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In this paper, we first point out a gap in Yang (2012). Next, strong convergence theorem for the common solution for a finite family of φ -strongly accretive operator equations in Banach spaces is established without any bounded assumption, and we also give an example to show universality of the result of this paper, which improve and extend some recent results. [ABSTRACT FROM AUTHOR]

Abstract: Comment on the paper “A class of methods based on non-polynomial spline functions for the solution of a special fourth-order boundary-value problems with engineering applications” in Applied Mathematics and Computation 174 (2006) 1169–1180. The paper considered a class of two-point boundary-value problems of the form where f(x) and g(x) are continuous on [a, b], and A i and B i (i =1,2) are finite real constants. Here we correct some mistake in derivation of non-polynomial spline, boundary formulas, truncation errors, convergence analysis and computational experiments. [Copyright &y& Elsevier]

Abstract: This work presents a proof of convergence of a discrete solution to a continuous one. At first, the continuous problem is stated as a system of equations which describe the filtration process in the pressing section of a paper machine. Two flow regimes appear in the modeling of this problem. The model for the saturated flow is presented by the Darcy’s law and the mass conservation. The second regime is described by the Richards’ approach together with a dynamic capillary pressure model. The finite volume method is used to approximate the system of PDEs. Then, the existence of a discrete solution to the proposed finite difference scheme is proven. Compactness of the set of all discrete solutions for different mesh sizes is proven. The main theorem shows that the discrete solution converges to the solution of the continuous problem. At the end we present numerical studies for the rate of convergence. [Copyright &y& Elsevier]

Abstract: In this short note an addition to the paper [A.G. Bratsos, M. Ehrhardt, I.Th. Famelis, A discrete Adomian decomposition method for discrete nonlinear Schrödinger equations, Appl. Math. Comput. 197(1) (2008) 190–205] using the modulus of the terms evaluated from the Adomian decomposition method on p. 194 and their relation to the convergence of the resulting series is presented. Conclusions for the accuracy of the approximated solution are derived. [Copyright &y& Elsevier]

Abstract: In this note, we point out an error in the recently published article [R.K. Mohanty, M.K. Jain, D. Dhall, A cubic spline approximation and application of TAGE iterative method for the solution of two-point boundary value problems with forcing function in integral form, Appl. Math. Model. 35 (2011) 3036–3047] and then correct it. [Copyright &y& Elsevier]

Abstract: A counterexample is provided in this short note to show that some of local convergence theorems established in [D.K.R. Babajee, M.Z. Dauhoo, An analysis of the properties of the variants of Newton’s method with third order convergence, Appl. Math. Comput. 183 (2006) 659–684] are not always true. Some mistakes in the proofs of these theorems are pointed out. [Copyright &y& Elsevier]

Abstract: The purpose of this note is to correct two convergence theorems for the generalized fuzzy integrals given in Fang [On the convergence theorems of generalized fuzzy integral sequence, Fuzzy Sets and Systems 124 (2001) 117–123]. [Copyright &y& Elsevier]

Abstract: In a recent paper by Jin Erdong and Sun Zhaowei [Robust controllers design with finite time convergence for rigid spacecraft attitude tracking control, Aerospace Science and Technology 12 (2008) 324–330], a terminal sliding mode control technique has been applied to the attitude control problem of rigid spacecraft. Unfortunately, the controller has singularity problem which will cause the instability of the closed-loop system of attitude tracking errors. In this article, a nonsingular terminal sliding mode controller is presented to overcome this problem. [Copyright &y& Elsevier]

Abstract: In this note, we will modify several gaps in Gurudwan and Sharma [N. Gurudwan, B.K. Sharma, Convergence theorem for the common solution for a finite family of -strongly accretive operator equations, Appl. Math. Comput. 217 (2011) 6748–6754]. [Copyright &y& Elsevier]

Abstract: In abstract of the paper [A. Rafiq, A note on “A family of methods for solving nonlinear equations”, Appl. Math. Comput. 195 (2008) 819–821] we can find the following sentences. We cite: Ujević et al. introduced a family of methods for solving nonlinear equations. However the main Algorithm 1 put forward by Ujević et al. (p. 7) is wrong. This is the main aim of this note. We also point out some major bugs in the results of Ujević et al. – the end of the citation. Here it is shown that all of the mentioned assertions are not true. In other words, the Algorithm 1 is correct (up to an obvious misprint, which is not mentioned in the above paper) and there are no major bugs in the paper by Ujević et al. In fact, these observations, which will be given in this note, show that the main aim of the paper by Rafiq is wrong. [Copyright &y& Elsevier]

This paper concerns the convergence of empirical measures in high dimensions. We propose a new class of probability metrics and show that under such metrics, the convergence is free of the curse of dimensionality (CoD). Such a feature is critical for high-dimensional analysis and stands in contrast to classical metrics (e.g. , the Wasserstein metric). The proposed metrics fall into the category of integral probability metrics, for which we specify criteria of test function spaces to guarantee the property of being free of CoD. Examples of the selected test function spaces include the reproducing kernel Hilbert spaces, Barron space, and flow-induced function spaces. Three applications of the proposed metrics are presented: 1. The convergence of empirical measure in the case of random variables; 2. The convergence of n -particle system to the solution to McKean–Vlasov stochastic differential equation; 3. The construction of an ɛ -Nash equilibrium for a homogeneous n -player game by its mean-field limit. As a byproduct, we prove that, given a distribution close to the target distribution measured by our metric and a certain representation of the target distribution, we can generate a distribution close to the target one in terms of the Wasserstein metric and relative entropy. Overall, we show that the proposed class of metrics is a powerful tool to analyze the convergence of empirical measures in high dimensions without CoD. [ABSTRACT FROM AUTHOR]

