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Stochastic cellular automata for rock-paper-scissors games are related to Lotka-Volterra model. Simulations are usually performed by two methods local and global interactions. It is well known that the population dynamics with local interaction is stable, where all species coexist. In contrast, global interaction leads to extinction. So far, theories such as mean-field theory and pair approximation have been presented, but they never explained the stable dynamics in local simulation. In the present article, we apply effective medium approximation (EMA) which has been developed in Physics. The effective medium is determined in a self-consistent way. The EMA theory well predicts the stability of population dynamics. Moreover, it fairly explains the aggregation of each species observed in the stationary state. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in the displacement of two incompressible phases in a Darcy–Brinkman flow in a porous media. The equations are obtained by the conservation of the mass and by considering the Brinkman regularization velocity of each phase. This model is treated in its general form with the whole nonlinear terms. This paper deals with construction and convergence analysis of a combined finite volume–nonconforming finite element scheme together with a phase-by-phase upstream according to the total velocity. [ABSTRACT FROM AUTHOR]

In Jung and Roh (2017), we investigated some properties of approximate solutions of the second-order inhomogeneous linear differential equations. In this paper as an application of above paper we will study the stability of the time independent Schrödinger equation with a potential box of finite walls. [ABSTRACT FROM AUTHOR]

This paper presents an effective method to automatically construct trivariate tensor-product spline models of complicated geometry and arbitrary topology. Our method takes as input a solid model defined by its triangulated boundary surface. Using cuboid decomposition, an initial polycube approximating the input boundary mesh is built. This polycube serves as the parametric domain of the tensor-product spline representation required for isogeometric analysis. The polycube’s nodes and arcs decompose the input model’s boundary into quadrilateral patches, and these patches form hexahedral domains. Using aligned global parameterization, the nodes are re-positioned and the arcs are re-routed across the surface in a way to achieve low overall patch distortion, and alignment to principal curvature directions and sharp features. The optimization process is based on one of the main contributions of this paper: a novel way to design cross fields with topological (i.e., imposed singularities) and geometrical (i.e., imposed directions) constraints by solving only sparse linear systems. Based on the optimized polycube and parameterization, compatible B-spline boundary surfaces are reconstructed. Finally, the interior volumetric parameterization is computed using Coon’s interpolation. In the context of parametric studies based on geometrical parameters, this method can be used to compute the morphing required for reduced order modeling. For different parametric instances with the same topology but different geometries, this method allows to have the same representation: i.e., meshes (or parameterizations) with the same topology. The efficiency and the robustness of the proposed approach are illustrated by several examples. [ABSTRACT FROM AUTHOR]

Abstract In this paper we study the approximation ratio of the solutions achieved after an ϵ -approximate one-round walk in non-atomic congestion games. Prior to this work, the solution concept of one-round walks had been studied for atomic congestion games with linear latency functions only (Christodoulou et al. [1] , Bilò et al. [2]). We give an explicit formula to determine the approximation ratio for non-atomic congestion games having general latency functions. In particular, we focus on polynomial latency functions, and, we prove that the approximation ratio is exactly ((1 + ϵ) (p + 1)) p + 1 for every polynomial of degree p. Then, we show that, by resorting to static (resp. dynamic) resource taxation, the approximation ratio can be lowered to (1 + ϵ) p + 1 (p + 1) p (resp. (1 + ϵ) p + 1 (p + 1) !). [ABSTRACT FROM AUTHOR]

Abstract In this paper, we address the Approximate Agreement problem in the Mobile Byzantine Fault model. Our contribution is three-fold. First, we refine the problem specification to adapt it to the Mobile Byzantine Fault environment. Then, we propose the first mapping from the existing variants of Mobile Byzantine models to the Mixed-mode Fault model. This mapping further help us to prove the correctness of MSR (Mean-Subsequence-Reduce) algorithms class in our context and it is of independent interest. We also prove lower bounds for solving Approximate Agreement under all existing Mobile Byzantine fault models. [ABSTRACT FROM AUTHOR]

