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The purpose of this paper is to introduce a class of total quasi-f-asymptotically nonexpansivenonself mappings and to study the strong convergence under a limit condition only in the framework of Banach spaces. As an application, we utilize our results to study the approximation problem of solution to a system of equilibrium problems. The results presented in the paper extend and improve the corresponding results announced by some authors recently. [ABSTRACT FROM AUTHOR]

This paper proposes and analyzes a stabilized finite-volume method (FVM) for the threedimensional stationary Navier-Stokes equations approximated by the lowest order finite element pairs. The method studies the new stabilized FVM with the relationship between the stabilized FEM (FEM) and the stabilized FVM under the assumption of the uniqueness condition. The results have three prominent features in this paper. Firstly, the error analysis shows that the stabilized FVM provides an approximate solution with the optimal convergence rate of the same order as the usual stabilized FEM solution solving the stationary Navier-Stokes equations. Secondly, superconvergence results on the solutions of the stabilized FEM and stabilized FVM are derived on the H¹-norm and the L²-norm for the velocity and pressure. Thirdly, residual technique is applied to obtain the L²-norm error for the velocity without additional regular assumption on the exact solution. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to prove strong convergence theorems for common fixed points of two countable families of relatively quasi nonexpansive mappings in a uniformly convex and uniformly smooth real Banach space using the properties of generalized f -projection operator. In order to get the strong convergence theorems, a new iterative scheme by monotone hybridmethod is presented and is used to approximate the common fixed points. Then, two examples of countable families of uniformly closed nonlinear mappings are given. The results of this paper modify and improve the results of Li et al. (2010), the results of Takahashi and Zembayashi (2008), and many others. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to consider a modified hybrid steepest-descent method by using a viscosity approximation method with a weakly contractive mapping for finding the common element of the set of a common fixed point for an infinite family of nonexpansive mappings and the set of solutions of a system of an equilibrium problem. The sequence is generated from an arbitrary initial point which converges in norm to the unique solution of the variational inequality under some suitable conditions in a real Hilbert space. The results presented in this paper generalize and improve the results of Moudafi (2000), Marino and Xu (2006), Tian (2010), Saeidi (2010), and some others. Finally, we give an application to minimization problems and a numerical example which support our main theorem in the last part. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present new results related to the convergence of the sequence of the q-Bernstein polynomials {Bn,q(f; x)} in the case q > 1, where f is a continuous function on ［0, 1］. It is shown that the polynomials converge to f uniformly on the time scale Jq = {q-j}... ⋓ {0}, and that this result is sharp in the sense that the sequence {Bn,q(f; x)}... may be divergent for all x ε R \ Jq. Further, the impossibility of the uniform approximation for the Weierstrass-type functions is established. Throughout the paper, the results are illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach to segmentation of dermoscopic images based on wavelet transformwhere the approximation coefficients have been shown to be efficient in segmentation. The three novel frameworks proposed in this paper, W-FCM, WCPSFCM, and WK-Means, have been employed in segmentation using ROC curve analysis to demonstrate sufficiently good results. The novel W-CPSFCM algorithm permits the detection of a number of clusters in automatic mode without the intervention of a specialist. [ABSTRACT FROM AUTHOR]

This paper contains a surprisingly large amount of material and indeed can serve as an introduction to some of ideas and methods of singular perturbation theory. The work done in this area during the periods 1984-2000 and 2000-2005 has already been surveyed in 2002 and 2007 but our main objective is to produce a collection of important research articles of physical significance. In this paper, the crux of research articles published by numerous researchers during 2006-2010 in referred journals has been presented, and this leads to conclusions and recommendations about what methods to use on singular perturbation problems. [ABSTRACT FROM AUTHOR]

Retrial queues can only be solved in a closed form in very few and simple cases, so researchers must resort to approximate models. However, most of the papers that propose approximate models assume the convergence of the proposed models to their exact counterparts, without providing a rigorous mathematical proof. In this paper we demonstrate the convergence of finite truncated models with two reattempt orbits. [ABSTRACT FROM AUTHOR]

This paper reviewed the research on the nonlinear free vibration of pre-stressed orthotropic membrane, which is commonly applied in building membrane structures. We applied the L-P perturbation method to solve the governing equations of large amplitude nonlinear free vibration of rectangular orthotropic membranes and obtained a simple approximate analytical solution of the frequency and displacement function of large amplitude nonlinear free vibration of rectangular membrane with four edges simply supported. By giving computational examples, we compared and analyzed the frequency results. In addition, vibration mode of the membrane and displacement and time curve of each feature point on the membrane surface were analyzed in the computational example. Results obtained from this paper provide a simple and convenient method to calculate the frequency and lateral displacement of nonlinear free vibration of rectangular orthotropic membranes in large amplitude. Meanwhile, the results provide some theoretical basis for solving the response of membrane structures under dynamic loads and provide some computational basis for the vibration control and dynamic design of building membrane structures. [ABSTRACT FROM AUTHOR]