Due to the attractiveness of household gas-electric tools, in this paper, an optimization technique is suggested based on the integrated demand response (IDR) and degree of tolerance for household energy management. The proposed method is mostly used to express the dynamic change in the forms of energy and undetermined variables in the systems, resulting from household and photovoltaic (PV) load. Thermostatically controlled demands include gas-electricity and air conditioning, and cut-able loads include gas-electric stove and washing machine. The interval optimization is modeled for optimizing the operation and greenhouse gas emission costs in multi-purpose systems. The undetermined variables are formulated as interval statistics and the limitations are simplified by degree of tolerance. In order to solve it, the interval optimization technique is converted into certainty optimization with the interval order relationship and the delayed probability degree. Then, the developed grasshopper search algorithm is based on the chaos theory to solve the interval optimization model in order to respond to uncertainty and demands of the users, such that degree of tolerance of cost that is acceptable by users is optimized. Contrary to other optimization algorithms, the grasshopper search algorithm can be combined with other methods. In this paper, the chaos theory is adopted to find a better solution. Since the information is placed in the search space without order, using this technique considerably leads to good convergence speed, precise final solution finding, not being trapped in local minima, lower SD, and robustness. Both methods of IDR and degree of tolerance for the household gas-electric equipment manage to reduce energy consumption by about 25% compared to traditional methods. • Gas-electric equipment is integrated in household energy management. • A novel IDR method in HMES is proposed, while uncontrollable loads are also executed. • To deal with HMES uncertainty with electric equipment, interval optimization is used. • The users' degree of tolerance in HMES with gas-electric equipment is modeled. • New model of the GSA based on chaos theory is introduced. [ABSTRACT FROM AUTHOR]

This paper focuses on stability of stochastic hybrid systems with random delay driven by a singularly perturbed Markov chain. By weak convergence and the martingale method, the limit system is obtained. Using the limit system as a bridge, this paper establishes the moment exponential stability of the original system by Razumikhin-type techniques. Finally, an example is given to illustrate this result. [ABSTRACT FROM AUTHOR]

This paper considers a novel multi-agent linear stochastic approximation algorithm driven by Markovian noise and general consensus-type interaction, in which each agent evolves according to its local stochastic approximation process which depends on the information from its neighbors. The interconnection structure among the agents is described by a time-varying directed graph. While the convergence of consensus-based stochastic approximation algorithms when the interconnection among the agents is described by doubly stochastic matrices (at least in expectation) has been studied, less is known about the case when the interconnection matrix is simply stochastic. For any uniformly strongly connected graph sequences whose associated interaction matrices are stochastic, the paper derives finite-time bounds on the mean-square error, defined as the deviation of the output of the algorithm from the unique equilibrium point of the associated ordinary differential equation. For the case of interconnection matrices being stochastic, the equilibrium point can be any unspecified convex combination of the local equilibria of all the agents in the absence of communication. Both the cases with constant and time-varying step-sizes are considered. In the case when the convex combination is required to be a straight average and interaction between any pair of neighboring agents may be uni-directional, so that doubly stochastic matrices cannot be implemented in a distributed manner, the paper proposes a push-sum-type distributed stochastic approximation algorithm and provides its finite-time bound for the time-varying step-size case by leveraging the analysis for the consensus-type algorithm with stochastic matrices and developing novel properties of the push-sum algorithm. Distributed temporal difference learning is discussed as an illustrative application. [ABSTRACT FROM AUTHOR]

In designing the extended state observer (ESO), one of the most challenging issues is its performance improvement. In this paper, a simple fuzzy system is proposed to improve the performance of ESO and changes this observer into fuzzy extended state observer (FESO). This FESO is an intelligent linear form of the ESO. The fuzzy system, which is applied to tune the observer gains in an intelligent manner, directs the observer to deliver an appropriate estimation performance. To design this fuzzy system, a simple input–output form is applied to reduce the number of fuzzy rules. The linear form of FESO simplifies the convergence analysis of this observer, which is analyzed through a Lyapunov function. The performance of FESO in the fields of fault diagnosis and active disturbance rejection control (ADRC) are shown by simulation examples and compared with traditional forms of ESO. In this paper, it is revealed that this new proposed ESO embodies advantages of the simple linear structure and provides a good performance, confirmed by its results. • A fuzzy extended state observer (FESO) is designed to obtain a good estimation performance. • A simple SISO form of the fuzzy system is introduced to tune the observer gains. • The FESO performance is investigated in the fields of fault diagnosis and ADRC. [ABSTRACT FROM AUTHOR]

This study extends the research on the convergence analysis of energy-related variables to cover renewable energy intensity by focusing on 26 OECD countries from 1990 to 2021. While there have been several studies on the convergence of different energy variables including renewable energy, the intensity dimension has been largely ignored in the literature. As some non-zero carbon emissions are associated with deploying various forms of renewable energy resources, ignoring their intensity of GDP fails to address the question of efficiency. To address this gap, this study employed a battery of econometric techniques including the novel panel unit root tests that capture abrupt or smooth breaks in the presence of cross-sectional dependence to test for the presence of unit roots in relative renewable energy intensity. The study also examined different clusters of the sample to check the existence of convergence or otherwise at different levels. The results suggest that 21 countries are convergent and only Germany, Japan, Netherlands, Poland and Switzerland are not convergent when the full sample is considered. However, these countries are convergent when other clusters of the countries are examined. Policy implications of the study have been discussed in the paper. [Display omitted] [ABSTRACT FROM AUTHOR]