Abstract This article deals with a backward diffusion problem for an inhomogeneous backward diffusion equation with fractional Laplacian in R : u t (x , t) + − Δ α u (x , t) = f (x , t) , (x , t) ∈ R × [ 0 , T ] , u (x , T) = g (x) , x ∈ R , lim x → ± ∞ u (x , t) = 0. This problem is an ill-posed problem due to the instability in solution. The goal of this paper is not only to provide a simple but effective regularization scheme to obtain the Hölder convergence rate, but also to give an approximation of solution of the equation with fractional diffusion to the one of the equation with Laplacian in both L 2 (R) and L p (R) setting. This result holds, in particular, when f (x , t) is spatially compactly supported, in which the difficulties due to the fractional Laplacian have been successfully overcome thanks to an additional condition on Fourier transform of f. We further study the convergence of solution of inhomogeneous problem to that of the homogeneous problem. Finally, numerical simulations, with finite difference schemes, based on Discrete Fourier Transform (DFT) algorithm are also presented to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper develops an analytical method to measure the performance of a multi-product unreliable production line with finite buffers between workstations. The performance measure used in this paper is Total Cycle Time. The proposed method is an approximation that generalizes the processing times to ease the variation of product types in a multi-product system. A decomposition method is then employed to approximate the production rate of a multi-product production line. The decomposition method considers generally distributed processing times as well as random failure and repair. A GI/G/1/N queuing model is also applied to obtain parameters such as blocking and starvation probabilities that are needed for the approximation procedure. Several numerical experiments under different scenarios are performed and results are validated by simulation models in order to assess the accuracy and strength of the proposed method. Consequent analysis and discussion of the results are also presented. [ABSTRACT FROM AUTHOR]

Motivated by a recent paper by the RBC–UKQCD Collaboration, which observes large violations of the naïve factorization hypothesis in K → π π decays, we study in this paper the accuracy of the Vacuum Insertion Approximation (VIA) for the matrix elements of the complete basis of four-fermion Δ F = 2 operators. We perform a comparison between the matrix elements in QCD, evaluated on the lattice, and the VIA predictions. We also investigate the dependence on the external meson masses by computing matrix elements for K , D s , B s and static mesons. In commonly used renormalization schemes, we find large violations of the VIA in particular for one of the two relevant Wick contractions in the kaon sector. These deviations, however, decrease significantly as the meson mass increases and the VIA predictions turn out to be rather well verified for B -meson matrix elements and, even better, in the infinite mass limit. [ABSTRACT FROM AUTHOR]

In this paper, we define analysis-suitable++ (AS++) T-splines which include analysis-suitable (AS) T-splines as a special case and maintain all the good mathematical properties as AS T-splines. We prove that AS++ T-splines are always linear independent regardless of the knot values and show that the classical construction of the dual basis for tensor-product B-splines and AS T-splines can be generalized to AS++ T-spline spaces. We also discuss how all of these issues pave the way to a mathematical theory for AS++ T-splines. [ABSTRACT FROM AUTHOR]

Confined concrete has superior anti-penetration performance over unconfined concrete. A finite dynamic spherical cavity-expansion approximation model with radially elastic confinement is proposed to analyze the confinement on concrete targets and predict the depth of penetration (DOP), taking steel-tube-confined concrete (STCC) targets normally penetrated by rigid projectiles as an example. Firstly, the validity of a nonlinear failure criterion to describe strength feature of concrete in the comminuted region is demonstrated by triaxial compressible tested data and the reference range of dimensionless parameter m in the modified Griffith criterion is recommended. Secondly, the relationship between the stresses in concrete and cavity-expansion velocity is developed. Furthermore, the confinement effects on response modes of confined concrete, radial stress at cavity wall and stresses distribution in concrete are analyzed. Lastly, an engineering model is also established to predict the DOP of STCC targets normally penetrated by rigid projectiles. The results show that the radial stress at cavity wall is not a constant during the cavity-expansion process in finite concrete with radially elastic confinement, which is different from the steady spherical cavity-expansion of infinite material in which the radial stress at cavity wall is a constant with constant cavity-expansion velocity. The possible response phases of confined concrete targets normally penetrated by rigid projectiles include “elastic-cracked-comminuted”, “cracked-comminuted” and “full-comminuted”, depending on the relationship among cavity-expansion velocity, radial confining stiffness and radius ratio of cavity to target. The DOP data from the engineering model established in this paper agree well with those of experiments in the published references. [ABSTRACT FROM AUTHOR]

