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The traditional parabolic equation (PE) method is based on the finite difference (FD) scheme. However, the scattering object cannot be well approximated for complex geometries. As a result, a large number of meshes are needed to discretize the complex scattering objects. In this paper, the spectral element method is introduced to better approximate the complex geometry in each transverse plane, while the FD scheme is used along the paraxial direction. This proposed algorithm begins with expanding the reduced scattered fields with the Gauss–Lobatto–Legendre polynomials and testing them by the Galerkin’s method in each transverse plane. Then, the calculation can be taken plane by plane along the paraxial direction. Numerical results demonstrate that the accuracy can be improved by the proposed method with larger meshes when compared with the traditional PE method. [ABSTRACT FROM AUTHOR]

A result due to Djordjević shows that the accumulation points of the approximate point spectrum of an operator are invariant under commuting finite rank perturbations. In this paper, we extend it to power finite rank perturbations. Some applications to polaroid operators, a-polaroid operators, generalized Drazin spectrum, generalized Weyl’s theorem, generalized a-Weyl’s theorem, propertyand propertyare given. [ABSTRACT FROM AUTHOR]

Letbe a non-negative matrix. Denote by, the infimum of thosesatisfying the following inequality: where,andis the Fibonacci numbers sequence andis a decreasing, non-negative sequence of real numbers. In this paper, first, the Fibonacci weighted sequence spaceis introduced. Then, we focus on the evaluation of, whereis the Hausdorff matrix operator or the Nörlund matrix operator or the transpose of the Nörlund matrix operator. For the case of Hausdorff matrices, a Hardy-type formula is established as an upper estimate. Also, a general upper estimate is established for the case of Nörlund matrices and their transpose. In particular, we apply our results to Cesàro matrices, Hölder matrices, Euler matrices and Gamma matrices. [ABSTRACT FROM AUTHOR]

This paper presents the design of an adaptive fuzzy sliding mode control (AFSMC) for uncertain discrete-time nonlinear dynamic systems. The dynamic systems are described by a discrete-time state equation with nonlinear uncertainties, and the uncertainties include the modelling errors and the external disturbances to be unknown but nonlinear with the bounded properties. The states are measured by the restriction of measurement sensors and the contamination with independent measurement noises. The nonlinear uncertainties are approximated by using the fuzzy IF-THEN rules based on the universal approximation theorem, and the approximation error is compensated by adding an adaptive complementary term to the proposed AFSMC. The fuzzy inference approach based on the extended single input rule modules is proposed to reduce the number of the fuzzy IF-THEN rules. The estimates for the un-measurable states and the adjustable parameters are obtained by using the weighted least squares estimator and its simplified one. It is proved that under some conditions the estimation errors will remain in the vicinity of zero as time increases, and the states are ultimately bounded subject to the proposed AFSMC. The effectiveness of the proposed method is indicated through the simulation experiment of a simple numerical system. [ABSTRACT FROM PUBLISHER]

This paper considers the promotion cost sharing decision between a supplier and a retailer. The customer demand is affected by both national and local promotional effects while the local promotional effect on a customer is dependent on the distance between the retailer and this customer. We propose a continuous approximation approach to modelling the sum of the customer demand in the whole market area served by the retailer. A model is provided to help managers decide on the retail price, the local advertising expenditure, the national advertising expenditure, and the supplier participation rate, with consideration of the influence of distance on the promotional effect. We also find that the supplier's promotion cost sharing rate increases as the market size increases or the influence of distance on the promotional effect decreases. A numerical example is given to show that the nature of distance-dependent promotional effect has a significant impact on the decisions and profits. [ABSTRACT FROM PUBLISHER]

A new Pareto front approximation method is proposed for multiobjective optimization problems (MOPs) with bound constraints. The method employs a hybrid optimization approach using two derivative-free direct search techniques, and intends to solve black box simulation-based MOPs where the analytical form of the objectives is not known and/or the evaluation of the objective function(s) is very expensive. A new adaptive weighting scheme is proposed to convert a multiobjective optimization problem to a single objective optimization problem. Another contribution of this paper is the generalization of the star discrepancy-based performance measure for problems with more than two objectives. The method is evaluated using five test problems from the literature, and a realistic engineering problem. Results show that the method achieves an arbitrarily close approximation to the Pareto front with a good collection of well-distributed nondominated points for all six test problems. [ABSTRACT FROM AUTHOR]