The paper aims to solve the problem of multi-agent path planning in complex environment using optimization algorithm. To address the issue of local optimum and premature convergence, a new method is proposed based on the whale optimization algorithm, combining the chaotic initialization, the reverse search and the differential evolution methods. It is theoretically proved that this algorithm is globally convergent in probability. When applied to path planning problems, the proposed optimization algorithm can effectively find a globally optimal and smoother path. Through simulation experiments with multi-UAVs, it is demonstrated that the proposed algorithm has better performance than the state-of-the-art methods in environment with both static and dynamic obstacles, reflecting the global convergence and robustness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze an adaptive time-stepping fully discrete scheme which possesses the optimal strong convergence order for the stochastic nonlinear Schrödinger equation with multiplicative noise. Based on the splitting skill and the adaptive strategy, the H 1 -exponential integrability of the numerical solution is obtained, which is a key ingredient to derive the strong convergence order. We show that the proposed scheme converges strongly with orders 1 2 in time and 2 in space. To investigate the numerical asymptotic behavior, we establish the large deviation principle for the numerical solution. This is the first result on the study of the large deviation principle for the numerical scheme of stochastic partial differential equations with superlinearly growing drift. And as a byproduct, the error of the masses between the numerical and exact solutions is finally obtained. [ABSTRACT FROM AUTHOR]

Several benefits of consuming fishery and aquaculture products have been documented by the extant literature. However, the literature has been largely silent on few dimensions of aquaculture products, including the convergence of aquatic products consumption. An importance of investigating the convergence of aquatic products is that it provides hindsight on which countries should be the focus of exporters of the products. Convergence analysis of aquatic products consumption provides information that is relevant to the need to boost local production of aquatic products, and to conserve foreign exchange earnings. The aim of this study is to investigate the convergence of total aquatic products consumption per capita in 27 European Union countries plus United Kingdom, during 1993–2019. We have further considered the convergence of the components of total aquatic products consumption, which include aquatic animals, cephalopods, crustaceans, demersal fish, freshwater fish, marine fish, molluscs, and pelagic fish. Additionally, we have examined conditional convergence by evaluating the determinants of convergence of total aquatic products consumption. Using recently introduced unit root tests that provide for both smooth and sharp breaks, the results provide support for stochastic convergence of total aquatic products consumption per capita. Using a new conditional convergence approach, the analysis demonstrates that population growth rate, real gross domestic product, and prices of aquatic products are factors that enable the convergence of total aquatic products. The results are not materially different across the components of total aquatic products consumption. The implications of the results are discussed in the paper. [ABSTRACT FROM AUTHOR]

Highlights • Sampling-based algorithms are commonly used in motion planning problems. • The RRT* algorithm incrementally builds a tree of motion to find a solution. • Taking a shortcut to the ancestry increases the convergence rate to the optimal. • Combination with sampling strategies further improves the performance. Abstract The Rapidly-exploring Random Tree (RRT) algorithm is a popular algorithm in motion planning problems. The optimal RRT (RRT*) is an extended algorithm of RRT, which provides asymptotic optimality. This paper proposes Quick-RRT* (Q-RRT*), a modified RRT* algorithm that generates a better initial solution and converges to the optimal faster than RRT*. Q-RRT* enlarges the set of possible parent vertices by considering not only a set of vertices contained in a hypersphere, as in RRT*, but also their ancestry up to a user-defined parameter, thus, resulting in paths with less cost than those of RRT*. It also applies a similar technique to the rewiring procedure resulting in acceleration of the tendency that near vertices share common parents. Since the algorithm proposed in this paper is a tree extending algorithm, it can be combined with other sampling strategies and graph-pruning algorithms. The effectiveness of Q-RRT* is demonstrated by comparing the algorithm with existing algorithms through numerical simulations. It is also verified that the performance can be further enhanced when combined with other sampling strategies. [ABSTRACT FROM AUTHOR]

Abstract This paper is concerned with the superconvergence properties of the quadratic finite volume method (FVM) on triangular meshes for elliptic equations. We proved the 3rd order superconvergence rate of the gradient approximation ‖ u h − u I ‖ 1 = O (h 3) and the 4th order superconvergence rate of the function value approximation ‖ u h − u I ‖ 0 = O (h 4) for the quadratic FVM on triangular meshes. Here u h is the FVM solution and u I is the piecewise quadratic Lagrange interpolation of the exact solution. It should be pointed out that the superconvergence phenomena of FVM strongly depends on the construction of dual mesh. Specially for quadratic FVMs, the scheme presented in this paper is the unique scheme which holds superconvergence. [ABSTRACT FROM AUTHOR]

Abstract Twenty years after the classical book of Ortega and Rheinboldt was published, five definitions for the Q -convergence orders of sequences were independently and rigorously studied (i.e., some orders characterized in terms of others), by Potra (1989), resp. Beyer, Ebanks and Qualls (1990). The relationship between all the five definitions (only partially analyzed in each of the two papers) was not subsequently followed and, moreover, the second paper slept from the readers attention. The main aim of this paper is to provide a rigorous, selfcontained, and, as much as possible, a comprehensive picture of the theoretical aspects of this topic, as the current literature has taken away the credit from authors who obtained important results long ago. Moreover, this paper provides rigorous support for the numerical examples recently presented in an increasing number of papers, where the authors check the convergence orders of different iterative methods for solving nonlinear (systems of) equations. Tight connections between some asymptotic quantities defined by theoretical and computational elements are shown to hold. [ABSTRACT FROM AUTHOR]

