paper, we explore the question of which non-linear inverse problems, which are solved by a selected regularization method, may have so-called linear a priori accuracy estimates – that is, the accuracy of corresponding approximate solutions linearly depends on the error level of the data. In particular, we prove that if such a linear estimate exists, then the inverse problem under consideration is well posed, according to Tikhonov. For linear inverse problems, we find that the existence of linear estimates lead to, under some assumptions, the well-posedness (according to Tikhonov) on the whole space of solutions. Moreover, we consider a method for solving inverse problems with guaranteed linear estimates, calledthe residual method on the correctness set(RMCS). The linear a priori estimates of absolute and relative accuracy for the RMCS are presented, as well as analogous a posteriori estimates. A numerical illustration of obtaining linear a priori estimates for appropriate parametric sets of solutions using RMCS is given in comparison with Tikhonov regularization. The a posteriori estimates are calculated on these parametric sets as well. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate a fully discrete local discontinuous Galerkin approximation of a non-linear non-Fickian diffusion model in viscoelastic polymers. For the spatial discretization, we adopt local discontinuous Galerkin finite element method and for the time discretization we use backward Euler method. We derive the stability estimate and a priori error estimate for the discrete scheme. Numerical examples are given to verify the theoretical findings. [ABSTRACT FROM PUBLISHER]

In this paper, we establish hierarchic control for the linear heat equation in ℝNwith potentials. Our strategy is inspired by the techniques developed by Díaz and Lions [On the approximate controllability of Stackelberg-Nash strategies. In: Díaz JI, editor. Ocean circulation and pollution control mathematical and numerical investigations. Berlin: Springer; 2005. p. 17–27]; however, many new difficulties arise due to lack of compactness of Sobolev embeddings. We manage these adversities by employing similarity variables and weighted Sobolev spaces. [ABSTRACT FROM PUBLISHER]

Independent component analysis (ICA) is a popular blind source separation technique used in many scientific disciplines. Current ICA approaches have focused on developing efficient algorithms under specific ICA models, such as instantaneous or convolutive mixing conditions, intrinsically assuming temporal independence or autocorrelation of the sources. In practice, the true model is not known and different ICA algorithms can produce very different results. Although it is critical to choose an ICA model, there has not been enough research done on evaluating mixing models and assumptions, and how the associated algorithms may perform under different scenarios. In this paper, we investigate the performance of multiple ICA algorithms under various mixing conditions. We also propose a convolutive ICA algorithm for echoic mixing cases. Our simulation studies show that the performance of ICA algorithms is highly dependent on mixing conditions and temporal independence of the sources. Most instantaneous ICA algorithms fail to separate autocorrelated sources, while convolutive ICA algorithms depend highly on the model specification and approximation accuracy of unmixing filters. [ABSTRACT FROM PUBLISHER]

In this paper, a new method for the design of variable bandwidth linear-phase finite impulse response filters using Bernstein polynomial Multiwavelets is proposed. In this method, approximation has been achieved by linearly combining the fixed coefficient linear phase filters with Bernstein multiwavelets, which are used to tune bandwidth of the filter. Optimisation has been achieved by minimising the mean square error between the desired and actual filter response which leads to a system of linear equations. The matrix elements can be expressed in form of Toeplitz-plus-Hankel matrix, which reduces the computational complexity. The simulation results illustrate significant improvement in errors in passband (ep), and stopband (es) as compared to earlier published work. [ABSTRACT FROM AUTHOR]

Sufficient conditions for a weak local minimizer in the classical calculus of variations can be expressed without reference to conjugate points. The local quadratic convergence of Newton’s method follows from these sufficient conditions. Newton’s method is applied in the minimization form; that is, the step is generated by minimizing the local quadratic approximation. This allows the extension to a globally convergent line search based algorithm (which will be presented in a future paper). [ABSTRACT FROM PUBLISHER]

