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The covariance matrix adaptation evolution strategy (CMA-ES) is one of the most successful evolutionary algorithms. CMA-ES incrementally learns the variable metric by evolving a full covariance matrix. Yet, it suffers from high computational overload. In this paper, we propose two efficient variants of CMA-ES, termed mutation matrix adaptation (MMA-ES) and exponential MMA-ES (xMMA-ES). These variants are derived by taking the first order approximation of the update of the covariance matrix in CMA-ES. Both variants avoid the computational costly matrix decomposition while keeping the simplicity of the update scheme of CMA-ES. We analyze the properties and connections of MMA-ES and xMMA-ES to other variants of evolution strategies. We have experimentally studied the proposed algorithms’ behaviors and performances. xMMA-ES and MMA-ES generally outperform or perform competitively to CMA-ES. We have investigated the performance of MMA-ES with the BiPop restart strategy on the BBOB benchmarks. The experimental results validate the performance of the proposed algorithms.

A special point on each time interval is found for the approximation of the variable-order time Caputo derivative, which makes at least second order approximation accuracy be obtained. On this basis, two difference schemes are proposed for the multi-dimensional variable-order time fractional sub-diffusion equations, which have second order accuracy in time, second order and fourth order accuracy in space, respectively. The obtained difference schemes are proved to be uniquely solvable. The convergence and stability of the schemes in the discrete H 1 -norm are analyzed by utilizing the energy method. Some numerical examples are presented to verify the theoretical results.

This paper proposes a stochastic model for mixed traffic flow with human-driven vehicles (HVs) and automated vehicles (AVs). The model is formulated in Lagrangian coordinates considering the heterogeneous behavior of human drivers. We further derive a first and second order approximation of the stochastic model describing the mean and the covariance dynamics, respectively, under different combinations of HVs and AVs in the traffic stream (e.g., randomly distributed in the stream, at the front of the stream, in the middle of the stream and in the rear of the stream). The proposed model allows us to explicitly investigate the interaction between AVs and HVs considering the uncertainty of human driving behavior. Six performance metrics are proposed to measure the impact of AVs on the uncertainty of HVs’ behavior, as well as on the stability of the system. The numerical experiment results show that AVs have significant impact on the uncertainty and stability of the mixed traffic flow system. Larger AV penetration rates can reduce the uncertainty inherent in HV behavior and improve the stability of the mixed flow substantially. Whereas AVs’ reaction time only has subtle impact on the uncertainty of the mixed stream; as well as the position of AVs in the traffic stream has marginal influence in terms of reducing uncertainty and improving stability.

In this paper, we consider the problem of sequentially estimating the unknown parameter in a particular exponential family of distributions under an asymmetric LINEX loss function and fixed cost for each observation within a Bayesian framework. Under a gamma prior distribution, the second order approximation for the Bayes risks of the asymptotically pointwise optimal rule and the optimal stopping rule are derived. It is shown that the asymptotically pointwise optimal rule is asymptotically non-deficient in the sense of Woodroofe (1981).

By using the perturbation expansion method and self-consistent iterative method, we evaluate the effect of the conduction band nonprabolicity on the wave vector ( k t ) dependent Rashba coefficient ( α ) and nonlinear Rashba spin splitting (Δ E ) in the Al 0.5 Ga 0.5 N/GaN quantum well (QW). The effective mass (energy) under the first order approximation m t1 ( E k1 ) is in proximity to the iterative result m tp ( E kp ) and m t1 > m tp , E k1 E kp , showing the higher order contributions to m t ( E k ) are small. The sign of the nonparabolic correction to E k is just opposite to that of the correction to m t . The increase of α and Δ E due to the conduction band nonparabolicity reaches about 3% at k t =1 nm −1 . Around the left heterointerface, the probability density is high and E k0 > E kp > E k1 , so α 0 α p α 1 , Δ E 0 E p E 1 . With increasing k t , α decreases, and Δ E increases slowly. For small k t , α 0 (Δ E 0 ), α 1 (Δ E 1 ) and α p (Δ E p ) are nearly the same. While for large k t , the difference between α 0 and α 1 ( α p ) increases rapidly, but the difference between Δ E 0 and Δ E 1 (Δ E p ) increases slowly.