Recently a WENO scheme, with smoothness indicators constructed based on L 1 measure is introduced by Ha et al. (2013) and the improved version of this scheme is presented by Kim et al. (2016), referred to as WENO-NS and WENO-P schemes respectively. These schemes perform better than the existing many fifth-order WENO schemes for the problems which contain discontinuities and attain fifth-order accuracy at the critical points where the first derivative vanishes but not at the points where the second derivatives are zero. This paper deals with modification of the above said methods to obtain a new fifth-order weighted essentially non-oscillatory (WENO) scheme. A new global-smoothness indicator is proposed which shows an improved behavior over the solutions of WENO-NS and WENO-P schemes and the proposed scheme attains an optimal order of approximation, even at the critical points where the first and second derivatives vanish but not the third derivative. Examples are taken in the numeric section to check the robustness and accuracy of the proposed scheme for one and two-dimensional system of Euler equations. [ABSTRACT FROM AUTHOR]

It is well understood that during the pharmaceutical aqueous film coating process the amount of liquid water that interacts with the porous tablet core can affect the quality of the final product. Therefore, understanding and simulating the mechanisms of water droplet spreading, absorption and evaporation is crucial for controlling the process and optimising the shelf-life of the tablets. The purpose of the work presented in this paper is to define and describe the spreading, absorption and evaporation phenomena after droplet impingement on a tablet. We divided the droplet behaviour into three phases of different dynamics and duration: the kinematic, capillary and evaporation phases. To model the kinematic phase, we combined and modified 1-D spreading models from the literature which solve the kinetic energy balance equation for the first milliseconds of spreading. For the capillary phase, we simplified and solved the continuity and Navier-Stokes equations using the lubrication approximation theory. Finally, for the evaporation phase, we adopted a modelling approach for the second drying stage of slurry droplets inside a spray dryer. During this stage, one can no longer describe the droplet as a liquid system containing solids, having to regard it as a wet particle with a dry crust and a wet core. In our work, we represented in a novel way the crust as the dry surface of the tablet and the wet core as the wetted area inside the porous matrix. We implemented the mathematical model presented in this work in gPROMS, employing the Modelbuilder platform. Our numerical results (droplet height and spreading, wetting, evaporation front profiles) are in good agreement with recent experimental data that we found in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we study the hedging problem based on the CVaR in incomplete markets. As the superhedging is quite expensive in terms of initial capital, we construct a self-financing strategy that minimizes the CVaR of hedging risk under a budget constraint on the initial capital. In incomplete markets, no explicit solution can be provided. To approximate the problem, we apply the Neyman–Pearson lemma approach with a specific equivalent martingale measure. Afterwards, we explicit the solution for call options hedging under the exponential-Lévy class of price models. This approach leads to an efficient and easy to implement method using the fast Fourier transform. We illustrate numerical results for the Merton model. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and investigate the Minimum Eccentricity Shortest Path (MESP) problem in unweighted graphs. It asks for a given graph to find a shortest path with minimum eccentricity. Let n and m denote the number of vertices and the number of edges of a given graph. We demonstrate that: • a minimum eccentricity shortest path plays a crucial role in obtaining the best to date approximation algorithm for a minimum distortion embedding of a graph into the line; • the MESP problem is NP-hard for planar bipartite graphs with maximum degree 3 and W[2]-hard for general graphs; • a shortest path of minimum eccentricity k can be computed in O ( n 2 k + 2 m ) time; • a 2-approximation, a 3-approximation, and an 8-approximation for the MESP problem can be computed in O ( n 3 ) time, in O ( n m ) time, and in O ( m ) time, respectively; • in a graph with a shortest path of eccentricity k , a k -dominating set can be found in n O ( k ) time. [ABSTRACT FROM AUTHOR]

We are promoting the use of variational principles as some generalizing idea that allows us to create consistent approximations of mathematical models. In this paper, we formulate a computing technology to solve direct and inverse problems of atmospheric dynamics and chemistry. For the implementation, we use functional decomposition methods, splitting techniques, and integrating factors designed as the solutions of some adjoint problems. One of the main purposes of the paper is to relate the theory of approximation with the concept of Eulerian integrating factors that plays the fundamental role in the theory of differential equations. We demonstrate the utility and versatility of the concept applying it to solve the systems of differential equations of convection–diffusion (with dominant convection) and stiff systems of kinetic equations. To identify the prospects of our approach, we briefly introduce how to use integrating factors in the case of unstructured grids. [Copyright &y& Elsevier]