For a large class of models involving several species competing for a single resource in ahomogeneousenvironment, it is known that the competitive exclusion principle (CEP) holds: only one species survives eventually. Various works indicate though that coexistence of many species is possible when the competition occurs in aheterogeneousenvironment. We propose here a spatially heterogeneous system modeling several species competing for a single resource, and migrating in the spatial domain. For this model, it is known, at least in particular cases, that if migrations areslowenough, then coexistence occurs. In this paper, we show at variance that if the spatial migrations arefastenough, then our system can be approximated by a spatially homogeneous system called aggregated model, which can be explicitly computed, and we show that if the CEP holds for the aggregated model, then it holds as well for the original, spatially heterogeneous model. In other words, we show the persistence of the CEP in the spatially heterogeneous situation when migrations are fast. As a consequence, for fast migrations only one species may survive, namely the best competitorin average. We last study which is the best competitorin averageon some examples, and draw some ecological consequences. [ABSTRACT FROM AUTHOR]

The asymptotic waveform evaluation (AWE) technique is utilized to deal with broadband electromagnetic problems of surface–wire junction geometries in this paper. To ensure the current continuity, triangles-to-segments junction model is used and the Rao–Wilton–Glisson (RWG) and triangular basis functions are used to solve the distributions of current on perfect electric conductor and wire, respectively. Then, the current on surface conductor, wire, and junctions are expanded in a rational function via Padé approximation. The AWE technique needs to store the high-order derivatives of the self-impedance and mutual-impedance matrices of surface–wire, which increase the memory requirements. Thus, the adaptive integral method is employed to reduce memory requirements and to accelerate the matrix-vector multiplications in an iterative solver. Finally, some numerical examples are shown to demonstrate the efficiency and accuracy of the proposed method [ABSTRACT FROM AUTHOR]

This paper proposed a modified ratio-cum-product estimator of finite population mean using information on coefficient of variation and coefficient of kurtosis of auxiliary variable in ranked set sampling. It has been shown that this method is highly beneficial to the estimation based on simple random sampling (SRS). The bias and mean squared error of the proposed estimators with large sample approximation are derived. Theoretically, it is shown that the suggested estimators are more efficient than the estimators in SRS. In addition, we support this theoretical result with the numerical illustration. [ABSTRACT FROM AUTHOR]

The analysis of polycrystalline materials benefits greatly from accurate quantitative descriptions of their grain structures. Laguerre tessellations approximate such grain structures very well. However, it is a quite challenging problem to fit a Laguerre tessellation to tomographic data, as a high-dimensional optimization problem with many local minima must be solved. In this paper, we formulate a version of this optimization problem that can be solved quickly using the cross-entropy method, a robust stochastic optimization technique that can avoid becoming trapped in local minima. We demonstrate the effectiveness of our approach by applying it to both artificially generated and experimentally produced tomographic data. [ABSTRACT FROM PUBLISHER]

In this paper, we consider a general class of two-time-scale Markov chains whose transition rate matrix depends on a parameter. We assume that some transition rates of the Markov chain will tend to infinity as. We divide the state space of the Markov chaininto a fast state space and a slow state space and define a reduced chainon the slow state space. Our main result is that the distribution of the original chainwill converge in total variation distance to that of the reduced chainuniformly in timeas. [ABSTRACT FROM AUTHOR]

The idea of spatial filtering is central in approximate deconvolution large-eddy simulation (AD-LES) of turbulent flows. The need for low-pass filters naturally arises in the approximate deconvolution approach which is based solely on mathematical approximations by employing repeated filtering operators. Two families of low-pass spatial filters are studied in this paper: the Butterworth filters and the Padé filters. With a selection of various filtering parameters, variants of the AD-LES are systematically applied to the decaying Burgers turbulence problem, which is a standard prototype for more complex turbulent flows. Comparing with the direct numerical simulations, it is shown that all forms of the AD-LES approaches predict significantly better results than the under-resolved simulations at the same grid resolution. However, the results highly depend on the selection of the filtering procedure and the filter design. It is concluded that a complete attenuation for the smallest scales is crucial to prevent energy accumulation at the grid cut-off. [ABSTRACT FROM AUTHOR]

