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An adaptive fuzzy sliding control (AFSMC) approach is adopted in this paper to address the problem of angular position control and vibration suppression of rotary flexible joint systems. AFSMC consists of fuzzy-based singleton control action and switching control law. By adjusting fuzzy parameters with the self-learning ability to discard system nonlinearities and uncertainties, singleton control based on fuzzy approximation theory can estimate the perfect control law of feedback linearization. To enhance robustness, an additional switching control law is incorporated to reduce the approximation error between the derived singleton control action and the perfect control law of feedback linearization. AFSMC's closed-loop stability will be demonstrated via sliding surface and Lyapunov function analysis of error function. In order to demonstrate the effectiveness of the AFSMC in tracking performance as well as its ability to respond to model uncertainties and external perturbations, simulations are carried out using Simulink and Matlab in order to demonstrate how well it adapts to these situations. Based on these results, it can be concluded that the AFSMC performs satisfactorily in terms of tracking. [ABSTRACT FROM AUTHOR]

The flow of non-Newtonian fluids is extremely important in a variety of industrial applications and processes, including painting, printing, and coating. The goal of this paper is to develop a mathematical model for an incompressible, non-isothermal third-grade fluid as it travels through a minor gap between two heated rolls that are revolving in the opposite direction. Using appropriate dimensionless parameters, the dimensionless version of the governing equations is constructed. To simplify the nondimensional form of the governing equations, the LAT (lubrication approximation theory) is applied. It is mentioned that the perturbation approach should be used. It is a very important tool in modern mathematical physics and practical fluid mechanics, and it is used a lot. Through perturbation techniques, exact solutions for velocity distribution, flow rate, temperature distribution, and pressure gradient are offered. To observe the flow pattern, streamlines are also drawn. Numerical outcomes of some substantial engineering quantities like flow rate, roll separation force, power input, and pressure distribution are found. Some outcomes are displayed graphically although others are presented in tabular form. We have observed that the third-grade parameters give a way to control velocity, pressure gradients, flow rate, and coating thickness. Further, increasing the velocities ratio values lowers the coating thickness on the web. Furthermore, the Brickman number has a significant influence on the temperature profile and has increased with the increase in the Brickman number. Both the model and the numerical calculations are in agreement with the viscous fluid model that is already present in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we mainly study the best approximation theory in Riesz space, which is not constructed by the norm, but only rely on the order structure. Based on the order structure, we propose the concept of the order best approximation in Riesz space and discuss some problems related to the order best approximation, including some sufficient and necessary conditions for satisfying the order best approximation set. Finally, we consider the order best approximation projection and its related properties. [ABSTRACT FROM AUTHOR]

To analyze the problem of vibration and bifurcation in the rotor system of the aeroengine with the elastic ring squeeze film damper (ERSFD) and elastic supports, the theoretical equation of the dynamic rotor system is developed in this paper, based on the rotor system, elastic ring squeeze film damper (ERSFD), and three elastic supports. The estimated analytical solution of the oil film force is solved using the short bearing approximation theory and the semi-oil film inference theory in the suspension and the inner and outer boss contact. Considering the oil film stiffness and damping of rolling bearings, the rolling bearing force model is established based on the elastohydrodynamic lubrication (EHL) theory. By the average method, the vibration and bifurcation modes are obtained concerning the bearing coefficient and parameters. The range optimization of parameters can be appropriately improved to enhance the dynamic characteristics of the device given different parameters of the hole of oil seepage, the stiffness, the position of elastic supports, and other structural parameters. [ABSTRACT FROM AUTHOR]

In this paper, the fuzzy polynomial is introduced and applied to investigate the least squares approximation problem based on LR fuzzy numbers. A new and simple approach to solve the original problem is constructed by using approximate fuzzy polynomial. Two numerical examples are given to illustrate the proposed method. Since a large number of data exist as an uncertain property and need a function relation to reflect the laws between different variables, our results enrich fuzzy numerical approximation theory. [ABSTRACT FROM AUTHOR]

This paper presents a mathematical model for the thin film roll coating process of an incompressible Williamson material, passing through a closed passage between a rotating roll and a web. In light of lubrication approximation theory, the flow equations are nondimensionalized. The regular perturbation approach is used to provide solutions for the velocity profile, pressure gradient, flow rate per unit width, and shear stress at the roll surface. Important engineering quantities such as coating thickness, maximum pressure, separation point, roll/sheet separating force, and roll-transmitted power to the fluid are also obtained. The effects of several factors are graphically projected. The study shows that the material factors that are involved determine the operating variables. Coating thickness and separation point are controlled by Weissenberg's number, therefore acting as a controlling parameter for the rate of flow, thickness in coating, power contribution, pressure, roll separating force, and separation point. In comparison to the existing results in the literature, the current results are broader and zero-order results are more accurate. [ABSTRACT FROM AUTHOR]