The efficient iterative method of moments and physical optics (EI-MoM–PO) hybrid formulation combined with the best uniform approximation is proposed to analyze the antenna array around the electrically large platform in this paper. In the conventional MoM–PO method, the computation of the mutual interaction matrix between the MoM and PO region is very time consuming. To facilitate the analysis of electrically large problems, the EI-MoM–PO method provides a possible way to avoid the calculation of the PO contribution in matrix form. On the other hand, the best uniform approximation is utilized to obtain the frequency response of antennas quickly and easy to be applied in EI-MoM–PO method. Finally, the frequency response of the bowtie antenna array around the electrically large platform is analyzed by the presented algorithm and the conventional one. Numerical results demonstrate the capability of the proposed technique. [ABSTRACT FROM AUTHOR]

This paper is aimed at deriving the error asymptotic expansion of trapezoidal rule approximation to integrals for the functions with fractional derivatives or algebraic singularities at some points and from which to design a modified Romberg extrapolation algorithm to effectively compute some singular integrals. Firstly, high-order local fractional derivatives are defined, then a general fractional Taylor's expansion is derived. Secondly, the error asymptotic expansion of trapezoidal rule for these integrals is obtained directly by using the formula of sums of non-integer powers and the general fractional Taylor's expansion. This method is different from the previous work. Thirdly, a modified Romberg extrapolation algorithm is designed to get numerical results efficiently. Finally, numerical examples are presented to verify the correctness of the theoretical analysis and the effectiveness of the extrapolation method. [ABSTRACT FROM AUTHOR]

In this paper, when a jointly Type-II censored sample arising fromkindependent exponential populations is available, the conditional MLEs of thekexponential mean parameters are derived. The moment generating functions and the exact densities of these MLEs are obtained using which exact confidence intervals are developed for the parameters. Moreover, approximate confidence intervals based on the asymptotic normality of the MLEs and credible confidence regions from a Bayesian viewpoint are also discussed. An empirical comparison of the exact, approximate, bootstrap, and Bayesian intervals is also made in terms of coverage probabilities. Finally, an example is presented in order to illustrate all the methods of inference developed here. [ABSTRACT FROM AUTHOR]

The aim of the paper is to investigate the Monge–Ampère measures of maximal subextensions of plurisubharmonic functions with given boundary values. As an application, we study the approximation of negative plurisubharmonic function with given boundary values by an increasing sequence of plurisubharmonic functions defined in larger domains. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamical behaviour of the fractional delayed damped Mathieu equation. This system includes three different phenomena (fractional order, time delay, parametric resonance). The method of harmonic balance is employed to achieve approximate expressions for the transition curves in the parameter plane. Then= 0 andn= 1 transition curves (both lower and higher order approximations) are obtained. The dependencies of these curves on the system parameters and fractional orders are determined. Previous results for the transition curves reported for the damped Mathieu equation, delayed second-order oscillator, and fractional Mathieu equation are confirmed as special cases of the results for the current system. [ABSTRACT FROM PUBLISHER]

In this paper, we consider an optimal co with state and control constraints, where a prespecified sequence of active subsystems is given. Both the switching instants and the control function are to be chosen such that the cost functional is minimized. Firstly, we convert the problem into a conventional optimal control problem based on parameterization of the switching instants. Next, through discretizing the control space, applying a time-scaling transformation and using the smoothing technique, the optimal control problem is approximated by a non-linear optimization problem with linear constraints and bounds on the variables. Furthermore, an algorithm that finds a suboptimal solution to the original problem is proposed. One major advantage with the new algorithm implementation is the only need to solve a non-linear optimization problem with linear constraints and bounds on the variables. The gradients of these linear constraints and the objective function can be easily obtained. Therefore, the original optimization problem can be solved efficiently using any gradient-based method, such as sequential quadratic programming algorithm. Finally, a flight planning example illustrates the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, we consider the stochastic facility location problem with submodular penalties. By exploring the structural properties of submodular function, we present a primal-dual-approximation algorithm for the problem. [ABSTRACT FROM AUTHOR]

