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This paper explores an inverse problem pertaining to the determination of a source function in non‐divergence parabolic equations, where the solution is known at a discrete set of points. Being different from other ordinary inverse source problems, which are often dependent on only one variable, the unknown coefficient in this paper not only depends on the space variable x$$ x $$ but also depends on the time t$$ t $$. On the basis of the optimal control framework, the existence of the optimal solution of the control function is proved. The necessary conditions to be satisfied by the optimal solution are given. The convergence of the optimal solution when the mesh parameters tend to zero is obtained. The conjugate gradient method is applied to the inverse problem and some numerical results are presented for various typical test examples. [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]

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 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]

In this paper, we first develop the modified gradient‐based iterative (MGI) method for the complex conjugate and transpose matrix equations A1XB1+A2X‾B2+A3XTB3+A4XHB4=E$$ {A}_1X{B}_1+{A}_2\overline{X}{B}_2+{A}_3{X}^T{B}_3+{A}_4{X}^H{B}_4=E $$. By adopting the updated technique, we can make full use of the latest information to compute the next result, which leads to a faster convergence rate. In theory, we apply the real representation of a complex matrix and the vec‐operator to prove the convergence properties. Furthermore, we extend the MGI algorithm to solve the generalized complex conjugate and transpose matrix equations. Then, the necessary and sufficient conditions for convergence of the MGI algorithm are presented. Lastly, three numerical examples are introduced to testify the efficiency of our methods. [ABSTRACT FROM AUTHOR]

The electrification of vehicles has emerged as a pivotal technique for addressing environmental concerns and reducing reliance on conventional fuel sources. Conversely, the best way to incorporate renewable energy into electric vehicles (EVs) is still a challenging task, particularly in enhancing the performance of EVs through efficient energy management. The transition to EVs has gained momentum as part of global efforts to mitigate environmental impacts and reduce dependence on fossil fuels. This paper proposes a hybrid method for enhancing EV performance through buck‐boost converters with renewable energy integration. The proposed technique is the joined execution of Flying Foxes Optimization (FFO) and Viscoelastic Constitutive Artificial Neural Networks (vCANNs) techniques. The proposed method's goal is to enhance the energy efficiency, minimize EV charging cost, and mitigating environmental impacts. The renewable energy sources: solar panels, fuel cells, and wind turbines, are integrated into the EV power system through buck‐boost converters. The buck‐boost converter's control signal is optimized through the FFO method. vCANNs are used to predict these control parameters. The proposed strategy is executed in MATLAB software and is compared with existing strategies. In comparison with other current approaches like particle swarm optimization, heap based optimizer, and wild horse optimize, the proposed method achieves a high efficiency of 99% and low cost of 0.05 €/KWh. [ABSTRACT FROM AUTHOR]

To improve the convergence of the gradient iterative (GI) algorithm and the Jacobi‐gradient iterative (JGI) algorithm [Bayoumi, Appl Math Inf Sci, 2021], a shift‐splitting Jacobi‐gradient iterative (SSJGI) algorithm for solving the matrix equation A풱−풱‾B=C is presented in this paper, which is based on the splitting of the coefficient matrices. The proposed algorithm converges to the exact solution for any initial value with some conditions. To demonstrate the effectiveness of the SSJGI algorithm and to compare it to the GI algorithm and the JGI algorithm [Bayoumi, Appl Math Inf Sci, 2021], numerical examples are provided. [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]

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]

The present paper is dedicated to the structural stability of the linear model of a mixture of two porous solids. It is shown that the variation of the characteristic coefficients that describe the coupling of the various mechanical effects involved in the model in concern does not destroy its structure. This means that any small variation of these coefficients leads to small variations in the corresponding solutions of the associated initial boundary value problems. For this purpose, more mathematical estimates are presented describing precisely the continuous dependence of the solutions with respect to all external given data of the initial boundary value problem, as well as with respect to appropriate measures of the set of coupling parameters. This allows the conclusion that the model of the mixture of porous materials is consistent. In particular, it is believed that the estimates obtained in terms of structural stability are particularly meaningful with regard to the materials used in building contexts and the related decay phenomena. [ABSTRACT FROM AUTHOR]