In this paper, we study a kind of conjugate gradient viscosity approximation algorithm for finding a common solution of split generalized equilibrium problem and variational inequality problem. Under mild conditions, we prove that the sequence generated by the proposed iterative algorithm converges strongly to the common solution. The conclusion presented in this paper is the generalization, extension, and supplement of the previously known results in the corresponding references. Some numerical results are illustrated to show the feasibility and efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Management of electric equipment has a direct impact on companies’ performance and profitability. Considering the critical role that electric power materials play in supporting maintenance operations and preventing equipment failure, it is essential to maintain an inventory to a reasonable level. However, a majority of these electric power materials exhibit an intermittent demand pattern characterized by random arrivals interspersed with time periods with no demand at all. These characteristics cause additional difficulty for companies in managing these electric power material inventories. In response to the above problem, this paper, based on the electric power material demand data of Shanghai Electric Power Company, develops a new method to determine the optimal order quantity Q⁎ in a cost-oriented periodic review (T,Q) system, whereby unsatisfied demands are backordered and demand follows a compound Erlang distribution. Q⁎corresponds to the value of Q that gives the minimum expected total inventory holding and backordering cost. Subsequently, an empirical investigation is conducted to compare this method with the Newsvendor model. Results verify its superiority in cost savings. Ultimately, considering the complicated calculation and low efficiency of that algorithm, this paper proposes an approximation and a heuristic algorithm which have a higher level of utility in a real industrial context. The approximation algorithm simplifies the calculation process by reducing iterative times while the heuristic algorithm achieves it by generalizing the relationship between the optimal order quantity Q⁎ and mean demand interarrival rate λ. [ABSTRACT FROM AUTHOR]

This paper is for the purpose of introducing and studying a class of new two-step viscosity iteration approximation methods for finding fixed points of set-valued nonexpansive mappings in CAT(0) spaces. By means of some properties and characteristic to CAT(0) space and using Cauchy-Schwarz inequality and Xu’s inequality, strong convergence theorems of the new two-step viscosity iterative process for set-valued nonexpansive and contraction operators in complete CAT(0) spaces are provided. The results of this paper improve and extend the corresponding main theorems in the literature. [ABSTRACT FROM AUTHOR]

The approximations for the Q-function reported in the literature so far have mainly been developed to overcome not only the difficulties, but also the limitations, caused in different research areas, by the nonexistence of the closed form expression for the Q-function. Unlike the previous papers, we propose the novel approximation for the Q-function not for solving some particular problem. Instead, we analyze this problem in one general manner and we provide one general solution, which has wide applicability. Specifically, in this paper, we set two goals, which are somewhat contrary to each other. The one is the simplicity of the analytical form of Q-function approximation and the other is the relatively high accuracy of the approximation for a wide range of arguments. Since we propose a two-parametric approximation for the Q-function, by examining the effect of the parameters choice on the accuracy of the approximation, we manage to determine the most suitable parameters of approximation and to achieve these goals simultaneously. The simplicity of the analytical form of our approximation along with its relatively high accuracy, which is comparable to or even better than that of the previously proposed approximations of similar analytical form complexity, indicates its wide applicability. [ABSTRACT FROM AUTHOR]

This paper addresses an energy-based extension of the Multimode Resource-Constrained Project Scheduling Problem (MRCPSP) called MRCPSP-ENERGY. This extension considers the energy consumption as an additional resource that leads to different execution modes (and durations) of the activities. Consequently, different schedules can be obtained. The objective is to maximize the efficiency of the project, which takes into account the minimization of both makespan and energy consumption. This is a well-known NP-hard problem, such that the application of metaheuristic techniques is necessary to address real-size problems in a reasonable time. This paper shows that the Activity List representation, commonly used in metaheuristics, can lead to obtaining many redundant solutions, that is, solutions that have different representations but are in fact the same. This is a serious disadvantage for a search procedure. We propose a genetic algorithm (GA) for solving the MRCPSP-ENERGY, trying to avoid redundant solutions by focusing the search on the execution modes, by using the Mode List representation. The proposed GA is evaluated on different instances of the PSPLIB-ENERGY library and compared to the results obtained by both exact methods and approximate methods reported in the literature. This library is an extension of the well-known PSPLIB library, which contains MRCPSP-ENERGY test cases. [ABSTRACT FROM AUTHOR]

In this paper, we propose a parameter perturbation homotopy continuation method for solving fixed point problems on more general nonconvex sets with both inequality and equality constraints. By adopting appropriate techniques, we make the initial points not certainly in the set consisting of the equality constraints. This point can improve the computational efficiency greatly when the equality constraints are complex. In addition, we also weaken the assumptions of the previous results in the literature so that the method proposed in this paper can be applied to solve fixed point problems in more general nonconvex sets. Under suitable conditions, we obtain the global convergence of this homotopy continuation method. Moreover, we provide several numerical examples to illustrate the results of this paper. [ABSTRACT FROM AUTHOR]