Highlights • The heat equation with nonlocal initial condition is considered. • Several finite difference schemes are constructed and analyzed. • The stability of the schemes is the main objective of investigation. • Time step size bound obtained in previous paper is revised. • Numerical experiments with linear and nonlinear problems confirm the theoretical results. Abstract In this paper, the two-level finite difference schemes for the one-dimensional heat equation with a nonlocal initial condition are analyzed. As the main result, we obtain conditions for the numerical stability of the schemes. In addition, we revise the stability conditions obtained in [21] for the Crank–Nicolson scheme. We present several numerical examples that confirm the theoretical results within linear, as well as nonlinear problems. In some particular cases, it is shown that for small regions of the time step size values, the explicit FTCS scheme is stable while certain implicit methods, such as Crank–Nicolson scheme, are not. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we propose a Strongly Stable generalized finite element method (SSGFEM) for a non-smooth interface problem, where the interface has a corner. The SSGFEM employs enrichments of 2 types: the nodes in a neighborhood of the corner are enriched by singular functions characterizing the singularity of the unknown solution, while the nodes close to the interface are enriched by a distance based function characterizing the jump in the gradient of the unknown solution along the interface. Thus nodes in the neighborhood of the corner and close to the interface are enriched with two enrichment functions. Both types of enrichments have been modified by a simple local procedure of "subtracting the interpolant." A simple local orthogonalization technique (LOT) also has been used at the nodes enriched with both enrichment functions. We prove that the SSGFEM yields the optimal order of convergence. The numerical experiments presented in this paper indicate that the conditioning of the SSGFEM is not worse than that of the standard finite element method, and the conditioning is robust with respect to the position of the mesh relative to the interface. Highlights • GFEM for 2D non-smooth interface problem. • Singular enrichment functions in addition to distance based enrichment functions. • Proof of optimal convergence of the GFEM. • Experimental study of conditioning and robustness of GFEM. • The notion of Strongly Stable GFEM (SSGFEM). [ABSTRACT FROM AUTHOR]

Abstract In this paper various hybrid hp -finite element methods are discussed for elliptic model problems. In particular, a stabilized primal-hybrid hp -method is introduced which approximatively ensures continuity conditions across element interfaces and avoids the enrichment of the primal discretization space as usually required to fulfill some discrete inf-sup condition. A priori as well as a posteriori error estimates are derived for this method. The stabilized primal-hybrid hp -method is also applied to a model obstacle problem since it admits the definition of pointwise constraints. The paper also describes some extensions of primal, primal-mixed and dual-mixed methods as well as their hybridizations to hp -finite elements. In numerical experiments the convergence properties of the stabilized primal-hybrid hp -method are discussed and compared to all the other hp -methods introduced in this paper. The applicability of the a posteriori error estimates to drive h - and hp -adaptive schemes is also investigated. [ABSTRACT FROM AUTHOR]

Abstract This paper presents a neurodynamic approach to nonlinear optimization problems with affine equality and convex inequality constraints. The proposed neural network endows with a time-varying auxiliary function, which can guarantee that the state of the neural network enters the feasible region in finite time and remains there thereafter. Moreover, the state with any initial point is shown to be convergent to the critical point set when the objective function is generally nonconvex. Especially, when the objective function is pseudoconvex (or convex), the state is proved to be globally convergent to an optimal solution of the considered optimization problem. Compared with other neural networks for related optimization problems, the proposed neural network in this paper has good convergence and does not depend on some additional assumptions, such as the assumption that the inequality feasible region is bounded, the assumption that the penalty parameter is sufficiently large and the assumption that the objective function is lower bounded over the equality feasible region. Finally, some numerical examples and an application in real-time data reconciliation are provided to display the well performance of the proposed neural network. [ABSTRACT FROM AUTHOR]

Abstract We present a new framework for expressing finite element methods on multiple intersecting meshes: multimesh finite element methods. The framework enables the use of separate meshes to discretize parts of a computational domain that are naturally separate; such as the components of an engine, the domains of a multiphysics problem, or solid bodies interacting under the influence of forces from surrounding fluids or other physical fields. Such multimesh finite element methods are particularly well suited to problems in which the computational domain undergoes large deformations as a result of the relative motion of the separate components of a multi-body system. In the present paper, we formulate the multimesh finite element method for the Poisson equation. Numerical examples demonstrate the optimal order convergence, the numerical robustness of the formulation and implementation in the face of thin intersections and rounding errors, as well as the applicability of the methodology. In the accompanying paper (Johansson et al., 2018), we analyze the proposed method and prove optimal order convergence and stability. [ABSTRACT FROM AUTHOR]

Abstract In this paper, by combining the p -order block boundary value methods with the m -th Lagrange interpolation, a class of new numerical methods for solving nonlinear fractional differential equations with the γ -order (0 < γ < 1) Caputo derivatives are obtained. It is proved under some appropriate conditions that the induced methods are convergent of order min ⁡ { p , m − γ + 1 } and globally stable. Several numerical examples are given to illustrate the theoretical results and the computational effectiveness and accuracy of the methods. Highlights • This paper deals with numerical computation and analysis for nonlinear fractional differential equations (FDEs) with γ -order Caputo derivatives. • A class of extended block boundary value methods (EBBVMs) for solving the FDEs are obtained. • The EBBVMs are proved to be convergent of order min ⁡ { p , m − γ + 1 } and globally stable under the appropriate conditions. • Several numerical examples are given to illustrate the theoretical results and the computational effectiveness and accuracy of the methods. [ABSTRACT FROM AUTHOR]

Abstract In order to assess how seasonality affects disparities in natural gas consumption among sectors, this paper aims to study the pattern of convergence in natural gas consumption in a sample of 11 sectors in the United States between January 1973 and February 2017. In addition to the full sample, the existence of convergence is also examined in five subsets of sectors: residential, commercial, industrial, transport and electric power. By using various types of unit root tests, empirical results provide significant support for the convergence of disaggregated natural gas consumption across sectors in the United States. Another important finding of this paper is that natural gas consumption, despite being convergent, is very persistent. Highlights • This study is to test the hypothesis of the convergence in disaggregated natural gas consumption for the United States. • We use various types of unit root tests. • The energy conservation policies oriented towards the reduction of the seasonal effects of natural gas consumption. [ABSTRACT FROM AUTHOR]

