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In this paper we propose an approximation method based on the classical Schoenberg-Marsden variation diminishing operator with applications to the construction of new quadrature rules. We compare the new operator with the multilevel one studied in [12] in order to characterize both of them with respect to the well known classical one. We discuss convergence properties and present numerical experiments. [ABSTRACT FROM AUTHOR]

In recent years, the utilization of fractional calculus has witnessed a notable surge across various scientific and engineering domains. This manuscript delves into the exploration of adapted iterative techniques tailored for solving nonlinear equations, capitalizing on the diverse range of derivatives available for addressing different problem contexts. We scrutinize previously developed iterative methods, enhancing their efficacy by introducing an auxiliary parameter to the root search process for nonlinear equations (NLE), alongside a fixed order of fractional derivatives. The selection of the auxiliary parameter is confined to the interval (0,1] for convenience. A thorough convergence analysis is conducted, employing a fractional power series expansion of f(x) in terms of fractional derivatives. Subsequently, a series of NLEs is solved to showcase and contrast the efficiency of our proposed methods with established iterative techniques. This refined abstract aims to succinctly elucidate the objectives and contributions of our study, providing readers with a clearer understanding of the manuscript’s scope and significance. [ABSTRACT FROM AUTHOR]

We mainly study the negligibility of haptotaxis effect on global existence, boundedness and convergence of classical solutions to a four-component chemotaxis-haptotaxis system with indirect signal production: { u t = Δ u − χ ∇ ⋅ (u ∇ v) − ξ ∇ ⋅ (u ∇ w) in Ω × (0 , ∞) , v t = Δ v − v + m in Ω × (0 , ∞) , m t = Δ m − m + u in Ω × (0 , ∞) , w t = − v w + η w (1 − w) in Ω × (0 , ∞) , in a bounded and smooth domain Ω ⊂ R n (1 ≤ n ≤ 5) with nonnegative parameters χ , ξ , η , nonnegative regular initial data (u 0 , v 0 , m 0 , w 0) and homogeneous Neumann boundary conditions. When n ≤ 3 , it is proven that solutions to the corresponding Neumann initial-boundary value problem exist globally in time for any η ≥ 0 and remain bounded for small η ≥ 0 ; when n = 4 , η = 0 and Ω is a ball centered at the origin, global boundedness of radially symmetric solutions is shown under ‖ u 0 ‖ L 1 (Ω) < (8 π) 2 χ ; and when n ∈ { 4 , 5 } , η = 0 and χ = 0 , global boundedness of solutions is shown. In either case, the global bounded w -solution component is shown to decay exponentially in W 1 , ∞ (Ω) and the global bounded (u , v , m) -solution component converges exponentially in L ∞ (Ω) to that of the corresponding indirect chemotaxis-only model for suitably small χ ≥ 0. This project incorporates a biological mechanism modeling indirect signal production in chemotaxis-haptotaxis models and our results extend the previous work of Fujie & Senba (2017) [11] on indirect chemotaxis-only system (w ≡ 0) to indirect chemotaxis-haptotaxis one, revealing that the effect of haptotaxis can be neglected even in a chemotaxis system with indirect signal production. Furthermore, our findings demonstrate that indirect chemotaxis mechanism has positive effect on boundedness and enlarges critical blow-up mass comparing to the existing result of Jin & Xiang (2021) [19] on the corresponding direct chemotaxis-haptotaxis model, providing a further understanding about this indirect mechanism in chemotaxis-haptotaxis settings. [ABSTRACT FROM AUTHOR]

In this work, a new solution for the bipolar-fuzzy initial value problem is proposed. This method is obtained by approximating the solution by piece-wise polynomial of order three. The existence and uniqueness of the solution and convergence of the method are discussed in detail. Finally, for more explanation, several numerical examples are solved. [ABSTRACT FROM AUTHOR]

