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The Internet convulsed journalism and created new press models based on budgets radically different from those that traditionally shaped the performance of the profession. Although at first the newspapers created different work structures for paper and web media, the final decision of the journalistic companies was to create a single newsroom for paper and web media. This article investigates if from the theory of Communication, and especially from the works of McLuhan, this decision is or is not justified in a correct way. [ABSTRACT FROM AUTHOR]

Background: Online interaction in blended learning is leveraged through social presence and convergence. However, little systematic work currently exists on how researchers have explored these challenges in higher education institutions and no studies have synthesised these challenges. Objectives: The purpose of this study is to give a novel overview of social presence and convergence to improve online interaction in blended learning in higher education. The findings will be synthesised into blended learning design principles. Method: Two systematic literature reviews, one on each challenge, were carried out through the Web of Science databases and consulting cited sources in review articles. Accordingly, 28 distinct studies were selected through the guidelines of the PRISMA statement, using predefined selection criteria. Results and Conclusions: The results show that social presence in blended learning is mostly evoked through course design, introductory f2f meetings, collaborative activities, prompt online feedback, the teacher's presence, and planned facilitation. To establish convergence, it is recommended to make basic theory available online through video clips, web‐lectures, articles, followed by simple online assignments or self‐study to increase understanding, thereby creating opportunities for deep learning during face‐to‐face through discussions and collaborative activities. Implications: This paper adds to the theory on blended learning and instructional design in higher education, and further offers an elaborate set of design principles for educational practice. Future research on instructional design may investigate in particular how a target group or student factors, are affected by the blended learning environment in order to tailor designs for a specific target group. Lay Description: What is known?: Online interaction is pivotal in blended learningOnline interaction is leveraged through social presence and convergenceSocial presence prevents the online student from feeling lonelyConvergence entails deciding the best‐suited delivery mode: online or face‐to‐face What this paper adds: A novel overview and critical analysis of social presence in blended learningA novel overview and critical analysis of convergence in blended learningA synthesis of the findings on social presence and convergenceExtraction of the findings into blended learning design principles Implications for practitioners: The teacher's presence through design and accessibility fosters students' social presencePlacing concepts online leaves room for deep learning during face‐to‐faceCollaborative activities evoke social presence and facilitate deep learningBlended learning designs should be further tailored for the target group [ABSTRACT FROM AUTHOR]

This paper considers the problem of kernel regression and classification with possibly unobservable response variables in the data, where the mechanism that causes the absence of information can depend on both predictors and the response variables. Our proposed approach involves two steps: First we construct a family of models (possibly infinite dimensional) indexed by the unknown parameter of the missing probability mechanism. In the second step, a search is carried out to find the empirically optimal member of an appropriate cover (or subclass) of the underlying family in the sense of minimizing the mean squared prediction error. The main focus of the paper is to look into some of the theoretical properties of these estimators. The issue of identifiability is also addressed. Our methods use a data-splitting approach which is quite easy to implement. We also derive exponential bounds on the performance of the resulting estimators in terms of their deviations from the true regression curve in general L p norms, where we allow the size of the cover or subclass to diverge as the sample size n increases. These bounds immediately yield various strong convergence results for the proposed estimators. As an application of our findings, we consider the problem of statistical classification based on the proposed regression estimators and also look into their rates of convergence under different settings. Although this work is mainly stated for kernel-type estimators, it can also be extended to other popular local-averaging methods such as nearest-neighbor and histogram estimators. [ABSTRACT FROM AUTHOR]

This paper reports on research into co-creation labs as a tool for exploring environmental communication. Co-creation labs are novel spaces for experimentation, social learning, and trans-disciplinary as well as cross-sectoral collaboration for sustainability transformations. This paper examines the approach taken by researchers to theorising, via a repurposing of the 2×2 scenario matrix, a series of "labs" that represent diverse spaces in which to explore co-creative convergence through transformative learning processes. In addition, examples from work done to date are offered to illustrate progress in implementing these labs and testing the strengths and weaknesses of these co-creative spaces. [ABSTRACT FROM AUTHOR]

Recently, convergence has been presented as one of the technical innovations in many industrial sectors and diffusion has been discussed as providing the main influence on convergence. The present study used the VOSviewer to analyze convergence trends and the current state of joint research, complemented by quantitative analysis using information from scientific papers published in 2015 obtained through the Scopus database. The results of this study illustrate that convergence of research occurring in Korea is evident in a variety of sectors, e.g. chemistry, material science, mechanics and the electrical and electronics sectors. We discovered that a sector performing research characterized by convergence also was actively involved in joint research. We also discovered that institutions conducting many studies were doing so as partners within joint research with other institutions. There are two important applications: The present study identified important information that can be used to monitor convergence and diffusion appears to provide the most influence on convergence. [ABSTRACT FROM AUTHOR]