In this paper we introduce a novel method for obtaining good quality paths for autonomous road vehicles (e.g., cars or buses) in narrow environments. There are many traffic situations in urban scenarios where nontrivial maneuvering in narrow places is necessary. Navigating in cluttered parking lots or having to avoid obstacles blocking the way and finding a detour even in narrow streets are challenging, especially if the vehicle has large dimensions like a bus. We present a combined approximation-based approach to solve the path planning problem in such situations. Our approach consists of a global planner which generates a preliminary path consisting of straight and turning-in-place primitives and a local planner which is used to make the preliminary path feasible to car-like vehicles. The approximation methodology is well known in the literature; however, both components proposed in this paper differ from existing similar planning methods. The approximation process with the proposed local planner is proven to be convergent for any preliminary global paths. The resulting path has continuous curvature which renders our method well suited for application on real vehicles. Simulation experiments show that the proposed method outperforms similar approaches in terms of path quality in complicated planning tasks. [ABSTRACT FROM AUTHOR]

Short-term load forecasting model based on quantum Elman neural networks was constructed in this paper. The quantum computation and Elman feedback mechanism were integrated into quantum Elman neural networks. Quantum computation can effectively improve the approximation capability and the information processing ability of the neural networks. Quantum Elman neural networks have not only the feedforward connection but also the feedback connection. The feedback connection between the hidden nodes and the context nodes belongs to the state feedback in the internal system, which has formed specific dynamic memory performance. Phase space reconstruction theory is the theoretical basis of constructing the forecasting model. The training samples are formed by means of K-nearest neighbor approach. Through the example simulation, the testing results show that the model based on quantum Elman neural networks is better than the model based on the quantum feedforward neural network, the model based on the conventional Elman neural network, and the model based on the conventional feedforward neural network. So the proposed model can effectively improve the prediction accuracy. The research in the paper makes a theoretical foundation for the practical engineering application of the short-term load forecasting model based on quantum Elman neural networks. [ABSTRACT FROM AUTHOR]

This survey is devoted to a series of investigations developed in the last fifteen years, starting from the introduction of a sequence of positive linear operators which modify the classical Bernstein operators in order to reproduce constant functions and x2 on [0,1]. Nowadays, these operators are known as King operators, in honor of J. P. King who defined them, and they have been a source of inspiration for many scholars. In this paper we try to take stock of the situation and highlight the state of the art, hoping that this will be a useful tool for all people who intend to extend King's approach to some new contents within Approximation Theory. In particular, we recall the main results concerning certain King-type modifications of two well known sequences of positive linear operators, the Bernstein operators and the Szász-Mirakyan operators. [ABSTRACT FROM AUTHOR]

In order to solve (partial) differential equations, implicit midpoint rules are often employed as a powerful numerical method. The purpose of this paper is to introduce and study a class of new Picard-Mann iteration processes with mixed errors for the implicit midpoint rules, which is different from existing methods in the literature, and to analyze the convergence and stability of the proposed method. Further, some numerical examples and applications to optimal control problems with elliptic boundary value constraints are considered via the new Picard-Mann iterative approximations, which shows that the new Picard-Mann iteration process with mixed errors for the implicit midpoint rule of nonexpansive mappings is brand new and more effective than other related iterative processes. [ABSTRACT FROM AUTHOR]

The Berry-Esseen bound for the random variable based on the sum of squared sample correlation coefficients and used to test the complete independence in high diemensions is shown by Stein's method. Although the Berry-Esseen bound can be applied to all real numbers in R, a nonuniform bound at a real number z usually provides a sharper bound if z is fixed. In this paper, we present the first version of a nonuniform bound on a normal approximation for this random variable with an optimal rate of 1/0.5+|z|·O1/m by using Stein's method. [ABSTRACT FROM AUTHOR]

An overview of current debates and contemporary research devoted to the modeling of decision-making processes and their facilitation directs attention to the quality of priority ratios estimation through pairwise comparisons. At the core of the process are various approximation procedures for a pairwise comparison matrix which, in a sense, reflects preferences of decision-makers. Certainly, when judgments regarding these preferences are perfectly consistent (cardinally transitive), all approximation procedures coincide and the quality of the prioritization process is exemplary. However, human judgments are very rarely consistent, and thus the quality of priority ratios estimation may significantly vary. Obviously, the range of these variations depends on the applied approximation procedure for a pairwise comparison matrix. Although there are many approximation procedures which can be applied in the prioritization process, it has been promoted for many decades that only one should be applied and no others qualify. This paper suggests this opinion is a fallacy. Research results argue that a genuine, commonly applied approximation procedure for a pairwise comparison matrix may deteriorate the quality of priority ratios estimation. Thus, a number of solutions are also proposed which can improve the process of priority ratios estimation. In order to provide credible and high quality results, the problem is studied via a properly designed and coded seminal simulation algorithm, executed in Wolfram Mathematica 8.0. [ABSTRACT FROM AUTHOR]