In this paper, we present and analyze fully discrete finite difference schemes designed for solving the initial value problem associated with the fractional Korteweg-de Vries (KdV) equation involving the fractional Laplacian. We design the scheme by introducing the discrete fractional Laplacian operator which is consistent with the continuous operator, and possesses certain properties which are instrumental for the convergence analysis. Assuming the initial data u 0 ∈ H 1 + α (R) , where α ∈ [ 1 , 2) , our study establishes the convergence of the approximate solutions obtained by the fully discrete finite difference schemes to a classical solution of the fractional KdV equation. Theoretical results are validated through several numerical illustrations for various values of fractional exponent α . Furthermore, we demonstrate that the Crank–Nicolson finite difference scheme preserves the inherent conserved quantities along with the improved convergence rates. [ABSTRACT FROM AUTHOR]

This paper mainly studies the convergence of time-varying discrete-time Altafini model. Firstly, we convert the bipartite consensus of the Altafini model with n nodes into consensus of the DeGroot model with $ 2n $ 2 n nodes by adopting lifting approach. Secondly, based on structural balance theory and node relabelling theory, the consensus of enlarged DeGroot model can be further equivalently converted into the consensus of one simple DeGroot model with n nodes. Thirdly, by using the equivalent transformation and the ergodic coefficient theory, we change the sufficient condition from 'repeatedly jointly strongly connected' graphs to 'repeatedly jointly scrambling' graphs, and verify that the new condition also can lead to the bipartite consensus of the Altafini model. This novel criterion allows for determining the bipartite consensus of the Altafini model without the condition of 'repeatedly jointly strongly connected' graphs. Next, we provide a concise proof for the case of opinions converging to 0 with the condition of 'repeatedly jointly strongly connected' by the ergodic coefficient theory. Finally, we develop a reasonable coevolution model to illustrate the effectiveness and strong applicability of our main theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the error estimates of the Crank-Nicolson-Leapfrog (CNLF) time-stepping scheme for the two-phase Cahn-Hilliard-Navier-Stokes (CHNS) incompressible flow equations based on scalar auxiliary variable (SAV) are strictly proved. Due to the complexity of the multiple variables and the strong coupling of the equations, it is not easy to prove rigorous error estimates. Under the corresponding regularity assumption and the superconvergence of the negative norm estimates of the two quasi-projections, we prove that the error estimates for phase-field ϕ in the H 1 -semi-norm and velocity u in the H 1 -norm are able to achieve second-order convergence rates in time and the O (h r + 1) (r ≥ 1) in space. The nonlocal variables Q and r also achieve the same convergence rate. In addition, the pressure p in the L 2 -norm can only reach first-order convergence rate in time and the O (h r) (r ≥ 1) in space. At the same time, several numerical examples are given to illustrate the accuracy and effectiveness of the numerical scheme. [ABSTRACT FROM AUTHOR]

By introducing two parameters in the splittings of the matrices A and B, this paper presents a parameterized accelerated iteration (PAI) method for solving the matrix equation A X B = C . The convergence property of the PAI method and the choices of the parameters are thoroughly investigated. Additionally, based on some special splittings of the matrices A and B, several variants of the PAI method are established. Furthermore, for some certain cases, the optimal parameters can be determined, and it is demonstrated that the PAI method is more efficient than the gradient-based iteration (GBI) method (Ding et al. Appl. Math. Comput. 197, 41–50 2008). Finally, by comparing it with several existing iteration methods, the effectiveness of the PAI method is verified through four numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, efficient algorithms will be studied for solving nonlinear saddle point problems from the elliptic optimal control problems. Based on the preconditioned inexact Uzawa (PIU) algorithmic framework, an improved preconditioned inexact Uzawa (I-PIU) algorithmic framework will first be constructed for solving a class of block-structured nonlinear systems, which possess a more general form of the nonlinear saddle point systems. When the I-PIU algorithmic framework is used for solving the block-structured nonlinear systems, a detailed theoretical analysis of the global convergence properties is proposed under the case that the nonlinear operator is single-valued. Besides, a special I-PIU method is established based on a new matrix splitting technique at the first iterative step of the I-PIU algorithmic framework, and then we establish the detailed theoretical results of the convergence. Finally, some numerical experiments are given to demonstrate the efficiency of the I-PIU method. [ABSTRACT FROM AUTHOR]