This paper is devoted to the following question: how to characterize convex nowhere dense subsets of normed linear spaces in terms of porosity? The motivation for this study originates from papers of V. Olevskii and L. Zaj´ıˇcek, where it is shown that convex nowhere dense subsets of normed linear spaces are porous in some strong senses. [ABSTRACT FROM AUTHOR]

Evaluating the reliability of a transportation network often involves an intensive simulation exercise to randomly generate and evaluate different possible network states. This paper proposes an algorithm to approximate the network reliability which minimizes the use of such simulation procedure. The algorithm will dissect and classify the network states into reliable, unreliable, and un-determined partitions. By postulating the monotone property of the reliability function, each reliable and/or unreliable state can be used to determine a number of other reliable and/or unreliable states without evaluating all of them with an equilibrium assignment procedure. The paper also proposes the cause-based failure framework for representing dependent link degradation probabilities. The algorithm and framework proposed are tested with a medium size test network to illustrate the performance of the algorithm. [ABSTRACT FROM AUTHOR]

This paper presents new results on modeling and analysis of dynamics of fractional-order discrete-time linear time-invariant single-input single-output (LTI SISO) systems by means of new, two-layer, “fractional-order discrete-time Laguerre filters.” It is interesting that the fractionality of the filters at the upper system dynamics layer is directly projected from the lower Laguerre-based approximation layer for the Grünwald-Letnikov difference. A new stability criterion for discrete-time fractional-order Laguerre-based LTI SISO systems is introduced and supplemented with a stability preservation analysis. Both the stability criterion and the stability preservation analysis bring up rather surprising results, which is illustrated with simulation examples. [ABSTRACT FROM AUTHOR]

The Cattaneo-Vernotte equation is a generalization of the heat and particle diffusion equations; this mathematical model combines waves and diffusion with a finite velocity of propagation. In disordered systems the diffusion can be anomalous. In these kinds of systems, the mean-square displacement is proportional to a fractional power of time not equal to one. The anomalous diffusion concept is naturally obtained from diffusion equations using the fractional calculus approach. In this paper we present an alternative representation of the Cattaneo-Vernotte equation using the fractional calculus approach; the spatial-time derivatives of fractional order are approximated using the Caputo-type derivative in the range (0,2]. In this alternative representation we introduce the appropriate fractional dimensional parameters which characterize consistently the existence of the fractional space-time derivatives into the fractional Cattaneo-Vernotte equation. Finally, consider the Dirichlet conditions, the Fourier method was used to find the full solution of the fractional Cattaneo-Vernotte equation in analytic way, and Caputo and Riesz fractional derivatives are considered. The advantage of our representation appears according to the comparison between our model and models presented in the literature, which are not acceptable physically due to the dimensional incompatibility of the solutions. The classical cases are recovered when the fractional derivative exponents are equal to 1. [ABSTRACT FROM AUTHOR]

During the last years, kriging has become one of the most popular methods in computer simulation and machine learning. Kriging models have been successfully used in many engineering applications, to approximate expensive simulation models. When many input variables are used, kriging is inefficient mainly due to an exorbitant computational time required during its construction. To handle high-dimensional problems (100+), one method is recently proposed that combines kriging with the Partial Least Squares technique, the so-called KPLS model. This method has shown interesting results in terms of saving CPU time required to build model while maintaining sufficient accuracy, on both academic and industrial problems. However, KPLS has provided a poor accuracy compared to conventional kriging on multimodal functions. To handle this issue, this paper proposes adding a new step during the construction of KPLS to improve its accuracy for multimodal functions. When the exponential covariance functions are used, this step is based on simple identification between the covariance function of KPLS and kriging. The developed method is validated especially by using a multimodal academic function, known as Griewank function in the literature, and we show the gain in terms of accuracy and computer time by comparing with KPLS and kriging. [ABSTRACT FROM AUTHOR]

We consider a one-dimensional Allen-Cahn equation with constraint from the viewpoint of numerical analysis. The constraint is provided by the subdifferential of the indicator function on the closed interval, which is the multivalued function. Therefore, it is very difficult to perform a numerical experiment of our equation. In this paper we approximate the constraint by the Yosida approximation. Then, we study the approximating system of the original model numerically. In particular, we give the criteria for the standard forward Euler method to give the stable numerical experiments of the approximating equation. Moreover, we provide the numerical experiments of the approximating equation. [ABSTRACT FROM AUTHOR]