In this paper, we intend to utilize the generalized scalar auxiliary variable (GSAV) approach proposed in recent paper (Ju et al., SIAM J. Numer. Anal., 60 (2022), 1905–1931) for the nonlocal coupled sine-Gordon equation to construct a class of fully decoupled, linear, and second-order accurate energy-preserving scheme. The unconditional unique solvability and discrete energy conservation law of the proposed scheme are rigorously discussed, and the unconditional convergence is then proved by the mathematical induction. Particularly, the convergence analysis covers the proposed scheme in multiple dimensions due to the corresponding nonlinear terms satisfy the global Lipschitz continuity straightforwardly. Finally, time evolution of dynamical behavior of the governing equation with different nonlocal parameters are observed, and ample numerical comparisons demonstrate that the proposed scheme manifests high efficiency in long-time computations. [ABSTRACT FROM AUTHOR]

Purpose: This study presents a two-step numerical iteration method specifically designed to solve absolute value equations. The proposed method is valuable and efficient for solving absolute value equations. Several numerical examples were taken to demonstrate the accuracy and efficiency of the proposed method. Design/methodology/approach: We present a two-step numerical iteration method for solving absolute value equations. Our two-step method consists of a predictor-corrector technique. The new method uses the generalized Newton method as the predictor step. The four-point open Newton-Cotes formula is considered the corrector step. The convergence of the proposed method is discussed in detail. This new method is highly effective for solving large systems due to its simplicity and effectiveness. We consider the beam equation, using the finite difference method to transform it into a system of absolute value equations, and then solve it using the proposed method. Findings: The paper provides empirical insights into how to solve a system of absolute value equations. Originality/value: This paper fulfills an identified need to study absolute value equations. [ABSTRACT FROM AUTHOR]

In this paper, we study a method of polynomial interpolation that lies in-between Lagrange and Hermite methods. The novelty is that we use very general nodal systems on the unit circle as well as on the bounded interval only characterized by a separation property. The way in which we interpolate consists in considering all the nodes for the prescribed values and only half for the derivatives. Firstly, we develop the theory on the unit circle, obtaining the main properties of the nodal polynomials and studying the convergence of the interpolation polynomials corresponding to continuous functions with some kind of modulus of continuity and with general conditions on the prescribed values for half of the derivatives. We complete this first part of the paper with the study of the convergence for smooth functions obtaining the rate of convergence, which is slightly slower than that when equidistributed nodal points are considered. The second part of the paper is devoted to solving a similar problem on the bounded interval by using nodal systems having good properties of separation, generalizing the Chebyshev–Lobatto system, and well related to the nodal systems on the unit circle studied before. We obtain an expression of the interpolation polynomials as well as results about their convergence in the case of continuous functions with a convenient modulus of continuity and, particularly, for differentiable functions. Finally, we present some numerical experiments related to the application of the method with the nodal systems dealt with. [ABSTRACT FROM AUTHOR]

In this study, we extended the applicability of a derivative-free algorithm to encompass the solution of operators that may be either differentiable or non-differentiable. Conditions weaker than the ones in earlier studies are employed for the convergence analysis. The earlier results considered assumptions up to the existence of the ninth order derivative of the main operator, even though there are no derivatives in the algorithm, and the Taylor series on the finite Euclidian space restricts the applicability of the algorithm. Moreover, the previous results could not be used for non-differentiable equations, although the algorithm could converge. The new local result used only conditions on the divided difference in the algorithm to show the convergence. Moreover, the more challenging semi-local convergence that had not previously been studied was considered using majorizing sequences. The paper included results on the upper bounds of the error estimates and domains where there was only one solution for the equation. The methodology of this paper is applicable to other algorithms using inverses and in the setting of a Banach space. Numerical examples further validate our approach. [ABSTRACT FROM AUTHOR]

Some new classes of general harmonic convex sets and convex functions are introduced and studied in this paper. The optimality criteria of the differentiable general harmonic functions is characterized by the general harmonic variational inequalities. Special cases are also pointed out as applications of the new concepts. Auxiliary principle technique involving an arbitrary operator is applied to suggest and analysis several inertial type methods are suggested. Convergence criteria is investigated of the proposed methods under weaker conditions. The results obtained in this paper may inspire further research along with implementable numerical methods for solving the general harmonic variational inequalities and related optimization problems. [ABSTRACT FROM AUTHOR]

The Last decade saw significant growth in the digital terrestrial television (DTT) subscribers. The High peak-to-average power ratio (PAPR) of the transmitted signal is implied by the large fluctuations in its amplitude, which is a serious issue in the contemporary and next generation DTT broadcasting systems. These large fluctuations prevent feeding the high power amplifier (HPA) at an operating point near its non-linear (NL) saturation region, thereby lowering its power efficiency. For a better future, energy-efficient green communications is the need of hour. This paper focuses on digital predistortion (DPD), which is among the widely used techniques for HPA linearization in order to minimize the NL effects. DPD technique requires a feedback signal. This paper proposes a novel adding signal-based digital predistortion, where the output of the HPA is gradually linearized by adding a signal at the input in an iterative manner. By Taylor series approximation, the DPD problem can be posed as a convex one. We prove that a tighter upper bound exists for the convergence factor and instead of directly solving the convex problem, we pick a convergence factor value within its bounds that offers a good trade-off between convergence speed and residual error value. The simulation results show that the proposed technique can quickly linearize the HPA with good convergence. [ABSTRACT FROM AUTHOR]