This paper aims to summarizing the different approaches in determining the implied volatility for the options. This value is of particular importance since it is the main component of theoptions price and because, among traders, options are quoted in terms of volatility rather than price. After a discussion on the approximation methods, a numerical approach is explained. It is shown that, in order to ensure a fast and reliable convergence, the selection of an appropriate starting point is key. The authors suggestion for choosing the first order approximation or the inflexion as initial point is also illustrated.

We use Monte Carlo experiments to evaluate whether “upward pricing pressure” (UPP) accurately predicts the price effects of mergers, motivated by the observation that UPP is a restricted form of the first order approximation derived in Jaffe and Weyl (2013). Results indicate that UPP is quite accurate with standard log-concave demand systems, but understates price effects if demand exhibits greater convexity. Prediction error does not systematically exceed that of misspecified simulation models, nor is it much greater than that of correctly-specified models simulated with imprecise demand elasticities. The results also support that UPP provides accurate screens for anticompetitive mergers.

Breaking the uncovered interest rate parity (UIP) condition is essential to accounting for the empirical behavior of exchange rates, and is a prerequisite for theoretical analysis of sterilized foreign exchange interventions. Gabaix and Maggiori (2015) account for some of the long-standing empirical exchange rate puzzles by introducing financial intermediaries that are willing to absorb international saving imbalances for a premium, thereby deviating from the UIP. In another important contribution, Fanelli and Straub (2019) lay down the principles for foreign exchange interventions. In their model, regulatory exposure limits and participation cost in the international financial markets drive a wedge in the UIP. This paper demonstrates that, to a first order approximation, these models are equivalent to a reduced-form portfolio adjustment cost model, as in Schmitt-Grohe and Uribe (2003). Therefore, to the extent that one is only concerned with first-order dynamics and second moments, there is no gain from adopting the rich microstructure of either models -- a simple portfolio adjustment cost is just as good.

This paper contributes by providing a new approach to study optimal macroprudential policies based on economy wide welfare. Following Gerba (2017), we pin down a welfare function based on a first-and second order approximation of the aggregate utility in the economy and use it to determine the merits of different macroprudential rules for Euro Area. With the aim to test this framework, we apply it to the model of Clerc et al. (2015). We find that the optimal level of capital is 15.6 percent, or 2.4 percentage points higher tan the 2001-2015 value. Optimal capital reduces significantly the volatility of the economy while increasing somewhat the total level of welfare in steady state, even with a time-invariant instrument. Expressed differently, bank default rates would have been 3.5 percentage points lower while credit and GDP 5% and 0.8% higher had optimal capital level been in place during the 2011-2013 crisis. Further, using a model-consistent loss function, we find that the optimal Countercyclical Capital Buffer (CCyB) rule depends on whether observed or optimal capital levels are already in place. Conditional on optimal capital level, optimal CCyB rule should respond to movements in total credit and mortgage lending spreads. Gains in welfare from optimal combination of instruments is higher than the sum of their individual effects due to synergies and positive mutual spillovers.

Observations of runout distances combined with velocity measurements suggest that “major” dry-mixed avalanches show a scale invariance to the total drop height HSC. This is in accordance to the proposed upper-limit envelope of the maximum velocity by McClung and Schaerer (2006). The observations are also supported by a simple scaling analysis using a simple mass block model on cycloidal and parabolic tracks (Gauer, 2018b), concluding U max ~ gH SC / 2 . In this supplementary paper, a simple mass block model is presented that includes basic observations of major dry-mixed avalanches, such as mass entrainment and deposition, and that reflects this scale invariance. Almost all model parameters can principally be observed in the field. Model results are compared with a series of avalanche observations of runout and velocity and match well, considering that the model is a first order approximation.

We consider the initial boundary value problem for the time-fractional diffusion equation with a homogeneous Dirichlet boundary condition and an inhomogeneous initial data a ( x ) ∈ L 2 ( D ) in a bounded domain D ⊂ R d with a sufficiently smooth boundary. We analyze the homogenized solution under the assumption that the diffusion coefficient κ ϵ ( x ) is smooth and periodic with the period ϵ > 0 being sufficiently small. We derive that its first order approximation measured by both pointwise-in-time in L 2 ( D ) and L p ( ( θ , T ) ; H 1 ( D ) ) for p ∈ [ 1 , ∞ ) and θ ∈ ( 0 , T ) has a convergence rate of O ( ϵ 1 / 2 ) when the dimension d ≤ 2 and O ( ϵ 1 / 6 ) when d = 3 . Several numerical tests are presented to demonstrate the performance of the first order approximation.