In this paper, it is described how the matrix mixing model updating technique can be combined with the local correspondence (LC) mode shape expansion algorithm, to give a new finite element (FE) model updating method. The matrix mixing method uses that the inverse mass and stiffness matrices can be expressed as a linear combination of outer products of FE mode shape vectors, where the low-frequency part of these sums are substituted with expanded test modes. The approach is meant to update FE models in one-step and is exact, except for the following two approximations: the mode shape smoothing and the mass scaling of the expanded experimental mode shapes. A simulation study illustrates the errors from the two approximations and shows the ability of the technique to improve the modal assurance criterion (MAC) values so that they get very close to unity. Finally, the performance of the proposed updating method is assessed by means of an application example in which the FE model is updated based on the test modes of a real structure. [ABSTRACT FROM AUTHOR]

Nowadays, a wide class of problems can be solved by using the classical newsboy model. However, in problems where uncertainty of events and randomness are omnipresent, there is a necessity to adapt the existing solutions and/or find new extensions that will properly answer all requirements. This paper considers a multistage assembly system where interrelated assembly operations with independent stochastic operation times should be planned in an optimal way. Delivery of items in a requested time implies that either delay costs or holding costs appear. The goal is to find optimal safety times. We propose an approximate technique based on successive application of the solution of simpler one-stage problem. The generalized mathematical model suggested is built up on the relaxed hypothesis and can be used in multistage assembly networks. The existence and uniqueness of the solution are proven. The preliminary tests are performed and our approximate technique is compared to exact results. [ABSTRACT FROM AUTHOR]

In this paper, we will consider the stationary Stokes equations with the periodic boundary condition and we will study approximation property of the solutions by using the properties of the Fourier series. Finally, we will discuss that our estimation for approximate solutions is optimal. [ABSTRACT FROM AUTHOR]

The differential problem given by a parabolic equation describing the purely viscous flow generated by a constant or an oscillating motion of a boundary is the well-known Stokes’ problem. The one-dimensional equation is generally solved for unbounded or bounded domains; for the latter, either free slip (i.e., zero normal gradient) or no-slip (i.e., zero velocity) conditions are enforced on one boundary. Generally, the analytical strategy to solve these problems is based on finding the solutions of the Laplace-transformed (in time) equation and on inverting these solutions. In the present paper this problem is solved by making use of the residuals theorem; as it will be shown, this strategy allows achieving the solutions of First and Second Stokes’ problems in both infinite and finite depth. The extension to generally periodic boundaries with the presence of a periodic pressure gradient is also presented. This approach allows getting closed form solutions in the time domain in a rather fast and simple way. An ad hoc numerical algorithm, based on a finite difference approximation of the differential equation, has been developed to check the correctness of the analytical solutions. [ABSTRACT FROM AUTHOR]

As an extension of Pawlak’s rough sets, rough fuzzy sets are proposed to deal with fuzzy target concept. As we know, the uncertainty of Pawlak’s rough sets is rooted in the objects contained in the boundary region, while the uncertainty of rough fuzzy sets comes from three regions (positive region, boundary region, and negative region). In addition, in the view of traditional uncertainty measures, the two rough approximation spaces with the same uncertainty are not necessarily equivalent, and they cannot be distinguished. In this paper, firstly, a fuzziness-based uncertainty measure is proposed. Meanwhile, the essence of the uncertainty for rough fuzzy sets and its three regions in a hierarchical granular structure is revealed. Then, from the perspective of fuzzy distance, we introduce a modified uncertainty measure based on the fuzziness-based uncertainty measure and present that our method not only is strictly monotonic with finer approximation spaces, but also can distinguish the two rough approximation spaces with the same uncertainty. Finally, a case study is introduced to demonstrate that the modified uncertainty measure is more suitable for evaluating the significance of attributes. These works are useful for further study on rough sets theory and promote the development of uncertain artificial intelligence. [ABSTRACT FROM AUTHOR]

Artificial Neural Network (ANN) is a widely used algorithm in pattern recognition, classification, and prediction fields. Among a number of neural networks, backpropagation neural network (BPNN) has become the most famous one due to its remarkable function approximation ability. However, a standard BPNN frequently employs a large number of sum and sigmoid calculations, which may result in low efficiency in dealing with large volume of data. Therefore to parallelize BPNN using distributed computing technologies is an effective way to improve the algorithm performance in terms of efficiency. However, traditional parallelization may lead to accuracy loss. Although several complements have been done, it is still difficult to find out a compromise between efficiency and precision. This paper presents a parallelized BPNN based on MapReduce computing model which supplies advanced features including fault tolerance, data replication, and load balancing. And also to improve the algorithm performance in terms of precision, this paper creates a cascading model based classification approach, which helps to refine the classification results. The experimental results indicate that the presented parallelized BPNN is able to offer high efficiency whilst maintaining excellent precision in enabling large-scale machine learning. [ABSTRACT FROM AUTHOR]