In this paper, a parallel Robin–Robin domain decomposition method for H(div)-elliptic problems is proposed. The convergence of the method is proved for both the continuous problem and the finite element approximation. Some numerical testes are also presented to demonstrate the effectiveness of the method. [ABSTRACT FROM PUBLISHER]

Copositive and completely positive matrices play an increasingly important role in Applied Mathematics, namely as a key concept for approximating NP-hard optimization problems. The cone of copositive matrices of a given order and the cone of completely positive matrices of the same order are dual to each other with respect to the standard scalar product on the space of symmetric matrices. This paper establishes some new relations between orthogonal pairs of such matrices lying on the boundary of either cone. As a consequence, we can establish an improvement on the upper bound of the cp-rank of completely positive matrices of general order and a further improvement for such matrices of order six. [ABSTRACT FROM AUTHOR]

Developing scales is a critical step in monitoring and evaluating ecotourism to ensure sustainability. Replicating studies to test if scales are enduring in evaluating visitors’ assessments of ecotourism is also essential to ensure reliability and credibility, and to track changes. This paper reports on a sample of 404 international visitors in Nepal's Annapurna Conservation Area, undertaken in 2012, to test for scale stability and change from a 2006 survey. The original scale was cross-validated by confirmatory factor analysis, and then mean-level change and rank-order stability of scale items were reported. There was strong support for the original factor model in the new sample; all items were loaded on a single construct; their loadings were statistically significant, the root-mean-square error of approximation was .076, the comparative fit index was .993, and the non-normed fit index was .987. Although a statistically significant decrease in the mean of scale items was found, the items’ rank-ordering remained similar. The Spearman's rank-order correlation between factor loadings of 2006 and 2012 was .714 and statistically significant. Cronbach's alpha was .845, comparable to the previous alpha of .910. The ecotourism evaluation scale showed temporal consistency but also detected changes in visitors’ attitudes requiring management attention. [ABSTRACT FROM PUBLISHER]

For nonlinear descriptor systems, this paper presents an approach to obtain a fuzzy controller with guaranteed finite-time stability and finite-time boundedness with non-zero initial state, which outperforms some recent work and additionally provides a precision estimation of model approximation. We prove necessary and sufficient conditions of finite-time stability and finite-time boundedness with non-zero initial state for nonlinear descriptor systems. Using Takagi–Sugeno fuzzy dynamic models and proposed sufficient conditions, we define fuzzy sets and use linear matrix inequalities to satisfy differential linear matrix inequalities. A simulation confirms efficiency and precision of the given method. [ABSTRACT FROM PUBLISHER]

In this paper an efficient numerical method for solving a class of multipoint boundary value problems with special boundary conditions of Birkhoff-type is presented. After a quick reference to Birkhoff-type interpolation polynomial which satisfies the particular conditions, and a result on the existence and uniqueness of solution of the given problem, an algorithm is introduced to find a polynomial that approximates the solution. It is a general collocation method. Then an a priori estimation of the error of this approximation is given. Finally, to show the efficiency and the applicability of the method, numerical results are presented. These numerical experiments provide favourable comparisons with the NDSolve command of Mathematica. [ABSTRACT FROM AUTHOR]

In this paper, we derive a high-order compact finite difference scheme for solving the reaction–subdiffusion equation with Neumann boundary value condition. The L1 method is used to approximate the temporal Caputo derivative, and the compact difference operator is applied for spatial discretization. We prove that the compact finite difference method is unconditionally stable and convergent with orderO(τ2−α+h4) inL2norm, where τ, α, andhare the temporal step size, the order of time fractional derivative and the spatial step size, respectively. Finally, some numerical experiments are carried out to show the effectiveness of the proposed difference scheme. [ABSTRACT FROM AUTHOR]