Abstract In this paper we investigate the problem of influence of parametric perturbations on the Lyapunov spectrum of the discrete linear time-varying system. The main result of the paper is that for any two sequences of positive real numbers and any rate of convergence there exist a discrete linear time-varying system and a perturbation tending to zero with the given rate of convergence such that the spectra of the perturbed and unperturbed systems coincide with the a priori given sequences. Moreover, we show that this phenomenon is possible even when the perturbations are different from zero, rarely, in a certain sense. Finally, as a conclusion from the main result, we obtain that the separation type and the index of exponential stability may vary arbitrarily under the influence of exponentially decreasing perturbations. [ABSTRACT FROM AUTHOR]

Abstract This paper is concerned with diffusion control problem of a tempered anomalous diffusion system based on fractional-order PI controllers. The contribution of this paper is to introduce fractional-order PI controllers into the tempered anomalous diffusion system for mobile actuators motion and spraying control. For the proposed control force, convergence analysis of the system described by mobile actuator dynamical equations is presented based on Lyapunov stability arguments. Moreover, a new Centroidal Voronoi Tessellation (CVT) algorithm based on fractional-order PI controllers, henceforth called FOPI-based CVT algorithm, is provided together with a modified simulation platform called Fractional-Order Diffusion Mobile Actuator-Sensor 2-Dimension Fractional-Order Proportional Integral (FO-Diff-MAS2D-FOPI). Finally, extensive numerical simulations for the tempered anomalous diffusion process are presented to verify the effectiveness of our proposed fractional-order PI controllers. [ABSTRACT FROM AUTHOR]

Highlights • This study investigates the convergence of two bibliometric approaches to the measurement of interdisciplinary research. • The above general tendency varies across disciplines, but noticeable exceptions are found at individual paper level. • The diversity of the reference list grows with the number of fields reflected in the authors' list and with the number of authors being equal the number of fields. • When fields reflected in the authors' list belong to different disciplines, the disparity in the reference list is accordingly higher. Abstract This study investigates the convergence of two bibliometric approaches to the measurement of interdisciplinary research: one based on analyzing disciplinary diversity in the reference list of publications, the other based on the disciplinary diversity of authors of publications. In particular we measure the variety, balance, disparity and integrated diversity index of, respectively, single-author, multi-author single-field, and multi-author multi-field publications. We find that, in general, the diversity of the reference list grows with the number of fields reflected in a paper's authors' list and, to a lesser extent, with the number of authors being equal the number of fields. Further, we find that when fields belonging to different disciplines are reflected in the authors' list, the disparity in the reference list is higher than in the case of fields belonging to the same discipline. However, this general tendency varies across disciplines, and noticeable exceptions are found at individual paper level. [ABSTRACT FROM AUTHOR]

Highlights • This paper proposes a quantitative future-oriented approach to technological opportunity discovery for convergence using patent information. • The proposed approach predicts potential technological knowledge flows between heterogeneous fields. • The technological opportunities between biotechnology and information technology are used to illustrate the proposed method. • This paper identifies technological opportunities for convergence with direction and strength of potential knowledge flows. Abstract As technological convergence has recently become a mainstream innovation trend, technological opportunities need to be explored in heterogeneous technology fields. Most of the previous convergence studies have taken a retrospective view in measuring the degree of convergence and monitoring the converging trends. This paper proposes a quantitative future-oriented approach to technological opportunity discovery for convergence using patent information. In a future-oriented approach, technological opportunities for convergence are suggested by predicting potential technological knowledge flows (TKFs) between heterogeneous fields. The potential TKFs are predicted by a link prediction method in a directed network, which is suggested in this paper to represent the direction of the predicted TKFs by adapting the concept of bibliographic coupling and edge-betweenness centrality. Converging technological opportunities are proposed as incremental and radical technological opportunities by extracting the potential increased knowledge flow links and emerging knowledge flow links. Moreover, the direction and themes of the predicted potential TKFs are provided as technological opportunities for convergence. As an illustration of the proposed method, the technological opportunities between biotechnology (BT) and information technology (IT) are explored. Firms and researchers can use the proposed method to seek out new technological opportunities from various technologies so that R&D policymakers can plan new R&D projects on technological convergence. [ABSTRACT FROM AUTHOR]

This paper introduces a nonlinear multigrid solver for mixed finite element discretizations based on the Full Approximation Scheme (FAS) and element-based Algebraic Multigrid (AMGe). The AMGe coarse spaces with approximation properties used in this work enable us to overcome the difficulties in evaluating the nonlinear coarse operators and the degradation in convergence rates that characterized previous attempts to extend FAS to algebraic multilevel hierarchies on general unstructured grids. Specifically, the AMGe technique employed in this paper allows to derive stable and accurate coarse discretizations on general unstructured grids for a large class of nonlinear partial differential equations, including saddle point problems. The approximation properties of the coarse spaces ensure that our FAS approach for general unstructured meshes leads to optimal mesh-independent convergence rates similar to those achieved by geometric FAS on a nested hierarchy of refined meshes. In the numerical results, Newton’s method and Picard iterations with state-of-the-art inner linear solvers are compared to our FAS algorithm for the solution of a nonlinear saddle point problem arising from porous media flow applications. Our approach outperforms – both in terms of number of iterations and computational time – traditional methods in all the experiments. [ABSTRACT FROM AUTHOR]

Data envelopment analysis (DEA) is a frontier analysis procedure for evaluating the relative performance of decision making units (DMUs) with multiple inputs and multiple outputs. To improve its discrimination power, an important extension is proposed as cross-efficiency, which uses peer DMUs’ optimal relative weights to evaluate the relative performance. However, the existing cross-efficiency methods show an inconsistent and unbalanced evaluation standard, since each DMU might determine a different total (or mean) efficiency value across all DMUs. The different values imply that the DMUs that have assigned larger cross-efficiency scores will have a larger effect in aggregating the ultimate cross-efficiency scores and different DMUs’ effects are unbalanced in cross-efficiency methods. In this paper, we will deal with this unbalanced cross-efficiency evaluation problem. To this end, we first suggest a practical adjustment measure to rectify the traditional cross-efficiency, which will provide a common evaluation standard for all DMUs and make each DMU dispatch an identical total efficiency score across all DMUs. Further, we propose a game-like iterative procedure to obtain the optimal balanced cross-efficiency. Finally, we present both a numerical example and an empirical study derived from the literature and a real-world problem to demonstrate the usefulness and efficacy of the new balanced cross-efficiency evaluation approach. The work presented in this paper can extend the traditional cross-efficiency approaches to situations involving unbalanced evaluation standards, and make the evaluation results more practical significance. [ABSTRACT FROM AUTHOR]