Globalisation, changes in technology and transportation, and isomorphic trends in the sector emphasise the need to identify the diversity of higher education institutions. As a response, classification mechanisms emerged in higher education in recent decades. While many studies on classification focus on the types and methodology, the examination of the utility of classifications is limited. Thus, this paper examines the perspectives of 14 people in critical positions on the Carnegie Basic Classification of Higher Education and is triangulated by institutional documents. The results revealed some important implications for policymakers and researchers. While the Carnegie Basic Classification seems to remain one of the significant sources in higher education, the availability of big data, along with varying new methodologies, began to threaten the usability of the classification system. Moreover, contrary to the role assigned to it earlier, Carnegie Basic Classification seems to contribute more to homogeneity in the system. [ABSTRACT FROM AUTHOR]

This paper presents three tensor randomized extended Kaczmarz methods for solving a tensor inconsistent linear system of equations under the t-product between tensors. The randomized extended Kaczmarz, the randomized extended block Kaczmarz, and the randomized extended greedy block Kaczmarz methods in tensor form are proposed to solve inconsistent tensor linear system of equations, respectively. The convergence of each method is proved. Several numerical examples are given to show the efficiency and effectiveness of our methods. [ABSTRACT FROM AUTHOR]

This paper proposes a new meta-heuristic optimization algorithm called Cleaner Fish Optimization algorithm (CFO) inspired by cleaner fish. The CFO simulates the movement behavior of cleaner fish when performing "cleaning services" and the behavior of female may change its sex to become a male, and defines two modes of position update. In addition, a two-generation cycle operation strategy is proposed to realize the optimization process. To verify the effectiveness of the CFO algorithm, 23 well-known CEC benchmark functions, CEC-2017 benchmark functions and 4 engineering design problems are adopted. Simulation results show that the proposed algorithm has a faster convergence rate and better optimal solution when it compared with several other meta-heuristic algorithms. [ABSTRACT FROM AUTHOR]

In this paper, an improved zeroing neural network (ZNN) model is proposed to obtain the positive definite solutions of the continuous coupled Lyapunov matrix equations (CLMEs) associated with continuous‐time Markovian jump (CMJ) systems. To achieve this, a general ZNN model is established by constructing a matrix‐valued error function. Then, to accelerate the convergence rate of the proposed ZNN model, the latest estimation is introduced to obtain an improved ZNN model. Some convergence conditions have been derived for the presented improved ZNN model through Lyapunov theory. Comparisons among the improved ZNN model and the existing results are conducted to illustrate the advantages of the proposed improved ZNN model in numerical examples. [ABSTRACT FROM AUTHOR]

This paper deals with speeding up the convergence of a class of two-step iterative methods for solving linear systems of equations. To implement the acceleration technique, the residual norm associated with computed approximations for each sub-iterate is minimized over a certain two-dimensional subspace. Convergence properties of the proposed method are studied in detail. The approach is further developed to solve (regularized) normal equations arising from the discretization of ill-posed problems. The results of numerical experiments are reported to illustrate the performance of exact and inexact variants of the method on several test problems from different application areas. [ABSTRACT FROM AUTHOR]

It has become a new trend for the future development of Chinese agriculture to accelerate the transformation from increasing production to improving quality and realizing green growth. This paper uses the sequential DEA to measure the agricultural green total factor productivity (GTFP) of 306 Chinese cities from 1996 to 2017, then tests its convergence. The results show that the average growth rate of Chinese agricultural GTFP is 0.58%; the main driving force coming from technical progress. The convergence of agricultural GTFP has dual characteristics of stages and regions, and the significant σ convergence only exists in the central region during 1996–2003. There is significant β convergence at the national level, in the eastern and central regions, and neither convergence nor divergence in the western region. However, during 2004–2017, only the eastern region had β convergence. Finally, the conditional convergence speed is higher than the absolute convergence, and the eastern region is higher than the central. [ABSTRACT FROM AUTHOR]

This paper explores the possibility of solving the one-dimensional Burgers' equation with a tailored finite point method (TFPM) based on an explicit stencil along with utilizing the Cole Hopf transformation. The proposed TFPM procedure operates on an explicit four-point stencil where the nodal solution at the advanced temporal level is written as a linear combination of the nodal solutions at the preceding temporal level. In order to bring the essence of the local exact solutions into the numerical approximations the scalar coefficients involved in the linear sum are determined by the application of the fundamental solutions into the stencil. The efficiency of the method is demonstrated through the comparisons of TFPM solutions for various examples with the exact solutions and solutions from well-established methodologies in the literature. [ABSTRACT FROM AUTHOR]

In this paper, several Kaczmarz-type numerical methods for solving the matrix equations AX = B and XA = C are proposed, where the coefficient matrix A may be full rank or deficient rank. These methods are iterative methods without matrix multiplication. Theoretically, the convergence of these methods is proved. The numerical results show that these methods are more efficient than iterative methods involving matrix multiplication for high-dimensional matrices. [ABSTRACT FROM AUTHOR]