The aim of the paper is to study a new class of coupled variational–hemivariational inequalities with unilateral constraints and history‐dependent operators. First, by employing a fixed‐point theorem for history‐dependent operators combined with surjectivity theorem, we establish the existence and uniqueness of solution for coupled system. Second, we obtain a convergence result, namely, related penalized problems of solutions converge to the solution to the original system. Finally, we conclude with a new contact problem of the body pressure of two elastic materials. [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]

Numerical methods have been extensively applied to fracture mechanics, while they cannot simulate the problems without the mechanical models or constitutive equations. Artificial neural networks (ANNs) can be utilized to predict complex fracture problems, but these approaches require large amounts of data for the training. Therefore, in this paper, to combine the advantages of the numerical methods and the ANNs, an improved back propagation neural network (BPNN) is proposed by introducing the enrichment used in the numerical methods into the activation function utilized in the neural networks. The enrichment is able to represent the crack tip field which can accelerate the convergence. At the field near the crack tip, the improved BP solution can converge to the analytical solutions which validate the high accuracy of the proposed method. Without sufficient data, especially the data are missing in the near field of the crack tip, the improved BP method can also achieve high accuracy and convergence, while the conventional BP method may not converge to the predetermined error bound. Numerical simulations of the quasi‐static and fatigue crack problems demonstrate that the improved BP method can accurately predict the crack propagation and its growth rate with relatively little data. [ABSTRACT FROM AUTHOR]

In this paper, we consider an optimal control and stabilization problem of linear mean-field (MF) system, where the quadratic cost functional is allowed to be indefinite. Inspired by the equivalent cost functional method, we introduce a subset, which helps us to investigate the convergence property of generalized differential Riccati equations arising in indefinite mean-field linear quadratic (MF-LQ) problems with finite horizon. A coupled generalized algebraic Riccati equation (GARE) is thus obtained. More importantly, the solution pair of corresponding GARE can be decomposed into a solution pair of a coupled standard algebraic Riccati equation (SARE) and a matrix pair in the subset we introduce. Thus, an equivalent relationship is established between GARE and SARE. With this equivalence, we derive necessary and sufficient conditions to stabilize linear MF-system with indefinite weighting matrices in mean-square sense. [ABSTRACT FROM AUTHOR]

Income mobility is a key issue for understanding the process of economic growth and distributional change. Some economists have used the concept of "pro‐poor growth" to examine, with individual‐level panel data, whether the poor benefit more than the rich from economic growth by tracking the extent of income mobility among different population subgroups. There is also literature in macroeconomics on the measurement of convergence. This paper introduces population‐weighted relative and absolute indices of mobility, convergence, and pro‐poor growth; it also distinguishes between anonymous and nonanonymous approaches to these issues. The empirical analysis is based on Chinese panel data for the period 2010–2018. In both absolute and relative terms, income growth in China was greater for individuals with an initially lower income but only for lower income deciles in relative terms. There was also an overall increase in individual welfare from anonymous and nonanonymous perspectives, which was higher among younger individuals. The welfare of the poor did not increase more than that of the nonpoor. These results shed light on the evolution of income distribution in China during the past decade's rapid economic growth. [ABSTRACT FROM AUTHOR]

When the sparse regularizer is convex and its proximal operator has a closed‐form, first‐order iterative algorithms based on proximal operators can effectively solve the sparse optimization problems. Recently, plug‐and‐play (PnP) algorithms have achieved significant success by incorporating advanced denoisers to replace the proximal operators in iterative algorithms. However, convex sparse regularizers such as the ℓ1$$ {\ell}_1 $$‐norm tend to underestimate the large values within the sparse solutions. In contrast, the convex non‐convex (CNC) sparse regularization enables the non‐convex regularizer while preserving the convexity of the objective function. In this paper, we propose several PnP algorithms for solving the CNC sparse regularization model and discuss their convergence properties. Specifically, we first derive the proximal operator for CNC sparse regularization in iterative form and subsequently integrate it with several first‐order algorithms to yield different PnP algorithms. Then, based on the monotone operator theory, we prove that the proposed PnP algorithms are convergent under the condition that the data‐fidelity term is strongly convex and the residuals of the denoisers are contractive. We also emphasized the significance of strong convexity in the data‐fidelity term for the CNC sparse regularization model. Additionally, we demonstrate the superiority of the proposed PnP algorithms through extensive image restoration tasks. [ABSTRACT FROM AUTHOR]