This paper proposes a new theoretic approach to a specific interaction of continuous and discrete dynamics in switched control systems known as a Zeno behaviour. We study executions of switched control systems with affine structure that admit infinitely many discrete transitions on a finite time interval. Although the real world processes do not present the corresponding behaviour, mathematical models of many engineering systems may be Zeno due to the used formal abstraction. We propose two useful approximative approaches to the Zeno dynamics, namely, an analytic technique and a variational description of this phenomenon. A generic trajectory associated with the Zeno dynamics can finally be characterized as a result of a specific projection or/and an optimization procedure applied to the original dynamic model. The obtained analytic and variational techniques provide an effective methodology for constructive approximations of the general Zeno-type behaviour. We also discuss shortly some possible applications of the proposed approximation schemes. [ABSTRACT FROM AUTHOR]

Due to large numbers of antennas and users, matrix inversion is complicated in linear precoding techniques for massive MIMO systems. Several approximated matrix inversion methods, including the Neumann series, have been proposed to reduce the complexity. However, the Neumann series does not converge fast enough. In this paper, to speed up convergence, a new joint Newton iteration and Neumann series method is proposed, with the first iteration result of Newton iteration method being employed to reconstruct the Neumann series. Then, a high probability convergence condition is established, which can offer useful guidelines for practical massive MIMO systems. Finally, simulation examples are given to demonstrate that the new joint Newton iteration and Neumann series method has a faster convergence rate compared to the previous Neumann series, with almost no increase in complexity when the iteration number is greater than or equal to 2. [ABSTRACT FROM AUTHOR]

Besides inheriting the properties of classical Bézier curves of degree n, the corresponding λ-Bézier curves have a good performance in adjusting their shapes by changing shape control parameter. In this paper, we derive an approximation algorithm for multidegree reduction of λ-Bézier curves in the L2-norm. By analysing the properties of λ-Bézier curves of degree n, a method which can deal with approximating λ-Bézier curve of degree n+1 by λ-Bézier curve of degree m  (m≤n) is presented. Then, in unrestricted and C0, C1 constraint conditions, the new control points of approximating λ-Bézier curve can be obtained by solving linear equations, which can minimize the least square error between the approximating curves and the original ones. Finally, several numerical examples of degree reduction are given and the errors are computed in three conditions. The results indicate that the proposed method is effective and easy to implement. [ABSTRACT FROM AUTHOR]

The aim of this paper is to determine the stabilizing PID parametric region for multivariable systems. Firstly, a general equivalent transfer function parameterization method is proposed to construct the multiloop equivalent process for multivariable systems. Then, based on the equivalent single loops, a model-based method is presented to derive the stabilizing PID parametric region by using the generalized Hermite-Biehler theorem. By sweeping over the entire ranges of feasible proportional gains and determining the stabilizing regions in the space of integral and derivative gains, the complete set of stabilizing PID controllers can be determined. The robustness of the design procedure against the approximation in getting the SISO plants is analyzed. Finally, simulation of a practical model is carried out to illustrate the effectiveness of the proposed technique. [ABSTRACT FROM AUTHOR]

A probabilistic method is presented to analyze the temperature and the maximum frequency for multicore processors based on consideration of workload variation, in this paper. Firstly, at the microarchitecture level, dynamic powers are modeled as the linear function of IPCs (instructions per cycle), and leakage powers are approximated as the linear function of temperature. Secondly, the microarchitecture-level hotspot temperatures of both active cores and inactive cores are derived as the linear functions of IPCs. The normal probabilistic distribution of hotspot temperatures is derived based on the assumption that IPCs of all cores follow the same normal distribution. Thirdly and lastly, the probabilistic distribution of the set of discrete frequencies is determined. It can be seen from the experimental results that hotspot temperatures of multicore processors are not deterministic and have significant variations, and the number of active cores and running frequency simultaneously determine the probabilistic distribution of hotspot temperatures. The number of active cores not only results in different probabilistic distribution of frequencies, but also leads to different probabilities for triggering DFS (dynamic frequency scaling). [ABSTRACT FROM AUTHOR]

Structural load types, on the one hand, and structural capacity to withstand these loads, on the other hand, are of a probabilistic nature as they cannot be calculated and presented in a fully deterministic way. As such, the past few decades have witnessed the development of numerous probabilistic approaches towards the analysis and design of structures. Among the conventional methods used to assess structural reliability, the Monte Carlo sampling method has proved to be very convenient and efficient. However, it does suffer from certain disadvantages, the biggest one being the requirement of a very large number of samples to handle small probabilities, leading to a high computational cost. In this paper, a simple algorithm was proposed to estimate low failure probabilities using a small number of samples in conjunction with the Monte Carlo method. This revised approach was then presented in a step-by-step flowchart, for the purpose of easy programming and implementation. [ABSTRACT FROM AUTHOR]