One of the most important issues in the design of distributed systems is process scheduling, which maps applications to resources in an attempt to reduce the application execution time or maximise resource utilisation. The complexity involved in finding good scheduling solutions has motivated the design of several heuristics and approximation algorithms. Although heuristics aim at finding good solutions within acceptable time constraints, they do not guarantee solution quality. On the other hand, approximation-based algorithms provide optimal solution bounds, but they are usually designed to address simple scenarios. In an attempt to combine the best of both algorithmic approaches, this paper proposes the min-heap-based scheduling algorithm (MHSA), which finds solutions for homogeneous and heterogeneous distributed environments within acceptable time constraints and optimal solution bounds. MHSA considers applications that can be bag-of-tasks or which communicate among each other. Such solutions minimise the application execution time and maximise resource utilisation; therefore, MHSA is a system-oriented scheduling algorithm. Results confirm that MHSA provides better solutions than schedulers such as Random, Round-Robin, Workload-Queue and List-Scheduling. In addition, MHSA provides an-approximation ratio for reaching optimal solution bounds. [ABSTRACT FROM AUTHOR]

This paper suggested an alternative ratio-cum-product type class of estimators of population mean using exponentiation method in simple random sampling. Approximate bias and mean squared error formulae of the suggested class of estimators have been obtained up to the first order of approximation. Asymptotic optimum estimator in the suggested class of estimators has been obtained with its mean squared error formula. Regions of preferences have been obtained under which the suggested class of estimators has been better than the usual unbiased, ratio and product estimators and the estimators according to Singh and Agnihotri (2008). Some examples are cited with numerical study. [ABSTRACT FROM PUBLISHER]

This paper presents an adaptive mesh refinement (AMR) algorithm to solve the non-isothermal multiphase flows in heterogeneous porous media comprising different rock types. To address the discontinuity coming from different rock types, we found that the ratios of relative permeability and oil-gas capillary pressure are continuous; hence they are chosen as the judging values for the regridding purpose. Moreover, because of the tensorial permeability and the complex topology of the AMR grid, a coupling flux solution based on the multipoint flux approximation was carefully designed. Numerical examples revealed the accuracy and efficiency of the proposed AMR algorithm. [ABSTRACT FROM PUBLISHER]

In recent years, dynamical modelling has been provided with a range of breakthrough methods to perform exact Bayesian inference. However, it is often computationally unfeasible to apply exact statistical methodologies in the context of large data sets and complex models. This paper considers a nonlinear stochastic differential equation model observed with correlated measurement errors and an application to protein folding modelling. An approximate Bayesian computation (ABC)-MCMC algorithm is suggested to allow inference for model parameters within reasonable time constraints. The ABC algorithm uses simulations of ‘subsamples’ from the assumed data-generating model as well as a so-called ‘early-rejection’ strategy to speed up computations in the ABC-MCMC sampler. Using a considerate amount of subsamples does not seem to degrade the quality of the inferential results for the considered applications. A simulation study is conducted to compare our strategy with exact Bayesian inference, the latter resulting two orders of magnitude slower than ABC-MCMC for the considered set-up. Finally, the ABC algorithm is applied to a large size protein data. The suggested methodology is fairly general and not limited to the exemplified model and data. [ABSTRACT FROM PUBLISHER]

The unified hybrid censoring is a mixture of generalized Type I and Type II hybrid censoring schemes. This paper presents the statistical inference and prediction of the Burr Type XII distribution for unified hybrid-censored data. The maximum likelihood estimators for estimating the unknown parameters are developed using the expectation-maximization algorithm. The Bayesian estimates of the unknown parameters under the assumption of independent gamma priors are obtained using two approximations, namely Lindley's approximation and the Markov Chain Monte Carlo (MCMC) technique. Also, MCMC samples are used to construct the highest posterior density credible intervals as well. Simulation experiments are performed to compare the different proposed methods. The prediction of the future observations based on a unified hybrid-censored sample is also provided. A real dataset representing the droplet splashing reported in 90° spray angle is used to illustrate the derived results. Furthermore, a useful interval say tracking interval is introduced for comparing the distance of the two rival models from the true model. [ABSTRACT FROM PUBLISHER]