In the present work we propose an analytical method for the algebraic calculation of the low frequency expansion of the solution of a scalar scattering problem upon a smooth starshaped scatterer. The method is based on the far field expansion theorem, introduced by Atkinson and Wilcox in the middle of the last century, applied in the low frequency realm. In this view, the need for solving elliptical boundary value problems to obtain the low frequency approximations is replaced by an analytical procedure, easily encoded in an algorithm including only algebraic operators. As a demonstration example, the method is applied to the acoustic scattering problem with plane wave excitation upon three different non-penetrable spherical scatterers. The first low frequency approximations are deduced, yielding the validity of the proposed method by both recovering already known results and accurately deriving higher orders of approximation.

An update of the former version of the database and software for the calculation of CO2–air absorption coefficients taking line-mixing into account [Lamouroux et al. J Quant Spectrosc Radiat Transf 2010;111:2321] is described. In this new edition, the data sets were constructed using parameters from the 2012 version of the HITRAN database and recent measurements of line-shape parameters. Among other improvements, speed-dependent profiles can now be used if line-mixing is treated within the first order approximation. This new package is tested using laboratory spectra measured in the 2.1 μm and 4.3 μm spectral regions for various pressures, temperatures and CO2 concentration conditions. Despite improvements at 4.3 μm at room temperature, the conclusions on the quality of this update are more ambiguous at low temperature and in the 2.1 μm region. Further tests using laboratory and atmospheric spectra are thus required for the evaluation of the performances of this updated package.

The safety behaviour of metal-fuelled fast breeder reactor cores may be assessed by their transient behaviour during anticipated unprotected transients. Out of such transients, unprotected loss of flow accident (ULOFA) has been recognized as an event important for determining reactor safety due to the positive sodium void coefficient of reactivity and the remote possibility of complete power failure as initiator. Reactor safety under ULOFA condition is particularly based on the inherent feedbacks, which is calculated using the removal worths and Doppler constants. As the removal worth is a strong function of reactor size, ULOF analyses are carried out in three different reactor size viz. 120 MWe, 500 MWe and 1000 MWe. The study reveals that smaller metal cores are safer than larger cores with respect to the ULOF accidents in the pre-disassembly phase. The present study also shows that the use of exact perturbation based reactivity worths introduce no significant changes in the safety behaviour of metal fuel reactor compared to that with the use of first order perturbation worths in pre-disassembly phase. The first order approximation is found to be valid as the expansion of materials in the core during ULOFA is small before the core enters the disassembly phase.

We describe three-dimensional and planar models of hyperelastic fiber reinforced materials characterized by statistical distribution of the fiber orientation. Our models are based on a second order approximation of the strain energy density in terms of the fourth pseudo-invariant I ¯ 4 , typically employed in the description of fiber reinforced materials. For a particular choice of the strain energy density associated to the fiber reinforcement, it is possible to derive the explicit expression of the material and spatial stress tensors and of the stress covariance tensors. The mechanical behavior of the models is assessed through uniaxial, biaxial and shear tests.

We present the results from the molecular dynamics (MD) simulations of nanodrops. A thermodynamic based method known as test area simulation method (TASM) developed by Gloor et al. [J. Chem. Phys. 123, 134703 (2005)] is employed to determine the surface tension. The results show that the value of surface tension decreases with the decrease of size of the drop. We have also determined the Tolman's gap and surface entropy of nanodrop–vapor interfaces for a better understanding of curvature effects on surface tension. Both these parameters are found to be size dependent properties. The thermodynamic perturbation theory (TPT) method is employed to validate the size effect of drops on surface tension. Second order approximation of TPT is found to be in good agreement with central difference TASM results.

This paper deals with the approximation of continuous functions by sequences of some modified Bernstein–Durrmeyer type operators that reproduce certain test functions. The orders of approximation of the new versions turn to be at least as good as the one of the genuine Bernstein–Durrmeyer operators. Moreover, by extrapolating techniques recently applied to the classical Bernstein operators, we present a one-parameter family of modified sequences of operators that reproduce certain polynomials and possess that popular genuine sequence as a limit case. Comparisons and some illustrative graphics are also presented.