Conic sections have many applications in industrial design, however, they cannot be exactly represented in polynomial form. Hence approximating conic sections with polynomials is a challenging problem. In this paper, we use the monomial form of Delgado and Peña (DP) curves and present a matrix representation for them. Using the matrix form and the least squares method, we propose a simple and efficient algorithm for approximating conic sections by DP curves of arbitrary degree with endpoint interpolation. Finally, we test and compare the proposed algorithm on some numerical examples which validates and confirms efficiency of it. [ABSTRACT FROM AUTHOR]

The goal of this paper is twofold: first, it investigates the effect of low-pass spatial filters for approximate deconvolution large eddy simulation (AD-LES) of turbulent incompressible flows. Second, it proposes the hyper-differential filter as a means of increasing the accuracy of the AD-LES model without increasing the computational cost. Box filters, Padé filters, and differential filters with a wide range of parameters are studied in the AD-LES framework. The AD-LES model, in conjunction with these spatial filters, is tested in the numerical simulation of the two-dimensional and three-dimensional Taylor–Green vortex problems. We show that the most accurate results are obtained with the hyper-differential filter, followed by the differential filter. We also demonstrate that the results highly depend on the selection of the filtering procedure. It seems that filters whose transfer function resembles that of the Fourier cut-off filter (such as the hyper-differential filters) tend to perform the best. [ABSTRACT FROM AUTHOR]

This paper deals with best nonlinear simultaneous approximation problems to two continuous functions under a general monotonic norm on. Characterizations results of Kolmogorov type and of alternation type and uniqueness results for the best simultaneous approximation are established. Applications are given to the set of rational functions. [ABSTRACT FROM PUBLISHER]

In this paper we consider the thin film equation with prescribed non-zero contact angle condition for a large class of mobility coefficients, in dimension 1. We prove the global in time existence of weak solutions by using a diffuse approximation of the free boundary condition. This approach, which can be physically motivated by the introduction of singular disjoining/conjoining pressure forces had been suggested in particular by Bertsch et al. in [11]. [ABSTRACT FROM AUTHOR]

This paper aims at studying, in the image space, an approximation of a vector optimization problem obtained by substituting the involved functions with their-derivatives. It is shown that, under the hypothesis of-differentiability, the existence of a lower semistationary point is equivalent to the linear separation between the image of the approximated problem and a suitable convex subset of the image space. Applications to optimality conditions are provided. [ABSTRACT FROM AUTHOR]

In the present paper, we consider a Cauchy problem for the Laplace equation in a rectangle domain. A new filtering method is presented for approximating the solution of this problem, and the Hölder-type error estimates are obtained by the different parameter choice rules. Numerical illustration shows that the proposed method works effectively. [ABSTRACT FROM PUBLISHER]

In the present paper we construct the cubic B-spline operational matrix of fractional derivative in the Caputo sense, and use it to solve fractional differential equation. The main characteristic of the approach is that it overcomes the computational difficulty induced by the memory effect. There is no need to save and call all historic information, which can save memory space and reduce computational complexity. Numerical results demonstrate the validity and applicability of the method to solve fractional differential equation. The results from this method are good in terms of accuracy. [ABSTRACT FROM PUBLISHER]

A new analytical method for the approximate computation of the time-dependent Green's function for the initial-boundary value problem of the three-dimensional wave equation on multi-layered bounded cylinder is suggested in this paper. The method is based on the derivation of eigenvalues and eigenfunctions for an ordinary differential equation with piecewise constant coefficients, and an approximate computation of Green's function in the form of the Fourier series with a finite number of terms relative to the orthogonal set of the derived eigenfunctions. The computational experiment confirms the robustness of the method. [ABSTRACT FROM PUBLISHER]