In the paper a new, fractional order, discrete model of a two-dimensional temperature field is addressed. The proposed model uses Grünwald-Letnikov definition of the fractional operator. Such a model has not been proposed yet. Elementary properties of the model: practical stability, accuracy and convergence are analysed. Analytical conditions of stability and convergence are proposed and they allow us to estimate the orders of the model. Theoretical considerations are validated using experimental data obtained with the use of a thermal imaging camera. Results of analysis supported by experiments point that the proposed model assures good accuracy and convergence for low order and relatively short memory length. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a time two-grid algorithm to get the numerical solution of nonlinear generalized viscous Burgers' equation, which is the first time that the two-grid method is used to solve this problem. Based on Crank–Nicolson finite difference scheme, we establish the time two-grid difference (TTGD) scheme which consists of three computational procedures to reduce the computational cost compared with the general finite difference (GFD) scheme. The cut-offf function method is applied to prove the conservation, unique solvability, the prior estimate and convergence in L 2 -norm and L ∞ -norm of the TTGD scheme on the coarse grid and fine grid, respectively. Comparing our TTGD scheme with GFD scheme in Zhang et al. (Appl Math Lett 112:106719, 2021), we provided the proof the uniqueness the solution of the nonlinear scheme, direct proof of convergence in L 2 -norm and the prior estimate both on the coarse mesh and fine mesh. The numerical results show that our TTGD scheme is more efficient than the GDF scheme in Zhang et al. (2021) in terms of the CPU time. Particularly, our method not only improves the efficiency, but also preserves the energy conservation of the original model. [ABSTRACT FROM AUTHOR]

In this paper, we study the improved block splitting (IBS) iteration method and its accelerated variant, the accelerated improved block splitting (AIBS) iteration method, for solving linear systems of equations stemming from the discretization of the complex Helmholtz equation. We conduct a comprehensive convergence analysis and derive optimal iteration parameters aimed at minimizing the spectral radius of the iteration matrix. Through numerical experiments, we validate the efficiency of both iteration methods. [ABSTRACT FROM AUTHOR]

Dynamic Pattern Synthesis (DPS) provides a new longitudinal method for evaluating the impacts of macroeconomic and public policy interventions. Situated within complexity theory and critical realism, it has evolved from the established methods of Cluster Analysis and Configurational Modelling approaches. Dynamic Pattern Synthesis identifies case convergence and divergence (using quantitative techniques), while remaining close to the qualitative uniqueness of each case. In this paper, the DPS approach is used to consider macroeconomic convergence across Sub-Saharan Africa during the Millennium Development Goals, and the possible impacts of IMF interventions in stimulating long-term macroeconomic outcomes. The findings reveal a high degree of economic instability experienced across the region and varying responses to an external shock. The importance of 'outliers' and inconsistency in country convergence are also observed. The DPS method highlights the importance of individual country experiences in relation to external shocks. When factoring in IMF interventions, the findings highlight multiple paths to a given policy outcome, rather than a single optimal economic strategy. This opens up the debate on policy issues associated with economic complexity, including how best to create an overall environment of stability that might promote convergence and reduce the instability that undermines planning and investment. [ABSTRACT FROM AUTHOR]

This paper examines the concepts and practical applications of the spanning tree protocol (STP). It also covers per-VLAN spanning tree (PVST), multiple spanning tree (MST), and rapid STP (RSTP). Moreover, practical scenarios are presented to help the reader understand the concepts and implementations of these protocols. This study analyzes protocols using seven metrics. All protocols have been evaluated using these metrics in both small and big topology scenarios to obtain the best results. In addition, all metrics are mentioned in the introduction chapter, and the way used to apply tests on the metrics is described in the methodology chapter. Based on the experiments, different STPs performance are compared, including STP, RSTP, PVST, and MST. In summary, findings show that STP is easy to use and performs well overall, but it consistently has high latency issues. RSTP is suitable for small networks and has quick convergence, but it cannot handle as much load as STP. PVST performed the best in the experiments, as it demonstrated high scalability and the ability to handle a lot of pressure, although it requires strong hardware. However, MST did not perform as well as expected, as it struggled with delay problems and high jitter. In conclusion, it is recommended to use RSTP for simple networks that require fast convergence with dependable delay and capacity, or STP for networks that require good scaling and bandwidth. PVST is an excellent option for those who can afford high-performance hardware, while MST is suitable for simple networks or those with outdated hardware. [ABSTRACT FROM AUTHOR]

This article, titled "Functions Almost Universal in the Sense of Signs with Respect to the Trigonometric System and the Walsh System," discusses the existence and structure of functions whose Fourier series are almost universal in the sense of signs with respect to the trigonometric system and the Walsh system. The paper explores various definitions and theorems related to universal functions and poses unanswered questions about the existence of certain types of universal functions. The authors provide examples and results from previous studies in the field of complex and real analysis. The article concludes with acknowledgments and funding information. [Extracted from the article]

In this paper, we extend SMSNS [Pourbagher M, Salkuyeh DK. On the solution of a class of complex symmetric linear systems. Appl Math Lett. 2018;76:14–20.] iteration method for solving a class of complex symmetric system of linear equations. We propose a successive-overrelaxation (SOR) acceleration scheme for SMSNS (SMSNSSOR), discuss the convergence conditions of it and give the optimal parameters which make the fast convergence. Numerical results demonstrate that SMSNSSOR iteration method is feasible and effective for solving complex symmetric systems, and performs better than some other usually used iteration methods. [ABSTRACT FROM AUTHOR]