To reduce contour error in contour-following tasks, a common approach is to design a controller based on the contour error information. Hence, real-time contouring error estimation plays an important role in contour-following control. However, the available second-order estimation formulas only apply to biaxial motion systems, and cannot be generalized to handle arbitrary contours tracked by multi-axis motion systems. In this paper, a point-to-curve distance function is defined, and its properties are investigated, especially, its second-order Taylor approximant is derived. On this basis, a novel second-order approach for calculating contour errors of arbitrary contours in real time is proposed. The inter-correlations between the present approach and four commonly used ones are classified. Simulation and experimental results demonstrate the effectiveness of the proposed contour error estimation algorithm.

In this paper we discuss the application of second-order adjoint based perturbation techniques to linear and nonlinear time dependent problems. These techniques are based on the property of the adjoint problem which allows calculating the set of first and second order coefficients by solving a number of adjoint systems. The derivation of a second order adjoint theory that can be used to calculate the second order Taylor components of a functional response is first presented for nonlinear problems, and then reformulated for linear systems. This implementation is based on the Adjoint Sensitivity Analysis Procedure, originally presented by Cacuci. The theoretical part is followed by the application of the technique to some classical reactor physics problems: a fuel depletion calculation, a linear and a nonlinear point-kinetic problem. The results obtained using the second order theory are compared with the values obtained using a first order approximation and a direct solution of the forward problem. Our first results show that the procedure provides good estimations in presence of higher order perturbation components, being able to reconstruct the responses of interest even in presence of large perturbations. The main differences between linear and nonlinear formulations and their computational implications are also discussed.

First order approximation in standard perturbation theory has been used for the safety analysis of Indian prototype fast breeder reactor (PFBR). Material void and Doppler worth distribution obtained with first order approximation has been used to find the response of PFBR core during reactivity transients like unprotected loss of flow accident (ULOFA) and unprotected transient over power accident (UTOPA) up to sodium voiding. The validity of first order approximation applied to larger perturbations during such accidents has been tested by developing an exact perturbation code PERTX. 2D diffusion code ALCIALMI and ABBN-93 evaluated nuclear data has been used for the analysis. European Reactor Analysis Optimized Calculation System (ERANOS) is a code system used for reliable neutronic calculations of current and advanced fast reactor cores. The results of perturbation analysis of PFBR done with IGCAR code systems have been compared with those obtained with ERANOS 2.1 and JEFF 3.1 nuclear data. The present study reveals the adequacy of the IGCAR perturbation methods in 2D for the safety analysis of PFBR core involving transients with fuel, structure and coolant temperatures change.

In this paper, a quantitative measure of partial observability is de_ned for PDEs. The quantity is proved to be consistent in well-posed approximation schemes. A first order approximation of an unobservability index using empirical gramian is introduced. For linear systems with full state observability, the empirical gramian is equivalent to the observability gramian in control theory. The consistency theorem is exemplified using a Burgers' equation.

Much of the controversy surrounding recent policy proposals to broaden the base for value added taxes (VAT) revolves around who ultimately bears the burden of these taxes. The typical assumption is that consumer prices fully reflect taxes, so that the main empirical question is how the tax induced price changes affect members of different income groups. However, the evidence base is scarce and market imperfections could generate both over and under-shifting of VAT to consumer prices. In this paper, we examine the incidence and distributional effects of VAT in a setting with plausibly exogenous variation in tax rates. The context of our study is a sharp change in the VAT policy on food items in Norway. Using a regression discontinuity design, we examine the direct impact of the policy change on the consumer prices of food items as well as any cross-price effects on other goods. Our estimates suggest that taxes levied on food items are completely shifted to consumer prices, whereas the pricing of other goods is not materially affected. To understand the distributional effects of the VAT reform, we use expenditure data and estimate the compensating variation of the tax induced price changes. We find that lowering the VAT on food attenuates inequality in consumer welfare, in part because households adjust their spending patterns in response to the price changes. By comparison, the usual first order approximation of the distributional effects, which ignores behavioral responses, seriously understates the redistributive nature of the VAT reform.