As a universal approximator, the first order Takagi–Sugeno fuzzy system possesses the capability to approximate widespread nonlinear systems through a group of IF THEN fuzzy rules. Although group lasso regularization has the advantage of inducing group sparsity and handling variable selection issues, it can lead to numerical oscillations and theoretical challenges in calculating the gradient at the origin when employed directly during training. The paper addresses the aforementioned obstacle by invoking a smoothing function to approximate group lasso regularization. On this basis, a gradient‐based neuro fuzzy learning algorithm with smoothing group lasso regularization for the first order Takagi–Sugeno fuzzy system is proposed. The convergence of the proposed algorithm is rigorously proved under gentle conditions. In addition, experimental outcomes acquired on two approximations and two classification simulations demonstrate that the proposed algorithm outperforms the algorithm with original group lasso regularization and L2 regularization in terms of error, pruned neurons, and accuracy. This is particularly evident in significant advancements in pruned neurons due to group sparsity. In comparison to the algorithm with L2 regularization, the proposed algorithm exhibits improvements of 6.3, 5.3, and 142.6 in pruned neurons during sin(πx)$(\pi x)$ function, Gabor function, and Sonar benchmark dataset simulations, respectively. [ABSTRACT FROM AUTHOR]

This paper analyzes environmental convergence and its determinants. We construct our analysis in a bilateral setting and hypothesize that, through foreign direct investment (FDI), one or more investor countries could impact the environmental performance of their hosts, leading thus to a possible environmental convergence between home and host economies. To do this, we construct an original database on bilateral FDI encompassing 128 countries for the period 2000-2012. Our results suggest that, in general, FDI does not directly impact environmental convergence, except for the case of FDI originating from major investor countries. Under specific conditions, FDI can be expected to influence environmental convergence along with other variables such as GDP per capita, industrial development, geographical proximity, or cultural and historical ties. Overall, these effects may vary depending on the type of partnership considered (North-North, North-South, South-North, and South-South). [ABSTRACT FROM AUTHOR]

The U.K. insurance industry has a dominant international presence, suggesting strong competitiveness and performance. Yet, its efficiency and productivity has rarely being investigated. The purpose of this paper is to provide an overview of insurers' performance in the U.K. insurance market from 1996 to 2017, using stochastic frontier analysis to measure efficiency scores and productivity at the firm level. Results show the U.K. insurance industry could improve by about 40% in terms of cost efficiency and by 70% in terms of profit efficiency. In addition, our model reveals a higher cost efficiency score compared to profit efficiency, implying that there are higher inefficiencies on the income side of the insurance industry as measured by our profit function. In terms of total factor productivity (TFP) growth, we report a steady decline over time while on average is negative. By decomposing TFP growth into its underlying components, we reveal that the reported negative trend in TFP growth over time has mainly been driven by the enhanced competition that resulted in a drop in markup, while the scale and cost efficiency has also driven TFP growth down. However, from a positive point of view, we report evidence of both β‐convergence and σ‐convergence in cost and profit efficiency. [ABSTRACT FROM AUTHOR]

Populations may adapt to similar environments via parallel or non‐parallel genetic changes, but the frequency of these alternative mechanisms and underlying contributing factors are still poorly understood outside model systems. We used QTL mapping to investigate the genetic basis of highly divergent craniofacial traits between the scale‐eater (Cyprinodon desquamator) and molluscivore (C. brontotheroides) pupfish adapting to two different hypersaline lake environments on San Salvador Island, Bahamas. We lab‐reared F2 scale‐eater x molluscivore intercrosses from two different lake populations, estimated linkage maps, scanned for significant QTL for 29 skeletal and craniofacial traits, female mate preference, and sex. We compared the location of QTL between lakes to quantify parallel and non‐parallel genetic changes. We detected significant QTL for six craniofacial traits in at least one lake. However, nearly all shared QTL loci were associated with a different craniofacial trait within each lake. Therefore, our estimate of parallel evolution of craniofacial genetic architecture could range from one out of six identical trait QTL (low parallelism) to five out of six integrated trait QTL (high parallelism). We suggest that pleiotropy and trait integration can affect estimates of parallel evolution, particularly within rapid radiations. We also observed increased adaptive introgression in shared QTL regions, suggesting that gene flow contributed to parallel evolution. Overall, our results suggest that the same genomic regions may contribute to parallel adaptation across integrated suites of craniofacial traits, rather than specific traits, and highlight the need for a more expansive definition of parallel evolution. [ABSTRACT FROM AUTHOR]