The Levenberg–Marquardt (LM) method is one of the most significant methods for solving nonlinear equations as well as symmetric and asymmetric linear equations. To improve the method, this paper proposes a new adaptive LM algorithm by modifying the LM parameter, combining the trust region technique and the non-monotone technique. It is interesting that the new algorithm is constantly optimized by adaptively choosing the LM parameter. To evaluate the effectiveness of the new algorithm, we conduct tests using various examples. To extend the convergence results, we prove the convergence of the new algorithm under the Hölderian local error bound condition rather than the commonly used local error bound condition. Theoretical analysis and numerical results show that the new algorithm is stable and effective. [ABSTRACT FROM AUTHOR]

In this paper, a high-accuracy conservative implicit algorithm for computing the space fractional coupled Schrödinger–Boussinesq system is constructed. Meanwhile, the conservative nature, a priori boundedness, and solvability of the numerical solution are presented. Then, the proposed algorithm is proved to be second-order convergence in temporal and fourth-order spatial convergence using the discrete energy method. Finally, some numerical experiments validate the effectiveness of the conservative algorithm and confirm the accuracy of the theoretical results for different choices of the fractional-order α. [ABSTRACT FROM AUTHOR]

This paper considers the secure distributed control consensus problem of linear multi‐agent systems (MASs) under switching topologies, subject to intermittent sequential scaling attacks, which was compelled to scaling factor, attack frequency, duration and cooperative‐competitive networks. First, the scenario of a fixed topology is considered, and a novel control protocol combined with a logarithmic quantizer and relative state measurements of neighbouring agents is discussed. The sighed graph is utilized to characterize the communication topology determined by the information flow directions and captured by the graph Laplacian matrix. After that, sufficient conditions for effectiveness of the developed control methods in guiding the MASs to secure bipartite leader‐following consensus are constructed. Second, the scenario of switching topologies is considered, and it is derived that the secure bipartite consensus will be achieved if the designed state feedback control protocol with the scaling factor, the attack duration, attack frequency and switching signal are selected properly. At last, to prove the effectiveness of the designed controllers, a simulation example depended on the real‐word actual military is introduced. [ABSTRACT FROM AUTHOR]

The paper demonstrates two approaches to constructing monotonic difference schemes for the transfer equation in divergent form from the family of semi-Lagrangian methods: Eulerian–Lagrangian and Lagrangian–Eulerian. Within each approach, a monotonic conservative difference scheme is proposed. It is shown that within the framework of the Lagrangian–Eulerian approach, based on the use of curvilinear grids formed by the characteristics of the approximated transfer operator, it is possible to construct monotonic difference schemes of second order accuracy. [ABSTRACT FROM AUTHOR]

• A distribution dynamics approach is employed to examine the converge of TFEE across Chinese PAA level cities. • The findings show a clear convergence in TFEE. • Convergence comes more from efficiency drops in high TFEE cities than from efficiency gains in low TFEE cities. • The environmental protection polices in key cities improved energy efficiency. • Large-sized cities show better performance in energy efficiency than small- and medium-sized cities. Improving energy efficiency is considered the most direct route to reducing carbon emissions on a massive scale. To examine the long-run trend of China's energy efficiency, this paper employs a distribution dynamics approach to analyze the convergence of total-factor energy efficiency (TFEE) across 286 Chinese cities between 2002 and 2014. The result suggests the existence of convergence, which comes more from the efficiency declines in the high TFEE cities rather than the efficiency gains in the low TFEE cities. Despite the fact that a few cities have performed well in energy efficiency, the majority of cities have converged to a low-efficiency point. Further analyses show that the inefficiency was attributed to inefficient energy use in small- and medium-sized cities. Our analysis provides strong scientific support for China's ongoing energy conservation and environmental protection policies. [ABSTRACT FROM AUTHOR]

In this paper, we consider the behaviour of solutions to a class of fully history-dependent variational-hemivariational inequalities with respect to the perturbation of the data. First, the existence and uniqueness of the solution to a class of fully history-dependent variational-hemivariational inequalities is obtained by using a fixed point theorem. Second, we obtain continuous dependence result of solutions with respect to all the data of variational-hemivariational inequalities. Meanwhile, the convergence results of the solutions for the special case of abstract variational inequalities are also given. Finally, to illustrate our main results, we consider a class of viscoelastic contact problem with a long memory. By using our abstract result, we get the continuous dependence of the solutions to frictional contact problem with respect to all the data. [ABSTRACT FROM AUTHOR]

In this paper, we study the convergence analysis of the inexact Newton–Landweber iteration method (INLIM) with frozen derivative in Hilbert as well as Banach spaces. To study the convergence analysis, we incorporate the Hölder stability of the inverse mapping and Lipschitz continuity of the Fréchet derivative of the forward mapping. Moreover, we derive the convergence rates of INLIM in Hilbert as well as Banach spaces without using any extra smoothness condition. Finally, we compare our convergence rates results with that of several other frozen methods proposed in the literature to solve inverse problems. [ABSTRACT FROM AUTHOR]