This paper presents a multiconstrained quality-of-service routing (QoSR) based on a differentially guided krill herd (DGKH) algorithm in mobile ad hoc networks (MANETs). QoSR is a NP-complete and significant problem with immense challenges in determining an optimum path that simultaneously satisfies various constraints in MANETs, where the topology varies constantly. Various heuristic algorithms are widely used to solve this problem with compromise on excessive computational complexities and/or low performance. This paper proposes a krill herd based algorithm called DGKH, where the krill individuals do not update the position in comparison with one-to-one (as usual), but instead it uses the information from various krill individuals and then searches to determine a feasible path. Experiment results on MANETs with different number nodes (routes) are considered with three constraints which are maximum allowed delay, maximum allowed jitter, and minimum requested bandwidth. It is demonstrated that the proposed DGKH algorithm is an effective approximation algorithm exhibiting satisfactory performance than the KHA and existing algorithms in the literature by determining an optimum path that satisfies more than one QoS constraint in MANETs. [ABSTRACT FROM AUTHOR]

Capacitive micromachined ultrasonic transducers (CMUTs) are one of the appealing MEMS devices. Most studies treat CMUTs as rigid plates vibrating in open air, ignoring the mechanical boundary conditions for simplification and resulting in cumulative errors in coupled fields. This paper presents a new analytical model for the pull-in characteristics of the flat circular CMUT cell featuring sealed cavity. Utilizing the plate theory coupled with Boyle’s law, the paper establishes a strong relation between the pressures inside the sealed cavity and the pull-in characteristics for the first time. Not only did we point out that the existence of the pressure inside the sealed cavity cannot be omitted, but we also quantified the direct effect of the pressure ratios on the pull-in phenomenon. The pull-in voltages increase while the pull-in ratios decrease with the pressure ratios of the pressure inside the sealed cavity to the ambient pressure. The proposed calculation process delivers a good approximation of the pull-in voltages and displacements, which are consistent with COMSOL simulation results. Particularly, the percentage error of our calculation process is 6.986% for the worst case. Therefore, our proposed analytical model accurately and efficiently predicts the pull-in characteristics and this paper offers new perspectives and reference value in designing and modeling the CMUTs. [ABSTRACT FROM AUTHOR]

In order to characterize the controllability of the aggregate demand response, that is, the aggregated consumer behaviors, the paper introduces the concept of controllability index which expresses the lowest occurrence probability in total electric consumption which can be changed by electric price. As the number of consumers is larger, it becomes difficult to directly analyze the controllability index. To resolve the difficulty of the large number of consumers, by using the central limit theorem, the paper approximates the controllability index and gives the solution maximizing the approximated controllability index. [ABSTRACT FROM AUTHOR]

Tilting pad bearings offer unique dynamic stability enabling successful deployment of high-speed rotating machinery. The model of dynamic stiffness, damping, and added mass coefficients is often used for rotordynamic analyses, and this method does not suffice to describe the dynamic behaviour due to the nonlinear effects of oil film force under larger shaft vibration or vertical rotor conditions. The objective of this paper is to present a nonlinear oil force model for finite length tilting pad journal bearings. An approximate analytic oil film force model was established by analysing the dynamic characteristic of oil film of a single pad journal bearing using variable separation method under the dynamic π oil film boundary condition. And an oil film force model of a four-tilting-pad journal bearing was established by using the pad assembly technique and considering pad tilting angle. The validity of the model established was proved by analyzing the distribution of oil film pressure and the locus of journal centre for tilting pad journal bearings and by comparing the model established in this paper with the model established using finite difference method. [ABSTRACT FROM AUTHOR]

Robust optimization is a powerful and relatively novel methodology to cope with optimization problems in the presence of uncertainty. The positive aspect of robust optimization approach is its computational tractability that attracts more and more attention. In this paper, we focus on an ambiguous P-model where probability distributions are partially known. We discuss robust counterpart (RC) of uncertain linear constraints under two refined uncertain sets by robust approach and further find the safe tractable approximations of chance constraints in the ambiguous P-model. Because of the probability constraints embedded in the ambiguous P-model, it is computationally intractable. The advantage of our approach lies in choosing an implicit way to treat stochastic uncertainty models instead of solving them directly. The process above can enable the transformation of proposed P-model to a tractable deterministic one under the refined uncertainty sets. A numerical example about portfolio selection demonstrates that the ambiguous P-model can help the decision maker to determine the optimal investment proportions of various stocks. Sensitivity analyses explore the trade-off between optimization and robustness by adjusting parameter values. Comparison study is conducted to validate the benefit of our ambiguous P-model. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying the analytical series solutions for the differential equations with variable coefficients. By a general residual power series method, we construct the approximate analytical series solutions for differential equations with variable coefficients, including nonhomogeneous parabolic equations, fractional heat equations in 2D, and fractional wave equations in 3D. These applications show that residual power series method is a simple, effective, and powerful method for seeking analytical series solutions of differential equations (especially for fractional differential equations) with variable coefficients. [ABSTRACT FROM AUTHOR]

Tensor exponential function is an important function that is widely used. In this paper, tensor Pade´-type approximant (TPTA) is defined by introducing a generalized linear functional for the first time. The expression of TPTA is provided with the generating function form. Moreover, by means of formal orthogonal polynomials, we propose an efficient algorithm for computing TPTA. As an application, the TPTA for computing the tensor exponential function is presented. Numerical examples are given to demonstrate the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