Autonomous vehicles need to perform social accepted behaviors in complex urban scenarios including human-driven vehicles with uncertain intentions. This leads to many difficult decision-making problems, such as deciding a lane change maneuver and generating policies to pass through intersections. In this paper, we propose an intention-aware decision-making algorithm to solve this challenging problem in an uncontrolled intersection scenario. In order to consider uncertain intentions, we first develop a continuous hidden Markov model to predict both the high-level motion intention (e.g., turn right, turn left, and go straight) and the low level interaction intentions (e.g., yield status for related vehicles). Then a partially observable Markov decision process (POMDP) is built to model the general decision-making framework. Due to the difficulty in solving POMDP, we use proper assumptions and approximations to simplify this problem. A human-like policy generation mechanism is used to generate the possible candidates. Human-driven vehicles’ future motion model is proposed to be applied in state transition process and the intention is updated during each prediction time step. The reward function, which considers the driving safety, traffic laws, time efficiency, and so forth, is designed to calculate the optimal policy. Finally, our method is evaluated in simulation with PreScan software and a driving simulator. The experiments show that our method could lead autonomous vehicle to pass through uncontrolled intersections safely and efficiently. [ABSTRACT FROM AUTHOR]

We investigate the convergence analysis of the following general inexact algorithm for approximating a zero of the sum of a cocoercive operator A and maximal monotone operators B with D(B)⊂H: xn+1=αnf(xn)+γnxn+δn(I+rnB)-1(I-rnA)xn+en, for n=1,2,…, for given x1 in a real Hilbert space H, where (αn), (γn), and (δn) are sequences in (0,1) with αn+γn+δn=1 for all n≥1, (en) denotes the error sequence, and f:H→H is a contraction. The algorithm is known to converge under the following assumptions on δn and en: (i) (δn) is bounded below away from 0 and above away from 1 and (ii) (en) is summable in norm. In this paper, we show that these conditions can further be relaxed to, respectively, the following: (i) (δn) is bounded below away from 0 and above away from 3/2 and (ii) (en) is square summable in norm; and we still obtain strong convergence results. [ABSTRACT FROM AUTHOR]

This paper proposes a two-level additive Schwarz preconditioning algorithm for the weak Galerkin approximation of the second-order elliptic equation. In the algorithm, a P1 conforming finite element space is defined on the coarse mesh, and a stable intergrid transfer operator is proposed to exchange the information between the spaces on the coarse mesh and the fine mesh. With the framework of the Schwarz method, it is proved that the condition number of the preconditioned system only depends on the rate of the coarse mesh size and the overlapping size. Some numerical experiments are carried out to verify the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates a homotopy-based method for embedding with hundreds of thousands of data items that yields a parallel algorithm suitable for running on a distributed system. Current eigenvalue-based embedding algorithms attempt to use a sparsification of the distance matrix to approximate a low-dimensional representation when handling large-scale data sets. The main reason of taking approximation is that it is still hindered by the eigendecomposition bottleneck for high-dimensional matrices in the embedding process. In this study, a homotopy continuation algorithm is applied for improving this embedding model by parallelizing the corresponding eigendecomposition. The eigenvalue solution is converted to the operation of ordinary differential equations with initialized values, and all isolated positive eigenvalues and corresponding eigenvectors can be obtained in parallel according to predicting eigenpaths. Experiments on the real data sets show that the homotopy-based approach is potential to be implemented for millions of data sets. [ABSTRACT FROM AUTHOR]

The paper aims at establishing a fast numerical algorithm for Bk(f), where f is any function in the Hardy space H2(Td) and k is the scale level. Here, Bk(f) is an approximation to f we recently constructed by applying the multiscale transform to the Cauchy kernel. We establish the matrix expression of Bk(f) and find that it has the structure of a multilevel Hankel matrix. Based on the structure, a fast numerical algorithm is established to compute Bk(f). The computational complexity is given. A numerical experiment is carried out to check the efficiency of our algorithm. [ABSTRACT FROM AUTHOR]