Standard interpolatory subdivision schemes and their underlying interpolating refinable functions are of interest in CAGD, numerical PDEs, and approximation theory. Generalizing these notions, we introduce and study n s -step interpolatory M -subdivision schemes and their interpolating M -refinable functions with n s ∈ N ∪ { ∞ } and a dilation factor M ∈ N \ { 1 } . We completely characterize C m -convergence and smoothness of n s -step interpolatory subdivision schemes and their interpolating M -refinable functions in terms of their masks. Inspired by n s -step interpolatory stationary subdivision schemes, we further introduce the notion of r-mask quasi-stationary subdivision schemes, and then we characterize their C m -convergence and smoothness properties using only their masks. Moreover, combining n s -step interpolatory subdivision schemes with r-mask quasi-stationary subdivision schemes, we can obtain r n s -step interpolatory subdivision schemes. Examples and construction procedures of convergent n s -step interpolatory M -subdivision schemes are provided to illustrate our results with dilation factors M = 2 , 3 , 4 . In addition, for the dyadic dilation M = 2 and r = 2 , 3 , using r masks with only two-ring stencils, we provide examples of C r -convergent r-step interpolatory r-mask quasi-stationary dyadic subdivision schemes. [ABSTRACT FROM AUTHOR]

Although the multiobjective evolutionary algorithms (MOEAs) have been proved to bring promising prospects for solving multiobjective optimization problems (MOPs), the performance of the algorithm deteriorates sharply in high-dimensional objective space due to the weak selection pressure and the unregulated balance, which is caused by the increase of objective space dimension. Some current MOEAs with two-stage strategy (TS) strive to address above issues by dividing the evolutionary process into two independent stages, in which convergence and diversity are handled separately within successive generations of different stages. However, TS-MOEAs have some weaknesses, such as sensitivity to stage division, and incomplete separation of convergence and diversity. In this paper, TS/KW-MaOEA is proposed for solving many-objective optimization problems (MaOPs), which keeps TS as the central and equips a perfect control mechanism for separated balance. More specifically, TS/KW-MaOEA can automatically adjust the balance trend and provide appropriate selection pressure for MaOPs according to the Kondratiev wave (KW) search model and the objective space dimension. To verify the effectiveness of the proposed algorithm, a series of experiments are carried out against seven state-of-the-art many-objective optimization algorithms on 15 benchmark problems with up to 30 objectives. Experimental results indicate that the proposed algorithm is highly competitive against peer competitors. [ABSTRACT FROM AUTHOR]

In line with Pollitt's call to clarify convergence in public management reforms, this research explores the decisional convergence in the context of performance budgeting reforms. Applying longer, deeper and comparative approaches, this research analyzes decades of experiences and comprehensive performance budgeting written foundations between two countries under the same framework. We found convergence of reform direction and transferability of key dimensions of reform. However, the important decisional divergences lie in evolution paths, reform speeds and the uneven, and sometimes surprisingly differential specifications of measurement, integration, accountability, and culture in performance budgeting foundations between the two countries. Adaptations and aspirations as sources of divergence, theoretical implications of T-form reform, and implications for generally accepted performance principles are explored. [ABSTRACT FROM AUTHOR]

Many-objective evolutionary algorithms often struggle to strike a balance between convergence and diversity when solving many-objective optimization problems. Consequently, an adaptive boundary-based selection many-objective evolutionary algorithm with density estimation, MaOEA/ABS-DE, is proposed. Specifically, the algorithm initially utilizes prior information regarding the adaptive estimation of the shape of the Pareto front to perform coordinate transformation on the population, thus guiding the population towards the approximate boundary of the current Pareto front. Subsequently, a novel approach for estimating the neighboring density of individuals is introduced by utilizing the distribution information of the transformed population. Furthermore, adaptive boundary-based selection and shifted-based density estimation selection strategies are designed for the environmental selection process. The environmental selection process is completed through a two-step selection. In the first step, a candidate pool is formed by selecting solutions with lower neighboring density, which aims to maintain a broad search for the population in the objective space. In the second step, the SDE is introduced to compare the convergence of individuals in the candidate pool, and those with the optimal SDE values are selected. Finally, extensive comparative experiments are conducted on two benchmark test suites, MaF (Many-objective Functions) and WFG (Walking Fish Group), as well as on two practical cases. The MaOEA/ABS-DE is compared with five representative many-objective evolutionary algorithms, including 1by1EA, NSGA-III, MaOEA-CSS, RVEA, and SPEA2 + SDE. Experimental results demonstrate that the proposed algorithm outperforms or at least matches the performance of the five algorithms on 87.04%, 92.59%, 87.04%, 88.89%, and 87.04% of the test instances, respectively. [ABSTRACT FROM AUTHOR]