The influence of the quadratic and cubic terms on non-linear dynamic characteristics of the angle-ply composite laminated rectangular plate with parametric and external excitations is investigated. The method of multiple time scale perturbation is applied to solve the non-linear differential equations describing the system up to and including the second-order approximation. All possible resonance cases are extracted and investigated at this approximation order. Two cases of the sub-harmonic resonances cases (Ω2 ≅ 2ω1 and Ω2 ≅ 2ω2) in the presence of 1:2 internal resonance ω2 ≅ 2ω1 are considered. The stability of the system is investigated using both frequency response equations and phase-plane method. It is quite clear that some of the simultaneous resonance cases are undesirable in the design of such system as they represent some of the worst behavior of the system. Such cases should be avoided as working conditions for the system. Some recommendations regarding the different parameters of the system are reported. Comparison with the available published work is reported.

We derive in this paper the mathematical model, describing the single mode dynamics of a beam subjected to external loads. Taking into account the geometrical nonlinearities and considering the second order approximation of the deflected length of the beam, we show that the single mode dynamics of a simply supported (hinged–hinged) beam can be described by a ϕ6 potential with various configurations.

Using 3-D petrological-thermo-mechanical subduction models, we investigate how the buoyancy of partially molten rock affects the development of thermal–chemical plumes and melt productivity in the mantle wedge. As a first order approximation we limit the positive buoyancy of partially molten rock (compared to non-molten rock), which can be decreased due to rapid melt extraction and removal to the surface. Our simulations show that a large to moderate density contrast (�� ) of >200 kg/m

In this paper we present a new parallel multi-frontal direct solver, dedicated for the hp Finite Element Method (hp-FEM). The self-adaptive hp-FEM generates in a fully automatic mode, a sequence of hp-meshes delivering exponential convergence of the error with respect to the number of degrees of freedom (d.o.f.) as well as the CPU time, by performing a sequence of hp refinements starting from an arbitrary initial mesh. The solver constructs an initial elimination tree for an arbitrary initial mesh, and expands the elimination tree each time the mesh is refined. This allows us to keep track of the order of elimination for the solver. The solver also minimizes the memory usage, by de-allocating partial LU factorizations computed during the elimination stage of the solver, and recomputes them for the backward substitution stage, by utilizing only about 10% of the computational time necessary for the original computations. The solver has been tested on 3D Direct Current (DC) borehole resistivity measurement simulations problems. We measure the execution time and memory usage of the solver over a large regular mesh with 1.5 million degrees of freedom as well as on the highly non-regular mesh, generated by the self-adaptive hp-FEM, with finite elements of various sizes and polynomial orders of approximation varying from p=1 to p=9. From the presented experiments it follows that the parallel solver scales well up to the maximum number of utilized processors. The limit for the solver scalability is the maximum sequential part of the algorithm: the computations of the partial LU factorizations over the longest path, coming from the root of the elimination tree down to the deepest leaf.

In this study, an accurate analytical solution for Duffing equations with cubic and quintic nonlinearities is obtained using the Homotopy Analysis Method (HAM) and Homotopy Pade technique. Novel and accurate analytical solutions for the frequency and displacement are derived. Comparison between the obtained results and numerical solutions shows that only the first order approximation of the Homotopy Pade technique leads to accurate solution with a maximum relative error less than 0.4%.

This paper deals with the non-variational Galerkin- B -spline method recently developed by the authors. It is applied to circular thin flexible plates within the context of Von Karman equations. Our main result shows that the low orders of approximation have been sufficient to build the solutions from the basis functions in a high quality. Comparison of solutions obtained to variational approach with known ones is performed.

In this paper we study analytically a class of waves in the variant of the classical second-order approximation Boussinesq system given by ∂ t u − b ∂ x x t u + c ∂ x x x x t u = − ∂ x v − ∂ x ( u v ) − ( 1 3 − 2 b ) ∂ x x x v + b ∂ x x x ( u v ) + b ∂ x ( u ∂ x x v ) − a ∂ x x x x x v , ∂ t v − b ∂ x x t v + c ∂ x x x x t v = − ∂ x u + 1 2 ∂ x x x u − v ∂ x v − ∂ x ( u ∂ x x u ) + b ∂ x ( v ∂ x x v ) − d ∂ x x x x x u , where a , b , c , d are some real constants. This equation is ill-posed and most initial conditions do not lead to solutions. Nevertheless, we show that, for almost every a , b , c and d it admits solutions that are quasiperiodic in time.

This paper compares the welfare implications of two widely used pricing assumptions in the New-Keynesian literature: Calvo-pricing vs. Rotemberg-pricing. We show that despite the strong similarities between the two assumptions to a first order of approximation, in general they might entail different welfare costs at higher order of approximation.