Abstract: In this paper we present low-residual approximate solutions for nonlocal 1D and 2D elasticity problems defined according to Eringen’s integral model. The benchmarks in the 1D cases are defined by prescribing the stress field while the unknown fields are the strains or the displacements. For the 2D cases we define problems with equilibrated tractions and evaluate the approximate displacement field. Meanwhile a Fourier series as well as a set of Chebyshev polynomials are used as the basis functions for the main unknown fields. We increase the number of the approximation functions to decrease the norm of the residuals and repeat the procedure until reasonable accuracy is obtained for the final solution. Since the procedure is very time consuming, in some benchmark problems we present the calculated coefficients and in some other we give some point-wise values for further use. The results presented in this paper are particularly useful for the validation and convergence studies when numerical methods are to be used for the solution of the nonlocal elasticity problems. [Copyright &y& Elsevier]

Abstract: The subject of this paper is the plate composed of two relatively stiff outer layers (skins) and a more compliant inner layer (soft interlayer, called core), i.e., three-layered (sandwich) plate. This system may represent composite and laminated plates, e.g., sandwich panels and decks. This paper presents a model that describes the behavior of three-layered plate by a system of exact analytical (explicit) equations, derived from the Kirchhoff–Love plate assumptions. Accordingly, this system of equations corresponds to the Kirchhoff–Love equation of the plate. The pie-chart of research on sandwiches allots only a slight slice to analytical modeling, while it allots the largest slice to approximate prediction methods. In particular, the three-layered plate lacked the two-dimensional governing equations. Empirical or semi-empirical formulations, finite element models, a priori formulas based on simplified or rough theories may represent more accessible research topics; however, they suffer from high layer-to-interlayer stiffness ratios, which impinge on their results. Thus, these approximate prediction methods provide unsatisfactory results for the continuously increasing ratios that the industry is developing, and will be developing, to increase ever more the stiffness-to-density and strength-to-density ratios of the sandwiches. Conversely, this model, whose formulation is exact, does not suffer whatsoever from high skin-to-core elastic modulus ratios, and therefore it is specifically dedicated to modern, advanced, and innovative sandwich plates. To apply this exact model is less time consuming than to generate any finite element mesh or to apply any approximate method. Consequently, approximate methods become completely unnecessary for the three-layered plates that comply with Kirchhoff–Love plate assumptions. On the contrary, for the three-layered plates that do not comply with these assumptions, the finite element models continue to represent a viable means, provided that beforehand their reliability is checked and their free parameters are calibrated. To facilitate check and calibration, exact results from the model are provided in the paper, which finite element results can be compared to. [Copyright &y& Elsevier]

Abstract: This paper presents the complex modal analysis for a proportionally damped structure equipped with linear non-proportionally damped viscous elements (substructures or discrete real devices) giving a low-rank contribution (r) to the non-proportional part of the damping matrix. Using the classical undamped modes and a special low-rank matrix update formulation of the problem, the original Quadratic Eigenproblem (QEP) is hugely deflated, without approximations, to an equivalent Rational Eigenproblem (REP) of dimension r ≪ n (), as an alternative to the linearized Standard Eigenproblem of order 2n over the complex field. The existence of classical modes in non-classically damped structures is also discussed. The REP is solved by the homotopy method: a robust predictor–corrector continuation algorithm is designed in order to determine the required eigenpairs. Some applications to simple models of both traditional and base-isolated structures, together with an outline of future work, end the paper. [Copyright &y& Elsevier]

Abstract: The problem of reconstructing signals and images from degraded ones is considered in this paper. The latter problem is formulated as a linear system whose coefficient matrix models the unknown point spread function and the right hand side represents the observed image. Moreover, the coefficient matrix is very ill-conditioned, requiring an additional regularization term. Different boundary conditions can be proposed. In this paper antireflective boundary conditions are considered. Since both sides of the linear system have uncertainties and the coefficient matrix is highly structured, the Regularized Structured Total Least Squares approach seems to be the more appropriate one to compute an approximation of the true signal/image. With the latter approach the original problem is formulated as an highly nonconvex one, and seldom can the global minimum be computed. It is shown that Regularized Structured Total Least Squares problems for antireflective boundary conditions can be decomposed into single variable subproblems by a discrete sine transform. Such subproblems are then transformed into one-dimensional unimodal real-valued minimization problems which can be solved globally. Some numerical examples show the effectiveness of the proposed approach. [Copyright &y& Elsevier]