The nonlinear Klein-Gordon equation (KGE) models many nonlinear phenomena. In this paper, we propose a scheme for numerical approximation of solutions of the one-dimensional nonlinear KGE. A common approach to find a solution of a nonlinear system is to first linearize the equations by successive substitution or the Newton iteration method and then solve a linear least squares problem. Here, we show that it can be advantageous to form a sum of squared residuals of the nonlinear problem and then find a zero of the gradient. Our scheme is based on the Sobolev gradient method for solving a nonlinear least square problem directly. The numerical results are compared with Lattice Boltzmann Method (LBM). The L2, L∞, and Root-Mean-Square (RMS) values indicate better accuracy of the proposed method with less computational effort. [ABSTRACT FROM AUTHOR]

Rough sets theory and fuzzy sets theory are important mathematical tools to deal with uncertainties. Rough fuzzy sets and fuzzy rough sets as generalizations of rough sets have been introduced. Type-2 fuzzy set provides additional degree of freedom, which makes it possible to directly handle high uncertainties. In this paper, the rough type-2 fuzzy set model is proposed by combining the rough set theory with the type-2 fuzzy set theory. The rough type-2 fuzzy approximation operators induced from the Pawlak approximation space are defined. The rough approximations of a type-2 fuzzy set in the generalized Pawlak approximation space are also introduced. Some basic properties of the rough type-2 fuzzy approximation operators and the generalized rough type-2 fuzzy approximation operators are discussed. The connections between special crisp binary relations and generalized rough type-2 fuzzy approximation operators are further examined. The axiomatic characterization of generalized rough type-2 fuzzy approximation operators is also presented. Finally, the attribute reduction of type-2 fuzzy information systems is investigated. [ABSTRACT FROM AUTHOR]

Correct description of optical properties of layers of disordered interacting nanoparticles is the problem. Contrary to volumes of nanocomposites, when standard models of effective-medium approximations (EMA) work well, two-dimensional case of layers has intrinsic anisotropy, which influences interparticle interactions. The deficiency of standard Maxwell-Garnett model in the application to the ellipsometry of layers of gold nanoparticles is demonstrated. It demands the modification of EMA models and one way of this is considered in this paper. Contrary to existing 2D models with phenomenological parameters, the proposed Green function approach uses the same number of parameters as standard 3D EMA models for explicit calculations of effective parameters of layers of disordered nanoparticles. [ABSTRACT FROM AUTHOR]

Let P∈Cm×m and Q∈Cn×n be Hermitian and {k+1}-potent matrices; that is, Pk+1=P=P⁎ and Qk+1=Q=Q⁎, where ·⁎ stands for the conjugate transpose of a matrix. A matrix X∈Cm×n is called {P,Q,k+1}-reflexive (antireflexive) if PXQ=X (PXQ=-X). In this paper, the system of matrix equations AX=C and XB=D subject to {P,Q,k+1}-reflexive and antireflexive constraints is studied by converting into two simpler cases: k=1 and k=2. We give the solvability conditions and the general solution to this system; in addition, the least squares solution is derived; finally, the associated optimal approximation problem for a given matrix is considered. [ABSTRACT FROM AUTHOR]

This paper addresses a free vibration analysis of thin-walled isotropic beams via higher-order refined theories. The unknown kinematic variables are approximated along the beam cross section as a N-order polynomial expansion, where N is a free parameter of the formulation. The governing equations are derived via the dynamic version of the Principle of Virtual Displacements and are written in a unified form in terms of a “fundamental nucleus.” This latter does not depend upon order of expansion of the theory over the cross section. Analyses are carried out through a closed form, Navier-type solution. Simply supported, slender, and short beams are investigated. Besides “classical” modes (such as bending and torsion), several higher modes are investigated. Results are assessed toward three-dimensional finite element solutions. The numerical investigation shows that the proposed Unified Formulation yields accurate results as long as the appropriate approximation order is considered. The accuracy of the solution depends upon the geometrical parameters of the beam. [ABSTRACT FROM AUTHOR]

The calculation of average material contact pressure to rolls base on mathematical theory of rolling process given by Karman equation was solved by many authors. The solutions reported by authors are used simplifications for solution of Karman equation. The simplifications are based on two cases for approximation of the circular arch: (a) by polygonal curve and (b) by parabola. The contribution of the present paper for solution of two-dimensional differential equation of rolling is based on description of the circular arch by equation of a circle. The new term relative stress as nondimensional variable was defined. The result from derived mathematical models can be calculated following variables: normal contact stress distribution, front and back tensions, angle of neutral point, coefficient of the arm of rolling force, rolling force, and rolling torque during rolling process. Laboratory cold rolled experiment of CuZn30 brass material was performed. Work hardening during brass processing was calculated. Comparison of theoretical values of normal contact stress with values of normal contact stress obtained from cold rolling experiment was performed. The calculations were not concluded with roll flattening. [ABSTRACT FROM AUTHOR]