In this paper, the concept of the second order approximation of f is redefined and second order optimality conditions for the minimizing problem (P) min 0 ∈ F ( x ) f ( x ) have been established, where f and the support function of the set valued map F have compact second order approximations at ( x ¯ , 0 ).

We present a closed form solution for the upscaled diffusion coefficient and derive a first-order homogenized approximation to linear flow equations with periodic and rapidly oscillating coefficients. The coefficients are defined as step functions describing inclusions of various shapes in a main matrix. This constitutes the n-dimensional upscaled version of Darcy’s law for linear flow in such systems. We consider the two-scale asymptotic expansion of the solution of the flow equation, and develop a corrector to an analytical approximation for the solution of the periodic cell-problem. We demonstrate that the proposed analytical form for the effective coefficient satisfies the generalized Voigt–Reiss’ inequality and is in agreement with other known theoretical results, including the geometric average for the checkerboard geometry, and with some published numerical results. The zeroth-order approximation in H1(Ω) is readily obtained and the first-order approximation in L2(Ω) is derived from the proposed analytical approximation to the basis functions. The analytical basis functions are also used to define a correction function that incorporates the heterogeneous features into the zeroth-order approximation to the gradient and flux, which considerably improves the convergence results. We illustrate the procedure with coefficients describing square inclusions with contrast ratios between the inclusion and the matrix as 10:1, 100:1, 1000:1 and 1:10, respectively. We demonstrate numerically that the convergence properties of the proposed approximations agree with the classical theoretical results in homogenization theory.

This paper presents an approach for robust open-loop and closed-loop control of biological production processes described by models with parameter uncertainties. The approach leads to trajectories that show small variations of the product amount if uncertain parameters and uncertain initial conditions are present. The algorithm utilizes a second order approximation to calculate the first two statistical moments of the system's output as a function of the stochastic system's state and uncertain model parameters.

Information feasible regulatory mechanisms (that do not require the regulator to acquire firm level information) have been proposed long ago for stochastic non-point emission problems. These mechanisms do not take polluter cooperation and firm entry–exit incentives simultaneously into account, nor are these issues addressed in an informationally efficient way. In this paper we propose an informationally feasible self-reporting mechanism that is robust to cooperation among polluters while giving participating firms correct abatement incentives as well as giving entry–exit incentives that are correct to a first order approximation.

This paper studies a general method for estimating the length of a parametric curve using only samples of points. We show that by making a special choice of points, namely the Gauss–Lobatto nodes, we get higher orders of approximation, similar to the behaviour of Gauss quadrature, and we derive some explicit examples.

Spline functions are widely used in the field of approximation theory and its applications. In this article, we propose the use of @p functions which are spline functions of degree two, as membership functions of the input variables. At first, we show by a constructive theory that multi-input-single-output (MISO) Sugeno Fuzzy Logic Systems with @p input variables membership functions are universal approximators to every continuously differentiable function defined on a compact subset of R^n. Moreover they are of first order approximation accuracy. Then, we show that with appropriately chosen parameters of the @p functions, fuzzy logic systems with @p input variables membership functions are universal approximators not only for the function itself but also for its first order derivative.

In this paper we discuss a generalization of the extended Luenberger observer for multi-output systems. Our approach can be interpreted as approximate error linearization. While the extended Luenberger observer results from a first order approximation of exact error dynamics, this paper provides an explicit formula for a second order approximation. The design procedure is formulated in terms of Lie derivatives and Lie brackets.

Two versions of multiple scales and Krylov–Bogoliubov–Mitropolsky (KBM) methods are extended to obtain the asymptotic solutions of a class of strongly nonlinear oscillators with slowly varying parameters. A comparison of the two methods is made to show that the multiple scales method is equivalent to the KBM method for the first order approximation. An example of pendulum with slowly varying length is given to illustrate the comparison of the two methods.

Simple straggling models had largely been abandoned in favor of Monte Carlo simulations of straggling which are accurate but time consuming, limiting their application in practice. The difficulty of simple analytic models is the failure to give accurate values past 85% of the particle range. A simple model is derived herein based on a second order approximation upon which rapid analysis tools are developed for improved understanding of material charged particle transmission properties.