In this paper, we propose Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM). The main goal of this paper is to design multiscale basis functions within GMsFEM framework such that the convergence of method is independent of the contrast and linearly decreases with respect to mesh size if oversampling size is appropriately chosen. We would like to show a mesh-dependent convergence with a minimal number of basis functions. Our construction starts with an auxiliary multiscale space by solving local spectral problems. In auxiliary multiscale space, we select the basis functions that correspond to small (contrast-dependent) eigenvalues. These basis functions represent the channels (high-contrast features that connect the boundaries of the coarse block). Using the auxiliary space, we propose a constraint energy minimization to construct multiscale spaces. The minimization is performed in the oversampling domain, which is larger than the target coarse block. The constraints allow handling non-decaying components of the local minimizers. If the auxiliary space is correctly chosen, we show that the convergence rate is independent of the contrast (because the basis representing the channels are included in the auxiliary space) and is proportional to the coarse-mesh size (because the constraints handle non-decaying components of the local minimizers). The oversampling size weakly depends on the contrast as our analysis shows. The convergence theorem requires that channels are not aligned with the coarse edges, which hold in many applications, where the channels are oblique with respect to the coarse-mesh geometry. The numerical results confirm our theoretical results. In particular, we show that if the oversampling domain size is not sufficiently large, the errors are large. To remove the contrast-dependence of the oversampling size, we propose a modified construction for basis functions and present numerical results and the analysis. [ABSTRACT FROM AUTHOR]

Highlights • This paper proposes a two stage method for identification of multiple-input single-output Hammerstein model with time delay. • The nonlinear part of Hammerstein model is approximated by the means of Radial Basis Function Neural Network. • The fractional order transfer function is applied to estimate the linear part of Hammerstein model. • The identification method is based on a hybrid scheme, including a novel evolutionary algorithm called Modified Genetic Algorithm (MGA) and the Recursive Least Squares method. • The MGA is inspired from the artificial genetic operation in some agronomic products. Abstract This paper deals with identification of the continuous-time Hammerstein systems with time delay using Genetic Algorithm (GA) combined with the Recursive Least-Squares (RLS) method. This model consists of the Radial Basis Function Neural Network (RBFNN) as its nonlinear static part and fractional order transfer function as its dynamic linear part. The fractional orders are identified by GA with an innovative strategy called Modified Genetic Algorithm (MGA). The main innovative idea is the selection and transferring the best characteristics or properties to the next generation. On the other hand, the centers and widths and the weighting parameters of the RBFNN and the transfer function coefficients of the linear dynamic part are updated by the RLS method. Simulation results are applied to illustrate the proposed method accuracy. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • In this paper, a modified BCO (MBCO) approach is proposed for data clustering. In the proposed MBCO, cloning and fairness concepts are used to improve the quality of clustering solution. • For every stage of allocation only data points which are unallocated in the previous stages of allocation are considered. • To obtain more diverse solution, a probability based selection ( Pbselection ) approach is proposed to assign the unallocated data to clusters in each iteration. • Next, to improve the convergence time, the current solution (centroid values) is always compared with the previous best solution. • In order to get global optimal and diverse solution, two hybridized approaches, i.e. MKCLUST and KMCLUST are proposed. Abstract Among the nature inspired heuristic or meta-heuristic optimization algorithms, Bee Colony Optimization (BCO) algorithms are widely used to solve clustering problem. In this paper, a modified BCO (MBCO) approach is proposed for data clustering. In the proposed MBCO, the forgiveness characteristics of bees and giving a fair chance to both trustworthy and untrustworthy bees are being taken care of. A probability based selection ( Pbselection ) approach is introduced in the proposed MBCO for assigning unallocated data points in every iteration. The result shows that, the proposed method gives faster convergence as compared to the existing well known algorithms. In order to improve the performance of MBCO further and to obtain global optimal and diverse solution, the proposed MBCO is hybridized with k -means algorithm. In average, the hybridized MKCLUST and KMCLUST give same or better result than the proposed MBCO. To validate the proposed algorithms, seven standard data sets are considered. From classification error percentages calculation, it is observed that the proposed algorithms perform better compared to some existing algorithms. The simulation results infer that the proposed algorithms can be efficiently used for data clustering. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • This paper proposed an improved version of fruit fly optimization (FOA). • Mutation adaptation mechanism is adopted to enhance the balance of FOA in terms of the exploitation and exploration ability. • The phase angle-based encoded strategy helps to achieve the high convergence performance. • The proposed method is used to find the optimal UAV path in the 3D environments. • Numerical experiments results show the proposed method is superior to several existing state-of-the-art optimization algorithms. Abstract This paper proposed an improved version of fruit fly optimization (FOA) to solve the unmanned aerial vehicle (UAV) path planning problem. The improved algorithm combines the phase angle-encoded and mutation adaptation mechanisms into the basic FOA and is referred to as θ-MAFOA. Mutation adaptation mechanism is adopted to enhance the balance of FOA in terms of the exploitation and exploration ability, while phase angle-based encoded strategy for fruit fly locations helps to achieve the high performance in the convergence process. Then, the proposed θ-MAFOA is used to find the optimal flight path for UAV in the complex three-dimensional (3D) terrain environments with various ground defense weapons. B-Spline curve that connects the start and target points is employed to represent a smooth path. Several performance criteria and constraints are taken into consideration to evaluate the cost of UAV paths. Numerical experiments are carried out on various test scenarios and the results show the proposed θ-MAFOA is superior to the basic and other two modified versions of FOA, and also more powerful than several existing state-of-the-art optimization algorithms. [ABSTRACT FROM AUTHOR]