This paper analyzes two key issues for the empirical implementation of parametric seasonal unit root tests, namely generalized least squares (GLS) versus ordinary least squares (OLS) detrending and the selection of the lag augmentation polynomial. Through an extensive Monte Carlo analysis, the performance of a battery of lag selection techniques is analyzed, including a new extension of modified information criteria for the seasonal unit root context. All procedures are applied for both OLS and GLS detrending for a range of data generating processes, also including an examination of hybrid OLS-GLS detrending in conjunction with (seasonal) modified AIC lag selection. An application to quarterly U.S. industrial production indices illustrates the practical implications of choices made. [ABSTRACT FROM PUBLISHER]

The boson-sampling problem has triggered a lot of interest in the scientific community because of its potential of demonstrating the computational power of quantum interference without the need of non-linear processes. However, the intractability of such a problem with any classical device relies on the realization of single photons approximately identical in their spectra. In this paper, we discuss the physics of boson sampling with non-identical single-photon sources, which is strongly relevant in view of scalable experimental realizations and triggers fascinating questions in the complexity theory. [ABSTRACT FROM PUBLISHER]

Our purpose in this paper is to obtain strong convergence result for approximation of solution to constrained convex minimization problem using a new iterative scheme in a real Hilbert space. Furthermore, we give numerical analysis of our iterative scheme. [ABSTRACT FROM AUTHOR]

In this paper, the effects of characteristics of incident light and the geometrical parameters to the reflectivity of dielectric Gaussian random rough surfaces are presented. The behaviors of the reflectivity vs. several parameters are quantified using approximate methods: the geometric optics approximation (GOA) and the Kirchhoff approximation (KA) and an exact method called integral method (IM). Finally, we determine the limits of validity of approximate methods by comparisons with IM results. The regions of validity of approximate methods depending of many geometrical and physical parameters: roughness, Brewster and shadowing effects, multiple reflections, surface materials, and nature of polarization. The broader domain of validity (DV) is for KA, at normal TE-polarized incident light, for the higher dielectric permittivity. However, the narrowed DV is for GOA, at normal TM-polarized incident light for lower dielectric permittivity. [ABSTRACT FROM AUTHOR]

In this paper, we develop efficient exact and approximate algorithms for computing a maximum independent set in random graphs. In a random graphG, each pair of vertices are joined by an edge with a probabilityp, wherepis a constant between 0 and 1. We show that a maximum independent set in a random graph that containsnvertices can be computed in expected computation time. In addition, we show that, with high probability, the parameterized independent set problem is fixed parameter tractable in random graphs and the maximum independent set in a random graph innvertices can be approximated within a ratio ofin expected polynomial time. [ABSTRACT FROM AUTHOR]

The asymptotic properties of the solutions of a class of linear, difference equations have been described—in increasing level of refinement—by many authors including H. Poincaré, O. Perron, and, finally, M. Pituk. In this paper we provide a proof of the constant coefficient case of Pituk’s theorem based on the recurrence properties of rotations of the torus. [ABSTRACT FROM AUTHOR]

Porteus (1986) explored an economic order quantity model with imperfect production processes that the approximate lot size is derived. Basically, he dealt with the lot size problem is rather meaningful. However, for mathematical simplicity, he adopted a truncated Taylor series expansion to present the approximate expected total cost function that results in overvalue of expected total cost. In this paper, we extend Porteus (1986) to present the optimal lot size model for defective items with a constant probability when the system is out-of-control and taking the maintenance cost into account. We show that there exists a unique optimal lot size such that the expected total cost is minimised. In addition, the bounds of optimal lot size are provided to develop the solution procedure. Finally, numerical examples are given to illustrate the theoretical results and compare optimal solutions obtained by using our approach and Porteus's approach. Numerical results show that our approach is better. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the problem of approximation of continuous multivariate functions by neural networks with a bounded number of neurons in hidden layers. We prove the existence of single-hidden-layer networks with bounded number of neurons, which have approximation capabilities not worse than those of networks with arbitrarily many neurons. Our analysis is based on the properties of ridge functions. [ABSTRACT FROM AUTHOR]