When superheated steam flows along the horizontal wellbore, it may change to saturated steam at some point of the wellbore. In this paper, to accurately predict the heat radius of cyclic superheated steam stimulation with horizontal wellbore, the distribution of thermophysical properties of superheated steam along the horizontal wellbore is considered. The heating process is divided into 4 stages for superheated steam and 3 stages for saturated steam when the phase change undergoes in the wellbore. On this basis, the mathematical model for heat radius of cyclic superheated steam stimulation with horizontal wellbore was established according to energy conservation principle and Laplace transformation method. The calculation result of the new mathematical model is in good agreement with that of the numerical simulation (CMG STARS) for the same parameters from a specific heavy oil reservoir, which verified the correctness of the new mathematical model. The effect of degree of superheat and the cycle of stimulation are analyzed in detail after the new mathematical model is validated. The results show that the heat radius of superheated zone, steam zone, and hot fluid zone all decrease with horizontal well length and increase with the cycle of stimulation. The higher the degree of superheat is, the farther from the heel of the horizontal wellbore the phase change undergoes. Besides, the radius of superheated zone, steam zone, and hot fluid zone increases with the degree of superheat, but the value increases little at steam zone and hot fluid zone. [ABSTRACT FROM AUTHOR]

This paper will study the high accuracy numerical solutions for elastic equations with nonlinear boundary value conditions. The equations will be converted into nonlinear boundary integral equations by the potential theory, in which logarithmic singularity and Cauchy singularity are calculated simultaneously. Mechanical quadrature methods (MQMs) are presented to solve the nonlinear equations where the accuracy of the solutions is of three orders. According to the asymptotical compact convergence theory, the errors with odd powers asymptotic expansion are obtained. Following the asymptotic expansion, the accuracy of the solutions can be improved to five orders with the Richardson extrapolation. Some results are shown regarding these approximations for problems by the numerical example. [ABSTRACT FROM AUTHOR]

Dealing with practical control systems, it is equally important to establish the controllability of the system under study and to find corresponding control functions explicitly. The most challenging problem in this path is the rigorous analysis of the state constraints, which can be especially sophisticated in the case of nonlinear systems. However, some heuristic considerations related to physical, mechanical, or other aspects of the problem may allow coming up with specific hierarchic controls containing a set of free parameters. Such an approach allows reducing the computational complexity of the problem by reducing the nonlinear state constraints to nonlinear algebraic equations with respect to the free parameters. This paper is devoted to heuristic determination of control functions providing exact and approximate controllability of dynamic systems with nonlinear state constraints. Using the recently developed approach based on Green’s function method, the controllability analysis of nonlinear dynamic systems, in general, is reduced to nonlinear integral constraints with respect to the control function. We construct parametric families of control functions having certain physical meanings, which reduce the nonlinear integral constraints to a system of nonlinear algebraic equations. Regimes such as time-harmonic, switching, impulsive, and optimal stopping ones are considered. Two concrete examples arising from engineering help to reveal advantages and drawbacks of the technique. [ABSTRACT FROM AUTHOR]

This paper designs a kind of adaptive fuzzy controller for robotic manipulator considering external disturbances and modeling errors. First, n-link uncertain robotic manipulator dynamics based on the Lagrange equation is changed into a two-order multiple-input multiple-output (MIMO) system via feedback technique. Then, an adaptive fuzzy logic control scheme is studied by using sliding theory, which adopts the adaptive fuzzy logic systems to estimate the uncertainties and employs a filtered error to make up for the approximation errors, hence enhancing the robust performance of robotic manipulator system uncertainties. It is proved that the tracking errors converge into zero asymptotically by using Lyapunov stability theory. Last, we take a two-link rigid robotic manipulator as an example and give its simulations. Compared with the existing results in the literature, the proposed controller shows higher precision and stronger robustness. [ABSTRACT FROM AUTHOR]

Detecting and counting elliptical objects are an interesting problem in digital image processing. There are real-world applications of this problem in various disciplines. Solving this problem is harder when there is occlusion among the elliptical objects, since in general these objects are considered as part of the bigger object (conglomerate). The solution to this problem focusses on the detection and segmentation of the precise number of occluded elliptical objects, while omitting all noninteresting objects. There are a variety of computational approximations that focus on this problem; however, such approximations are not accurate when there is occlusion. This paper presents an algorithm designed to solve this problem, specifically, to detect, segment, and count elliptical objects of a specific size when these are in occlusion with other objects within the conglomerate. Our algorithm deals with a time-consuming combinatorial process. To optimize the execution time of our algorithm, we implemented a parallel GPU version with CUDA-C, which experimentally improved the detection of occluded objects, as well as lowering processing times compared to the sequential version of the method. Comparative test results with another method featured in literature showed improved detection of objects in occlusion when using the proposed parallel method. [ABSTRACT FROM AUTHOR]