Rising coal price and increasingly stringent emission policy highlight the importance of balancing economic benefit and sustainable development of coal-fired power plants. In order to make the power plant operate economically and safely, and reduce the emission of pollutants as much as possible, this paper proposed a coal blending optimization framework for coal-fired power plants. This framework constructs a set of mathematical model based on the minimization objective function, including the economy, safety and environmental protection of coal. And a multi-strategy fusion multi-objective particle swarm optimization (MSF-MOPSO) method is proposed to optimize the coal blending model. The feasibility, effectiveness and superiority of the method are theoretically verified by convergence analysis and several sets of simulation experiments. And the practical application of this framework shows that under the coal blending strategy based on different weight combinations, the algorithm proposed in this paper can produce high-quality Pareto spatial distribution. Comparing with other state-of-the-art coal blending algorithms, this method can reduce the coal purchase cost by 4.42% and ${\rm{S}}{{\rm{O}}_{\rm{2}}}$SO2 emission by 5.11% at least under the same condition. It has significant environmental protection and economic benefit. [ABSTRACT FROM AUTHOR]

In order to address the convergence issue in fuzzy power flow calculations, this paper proposes an analytical approach based on the Levenberg–Marquardt method, aiming to improve the convergence of the fuzzy Newton power flow method. Firstly, a detailed analysis is conducted on the convergence theorem and convergence behavior of the fuzzy Newton method, revealing its poor convergence when the initial values are not properly selected. The Levenberg–Marquardt method is then selected as a means to enhance the convergence of the fuzzy Newton power flow calculations, specifically to tackle the problem of initial value deviation. Since the Jacobian matrix has a significant impact on the convergence region of the power flow, this paper reconstructs the Jacobian matrix based on the Levenberg–Marquardt method, effectively enlarging the convergence region. Through validation experiments on the IEEE 118 standard nodes and simulation comparative analysis, the results confirm the method's effectiveness in resolving the problem of initial value deviation and notably enlarging the convergence region, thereby improving the convergence of power flow calculations. [ABSTRACT FROM AUTHOR]

The study on how equilibria behave when perturbations occur in the data of a game is a fundamental theme, since actions and payoffs of the players may be affected by uncertainty or trembles. In this paper, we investigate the asymptotic behavior and the variational stability of the subgame perfect Nash equilibrium (SPNE) in one-leader one-follower Stackelberg games under perturbations both of the action sets and of the payoff functions. To pursue this aim, we consider a general sequence of perturbed Stackelberg games and a set of assumptions that fit the usual types of perturbations. We study if the limit of SPNEs of the perturbed games is an SPNE of the original game and if the limit of SPNE-outcomes of perturbed games is an SPNE-outcome of the original game. We fully positively answer when the follower's best reply correspondence is single-valued. When the follower's best reply correspondence is not single-valued, the answer is positive only for the SPNE-outcomes; whereas the answer for SPNEs may be negative, even if the perturbation does not affect the sets and affects only one payoff function. However, we show that under suitable non-restrictive assumptions it is possible to obtain an SPNE starting from the limit of SPNEs of perturbed games, possibly modifying the limit at just one point. [ABSTRACT FROM AUTHOR]

In the present paper, the expected-value (EV) reformulation of a class of stochastic vector variational inequalities (SVVI) is investigated. By using the regularized gap function, the EV reformulation of SVVI is transformed into a constrained optimization problem. Then a sample average approximation (SAA) method is proposed for solving the constrained optimization problem. Under suitable assumptions, the limiting behaviors of the optimal values and optimal solutions of the approximation problem are investigated. Finally, the rates of convergence in the different senses of optimal solutions for sample average approximation problem are discussed under the error bound condition. [ABSTRACT FROM AUTHOR]

Maxwell's equations describe the propagation of electromagnetic waves and are therefore fundamental to understanding many problems encountered in the study of antennas and electromagnetics. The aim of this paper is to propose and analyse an efficient fully discrete scheme for solving three-dimensional Maxwell's equations. This is accomplished by combining Fourier pseudospectral methods in space and exact formulation in time. Fast computation is efficiently implemented in the scheme by using the matrix diagonalisation method and fast Fourier transform algorithm which are well known in scientific computations. An optimal error estimate which is not encumbered by the CFL condition is established and the resulting scheme is proved to be of spectral accuracy in space and exact in time. Furthermore, the scheme is shown to have multiple conservation laws including discrete energy, helicity, momentum, symplecticity, and divergence-free field conservations. All the theoretical results of the accuracy and conservations are numerically illustrated by two numerical tests. [ABSTRACT FROM AUTHOR]