Deforestation poses a significant environmental challenge that demands global efforts to address, aiming to preserve forest ecosystems and promote sustainable development worldwide. This study investigates the global phenomenon of deforestation convergence from 1990 to 2020 across 149 countries, employing state transition probabilities assessed using Markov chains, dispersion indicators, and average deforestation rates. The analysis indicates a consistent decrease in dispersion indicators and average deforestation rates observed across the studied countries over three decades, coupled with high probabilities of maintaining current forest ecosystem states. These findings suggest the presence of sigma and beta convergence phenomena in the shift towards sustainable development, akin to patterns observed in economic growth. Furthermore, our research identifies the emergence of a Kuznets curve based on deforestation growth rates and dispersion indicators relative to GDP per capita since 2010. This also suggests a potential global convergence in sustainable forest-related activities. Hence, it is clear that coordinating environmental development policies among countries is crucial for achieving global ecological stability. This underscores the necessity for proactive measures to ensure worldwide forest conservation and sustainable management. [ABSTRACT FROM AUTHOR]

This paper focuses on the state estimate for a class of systems with both process noise and measurement noise under binary-valued observations, in which the Gaussian assumption on the predicted density of the state is not required. A recursive projected filter algorithm with time-varying thresholds is constructed to estimate the state under binary-valued observations. The time-varying thresholds are designed as the prediction value of the measurement, which can provide more information about the system state. The convergence property is established with some suitable stability, boundedness and observability conditions. In particular, the estimation error between state and estimate is proved to be asymptotically bounded in the mean-square sense, whose upper bound is related to the variance of process noise. Finally, the theoretical results are demonstrated via numerical examples of first-order and high-order systems. [ABSTRACT FROM AUTHOR]

Abstract Although the multiobjective evolutionary algorithms (MOEAs) have been proved to bring promising prospects for solving multiobjective optimization problems (MOPs), the performance of the algorithm deteriorates sharply in high-dimensional objective space due to the weak selection pressure and the unregulated balance, which is caused by the increase of objective space dimension. Some current MOEAs with two-stage strategy (TS) strive to address above issues by dividing the evolutionary process into two independent stages, in which convergence and diversity are handled separately within successive generations of different stages. However, TS-MOEAs have some weaknesses, such as sensitivity to stage division, and incomplete separation of convergence and diversity. In this paper, TS/KW-MaOEA is proposed for solving many-objective optimization problems (MaOPs), which keeps TS as the central and equips a perfect control mechanism for separated balance. More specifically, TS/KW-MaOEA can automatically adjust the balance trend and provide appropriate selection pressure for MaOPs according to the Kondratiev wave (KW) search model and the objective space dimension. To verify the effectiveness of the proposed algorithm, a series of experiments are carried out against seven state-of-the-art many-objective optimization algorithms on 15 benchmark problems with up to 30 objectives. Experimental results indicate that the proposed algorithm is highly competitive against peer competitors.

In the context of global systemic transformations, economic security has become a focal point in political and economic debates. The article explores how economic convergence within the European Union (EU) contributes to strengthening regional economic security. Using an innovative approach based on cluster analysis, the study reveals economic convergence trends among EU member states, highlighting the involvement of this process in promoting economic stability and security in the era of systemic changes. Our methodology involves applying clustering techniques to an extensive set of economic indicators to assess the dynamics of economic convergence between EU countries over the last two decades. The cluster analysis carried out allowed the grouping of countries based on their similar economic characteristics, thus providing a clear picture of the progress towards convergence. The results indicate a strong trend of economic alignment within the EU, with the formation of clusters suggesting a reduction in economic discrepancies. This process of convergence not only reflects greater economic cohesion, but also contributes to the macroeconomic stabilization of the region, an important aspect for economic security in the face of global volatility and uncertainties. The analysis shows that the EU is moving towards uniformity and economic convergence, with economic clusters becoming more similar over time.