The popular deep Q learning algorithm is known to be instability because of the Q-value’s shake and overestimation action values under certain conditions. These issues tend to adversely affect their performance. In this paper, we develop the ensemble network architecture for deep reinforcement learning which is based on value function approximation. The temporal ensemble stabilizes the training process by reducing the variance of target approximation error and the ensemble of target values reduces the overestimate and makes better performance by estimating more accurate Q-value. Our results show that this architecture leads to statistically significant better value evaluation and more stable and better performance on several classical control tasks at OpenAI Gym environment. [ABSTRACT FROM AUTHOR]

We consider convergence acceleration of the modified Fourier expansions by rational trigonometric corrections which lead to modified-trigonometric-rational approximations. The rational corrections contain some unknown parameters and determination of their optimal values for improved pointwise convergence is the main goal of this paper. The goal was accomplished by deriving the exact constants of the asymptotic errors of the approximations with further elimination of the corresponding main terms by appropriate selection of those parameters. Numerical experiments outline the convergence improvement of the optimal rational approximations compared to the expansions by the modified Fourier basis. [ABSTRACT FROM AUTHOR]

This paper provides a two-space stabilized mixed finite element scheme for the Stokes eigenvalue problem based on local Gauss integration. The two-space strategy contains solving one Stokes eigenvalue problem using the P1-P1 finite element pair and then solving an additional Stokes problem using the P2-P2 finite element pair. The postprocessing technique which increases the order of mixed finite element space by using the same mesh can accelerate the convergence rate of the eigenpair approximations. Moreover, our method can save a large amount of computational time and the corresponding convergence analysis is given. Finally, numerical results are presented to confirm the theoretical analysis. [ABSTRACT FROM AUTHOR]

We study the q-analogue of Euler-Maclaurin formula and by introducing a new q-operator we drive to this form. Moreover, approximation properties of q-Bernoulli polynomials are discussed. We estimate the suitable functions as a combination of truncated series of q-Bernoulli polynomials and the error is calculated. This paper can be helpful in two different branches: first we solve the differential equations by estimating functions and second we may apply these techniques for operator theory. [ABSTRACT FROM AUTHOR]

The information of temperature field distribution is complex but quite important for theoretical study and industrial applications, such as burning, drying, and heating, because it can reflect the internal running state of industrial equipment, assist to develop control strategy, and ensure safety in operation. Acoustic imaging is a kind of noncontact temperature measurement technique which is able to achieve temperature field distribution reconstruction. The process of temperature field distribution reconstruction using acoustic imaging is an inverse problem and its reconstruction performance depends on reconstruction algorithm. In this paper, a modified reconstruction algorithm is investigated. Compared with other reconstruction methods of least square algorithm and radial basis function approximation, the reconstruction results indicate that the modified reconstruction algorithm occupies the best information reflection of temperature field distribution and the reconstruction accuracy is improved. [ABSTRACT FROM AUTHOR]

This paper deals with the numerical approximation problem of the optimal control problem governed by the Euler-Bernoulli beam equation with local Kelvin-Voigt damping, which is a nonlinear coefficient control problem with control constraints. The goal of this problem is to design a control input numerically, which is the damping and distributes locally on a subinterval of the region occupied by the beam, such that the total energy of the beam and the control on a given time period is minimal. We firstly use the finite element method (FEM) to obtain a finite-dimensional model based on the original PDE system. Then, using the control parameterization method, we approximate the finite-dimensional problem by a standard optimal parameter selection problem, which is a suboptimal problem and can be solved numerically by nonlinear mathematical programming algorithm. At last, some simulation studies will be presented by the proposed numerical approximation method in this paper, where the damping controls act on different locations of the Euler-Bernoulli beam. [ABSTRACT FROM AUTHOR]

Attribute reduction is one of the most important problems in rough set theory. However, from the granular computing point of view, the classical rough set theory is based on a single granulation. It is necessary to study the issue of attribute reduction based on multigranulations rough set. To acquire brief decision rules from information systems, this paper firstly investigates attribute reductions by combining the multigranulations rough set together with evidence theory. Concepts of belief and plausibility consistent set are proposed, and some important properties are addressed by the view of the optimistic and pessimistic multigranulations rough set. What is more, the multigranulations method of the belief and plausibility reductions is constructed in the paper. It is proved that a set is an optimistic (pessimistic) belief reduction if and only if it is an optimistic (pessimistic) lower approximation reduction, and a set is an optimistic (pessimistic) plausibility reduction if and only if it is an optimistic (pessimistic) upper approximation reduction. [ABSTRACT FROM AUTHOR]

Hybrid automaton is a formal model for precisely describing a hybrid system in which the computational processes interact with the physical ones. The reachability analysis of the polynomial hybrid automaton is decidable, whichmakes the Taylor approximation of a hybrid automaton applicable and valuable. In this paper, we studied the simulation relation among the hybrid automaton and its Taylor approximation, as well as the approximate equivalence relation. We also proved that the Taylor approximation simulates its original hybrid automaton, and similar hybrid automata could be compared quantitatively, for example, the approximate equivalence we proposed in the paper. [ABSTRACT FROM AUTHOR]