Sung [On inverse moments for a class of nonnegative random variables. J Inequal Appl. 2010;2010:1–13. Article ID 823767, doi:10.1155/2010/823767] obtained the asymptotic approximation of inverse moments for a class of nonnegative random variables with finite second moments and satisfying a Rosenthal-type inequality. In the paper, we further study the asymptotic approximation of inverse moments for a class of nonnegative random variables with finite first moments, which generalizes and improves the corresponding ones of Wu et al. [Asymptotic approximation of inverse moments of nonnegative random variables. Statist Probab Lett. 2009;79:1366–1371], Wang et al. [Exponential inequalities and inverse moment for NOD sequence. Statist Probab Lett. 2010;80:452–461; On complete convergence for weighted sums of ϕ mixing random variables. J Inequal Appl. 2010;2010:1–13, Article ID 372390, doi:10.1155/2010/372390], Sung (2010) and Hu et al. [A note on the inverse moment for the nonnegative random variables. Commun Statist Theory Methods. 2012. Article ID 673677, doi:10.1080/03610926.2012.673677]. [ABSTRACT FROM PUBLISHER]

In this paper, an approximation approach is used to study existence of distributional solutions for degenerate quasilinear elliptic problems having multiple singularities in the whole space. [ABSTRACT FROM PUBLISHER]

In this paper, the approximate controllability of the semilinear functional differential equations with unbounded delays is first investigated. Then the regularity of solutions of the given system is addressed. Finally, a simple example to which our main result can be applied is given. [ABSTRACT FROM PUBLISHER]

This paper proposes an explicit model predictive control design approach for regulation of linear time-invariant systems subject to both state and control constraints, in the presence of additive disturbances. The proposed control law is implemented as a piecewise-affine function defined on a regular simplicial partition, and has two main positive features. First, the regularity of the simplicial partition allows one to efficiently implement the control law on digital circuits, thus achieving extremely fast computation times. Moreover, the asymptotic stability (or the convergence to a set including the origin) of the closed-loop system can be enforceda priori, rather than checkeda posteriorivia Lyapunov analysis. [ABSTRACT FROM PUBLISHER]

A generalized version of inverted exponential distribution (IED) is considered in this paper. This lifetime distribution is capable of modeling various shapes of failure rates, and hence various shapes of aging criteria. The model can be considered as another useful two-parameter generalization of the IED. Maximum likelihood and Bayes estimates for two parameters of the generalized inverted exponential distribution (GIED) are obtained on the basis of a progressively type-II censored sample. We also showed the existence, uniqueness and finiteness of the maximum likelihood estimates of the parameters of GIED based on progressively type-II censored data. Bayesian estimates are obtained using squared error loss function. These Bayesian estimates are evaluated by applying the Lindley's approximation method and via importance sampling technique. The importance sampling technique is used to compute the Bayes estimates and the associated credible intervals. We further consider the Bayes prediction problem based on the observed samples, and provide the appropriate predictive intervals. Monte Carlo simulations are performed to compare the performances of the proposed methods and a data set has been analyzed for illustrative purposes. [ABSTRACT FROM PUBLISHER]

In this paper, we suggest regression-type estimators for estimating the Bowley's coefficient of skewness using auxiliary information. To the first degree of approximation, the bias and mean-squared error expressions of the regression-type estimators are obtained, and the regions under which these estimators are more efficient than the conventional estimator are also determined. Further, a general class of estimators of the Bowley's coefficient of skewness is defined along with its properties. A class of estimators based on estimated optimum values is also defined. It is shown to the first degree of approximations that the variance of the class of estimators based on estimated optimum values is the same as that of the minimum variance of the proposed class of estimators. A simulation study is carried out to demonstrate the performance of the proposed difference estimator over the usual estimator. [ABSTRACT FROM AUTHOR]

In this paper, we propose an approximation method based on the Wiener–Ito chaos expansion for the pricing of European contingent claims. Our method is applicable to widely used option pricing models such as local volatility models, stochastic volatility models and their combinations. This method is useful in practice since the resulting approximation formula is not computationally expensive, hence it is suitable for calibration purposes. We will show through some numerical examples that our approximation remains quite good even for the long maturity and/or the high volatility cases, which is a desired feature. As an example, we propose a hybrid volatility model and apply our approximation formula to the JPY/USD currency option market obtaining very accurate results. [ABSTRACT FROM AUTHOR]