Abstract: In this paper, we study two variants of the problem of adding edges to a graph so as to reduce the resulting diameter. More precisely, given a graph , and two positive integers and , the Minimum-Cardinality Bounded-Diameter Edge Addition (MCBD) problem is to find a minimum-cardinality set of edges to be added to in such a way that the diameter of is less than or equal to , while the Bounded-Cardinality Minimum-Diameter Edge Addition (BCMD) problem is to find a set of edges to be added to in such a way that the diameter of is minimized. Both problems are well known to be NP-hard, as well as approximable within and (up to an additive term of 2), respectively. In this paper, we improve these long-standing approximation ratios to and to (up to an additive term of 2), respectively. As a consequence, we close, in an asymptotic sense, the gap on the approximability of MCBD, which was known to be not approximable within , for some constant , unless . Remarkably, as we further show in the paper, our approximation ratio remains asymptotically tight even if we allow for a solution whose diameter is optimal up to a multiplicative factor approaching . On the other hand, on the positive side, we show that at most twice of the minimal number of additional edges suffices to get at most twice of the required diameter. Some of our results extend to the edge-weighted version of the problems. [Copyright &y& Elsevier]

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

Abstract: Statistical analysis is an efficient method for the optimisation of any candidate mathematical model of creep rupture data, and for the comparative ranking of competing models. However, when a series of candidate models has been examined and the best of the series has been identified, there is no statistical criterion to determine whether a yet more accurate model might be devised. Hence there remains some uncertainty that the best of any series examined is sufficiently accurate to be considered reliable as a basis for extrapolation. This paper proposes that models should be validated primarily by parametric graphical comparison to rupture data and rupture gradient data. It proposes that no mathematical model should be considered reliable for extrapolation unless the visible divergence between model and data is so small as to leave no apparent scope for further reduction. This study is based on the data for a 12% Cr alloy steel used in BS PD6605:1998 to exemplify its recommended statistical analysis procedure. The models considered in this paper include a) a relatively simple model, b) the PD6605 recommended model and c) a more accurate model of somewhat greater complexity. [Copyright &y& Elsevier]

Abstract: This paper presents a fuzzy-Pareto dominance driven possibilistic model based planning of electrical distribution systems using multi-objective particle swarm optimization (MOPSO). This multi-objective planning model captures the possibilistic variations of the system loads using a fuzzy triangular number. The MOPSO based on the Pareto-optimality principle is used to obtain a set of non-dominated solutions representing different network structures under uncertainties in load demands and these non-dominated solutions are stored in an elite archive of limited size. Normally, choosing the candidate non-dominated solutions to be retained in the elite archive while maintaining the quality of the Pareto-approximation front as well as maintaining the diversity of solutions on this front is very much computationally demanding. In this paper, the principles of fuzzy Pareto-dominance are used to find out and rank the non-dominated solutions on the Pareto-approximation front. This ranking in turn is used to maintain the elite archive of limited size by discarding the lower ranked solutions. The two planning objectives are: (i) minimization of total installation and operational cost and (ii) minimization of risk factor. The risk factor is defined as a function of an index called contingency-load-loss index (CLLI), which captures the effect of load loss under contingencies, and the degree of network constraint violations. The minimization of the CLLI improves network reliability. The network variables that are optimized are: (i) number of feeders and their routes, and (ii) number and locations of sectionalizing switches. An MOPSO (developed by the authors), based on a novel technique for the selection and assignment of leaders/guides for efficient search of non-dominated solutions, is used as the optimization tool. The proposed planning approach is validated on a typical 100-node distribution system. Performance comparisons between the planning approaches with the possibilistic and deterministic load models are provided highlighting the relative merits and demerits. It is also verified that the proposed solution ranking scheme based on the fuzzy-Pareto dominance is very much better from both quality and computational burden point of view in comparison with the other well-known archive truncation techniques based on clustering and solution density measurement etc. [Copyright &y& Elsevier]

Abstract: Uniform resampling is the easiest to apply and is a general recipe for all problems, but it may require a large replication size . To save computational effort in uniform resampling, balanced bootstrap resampling is proposed to change the bootstrap resampling plan. This resampling plan is effective for approximating the center of the bootstrap distribution. Therefore, this paper applies it to neural model selection. Numerical experiments indicate that it is possible to considerably reduce the replication size . Moreover, the efficiency of balanced bootstrap resampling is also discussed in this paper. [Copyright &y& Elsevier]