In this paper, we first study in a Hilbertian framework the weak convergence of a general Gradient Projection Algorithm for minimizing a convex function of classover a convex constraint set. The way of selecting the stepsizes corresponds to the one used by López et al. for the particular case of the Split Feasibility Problem. This choice allows us to avoid the computation of operator norms. Afterwards, a relaxed version of the Gradient Projection Algorithm is considered where the feasible set is approximated by half-spaces making the projections explicit. Finally, to get the strong convergence, each step of the general Gradient Projection Method is combined with a viscosity step. This is done by adapting Halpern’s algorithm to our problem. The general scheme is then applied to the Split Equality Problem, and also to the Split Feasibility Problem. [ABSTRACT FROM AUTHOR]

The fuzzy rough set model and interval-valued fuzzy rough set model have been introduced to handle databases with real values and interval values, respectively. Variable precision rough set was advanced by Ziarko to overcome the shortcomings of misclassification and/or perturbation in Pawlak rough sets. By combining fuzzy rough set and variable precision rough set, a variety of fuzzy variable precision rough sets were studied, which cannot only handle numerical data, but are also less sensitive to misclassification. However, fuzzy variable precision rough sets cannot effectively handle interval-valued data-sets. Research into interval-valued fuzzy rough sets for interval-valued fuzzy data-sets has commenced; however, variable precision problems have not been considered in interval-valued fuzzy rough sets and generalized interval-valued fuzzy rough sets based on fuzzy logical operators nor have interval-valued fuzzy sets been considered in variable precision rough sets and fuzzy variable precision rough sets. These current models are incapable of wide application, especially on misclassification and/or perturbation and on interval-valued fuzzy data-sets. In this paper, these models are generalized to a more integrative approach that not only considers interval-valued fuzzy sets, but also variable precision. First, we review generalized interval-valued fuzzy rough sets based on two fuzzy logical operators: interval-valued fuzzy triangular norms and interval-valued fuzzy residual implicators. Second, we propose generalized interval-valued fuzzy variable precision rough sets based on the above two fuzzy logical operators. Finally, we confirm that some existing models, including rough sets, fuzzy variable precision rough sets, interval-valued fuzzy rough sets, generalized fuzzy rough sets and generalized interval-valued fuzzy variable precision rough sets based on fuzzy logical operators, are special cases of the proposed models. [ABSTRACT FROM PUBLISHER]

In their paper Barndorff-Nielsen et al. [4] employ so called ambit fields to model electricity spot-forward dynamics. We briefly introduce and discuss ambit fields, and introduce a novel method for approximating general ambit fields by a linear combination of ambit fields driven by exponential kernel functions (as has already been done in the null-spatial case of Lévy semistationary processes by Benth et al. [11]) by approximating the deterministic kernel function by a carefully selected finite sum. Moreover, we shall study examples, in the setting of modelling electricity forward markets, of ambit fields with singular kernel functions to illustrate the usefulness of our method for pricing purposes. [ABSTRACT FROM AUTHOR]

With a great capability of dealing with epistemic uncertainty, evidence theory has been utilised to conduct reliability analysis for engineering systems recently. Unfortunately, the discontinuous nature of uncertainty quantification using evidence theory incurs a huge computational cost. This paper proposes an efficient method to improve the computational efficiency of evidence theory for reliability analysis. In this method, evidence variables are transformed into random variables. Support vector regression is used to construct the approximation model of the limit-state function. The most probable point (MPP) of the approximate reliability problem with only random variables is searched out. Based on the MPP, the most probable focal element (MPFE) of the original problem with evidence variables is identified. According to the MPFE and the monotonicity of the limit-state function, contributions of some focal elements to belief and plausibility in evidence theory can be judged directly. Hence, the number of focal elements involved in the calculation of extreme values of the limit-state function is reduced. Four numerical examples are utilised to test the performance of the proposed method. Results indicate that the proposed method can reduce the computational cost on reliability analysis under epistemic uncertainty while ensuring the high accuracy of reliability analysis results. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the optimal control problem governed by multidimensional modified Swift–Hohenberg equation. After showing the relationship between the control problem and its approximation, we derive the optimality conditions for an optimal control of our original problem by using one of the approximate problems. [ABSTRACT FROM AUTHOR]