This paper discusses the use of polyhedral approximations in solvingp-order cone programming (pOCP) problems, or linear problems withp-order cone constraints, and their mixed-integer extensions. In particular, it is shown that the cutting-plane technique proposed in Krokhmal and Soberanis [Risk optimization with p-order conic constraints: A linear programming approach, Eur. J. Oper. Res. 201 (2010), pp. 653–671,http://dx.doi.org/10.1016/j.ejor.2009.03.053] for a special type of polyhedral approximations of pOCP problems, which allows for generation of cuts in constant time not dependent on the accuracy of approximation, is applicable to a larger family of polyhedral approximations. We also show that it can further be extended to form an exact solution method for pOCP problems withO(ϵ−1) iteration complexity. Moreover, it is demonstrated that an analogous constant-time cut-generating algorithm exists for recursively constructed lifted polyhedral approximations of second-order cones due to Ben-Tal and Nemirovski [On polyhedral approximations of the second-order cone, Math. Oper. Res. 26 (2001), pp. 193–205. Available athttp://dx.doi.org/10.1287/moor.26.2.193.10561]. It is also shown that the developed polyhedral approximations and the corresponding cutting-plane solution methods can be efficiently used for obtaining exact solutions of mixed-integer pOCP problems. [ABSTRACT FROM AUTHOR]

For a biped pole-climbing robot (BiPCR) with grippers, it is an essential demand to determine the target grasp configuration for climbing and transiting between poles, with the graspable region as a priori knowledge. The graspable region on the target pole is critically important for climbing path planning and motion control. To efficiently compute the graspable region for a BiPCR, we propose a novel binary approximating method in this paper. This method may also be applied to generate the three-dimensional (3-D) workspace of a manipulator with constant orientation. The grasping problem and the concept of graspable region for a BiPCR are first introduced. The binary approximating method and the corresponding algorithms are then presented to generate the graspable region. Additional constraints on a biped climbing robot with five degrees of freedom (DoFs) are presented as a supplement to the algorithm. A series of comprehensive simulations are conducted with the five-DoF and six-DoF climbing robots to verify the effectiveness of the proposed method. Finally, the dexterity of biped climbing robots with different DoFs is discussed. [ABSTRACT FROM PUBLISHER]

This paper presents a new family of fourth- compact finite difference schemes for the numerical solution of three-dimensional nonlinear biharmonic equations using coupled approach. The numerical solutions of unknown variable and its first- derivatives as well asv(=Δu) are obtained not only in the interior but also at the boundary. A prominent contribution of this work is that the boundary conditions for the variablevare approximated more accurately, which plays an important role for the efficiency of calculation. Finally, numerical experiments are conducted to verify the feasibility of this new method and the high accuracy of these schemes, including the steady Navier–Stokes equation in terms of vorticity-stream function formulation. [ABSTRACT FROM PUBLISHER]

This paper presents a method based on matrix-matrix multiplication concepts for determining the approximate (sparse) inverses of sparse matrices. The suggested method is a development on the well-known Schulz iteration and it can successfully be combined with iterative solvers and sparse approximation techniques as well. A detailed discussion on the convergence rate of this scheme is furnished. Results of numerical experiments are also reported to illustrate the performance of the proposed method. [ABSTRACT FROM PUBLISHER]

Approximations for general fractional order dynamic systems are of much theoretical and practical interest. In this paper, a new approximate method for fractional order integrator is proposed. The poles of the approximate model are unrelated to the order of integrator. This feature shows benefits on extending the algorithm to the systems containing various fractional orders. Then a unified approximate method is derived for general fractional order linear or nonlinear dynamic systems via combining the proposed new method with the distributed frequency model approach. Numerical examples are given to show the wide applicability of our method and to illustrate the acceptable accuracy for approximations as well. [ABSTRACT FROM AUTHOR]