Abstract: The computation of Global Climate Models (GCMs) presents significant numerical challenges. This paper presents new algorithms based on sparse occupancy trees for learning and emulating the long wave radiation parameterization in the NCAR CAM climate model. This emulation occupies by far the most significant portion of the computational time in the implementation of the model. From the mathematical point of view this parameterization can be considered as a mapping which is to be learned from scattered data samples , . Hence, the problem represents a typical application of high-dimensional statistical learning. The goal is to develop learning schemes that are not only accurate and reliable but also computationally efficient and capable of adapting to time-varying environmental states. The algorithms developed in this paper are compared with other approaches such as neural networks, nearest neighbor methods, and regression trees as to how these various goals are met. [Copyright &y& Elsevier]

Abstract: In this paper, the focus will be on approximating nonlinear large scale mathematical model of process systems using full order block-structured model. Further, the objective is to achieve a reduced order model for the nonlinear large model with reduced computational complexity, while at the same time being the good approximation of nonlinear model. The modeling approach used for this purpose is block structure models. Input–output Hammerstein structure referred to the classical Hammerstein model has been extended to new Hammerstein structure making use of states and inputs, hence called as input-state (IS) Hammerstein structure. In this paper it is shown that expansion of Taylor series leads to IS-Hammerstein structure. The accuracy of the approximation is improved by including higher order (second order) approximation. The input-state Hammerstein structure provides opportunities for model reduction in context of reducing the computational load by order reduction of states and Jacobians. IS-full order Hammerstein model has been implemented on a case study from the process industry namely the high purity distillation column. Within the operational domain of a process, the IS-Hammerstein structure provides a reduced order mode that can be used for online application purposes (i.e., optimization, model predictive control, etc.). [Copyright &y& Elsevier]

Abstract: Most design codes (Model Code 90, ACI-318-2008 and Eurocode–2-2004) suggest that the effect of a geometrical imperfection ought to be taken into account in the most unfavorable direction when designing slender reinforced concrete columns. If the bending plane of the beam–column is related to the strong axis, this imperfection acting in the opposite direction results in the column being subjected to axial load and biaxial bending, complicating the design procedure and increasing computational costs considerably. Such standards do not indicate when this geometrical imperfection generates a notable loss of resistance in the column. This paper proposes the geometrical slenderness of the weak axis as the variable that determines whether or not to consider the influence of such imperfection. This paper denominates this boundary value the “slenderness limit of the weak axis” (), and this is associated with a loss of resistance of 10% of the bending moment of the unbraced columns with respect to non-sway columns. An approximated equation of this limit is proposed using the results of a numerical simulation. The equation is valid for rectangular columns with doubly symmetric reinforcement and both normal and high strength concrete, and also for short-term and sustained loads. [Copyright &y& Elsevier]

Abstract: This paper presents a generic high dimensional model representation (HDMR) method for approximating the system response in terms of functions of lower dimensions. The proposed approach, which has been previously applied for problems dealing only with random variables, is extended in this paper for problems in which physical properties exhibit spatial random variation and may be modelled as random fields. The formulation of the extended HDMR is similar to the spectral stochastic finite element method in the sense that both of them utilize Karhunen–Loève expansion to represent the input, and lower-order expansion to represent the output. The method involves lower dimensional HDMR approximation of the system response, response surface generation of HDMR component functions, and Monte Carlo simulation. Each of the low order terms in HDMR is sub-dimensional, but they are not necessarily translating to low degree polynomials. It is an efficient formulation of the system response, if higher-order variable correlations are weak, allowing the physical model to be captured by the first few lower-order terms. Once the approximate form of the system response is defined, the failure probability can be obtained by statistical simulation. The proposed approach decouples the finite element computations and stochastic computations, and consecutively the finite element code can be treated as a black box, as in the case of a commercial software. Numerical examples are used to illustrate the features of the extended HDMR and to compare its performance with full scale simulation. [Copyright &y& Elsevier]