This paper presents an efficient exact analytical method for evaluating the performance of a two-machine manufacturing system with a finite buffer. Unlike existing work, it is assumed that the buffer is prone to time-dependent failure, that is, failure that can occur even when the buffer is not working. First, Markov model is established for the system. Then transition equations are derived based on the system state analysis. After that, a solution technique is provided to obtain the results. Finally, numerical cases are carried out to explore the internal laws of the system. The relationships between system parameters and system performance are investigated. Furthermore, the difference between buffer subject to time-dependent failure and buffer subject to operation-dependent failure is discussed. The proposed method is the building block of approximate analytical methods which can greatly improve the accuracy when analyzing long systems. [ABSTRACT FROM AUTHOR]

We propose a robust method for tracking nonlinear target with the fusion unscented Kalman filter (FUKF). We noticed that when some outliers exist in the measurements of the sensors, they cannot track the target accurately by using the standard Kalman filters. The robust statistics theory is used in this paper to solve this problem. The measurement noise variance which is at the time of the outlier is restructured through minimizing the designed cost function. Then, the standard fusion unscented Kalman filter is used to track the target in order to avoid the bias brought by the linear approximation. Compared to the traditional tracking method and Huber robust method (HFUKF), this method has a more accurate performance and can track the target efficiently while the outliers exist. Last, simulation examples in three different conditions are given and the simulation results show the advantages of the proposed method over the fusion unscented Kalman filter (FUKF) and the Huber robust method (HFUKF). [ABSTRACT FROM AUTHOR]

Adaptive Dynamic Programming (ADP) with critic-actor architecture is an effective way to perform online learning control. To avoid the subjectivity in the design of a neural network that serves as a critic network, kernel-based adaptive critic design (ACD) was developed recently. There are two essential issues for a static kernel-based model: how to determine proper hyperparameters in advance and how to select right samples to describe the value function. They all rely on the assessment of sample values. Based on the theoretical analysis, this paper presents a two-phase simultaneous learning method for a Gaussian-kernel-based critic network. It is able to estimate the values of samples without infinitively revisiting them. And the hyperparameters of the kernel model are optimized simultaneously. Based on the estimated sample values, the sample set can be refined by adding alternatives or deleting redundances. Combining this critic design with actor network, we present a Gaussian-kernel-based Adaptive Dynamic Programming (GK-ADP) approach. Simulations are used to verify its feasibility, particularly the necessity of two-phase learning, the convergence characteristics, and the improvement of the system performance by using a varying sample set. [ABSTRACT FROM AUTHOR]

This paper presents an Improved Genetic Algorithm with Two-Level Approximation (IGATA) to minimize truss weight by simultaneously optimizing size, shape, and topology variables. On the basis of a previously presented truss sizing/topology optimization method based on two-level approximation and genetic algorithm (GA), a new method for adding shape variables is presented, in which the nodal positions are corresponding to a set of coordinate lists. A uniform optimization model including size/shape/topology variables is established. First, a first-level approximate problem is constructed to transform the original implicit problem to an explicit problem. To solve this explicit problem which involves size/shape/topology variables, GA is used to optimize individuals which include discrete topology variables and shape variables. When calculating the fitness value of each member in the current generation, a second-level approximation method is used to optimize the continuous size variables. With the introduction of shape variables, the original optimization algorithm was improved in individual coding strategy as well as GA execution techniques. Meanwhile, the update strategy of the first-level approximation problem was also improved. The results of numerical examples show that the proposed method is effective in dealing with the three kinds of design variables simultaneously, and the required computational cost for structural analysis is quite small. [ABSTRACT FROM AUTHOR]

Most calculations in model reduction involve the solutions of a sequence of dual linear systems with multiple right-hand sides. To solve such systems efficiently, a new deflated BiCG method is explored in this paper. The proposed algorithm uses harmonic Ritz vectors to approximate left and right invariant subspaces inexpensively via small descenting direction vectors found by subsequent runs of deflated BiCG and then derives the deflated subspaces for the next pair of dual linear systems. This process leads to faster convergence for the next pair of systems. Numerical examples illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

More recently, with the increasing demand of web services on the World Wide Web used in the Internet of Things (IoTs), there has been a growing interest in the study of efficient web service quality evaluation approaches based on prediction strategies to obtain accurate quality-of-service (QoS) values. However, it is obvious that the web service quality changes significantly under the unpredictable network environment. Such changes impose very challenging obstacles to web service QoS prediction. Most of the traditional web service QoS prediction approaches are implemented only using a set of static model parameters with the help of designer’s a priori knowledge. Unlike the traditional QoS prediction approaches, our algorithm in this paper is realized by incorporating approximate dynamic programming- (ADP-) based online parameter tuning strategy into the QoS prediction approach. Through online learning and optimization, the proposed approach provides the QoS prediction with automatic parameter tuning capability, and prior knowledge or identification of the prediction model is not required. Therefore, the near-optimal performance of QoS prediction can be achieved. Experimental studies are carried out to demonstrate the effectiveness of the proposed ADP-based prediction approach. [ABSTRACT FROM AUTHOR]