A wireless network system is a pair (Ù;B), where B is a family of some base stations and Ù is a set of their users. To investigate the connectivity of wireless network systems, this paper takes covering approximation spaces as mathematical models of wireless network systems. With the help of covering approximation operators, this paper characterizes the connectivity of covering approximation spaces by their definable subsets. Furthermore, it is obtained that a wireless network system is connected if and only if the relevant covering approximation space has no nonempty definable proper subset. As an application of this result, the connectivity of a teacher-student interactive platform is discussed, which is established in the School of Mathematical Sciences of Soochow University. This application further demonstrates the usefulness of rough set theory in pedagogy andmakes it possible to research education by logical methods and mathematical methods. [ABSTRACT FROM AUTHOR]

The constrained convex minimization problem is to find a point xn with the property that xn ϵ C, and h(xn ) = min h(x), ∀x ϵ C, where C is a nonempty, closed, and convex subset of a real Hilbert space H, h(x) is a real-valued convex function, and h(x) is not Fréchet differentiable, but lower semicontinuous. In this paper, we discuss an iterative algorithm which is different from traditional gradient-projection algorithms. We firstly construct a bifunction F1 (x, y) defined as F1 (x, y) = h(y) - h(x). And we ensure the equilibrium problem for F1 (x, y) equivalent to the above optimization problem. Then we use iterative methods for equilibrium problems to study the above optimization problem. Based on Jung's method (2011), we propose a general approximation method and prove the strong convergence of our algorithm to a solution of the above optimization problem. In addition, we apply the proposed iterative algorithm for finding a solution of the split feasibility problem and establish the strong convergence theorem. The results of this paper extend and improve some existing results [ABSTRACT FROM AUTHOR]

It is expected in this paper to investigate the existence and uniqueness of positive solution for the following difference equation: -Δ²u(t - 1) = f(t, u(t)) + g(t, u(t)), t ∈ Z1, T, subject to boundary conditions either u(0) - βΔu(0) = 0, u(T + 1) = αu(η) or Δu(0) = 0,u(T + 1) = αu(η), where 0 < α < 1, β > 0, and η ∈2, T-1. The proof of the main result is based upon a fixed point theorem of a sum operator. It is expected in this paper not only to establish existence and uniqueness of positive solution, but also to show a way to construct a series to approximate it by iteration. [ABSTRACT FROM AUTHOR]

Most real-world engineering optimization problems are inherently multi objective, for example, searching for trade-off solutions of high quality and low cost. As no single optimal solution exists for such problems, multi objective optimizers provide sets of optimal (or near-optimal) trade-off solutions to choose from. The empirical attainment function (EAF) is a powerful tool that can be used to analyze and compare the performance of these optimizers. While the visualization of EAFs is rather straightforward in two objectives, the three-objective case presents a great challenge as we need to visualize a large number of 3D cuboids. This paper addresses the visualization of exact as well as approximated 3D EAF values and differences in these values provided by two competing multi objective optimizers. We show that the exact EAFs can be visualized using slicing and maximum intensity projection (MIP), while the approximated EAFs can be visualized using slicing, MIP, and direct volume rendering. In addition, the paper demonstrates the use of the proposed visualization techniques on a steel casting optimization problem. [ABSTRACT FROM AUTHOR]

Based on the moving least-squares (MLS) approximation, an improved interpolating moving least-squares (IIMLS) method based on nonsingular weight functions is presented in this paper. Then combining the IIMLS method and the Galerkin weak form, an improved interpolating element-free Galerkin (IIEFG) method is presented for two-dimensional potential problems. In the IIMLS method, the shape function of the IIMLS method satisfies the property of Kronecker δ function, and there is no difficulty caused by singularity of the weight function. Then in the IIEFG method presented in this paper, the essential boundary conditions are applied naturally and directly. Moreover, the number of unknown coefficients in the trial function of the IIMLS method is less than that of the MLS approximation; then under the same node distribution, the IIEFG method has higher computational precision than element-free Galerkin (EFG) method and interpolating element-free Galerkin (IEFG) method. Four selected numerical examples are presented to show the advantages of the IIMLS and IIEFG methods. [ABSTRACT FROM AUTHOR]

As a continuous state space problem, air combat is difficult to be resolved by traditional dynamic programming (DP) with discretized state space. The approximated dynamic programming (ADP) approach is studied in this paper to build a high performance decision model for air combat in 1 versus 1 scenario, in which the iterative process for policy improvement is replaced by mass sampling from history trajectories and utility function approximating, leading to high efficiency on policy improvement eventually. A continuous reward function is also constructed to better guide the plane to find its way to "winner" state from any initial situation. According to our experiments, the plane is more offensive when following policy derived from ADP approach other than the baseline Min-Max policy, in which the "time to win" is reduced greatly but the cumulated probability of being killed by enemy is higher. The reason is analyzed in this paper. [ABSTRACT FROM AUTHOR]