Abstract: This is a paper out of a series of three papers devoted to model- and hpq-adaptive finite element methods assigned for modeling and analysis of complex structures. In this paper we focus our attention on hierarchical models and hierarchical approximations, while the issues of error estimation and adaptivity control will be presented in the next papers of the series. In all the papers we consider the elastic structures of complex mechanical description. We apply 3D or 3D-based mechanical models, hierarchical modeling, and hierarchical approximations within our finite element formulation. In the proposed approach, the mechanical model and discretization parameters, such as the size h of the element, and the longitudinal and transverse approximation orders, p and q, can vary locally, i.e. they can be different in each finite element. The a posteriori error estimation is based on the residual equilibration methods applied to the assessment of the modeling and approximation errors. The error-controlled adaptive procedures are derived from a four-step strategy, with possible iterations on h- and p-steps. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes a centralized resource allocation (CRA) model for the enhanced Russell model. All the DMUs can be easily projected onto the efficient frontier by solving only one model. This projection can be made by transforming the proposed model to a linear programming problem. In this paper, instead of non-radially increasing or decreasing the inputs or outputs individually, we increase or decrease non-radially all of the inputs and outputs at the same time. By solving a single model, we can provide targets for all DMUs. By the proposed approximation, different targets can be found for all DMUs, as compared to those obtained by the previous approximations. The proposed model can be developed to CRA models. Finally, an applied example emphasizes the importance of the proposed model. [Copyright &y& Elsevier]

Abstract: Based on the Pawlak rough set theory, this paper investigates separations in covering approximation spaces, give some characterizations of these separations and some relations among these separations. As an application of these results, investigations on network security are converted into investigations on separations in covering approximation spaces by taking covering approximation spaces as mathematical models of networks. Results of this paper give further applications of the Pawlak rough set theory in pattern recognition and artificial intelligence, which makes it possible to research network security by logical methods and mathematical methods in computer science. This contributes to giving risk assessments of securities and to raise grades of securities for networks. [ABSTRACT FROM AUTHOR]

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

Abstract: For linear descriptor systems of the form , , this paper constructs reduced order systems associated with a given part of the finite spectrum of the pencil . It is known that the reduction can be obtained by a block diagonalization of the generalized Schur decomposition of . In this paper we consider the special case when and . This case is suited, in particular, for linearized hydrodynamic problems. We derive a sufficient condition under which the reduced system can approximate the initial one and show that it can be obtained in significantly cheap and efficient approaches. We consider first in detail the case when and is the identity matrix and then treat the general case. [Copyright &y& Elsevier]

Abstract: In this paper we investigate the approximations for the distribution function of a sum of lognormal random variables. These approximations are obtained by considering the conditional expectation of with respect to a conditioning random variable . The choice of is crucial in order to obtain accurate approximations. The different alternatives for that have been proposed in the literature to date are ‘global’ in the sense that is chosen such that the entire distribution of the approximation is ‘close’ to the corresponding distribution of the original sum . In an actuarial or a financial context one is often only interested in a particular tail of the distribution of . Therefore in this paper we propose approximations which are only locally optimal, in the sense that the relevant tail of the distribution of is an accurate approximation for the corresponding tail of the distribution of . Numerical illustrations reveal that local optimal choices for can improve the quality of the approximations in the relevant tail significantly. We also explore the asymptotic properties of the approximations and investigate links with results from [S. Asmussen, Rojas-Nandayapa, Sums of dependent lognormal random variables: Asymptotics and simulation, Stochastic Series at Department of Mathematical Sciences, University of Aarhus, Research Report number 469, 2005]. Finally, we briefly address the sub-optimality of Asian options from the point of view of risk averse decision makers with a fixed investment horizon. [Copyright &y& Elsevier]

Costas loop is a classical phase-locked loop (PLL) based circuit for carrier recovery and signal demodulation. The PLL is an automatic control system that adjusts the phase of a local signal to match the phase of the input reference signal. This tutorial is devoted to the dynamic analysis of the Costas loop. In particular the acquisition process is analyzed. Acquisition is most conveniently described by a number of frequency and time parameters such as lock-in range, lock-in time, pull-in range, pull-in time, and hold-in range. While for the classical PLL equations all these parameters have been derived (many of them are approximations, some even crude approximations), this has not yet been carried out for the Costas loop. It is the aim of this analysis to close this gap. The paper starts with an overview on mathematical and physical models (exact and simplified) of the different variants of the Costas loop. Then equations for the above mentioned key parameters are derived. Finally, the lock-in range of the Costas loop for the case where a lead-lag filter is used for the loop filter is analyzed. [ABSTRACT FROM AUTHOR]

Taylor series approximation like q ( t + τ ) ≈ q + τ ∂ q ∂ t are often used to derive, extend or interpret typical heat conduction models. Researchers may take it for granted that the single-phase-lagging (SPL) model can be considered as an extension of the Cattaneo–Vernotte (CV) model because there is such approximation relationship between them. We point out in this paper that this Taylor series approximation itself has some defects based on analyses in mathematics, physics and some examples first. Then, we show essential differences in both mathematics and physics between the CV and SPL models. It is found that their mathematical characteristics and accordance with the laws of thermodynamics are significantly different, which indicates that using this approximation to connect the two models may be defective in some cases. What’s more, higher order approximation can’t solve these problems and defects. [ABSTRACT FROM AUTHOR]