This paper is focused on an assessment of the state of the art of operational modal analysis (OMA) methodologies in estimating modal parameters from output responses of nonlinear structures. By means of the Volterra series, the nonlinear structure excited by random excitation is modeled as best linear approximation plus a term representing nonlinear distortions. As the nonlinear distortions are of stochastic nature and thus indistinguishable from the measurement noise, a protocol based on the use of the random phase multisine is proposed to reveal the accuracy and robustness of the linear OMA technique in the presence of the system nonlinearity. Several frequency- and time-domain based OMA techniques are examined for the modal identification of simulated and real nonlinear mechanical systems. Theoretical analyses are also provided to understand how the system nonlinearity degrades the performance of the OMA algorithms. [ABSTRACT FROM AUTHOR]

Piecewise-linear functions can approximate nonlinear and unknown functions for which only sample points are available. This paper presents a range of piecewise-linear models and algorithms to aid engineers to find an approximation that fits best their applications. The models include piecewise-linear functions with a fixed and maximum number of linear segments, lower and upper envelopes, strategies to ensure continuity, and a generalization of these models for stochastic functions whose data points are random variables. Derived from recursive formulations, the algorithms are applied to the approximation of the production function of gas-lifted oil wells. [ABSTRACT FROM AUTHOR]

Nodes in underwater wireless sensor networks (UWSNs) keep moving and dispersing due to force of water flow and aquatic creatures touching, and thus some isolated unknown nodes emerge. This type of isolated unknown nodes cannot directly communicate with enough beacons in their neighborhoods, which makes localizations for them disabled or the localization error unbearable. To this end, a multihops fitting localization approach is proposed in this paper. Firstly, some intermediate nodes between beacons and unknown nodes are set as routers to construct paths via a greedy method; then, the multihop paths are approximately fitted into straight lines; finally, the positions of unknown nodes can be estimated by trilateration. The proposed algorithm is analyzed and simulated in terms of localization error and error variance, and the results are proven preferable. [ABSTRACT FROM AUTHOR]

Here we construct different approximate solutions of the plane inverse boundary value problem of aerohydrodynamics. In order to do this we solve some conditional optimization problems in the norms ∥·∥2, ∥·∥∞, and ∥·∥1 and some of their generalizations. We present the example clarifying the mathematical constructions and show that the supremum norm generalization seems to be the optimal one of all the functionals considered in the paper. [ABSTRACT FROM AUTHOR]

Until now, all the investigations on fractional or generalized Navier-Stokes equations have been done under some restrictions on the different values that can take the fractional order derivative parameter β. In this paper, we analyze the existence and stability of nonsingular solutions to fractional Navier-Stokes equations of type (ut+u·∇u+∇p-Re-1(-∇)βu=f  in  Ω×(0,T]) defined below. In the case where β=2, we show that the stability of the (quadratic) convergence, when exploiting Newton’s method, can only be ensured when the first guess U0 is sufficiently near the solution U. We provide interesting well-posedness and existence results for the fractional model in two other cases, namely, when 1/2<β<1 and β≥1/2+(3/4). [ABSTRACT FROM AUTHOR]

Networked control system is a research area where the theory is behind practice. Closing the feedback loop through shared network induces time delay and some of the data could be lost. So the network induced time delay and data loss are inevitable in networked control Systems. The time delay may degrade the performance of control systems or even worse lead to system instability. Once the structure of a networked control system is confirmed, it is essential to identify the maximum time delay allowed for maintaining the system stability which, in turn, is also associated with the process of controller design. Some studies reported methods for estimating the maximum time delay allowed for maintaining system stability; however, most of the reported methods are normally overcomplicated for practical applications. A method based on the finite difference approximation is proposed in this paper for estimating the maximum time delay tolerance, which has a simple structure and is easy to apply. [ABSTRACT FROM AUTHOR]