This paper presents an inverse formulation of eigenvalue problem for optimising the dynamics behaviour of structures. The formulation is applied to one- and two-dimensional finite elements which are commonly used in simulation of real structures. Based on this formulation an algorithm is developed for accurate and efficient modification of structures stiffness and mass characteristics to achieve the desired natural frequencies and interpretation of results in terms of physical design parameters. The proposed algorithm is tested by conducting four case studies and the results are validated against exact solutions.

Self-calibration algorithms estimate both source directions of arrival (DOAs) and perturbed array response vector parameters, such as sensor locations. Calibration errors are usually assumed to be small and a first order approximation to the perturbed array response vector is often used to simplify the estimation procedure. In this paper, we develop a more robust procedure that does not rely on the small error assumption. It has better performance for large estimation errors, and when used to initialize the Weiss and Friedlander MUSIC-based iterative technique, we see significant improvement over existing techniques for both small and large errors.

Based on the basic equations of a rotating disk, we use the qualitative analysis theory of nonlinear equations and obtain a nonlinear dynamical model of formation of binary stars. Under certain conditions a pair of singular points results in the course of evolution, which corresponds to a binary star. Under other conditions these equations give a single central point, which corresponds to a single star. For example, in the first order approximation, when 8 φ x 2 > φ y 2 , there are two stable focal points; conversely, when 8 φ x 2 φ y 2 , there are two stable nodal points; when φ y = 0, there is only a central point. This new method and model may be extended and developed in other applications.

When there is a large detuning linear error in a phase shifting algorithm the first order approximation may not be accurate enough. An exact and a second order approximation for linear detuning error in a phase shifting are studied in this paper. If a detuning insensitive algorithm like the well known Schwider–Hariharan algorithm is shifted by moving the phase origin for the sampling points another detuning insensitive algorithm is obtained. It is well known that both algorithms are detuning insensitive in a first order approximation. Here we see that they are also equal if the detuning range is large.

Explicit formulae are given for the saddle connection of an integrable family of standard maps studied by Y. Suris [Func. Anal. Appl. 23 (1989) 74–76]. When the map is perturbed this connection is destroyed, and we use a discrete version of Melnikov's method to give an explicit formula for the first order approximation of the area of the lobes of the resultant turnstile. These results are compared with computations of the lobe area.

We consider sequential point estimation of a linear combination of means of k populations. Our procedure is shown to have asymptotically less risk when compared with the existing procedure for some class of distributions.

In his application of the homotopy perturbation (HP) method to the problem of the three-dimensional flow past a stretching sheet, P.D. Ariel [The three-dimensional flow past a stretching sheet and the homotopy perturbation method, Comput. Math. Appl. 54 (2007) 920–925] encountered secular terms in the second order approximation, which he could not avoid. It is shown here that these secular terms can be removed by coordinate straining. Moreover, the form of an HP solution, which is free from secular terms at all levels of approximation, and which can be determined recursively, is indicated.

In this note we relate two methods of convergence acceleration for ordinary continued fractions, the first one is due to Lorentzen and Waadeland (Jacobsen and Waadeland, 1980, 1998), the second one to Waadeland (1986, 1987, 1987, 1987, 1988). (C) 1999 Elsevier Science B.V. All rights reserved. AMS classification: 40A15; 65B99; 65Q05. ispartof: Journal of computational and applied mathematics vol:101 issue:1 pages:167-175 status: published

This paper provides methodologies for evaluating consumer benefits of infrastructure services using potentially observable information. We define benefit measures for consumers and, using general principles from the index number literature, derive alternative first and second order approximations to these measures under the assumption of fixed prices for market goods and services. We then describe how the benefit measures and their associated approximations can be used in quantifying the economic benefits when prices are allowed to change endogenously as the provision of infrastructure services changes. In addition, under quite unrestrictive assumptions, a measure of welfare change based only on potentially observable data is derived.

Here we propose a method of construction of the second order approximation for the ground state energy for a class of model Hamiltonians with a linear type of interaction with respect to Bose operators in the strong coupling case. For an application of the above-mentioned method we have considered the polaron model and proposed a set of nonlinear differential equations for the ground state energy calculation in the strong coupling case. We have considered also the radially symmetric case.

We consider a fifth-order singularly perturbed KdV equation. The direct perturbation method for solving it is investigated in the first order approximation for the travelling wave case. The application of the method leads to a general soliton of the first-order equation, which describes some arrays of wave crests. Analysis of the solution shows that the perturbation makes the soliton lower and narrower than an unperturbed KdV soliton.