We analyze the classical problem of the interaction between two charged surfaces separated by a solution containing neutralizing counter-ions. The focus is on obtaining a description where the solvent is treated explicitly rather than through a dielectric approximation as is conventionally done. We summarize the results of three papers where we have used a Stockmayer fluid model in Monte Carlo simulations. It is shown that the attractive ion–ion correlation mechanism is also operating when the solvent is described explicitly. There appears an oscillatory component to the force, but when this is accounted for, there is a semi-quantitative agreement between the continuum model and the model with explicit solvent. The properties of the continuum model can be reached in a molecular system by making the solvent molecules much smaller than the ions. It is demonstrated that having an explicit solvent model makes the analysis of force mechanisms more delicate due to the interplay between several different microscopic contributions to the force. Finally, it is argued that the agreement between the forces calculated using the continuum and the explicit solvent models, respectively, has as its basis the circumstance that the force between the surfaces is mainly caused by long-range ion–ion interactions, for which the dielectric approximation is most adequate. This argument applies equally well to an aqueous system as to the Stockmayer fluid. [ABSTRACT FROM AUTHOR]

A precise theoretical description of W- and Z-boson production in the resonance region is essential for the correct interpretation of high-precision measurements of the W-boson mass and the effective weak mixing angle. Currently, the largest unknown fixed-order contribution is given by the mixed QCD-electroweak corrections of O ( α s α ) . We argue, using the framework of the pole expansion for the NNLO QCD-electroweak corrections established in a previous paper, that the numerically dominant corrections arise from the combination of large QCD corrections to the production with the large electroweak corrections to the decay of the W / Z boson. We calculate these so-called factorizable corrections of “initial–final” type and estimate the impact on the W-boson mass extraction. We compare our results to simpler approximate combinations of electroweak and QCD corrections in terms of naive products of NLO QCD and electroweak correction factors and using leading-logarithmic approximations for QED final-state radiation as provided by the structure-function approach or QED parton-shower programs. We also compute corrections of “final–final” type, which are given by finite counterterms to the leptonic vector-boson decays and are found to be numerically negligible. [ABSTRACT FROM AUTHOR]

In this paper we propose a new iterative finite difference (IFD) scheme based on the Newton–Raphson–Kantorovich approximation method in function space to solve the classical one-dimensional Bratu’s problem. This new numerical method produces accurate solutions with low computational cost. The effectiveness and accuracy of the IFD method are confirmed through several numerical examples and compared to some existing numerical solvers. [ABSTRACT FROM AUTHOR]

In this paper, efficient numerical schemes are proposed for solving the fractional water wave models that describe the propagation of surface water wave. By using the weighted and shifted Grünwald–Letnikov (WSGL) formula to approximate the nonlocal fractional operators, we design a series of second order accurate difference schemes for the considered models. The existence, stability and convergence of numerical solutions of the proposed numerical schemes are established rigorously. The analysis shows that the proposed numerical schemes are unconditionally stable with second order accuracy for both temporal and spatial discretizations. Several numerical results are provided to verify the efficiency and accuracy of our theoretical analysis. [ABSTRACT FROM AUTHOR]

The goal of this paper is to obtain a numerical approximation of the effective Hamiltonian for a system of PDEs deriving from a second order discrete model for traffic flow. We will propose an explicit and an implicit discretization for this effective Hamiltonian and we will provide the corresponding error estimates of Crandall–Lions type. Finally, we will also present some numerical simulations. [ABSTRACT FROM AUTHOR]

Given an edge-weighted graph G = ( V , E ) and a subset R of V , a Steiner tree of G is a tree which spans all the vertices in R . A full Steiner tree is a Steiner tree which has all the vertices of R as its leaves. The full Steiner tree problem is to find a full Steiner tree of G with minimum weight. In this paper we consider the full Steiner tree problem when G is a unit disk graph. We present a 20-approximation algorithm for the full Steiner tree problem in G . As for λ -precise unit disk graphs we present a ( 10 + 1 λ ) -approximation algorithm, where λ is the length of the shortest edge in G . [ABSTRACT FROM AUTHOR]