In this paper, we present a comprehensive framework for studying Krylov subspace methods used to solve the linear system A x = f . These methods aim to achieve convergence within a specified number of iterations, denoted by m, given a particular initial estimate vector x 0 and its corresponding residual r 0 = f - A x 0 . Our analysis focuses on the minimal polynomial Φ m of degree m of A for the vector r 0 . We establish that these methods encompass Petrov-Galerkin methods and minimal seminorm methods as special cases. Additionally, we demonstrate that minimal seminorm methods satisfy implicit Petrov-Galerkin conditions. We provide a general formulation for the iterates based on generalized inverses. The choice of a specific left inverse and the method of constructing the Krylov basis are crucial distinguishing factors among different Krylov subspace methods. We describe and analyze the mathematical properties of these methods, emphasizing their dependency on two matrices. Notably, we prove that CMRH and QMR, as specific instances, also satisfy implicit Petrov-Galerkin orthogonality conditions. Furthermore, we explore techniques to improve the convergence behavior of these methods by carefully selecting vectors in their implementations. Through our investigation, we aim to deepen the understanding of Krylov subspace methods, provide insights into their convergence properties, and identify potential enhancements. We also consider some Krylov subspace methods, which are of product-type methods. In this case, the kth residual r k associated with the approximation x k of the exact solution is given by r k = Ψ k (A) Φ k (A) r 0 , and Ψ k is a polynomial of fixed or variable degree. We will examine particular choices of Ψ k involving local convergence, smoothing, fixed memory, and cost for each iteration. We will also give an enhancement of some product-type methods such as CGS. To illustrate the performance of the derived algorithms, we provide some numerical examples. [ABSTRACT FROM AUTHOR]

There are numerous phenomena in real world that their practical modeling in mathematics language deals with differential equations. Stochastic terms have significant roles in estimating behavior of these events such as machine tool vibrations, biology, traffic dynamics, neural networks and so on, it cannot be reasonable to consider an event without its past information, and it ends up with equations including time delays. The numerical solution of stochastic delay differential equations has always been of interest to researchers. In this paper, by using scaling function of the Daubechies wavelet, a collocation method is presented to solve a class of stochastic delay differential equations and it is tried to demonstrate the advantages of using this type of wavelet. Convergence of the method is provided and numerical experiments are reported to show application of the method in practice. [ABSTRACT FROM AUTHOR]

Tensor robust principal component analysis (TRPCA) aims at recovering the underlying low-rank clean tensor and residual sparse component from the observed tensor. The recovery quality heavily depends on the definition of tensor rank which has diverse construction schemes. Recently, tensor average rank has been proposed and the tensor nuclear norm has been proven to be its best convex surrogate. Many improved works based on the tensor nuclear norm have emerged rapidly. Nevertheless, there exist three common drawbacks: (1) the neglect of consideration on relativity between the distribution of large singular values and low-rank constraint; (2) the prior assumption of equal treatment for frontal slices hidden in tensor nuclear norm; (3) the missing convergence of whole iteration sequences in optimization. To address these problems together, in this paper, we propose a convex–concave TRPCA method in which the notion of convex–convex singular value separation (CCSVS) plays a dominant role in the objective. It can adjust the distribution of the first several largest singular values with low-rank controlling in a relative way and emphasize the importance of frontal slices collaboratively. Remarkably, we provide the rigorous convergence analysis of whole iteration sequences in optimization. Besides, a low-rank tensor recovery guarantee is established for the proposed CCSVS model. Extensive experiments demonstrate that the proposed CCSVS significantly outperforms state-of-the-art methods over toy data and real-world datasets, and running time per image is also the fastest. [ABSTRACT FROM AUTHOR]

The conventional approach of the local convergence analysis of an iterative method on R m , with m a natural number, depends on Taylor series expansion. This technique often requires the calculation of high-order derivatives. However, those derivatives may not be part of the proposed method(s). In this way, the method(s) can face several limitations, particularly the use of higher-order derivatives and a lack of information about a priori computable error bounds on the solution distance or uniqueness. In this paper, we address these drawbacks by conducting the local convergence analysis within the broader framework of a Banach space. We have selected an important family of high convergence order methods to demonstrate our technique as an example. However, due to its generality, our technique can be used on any other iterative method using inverses of linear operators along the same line. Our analysis not only extends in R m spaces but also provides convergence conditions based on the operators used in the method, which offer the applicability of the method in a broader area. Additionally, we introduce a novel semilocal convergence analysis not presented before in such studies. Both forms of convergence analysis depend on the concept of generalized continuity and provide a deeper understanding of convergence properties. Our methodology not only enhances the applicability of the suggested method(s) but also provides suitability for applied science problems. The computational results also support the theoretical aspects. [ABSTRACT FROM AUTHOR]

An efficient numerical method with high accuracy both in time and in space is proposed for solving d$$ d $$‐dimensional fractional diffusion equation with spectral fractional Laplacian. The main idea is discretizing the time by an s$$ s $$‐stage implicit Runge‐Kutta method and approximating the space by a spectral Galerkin method with Fourier‐like basis functions. In view of the orthogonality, the mass matrix of the spectral Galerkin method is an identity and the stiffness matrix is diagonal, which makes the proposed method is efficient for high‐dimensional problems. The proposed method is showed to be stable and convergent with at least order s+1$$ s+1 $$ in time, when the implicit Runge‐Kutta method with classical order p$$ p $$ (p≥s+1$$ p\ge s+1 $$) is algebraically stable. As another important contribution of this paper, we derive the spatial error estimate with optimal convergence order which depends on the regularity of the exact solution but not on the fractional parameter α$$ \alpha $$. This improves the previous result which depends on the fractional parameter α$$ \alpha $$. Numerical experiments verify and complement our theoretical results. [ABSTRACT FROM AUTHOR]