In this paper, we propose an augmented Lagrangian affine scaling (ALAS) algorithm for general nonlinear programming, for which a quadratic approximation to the augmented Lagrangian is minimized at each iteration. Different from the classical sequential quadratic programming (SQP), the linearization of nonlinear constraints is put into the penalty term of this quadratic approximation, which results in smooth objective of the subproblem and avoids possible inconsistency among the linearized constraints and trust region constraint. By applying affine scaling techniques to handle the strict bound constraints, an active set type affine scaling trust region subproblem is proposed. Through special strategies of updating Lagrange multipliers and adjusting penalty parameters, this subproblem is able to reduce the objective function value and feasibility errors in an adaptive well-balanced way. Global convergence of the ALAS algorithm is established under mild assumptions. Furthermore, boundedness of the penalty parameter is analyzed under certain conditions. Preliminary numerical experiments of ALAS are performed for solving a set of general constrained nonlinear optimization problems in CUTEr problem library. [ABSTRACT FROM AUTHOR]

Citizens are becoming increasingly likely to challenge the knowledge bases underlying policy programmes that deal with risks. This paper investigates how participants in online discussions engage in interactions between expert knowledge, ‘commons knowledge’ and policy assumptions. The concept of ‘boundary objects’, arrangements that allow different groups to work together without consensus, is used to analyse the role of online discussions in these interactions. Discussions on three Dutch online forums about the swine flu are investigated according to a framework for policy argumentation. Interaction between knowledge domains was limited, and it varied in focus and nature across the three forums. Each discussion functioned as a partial approximation of a boundary object. Government organizations should be more aware of the variety of online forums in which discussions about societal risks take place. Several practical options are presented for policy-making with regard to risks. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the Cauchy problem for both linear and semi-linear elliptic equations. In general, the equations have the form whereis a positive-definite, self-adjoint operator with compact inverse. As we know, these problems are well known to be ill-posed. On account of the orthonormal eigenbasis and the corresponding eigenvalues related to the operator, the method of separation of variables is used to give the solution in series representation. Thereby, we propose a modified method and show error estimations in many accepted cases. For illustration, two numerical examples, a modified Helmholtz equation and an elliptic sine-Gordon equation, are constructed to demonstrate the feasibility and efficiency of the proposed method. [ABSTRACT FROM PUBLISHER]

In dynamical systems saddle points partition the domain into basins of attractions of the remaining locally stable equilibria. This situation is rather common especially in population dynamics models, like prey–predator or competition systems. Focusing on squirrels population models with niche, in this paper we design algorithms for the detection and the refinement of points lying on the separatrix manifold partitioning the phase space. We consider both the two populations and the three populations cases. To reconstruct the separatrix curve and surface, we apply the Partition of Unity method, which makes use of Wendland's functions as local approximants. [ABSTRACT FROM PUBLISHER]

In this paper we study two inverse problems relating to reconstruction of the diffusion coefficientk(x), appearing in a linear partial parabolic equationut=(k(x)ux)x. One is concerned through overposed datau(x, T) and the other is with non-local boundary condition. We derive relations for these inverse problems, which show between changes ink(x) and changes in overposed data or the non-local boundary condition. They make us to help to construct an approximate solution based on the polynomial regression. We analyse the error in the approximation. Finally, some numerical experiments are presented. [ABSTRACT FROM PUBLISHER]

In this paper, the stability issue of Lur’e systems governed by a control law stabilising their forward Euler approximate model is investigated. More specifically, the considered control law is obtained by exploiting the advantages of a new Lur’e type Lyapunov function with disconnected level sets. This Lyapunov function is adapted to discrete-time Lur’e systems and to the structure of the forward Euler approximate model. The main result consists of linear matrix inequality conditions allowing to guarantee that the continuous-time Lur’e system associated with the proposed digital control law is globally asymptotically stable. The relevance of this approach is illustrated using a numerical example. [ABSTRACT FROM PUBLISHER]