This paper addresses the distributed cooperative stabilisation problem of continuous-time uncertain nonlinear multi-agent systems. By approximating the uncertain dynamics using neural networks, a distributed adaptive cooperative controller, based on the state information of the neighbouring agents, is proposed. The control design is developed for any undirected connected communication topologies without requiring the accurate model of each agent. This result is further extended to the output feedback case. An observer-based distributed cooperative controller is devised and a parameter dependent Riccati inequality is employed to prove stability of the overall multi-agent systems. This design is less complex than the other design methods and has a favourable decouple property between the observer design and the controller design for uncertain nonlinear multi-agent systems. For both cases, the developed controllers guarantee that all signals in the closed-loop network are uniformly ultimately bounded, and the states of all agents cooperatively converge to a small neighbourhood of origin. A comparative study is given to show the efficacy of the proposed method. [ABSTRACT FROM AUTHOR]

This paper attempts to develop a repetitive group sampling (RGS) plan by variables inspection for controlling the process fraction defective or the number of nonconformities when the quality characteristic follows a normal distribution and has only the lower or upper specification limit. The proposed sampling plan is derived by the exact sampling distribution rather than the approximation approach. The plan parameters are solved by a nonlinear optimization model which minimizes the average sample number required for inspection and fulfills the classical two-point conditions on the operating characteristic (OC) curve. The efficiency of the proposed variables RGS is examined and also compared with the existing variables single sampling plan in terms of the sample size required for inspection. The results indicate that the proposed variables RGS plan could significantly reduce samples required for inspection compared to the traditional variables single sampling plan. [ABSTRACT FROM AUTHOR]

In this paper, we study a Cauchy problem of an elliptic equation in a multi-dimensional case. Such a problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. To overcome the ill-posedness of the model problem, a new regularization method is applied to solve it. The corresponding error estimates between the exact solution and its regularization approximation are given. Finally, two numerical experiments are provided to illustrate the main results. [ABSTRACT FROM AUTHOR]

In this paper, a new improved regularization method is proposed to identify dynamic loads in practical engineering problems. Dynamic loads are expressed as the functions of time and the forward model for dynamic load identification is established through the discretized convolution integral of loads and the corresponding unit-pulse response functions of system. With measured responses containing noises, a regularization operator is proposed to construct a novel regularization method, and its regular property is proved. The improved regularization operator and L-curve method are combined to overcome the ill-condition of load reconstruction and to obtain the stable and approximate solutions of inverse problems. The theory is successfully applied to a mathematical problem and a vehicle hood problem in numerical simulations, which demonstrates the efficiency and robustness of the presented method. [ABSTRACT FROM AUTHOR]

Numerical evaluation of ruin probabilities in the classical risk model is an important problem. If claim sizes are heavy-tailed, then such evaluations are challenging. To overcome this, an attractive way is to approximate the claim sizes with a phase-type distribution. What is not clear though is how many phases are enough in order to achieve a specific accuracy in the approximation of the ruin probability. The goals of this paper are to investigate the number of phases required so that we can achieve a pre-specified accuracy for the ruin probability and to provide error bounds. Also, in the special case of a completely monotone claim size distribution we develop an algorithm to estimate the ruin probability by approximating the excess claim size distribution with a hyperexponential one. Finally, we compare our approximation with the heavy traffic and heavy tail approximations. [ABSTRACT FROM AUTHOR]

In this paper, a numerical method based on based quintic B-spline has been developed to solve systems of the linear and nonlinear Fredholm and Volterra integral equations. The solutions are collocated by quintic B-splines and then the integral equations are approximated by the four-points Gauss-Turán quadrature formula with respect to the weight function Legendre. The quintic spline leads to optimal approximation andO(h6) global error estimates obtained for numerical solution. The error analysis of proposed numerical method is studied theoretically. The results are compared with the results obtained by other methods which show that our method is accurate. [ABSTRACT FROM PUBLISHER]