An artificial neural network (ANN) in information technology is a system of hardware or software modeled after the operation of neurons in the human brain. ANNs, often known as "neural networks," are a form of deep learning technology that falls under the umbrella of Artificial Intelligence (AI). Commercial applications of these technologies typically focus on optimization and solving complex signal processing and pattern recognition problems. Multiple types of optimization techniques are utilized to determine the optimal neural network for a model. These procedures help determine and define the model's accuracy, dependability, functionality, and capacity. The convergence of the neural network helps determine the number of training iterations required to generate the fewest errors. In this paper, we investigate an activation function to help reduce the training time of the analog-to-digital converter (ADC). A new Hopfield ADC model is proposed by using the proteretic activation function property. We supported our research by simulating the new ADC converter and comparing the traditional Hopfield ADC, the hysteretic ADC, and the proteretic ADC. Experiment and simulation demonstrate that the proteretic function provides a faster rate of convergence than other functions, thereby enhancing the performance of the ADC application. [ABSTRACT FROM AUTHOR]

Nonlinear Kawarada equations have been used to model solid fuel combustion processes in the oil industry. An effective way to approximate solutions of such equations is to take advantage of the finite difference configurations. Traditionally, the nonlinear term of the equation is linearized while the numerical stability of a difference scheme is investigated. This leaves certain ambiguity and uncertainty in the analysis. Based on nonuniform grids generated through a quenching-seeking moving mesh method in space and adaptation in time, this paper introduces a completely new stability analysis of the approximation without freezing the nonlinearity involved. Pointwise orders of convergence are investigated numerically. Simulation experiments are carried out to accompany the mathematical analysis to strengthen our conclusions. [ABSTRACT FROM AUTHOR]

In this paper, for solving the vertical linear complementarity problem (VLCP) effectively, a two-step new modulus-based matrix splitting (TNMMS) iteration method is introduced. Its convergence properties are discussed in depth. The efficiency of the proposed method is confirmed by some numerical experiments from the 2-D boundary problem. Numerical results show that the proposed method is superior to some existing methods, such as the two modulus-based matrix splitting (TMMS) iteration method (Numer. Algor., 2011, 57: 83–99) and the new modulus-based matrix splitting (NMMS) iteration method (Optim., 2023, 72: 2499–2516). [ABSTRACT FROM AUTHOR]

Globalization has fueled the rise of international family disputes, which raise difficult legal issues that cannot be addressed by any court or jurisdiction working alone. These challenges require a considered and coherent response on the international front, supported by the willingness of individual family judges to communicate and cooperate to identify and implement practical solutions. To meet these new challenges, this paper proposes a vision of international family justice as collaborative justice. There are three aspects or phases to the proposed endeavor: (a) the articulation of common aspirations and values; (b) continuing cooperation and communication between family courts and institutions; and (c) convergence in the substantive norms and practice of international family law. Key points for the family court community: International family disputes raise difficult issues which cannot be addressed by any court or jurisdiction working alone. Such disputes call for cross‐border collaboration between judges, family lawyers, and a team of allied family justice professionals.Such collaboration should be directed toward three goals: (a) articulating common aspirations and values for family justice; (b) deepening cooperation and communication between family courts and other family justice institutions; and (c) promoting convergence in the substantive norms and practice of international family law. [ABSTRACT FROM AUTHOR]

This paper focuses on distributed consensus optimization problems with coupled constraints over time-varying multi-agent networks, where the global objective is the finite sum of all agents' private local objective functions, and decision variables of agents are subject to coupled equality and inequality constraints and a compact convex subset. Each agent exchanges information with its neighbors and processes local data. They cooperate to agree on a consensual decision vector that is an optimal solution to the considered optimization problems. We integrate ideas behind dynamic average consensus and primal-dual methods to develop a distributed algorithm and establish its sublinear convergence rate. In numerical simulations, to illustrate the effectiveness of the proposed algorithm, we compare it with some related methods by the Neyman–Pearson classification problem. [ABSTRACT FROM AUTHOR]

This paper proposes and analyzes an uncoupled and linearized compact finite difference scheme for the generalized dissipative symmetric regularized long‐wave (GDSRLW) equations. The unique solvability and some a priori estimates of the proposed difference scheme are rigorously proved based on the mathematical induction method. To obtain the ‖·‖∞$$ {\left\Vert \cdotp \right\Vert}_{\infty } $$‐norm estimation of numerical solutions, the discrete energy method is used to prove the convergence and stability of the difference scheme. The proposed difference scheme preserves the original energy dissipation property, and the convergence of the scheme is proved to be fourth‐order in space and second‐order in time in the ‖·‖∞$$ {\left\Vert \cdotp \right\Vert}_{\infty } $$‐norm for both u$$ u $$ and ρ$$ \rho $$. Some numerical experiments are given to verify the theoretical analysis and the reliability of the proposed difference scheme. [ABSTRACT FROM AUTHOR]