This paper is devoted to the blow up of analytic solutions with the emergence of irregular solutions. At first, we consider the Panov-Shelkovich system where such types of-wave solutions have been explicitly exhibited. We propose a method to reduce this system of nonlinear PDEs to a system of two ODEs in Banach spaces, which permits to obtain theoretical existence of approximate solutions for the Cauchy problem by constructing weak asymptotic solutions. Further, this method allows to study these PDEs through their ODEs representation by basic elementary numerical schemes whose construction is very easy. Then, we observe the expected results from the previous theoretical method; this also gives confidence in the mathematical proofs. We prove that this method gives back the classical analytic solutions using an abstract Cauchy-Kovalevska theorem in scales of Banach spaces. We also study solutions in the form offor other similar systems. Indeed, we show formation of very irregular shock waves when the existence time of a classical analytic solution is over. Finally, we sketch adaptations to provide weak asymptotic solutions to the 3-D Euler-Poisson equations with application to pressureless fluid dynamics and cosmology. [ABSTRACT FROM PUBLISHER]

In multilevel models for binary responses, estimation is computationally challenging due to the need to evaluate intractable integrals. In this paper, we investigate the performance of integrated nested Laplace approximation (INLA), a fast deterministic method for Bayesian inference. In particular, we conduct an extensive simulation study to compare the results obtained with INLA to the results obtained with a traditional stochastic method for Bayesian inference (MCMC Gibbs sampling), and with maximum likelihood through adaptive quadrature. Particular attention is devoted to the case of small number of clusters. The specification of the prior distribution for the cluster variance plays a crucial role and it turns out to be more relevant than the choice of the estimation method. The simulations show that INLA has an excellent performance as it achieves good accuracy (similar to MCMC) with reduced computational times (similar to adaptive quadrature). [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of systems of reaction-cross diffusion equations arising in population dynamics. New results of existence of weak solutions are presented, allowing to treat systems of two equations in which one of the cross diffusions is convex, while the other one is concave. The treatment of such cases involves a general study of the structure of Lyapunov functionals for cross diffusion systems, and the introduction of a new scheme of approximation, which provides simplified proofs of existence. [ABSTRACT FROM PUBLISHER]

This paper is concerned with the evaluation of natural frequencies for the design of simply supported girder bridges, continuous girder bridges, and continuous rigid frame bridges. There are two significant parameters affecting the vibration frequencies. The first parameter is called the span ratio γ while the second parameter is called the stiffness ratio κ. The approximate formulas in terms of these parameters are proposed for these three types of bridges. From the analysis results, it is found that the first mode shape of the continuous rigid frame bridge is mainly induced by the pier other than the superstructure, when the stiffness parameter κ is greater than 10. Finally, the method proposed herein may be adopted to investigate the natural frequency of other types of bridges. [ABSTRACT FROM PUBLISHER]

In this paper, a computational method for numerical solution of a class of integro-differential equations with a weakly singular kernel of fractional order which is based on Cos and Sin (CAS) wavelets and block pulse functions is introduced. Approximation of the arbitrary order weakly singular integral is also obtained. The fractional integro-differential equations with weakly singular kernel are transformed into a system of algebraic equations by using the operational matrix of fractional integration of CAS wavelets. The error analysis of CAS wavelets is given. Finally, the results of some numerical examples support the validity and applicability of the approach. [ABSTRACT FROM AUTHOR]

Based on the Moreau–Yosida regularization and a modified line search technique, this paper presents an implementable memory gradient method for solving a possibly non-differentiable convex minimization problem by converting the original objective function to a once continuously differentiable function. A main feature of this proposed method is that at each iteration, it sufficiently uses the previous multi-step iterative information and avoids the storage and computation of some matrices. Moreover, the proposed method makes use of approximate function and gradient values of the Moreau–Yosida regularization instead of the corresponding exact values. Under reasonable conditions, the convergence properties of the proposed algorithm are analysed. Preliminary numerical results show that the proposed method is efficient and can be applied to solve large-scale non-smooth optimization problems. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of capacitated covering with unit balls. In this problem, a set of weighted points in a metric spaceis given, and we want to cover them with a minimum number of the unit balls of that metric space provided that the total weight assigned to each unit ball is at most one. The problem is NP-hard as it generalizes the covering-with-unit-balls problem. We consider the problem in two cases: (1) the weight of each point can be split among several unit balls and (2) the unsplittable case. In the latter case, the problem is a generalization of the bin-packing problem even when, and thus it is not approximable under 1.5, unless P=NP. We design a polynomial-time approximation scheme (PTAS) for the splittable case whenis a fixed constant andis anmetric. This also results in a PTAS for the unsplittable case when all the points have the same weight. We also analyse several natural algorithms for this problem and prove that they achieve constant approximation factors. [ABSTRACT FROM AUTHOR]