Recently, Mao (2015) developed a new explicit method, called the truncated Euler–Maruyama (EM) method, for the nonlinear SDE and established the strong convergence theory under the local Lipschitz condition plus the Khasminskii-type condition. In his another follow-up paper (Mao, 2016), he discussed the rates of L q -convergence of the truncated EM method for q ≥ 2 and showed that the order of L q -convergence can be arbitrarily close to q ∕ 2 under some additional conditions. However, there are some restrictions on the truncation functions and these restrictions sometimes might force the step size to be so small that the truncated EM method would be inapplicable. The key aim of this paper is to establish the convergence rate without these restrictions. The other aim is to study the stability of the truncated EM method. The advantages of our new results will be highlighted by the comparisons with the results in Mao (2015, 2016) as well as others on the tamed EM and implicit methods. [ABSTRACT FROM AUTHOR]

This paper aims to provide a novel metaheuristic algorithm motivated from quantum motion entitled Multi-scale Quantum Harmonic Oscillator Algorithm (MQHOA). The calculation accuracy of MQHOA is adjustable. The physical model and mathematical analysis of the proposed algorithm are detailed and well interpreted in this paper. The structure of MQHOA is very simple, including merely two phases, the quantum harmonic oscillator process (QHO process) and multi-scale process (M process). Experiments are carried out to validate the effectiveness and efficiency of MQHOA by applying it to 30 well defined benchmark functions. We also compare MQHOA with several well-known metaheuristic algorithms, such as genetic algorithm (GA), simulated annealing (SA), particle swarm optimization (PSO) and quantum particle swarm optimization (QPSO). The comparative results indicate the competitive and superior performance of the proposed algorithm in both convergence speed and optimal solution accuracy. [ABSTRACT FROM AUTHOR]

In this paper, an indoor visible light localization system based on improved chaotic particle swarm optimization (CPSO) is proposed to achieve indoor 3-D positioning. In the field of visible light positioning, most of the localization is two-dimensional positioning under the condition of height determined. In addition, some three-dimensional visible light localization systems use a hybrid algorithm that greatly improves the computational complexity of the system, or requires the user to first provide a better initial point for three-dimensional positioning, which can’t be applied to life well. In order to solve the problems in the field of VLP, this paper proposes an indoor visible light positioning system based on improved chaotic particle swarm optimization. In this paper, the chaos algorithm is firstly used in the visible light positioning area. Meanwhile, the proposed algorithm combines chaos algorithm and particle swarm optimization algorithm, and obtains a high positioning accuracy in the simulation space of 3 m × 3 m × 4m. Chaos optimization algorithm can make use of visible light indoor positioning system to achieve the positioning accuracy greatly, and join the particle swarm algorithm can offset the slow convergence of the chaos algorithm. The simulation results show that the visible light positioning system based on CPSO algorithm can achieve the average error of less than 1.4 cm, and the positioning accuracy of 96.6% sampling points can reach within 3.55 cm. [ABSTRACT FROM AUTHOR]

In this paper we consider a family of high-order iterative methods which is more efficient than the Newton method to approximate a solution of symmetric algebraic Riccati equations. In fact, this paper is devoted to the convergence study of a k -steps iterative scheme with low operational cost and high order of convergence. We analyze their accessibility and computational efficiency. We also obtain results about the existence and localization of solution. Numerical experiments confirm the advantageous performance of the iterative scheme analyzed. [ABSTRACT FROM AUTHOR]

This paper examines convergence and stability of the two classes of theta-Milstein schemes for stochastic differential equations (SDEs) with non-global Lipschitz continuous coefficients: the split-step theta-Milstein (SSTM) scheme and the stochastic theta-Milstein (STM) scheme. For θ ∈ [ 1 ∕ 2 , 1 ] , this paper concludes that the two classes of theta-Milstein schemes converge strongly to the exact solution with the order 1. For θ ∈ [ 0 , 1 ∕ 2 ] , under the additional linear growth condition for the drift coefficient, these two classes of the theta-Milstein schemes are also strongly convergent with the standard order. This paper also investigates exponential mean-square stability of these two classes of the theta-Milstein schemes. For θ ∈ ( 1 ∕ 2 , 1 ] , these two theta-Milstein schemes can share the exponential mean-square stability of the exact solution. For θ ∈ [ 0 , 1 ∕ 2 ] , similar to the convergence, under the additional linear growth condition, these two theta-Milstein schemes can also reproduce the exponential mean-square stability of the exact solution. [ABSTRACT FROM AUTHOR]

For a Tychonoff space X , C p ( X ) is the space of all real-valued continuous functions with the topology of pointwise convergence. A subset A ⊂ X is said to be sequentially dense in X if every point of X is the limit of a convergent sequence in A . In this paper, the following 8 properties for C p ( X ) are considered. S 1 ( S , S ) ⇒ S f i n ( S , S ) ⇒ S 1 ( S , D ) ⇒ S f i n ( S , D ) ⇑ ⇑ ⇑ ⇑ S 1 ( D , S ) ⇒ S f i n ( D , S ) ⇒ S 1 ( D , D ) ⇒ S f i n ( D , D ) For example, a space X satisfies S 1 ( D , S ) (resp., S f i n ( D , S ) ) if whenever { D n : n ∈ N } is a sequence of dense subsets of X , one can take points x n ∈ D n (resp., finite F n ⊂ D n ) such that { x n : n ∈ N } (resp., ⋃ { F n : n ∈ N } ) is sequentially dense in X . Other properties are defined similarly. S 1 ( D , D ) (= R -separability) and S f i n ( D , D ) (= M -separability) for C p ( X ) were already investigated by several authors. In this paper, we have gave characterizations for C p ( X ) to satisfy other 6 properties above. [ABSTRACT FROM AUTHOR]