Image super-resolution (SR) aims at recovering the high-frequency (HF) details of a high-resolution (HR) image according to the given low-resolution (LR) image and some priors about natural images. Learning the relationship of the LR image and its corresponding HF details to guide the reconstruction of the HR image is needed. In order to alleviate the uncertainty in HF detail prediction, the HR and LR images are usually decomposed into 4 subbands after 1-level discrete wavelet transformation (DWT), including an approximation subband and three detail subbands. From our observation, we found the approximation subbands of the HR image and the corresponding bicubic interpolated image are very similar but the respective detail subbands are different. Therefore, an algorithm to learn 4 coupled principal component analysis (PCA) dictionaries to describe the relationship between the approximation subband and the detail subbands is proposed in this paper. Comparisons with various state-of-the-art methods by experiments showed that our proposed algorithm is superior to some related works. [ABSTRACT FROM AUTHOR]

The differential quadrature method has been widely used in scientific and engineering computation. However, for the basic characteristics of time domain differential quadrature method, such as numerical stability and calculation accuracy or order, it is still lack of systematic analysis conclusions. In this paper, according to the principle of differential quadrature method, it has been derived and proved that the weighting coefficients matrix of differential quadrature method meets the important V-transformation feature. Through the equivalence of the differential quadrature method and the implicit Runge-Kutta method, it has been proved that the differential quadrature method is A-stable and s-stage s-order method. On this basis, in order to further improve the accuracy of the time domain differential quadrature method, a class of improved differential quadrature method of s-stage 2s-order have been proposed by using undetermined coefficients method and Padé approximations. The numerical results show that the improved differential quadrature method is more precise than the traditional differential quadrature method. [ABSTRACT FROM AUTHOR]

One can reformulate chemical master equations of the stochastic reaction network into a partial differential equation (PDE) of a probability generating function (PGF). In this paper, we present two improvements in such PGF-PDE approach, based on perturbation and double-truncation, respectively. The stiff system that involves fast and slow reactions together often requires high computational cost. By applying the perturbation method to PGF-PDEs, we expand the equation in terms of a small reaction rate which is often responsible for such stiffness of the system. Also by doubly truncating, we dump relatively small terms and reduce the computational load significantly at each time step. The terms corresponding to rare events are sieved out through truncations of Taylor expansion. It is shown through numerical examples of enzyme kinetics, transition model, and Brusselator model that the suggested method is accurate and efficient for approximation of the state probabilities. [ABSTRACT FROM AUTHOR]

Control of quadrotor helicopters is difficult because the problem is naturally nonlinear. The problem becomes more challenging for common model based controllers when unpredictable uncertainties and disturbances in physical control system are taken into account. This paper proposes a novel intelligent controller design based on a fast online learning method called extreme learning machine (ELM). Our neural controller does not require precise system modeling or prior knowledge of disturbances and well approximates the dynamics of the quadrotor at a fast speed. The proposed method also incorporates a sliding mode controller for further elimination of external disturbances. Simulation results demonstrate that the proposed controller can reliably stabilize a quadrotor helicopter in both agitated attitude and position control tasks. [ABSTRACT FROM AUTHOR]

The Sudoku problem is a well-known logic-based puzzle of combinatorial number-placement. It consists in filling a n2 × n2 grid, composed of n columns, n rows, and n subgrids, each one containing distinct integers from 1 to n2. Such a puzzle belongs to the NP-complete collection of problems, to which there exist diverse exact and approximate methods able to solve it. In this paper, we propose a new hybrid algorithm that smartly combines a classic tabu search procedure with the alldifferent global constraint from the constraint programming world. The alldifferent constraint is known to be efficient for domain filtering in the presence of constraints that must be pairwise different, which are exactly the kind of constraints that Sudokus own. This ability clearly alleviates the work of the tabu search, resulting in a faster and more robust approach for solving Sudokus. We illustrate interesting experimental results where our proposed algorithm outperforms the best results previously reported by hybrids and approximate methods. [ABSTRACT FROM AUTHOR]

This paper deals with the hierarchical laminated shell elements with nonsensitivity to adverse conditions for linear static analysis of cylindrical problems. Displacement approximation of the elements is established by high-order shape functions using the integrals of Legendre polynomials to ensure C0 continuity at the interface between adjacent elements. For exact linear mapping of cylindrical shell problems, cylindrical coordinate is adopted. To find global response of laminated composite shells, equivalent single-layer theory is also considered. Thus, the proposed elements are formulated by the dimensional reduction from three-dimensional solid to two-dimensional plane which allows the first-order shear deformation and considers anisotropy due to fiber orientation. The sensitivity tests are implemented to show robustness of the present elements with respect to severe element distortions, very high aspect ratios of elements, and very large radius-to-thickness ratios of shells. In addition, this element has investigated whether material conditions such as isotropic and orthotropic properties may affect the accuracy as the element distortion ratio is increased. The robustness of present element has been compared with that of several shell elements available in ANSYS program. [ABSTRACT FROM AUTHOR]