This paper is concerned with model reduction for Markov chain models. The goal is to obtain alow-rank approximationto the original Markov chain. The Kullback–Leibler divergence rate is used to measure the similarity between two Markov chains; the nuclear norm is used to approximate the rank function. A nuclear-norm regularised optimisation problem is formulated to approximately find the optimal low-rank approximation. The proposed regularised problem is analysed and performance bounds are obtained through the convex analysis. An iterative fixed point algorithm is developed based on the proximal splitting technique to compute the optimal solutions. The effectiveness of this approach is illustrated via numerical examples. [ABSTRACT FROM AUTHOR]

The paper deals with a general class of linear positive approximation processes designed using series. For continuous and bounded functions defined on unbounded interval we give rate of convergence in terms of the usual modulus of smoothness. The main goal is to identify functions for which these operators provide uniform approximation over unbounded intervals. Particular cases are delivered. [ABSTRACT FROM AUTHOR]

In this paper, we study shifted Jacobi polynomials and develop a simple but highly accurate scheme for the numerical solution of coupled system of fractional differential equations. We derive some operational matrices of integration and differentiation of fractional order. By the application of these matrices we provide a theoretical treatment to approximate the solutions of the corresponding system. We use Matlab to perform necessary operations. The applicability of the technique is shown with some examples and the results are displayed graphically. [ABSTRACT FROM PUBLISHER]

The Kaczmarz method for finding the solution to an overdetermined consistent system of linear equationAx=b(A∈Rm×n) is an iterative algorithm that has found many applications ranging from computer tomography to digital signal processing. Recently, Strohmer and Vershynin proposed randomized Kaczmarz, and proved its exponential convergence. In this paper, motivated by idea of precondition, we present a modified version of the randomized Kaczmarz method where an orthogonal matrix was multiplied to both sides of the equationAx=b, and the orthogonal matrix is obtained by low-rank approximation. Our approach fits the problem whenmis huge andm≫n. Theoretically, we improve the convergence rate of the randomized Kaczmarz method. The numerical results show that our approach is faster than the standard randomized Kaczmarz. [ABSTRACT FROM PUBLISHER]

Road and track irregularities have an important influence on the dynamic behaviour of vehicles. Knowledge of their characteristics and magnitude is essential for the design of the vehicle but also for comparable homologation and acceptance tests as well as for the planning and management of track maintenance. Irregularities of tracks and roads are regularly measured using various measurement technologies. All have advantages and weaknesses and require several processing steps. Characterisation of irregularities is done in the distance as well as in the wavelength domain. For rail irregularities, various distance domain description methods have been proposed and are in use. Methods have been analysed and compared with regard to their processing steps. Several methods have been analysed using measured irregularity and vehicle response data. Characterisation in the wavelength domain is done in a similar way for track and road irregularities. Here, an important issue is the estimation of the power spectral densities and the approximation by analytical formulas. For rail irregularities, periodic defects also play an important role. The use of irregularities in simulations requires various processing steps if measured irregularities are used, as well as if synthetic data are utilised. This paper gives a quite complete overview of rail irregularities and points out similarities and differences to the road. [ABSTRACT FROM PUBLISHER]

In this paper, we study the Cauchy problem of the generalized Novikov equation. We first show that under suitable condition, the strong solution exists globally via somea prioriestimates. Then, we prove the existence and uniqueness of global weak solutions by the approximation method. We also obtain the exact peaked solutions. [ABSTRACT FROM PUBLISHER]

In this paper, we propose approximations of fluid flow that could be used for obtaining wall laws of higher order. We consider the two-dimensional laminar fluid flow, modeled by the incompressible Stokes system in a straight channel with a rough side. The roughness is periodic and the ratio of the amplitude of the rough part and the size of the flow domain is denoted by ϵ, being a small number. We impose periodic boundary conditions on the flow. We generalize the boundary layers needed for the construction of flow approximations of higher order with respect to ϵ. The existence of the layers and their features are discussed. Finally we give the error estimates for the approximations and establish an explicit wall law. [ABSTRACT FROM PUBLISHER]