The paper considers a class of nonsmooth neural networks where hard-limiter saturation nonlinearities are used to constrain solutions of a linear system with concentrated and distributed delays to evolve within a closed hypercube of R n . Such networks are termed delayed linear systems in saturated mode (D-LSSMs) and they are a generalization to the delayed case of a relevant class of neural networks previously introduced in the literature. The paper gives a rigorous foundation to the D-LSSM model and then it provides a fundamental result on convergence of solutions toward equilibrium points in the case where there are nonsymmetric cooperative (nonnegative) interconnections between neurons. The result ensures convergence for any finite value of the maximum delay and is physically robust with respect to perturbations of the interconnections. More importantly, it encompasses situations where there exist multiple stable equilibria, thus guaranteeing multistability of cooperative D-LSSMs. From an application viewpoint the delays in combination with the property of multistability make D-LSSMs potentially useful in the fields of associative memories, motion detection and processing of temporal patterns. [ABSTRACT FROM AUTHOR]

This paper presents a robust finite-time guidance (RFTG) law to a short-range interception problem. The main challenge is that the evasive strategy of the target is unpredictable because it is determined not only by the states of both the interceptor and the target, but also by external un-modeled factors. By robustly stabilizing a line-of-sight rate, this paper proposes an integrated continuous finite-time disturbance observer/bounded continuous finite-time stabilizer strategy. The design of this integrated strategy has two points: 1) effect of a target maneuver is modeled as disturbance and then is estimated by the second-order homogeneous observer; 2) the finite-time stabilizer is actively coupled with the observer. Based on homogeneity technique, the local finite-time input-to-state stability is established for the closed-loop guidance system, thus implying the proposed RFTG law can quickly render the LOS rate within a bounded error throughout intercept. Moreover, convergence properties of the LOS rate in the presence of control saturation are discussed. Numerical comparison studies demonstrate the guidance performance. [ABSTRACT FROM AUTHOR]

Nowadays, most of real world problems are complex and hence they cannot be solved by exact methods. So generally, we have to utilize approximate methods such as metaheuristics. So far, a significant amount of metaheuristic algorithms are proposed which are different with together in algorithm motivation and steps. Similarly, this paper presents the Tree Growth Algorithm (TGA) as a novel method with different approach to address optimization tasks. The proposed algorithm is inspired by trees competition for acquiring light and foods. Diversification and intensification phases and their tradeoff are detailed in the paper. Besides, the proposed algorithm is verified by using both mathematical and engineering benchmarks commonly used in this research area. This new approach in metaheuristic is compared and studied with well-known optimization algorithms and the comparison of TGA with standard versions of these employed algorithms showed the superiority of TGA in these problems. Also, convergence analysis and significance tests via some nonparametric technique are employed to confirm efficiency and robustness of the TGA. According to the results of conducted tests, the TGA can be considered as a successful metaheuristic and suitable for optimization problems. Therefore, the main purpose of providing this algorithm is achieving to better results, especially in continuous problems, due to the natural behavior inspired by trees. [ABSTRACT FROM AUTHOR]

This paper is devoted to studies of I wQN-spaces and some of their cardinal characteristics. Recently, Šupina in [32] proved that I is not a weak P-ideal if and only if any topological space is an I QN-space. Moreover, under p = c he constructed a maximal ideal I (which is not a weak P-ideal) for which the notions of I QN-space and QN-space do not coincide. In this paper we show that, consistently, there is an ideal I (which is not a weak P-ideal) for which the notions of I wQN-space and wQN-space do not coincide. This is a partial solution to [6, Problem 3.7] . We also prove that for this ideal the ideal version of Scheepers Conjecture does not hold (this is the first known example of such weak P-ideal). We obtain a strictly combinatorial characterization of non ( I wQN-space ) similar to the one given in [32] by Šupina in the case of non ( I QN-space ) . We calculate non ( I QN-space ) and non ( I wQN-space ) for some weak P-ideals. Namely, we show that b ≤ non ( I QN-space ) ≤ non ( I wQN-space ) ≤ d for every weak P-ideal I and that non ( I QN-space ) = non ( I wQN-space ) = b for every F σ ideal I as well as for every analytic P-ideal I generated by an unbounded submeasure (this establishes some new bounds for b ( I , I , Fin ) introduced in [31] ). As a consequence, we obtain some bounds for add ( I QN-space ) . In particular, we get add ( I QN-space ) = b for analytic P-ideals I generated by unbounded submeasures. By a result of Bukovský, Das and Šupina from [6] it is known that in the case of tall ideals I the notions of I QN-space ( I wQN-space) and QN-space (wQN-space) cannot be distinguished. Answering [6, Problem 3.2] , we prove that if I is a tall ideal and X is a topological space of cardinality less than co v ⁎ ( I ) , then X is an I wQN-space if and only if it is a wQN-space. [ABSTRACT FROM AUTHOR]

Motivated by truncated Euler–Maruyama (EM) method introduced by Mao (2015), a new explicit numerical method named modified truncated Euler–Maruyama method is developed in this paper. Strong convergence rates of the given numerical scheme to the exact solutions to stochastic differential equations are investigated under given conditions in this paper. Compared with truncated EM method, the given numerical simulation strongly converges to the exact solution at fixed time T and over a time interval [ 0 , T ] under weaker sufficient conditions. Meanwhile, the convergence rates are also obtained for both cases. Two examples are provided to support our conclusions. [ABSTRACT FROM AUTHOR]