All energy-related issues, including energy and energy economics, are issues that countries, policymakers, and researchers have been showing growing interest in. The demand for energy resources in the economies of all countries is growing, while access to energy resources is becoming more difficult, and the value of energy resources is increasing. It is becoming even more difficult for developing countries to access and utilize energy resources. This study examines the existence of convergence in per capita energy consumption for sub-Saharan African countries. The convergence analyses for 19 sub-Saharan African countries were conducted using annual data for the period 1971-2013. According to the Kapetanios, Shin and Snell (2003) test, per capita energy consumption converged in Angola, Benin, Mozambique, South Africa, and Tanzania. According to the nonlinear Güriş (2017) unit root test based on the Flexible Fourier Form, per capita energy consumption converges in South Africa, Zambia, and Zimbabwe. No evidence of convergence in per capita energy consumption was found in 12 sub-Saharan African countries.

Contemporary development policy concentrates predominantly on reducing noticeable economic differences in a spatial system, and an important role in this respect is played by EU Cohesion Policy. Owing to the considerable scale of financial exposure of Cohesion Policy, the assessment of effectiveness of the implemented measures and their greater reliance on evidence are of major significance. Despite numerous attempts to empirically verify the effects of EU funds spending, the problem remains unresolved, and the results of recent studies lead frequently to ambiguous conclusions.

Abstract 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.

The co-infection of HIV and COVID-19 is a pressing health concern, carrying substantial potential consequences. This study focuses on the vital task of comprehending the dynamics of HIV-COVID-19 co-infection, a fundamental step in formulating efficacious control strategies and optimizing healthcare approaches. Here, we introduce an innovative mathematical model grounded in Caputo fractional order differential equations, specifically designed to encapsulate the intricate dynamics of co-infection. This model encompasses multiple critical facets: the transmission dynamics of both HIV and COVID-19, the host’s immune responses, and the influence of treatment interventions. Our approach embraces the complexity of these factors to offer an exhaustive portrayal of co-infection dynamics. To tackle the fractional order model, we employ the Laplace-Adomian decomposition method, a potent mathematical tool for approximating solutions in fractional order differential equations. Utilizing this technique, we simulate the intricate interactions between these variables, yielding profound insights into the propagation of co-infection. Notably, we identify pivotal contributors to its advancement. In addition, we conduct a meticulous analysis of the convergence properties inherent in the series solutions acquired through the Laplace-Adomian decomposition method. This examination assures the reliability and accuracy of our mathematical methodology in approximating solutions. Our findings hold significant implications for the formulation of effective control strategies. Policymakers, healthcare professionals, and public health authorities will benefit from this research as they endeavor to curtail the proliferation and impact of HIV-COVID-19 co-infection.

Gender-related issues feature prominently on the EU’s agenda and in policies such as the Gender Equality Strategy 2020–2025 which identifies gender equality as a core principle of the EU. Within the broader convergence discourse which examines whether candidate countries are converging with the EU, prompted by Turkey’s withdrawal from the Council of Europe Istanbul Convention and the Sofagate incident, this paper conducts a gender-centric convergence analysis in the case Turkey. To this end, it uses five gender-focused indices compiled by the Varieties of Democracy (V-Dem) project. The empirical results from the convergence tests do not provide evidence supporting convergence in terms of these five gender-related indices. The findings of the present study concur with the existing relevant literature and should be viewed in the broader context of Turkey’s democratic backsliding and de-Europeanization process.

The “Kłodawa” salt mine, due to geological conditions and continuous salt extraction, is subject to a range of measurements documenting the speed of changes in the geometry of the chambers. Cyclic surveys are conducted under challenging conditions several hundred metres underground. Consequently, measurement methods used for determining the parameters of the ongoing clamping should be of high precision but also be resistant to dense dust (in fields of active mining) and strong gusts (near ventilation shafts).

The article analyzes the international experience of convergence of regional development. The features of the European development of regional policy are defined. The main stages of formation of regional policy of some European countries have been allocated. It is substantiated that the change of the conception of the Europe of nations into the conception of the Europe of regions has led to the formation of a single market, in which the regions are considered as independent players due to increasing their competitiveness. The main tasks of regional development support funds in European countries have been formed. It is determined that on the basis of support and implementation of socioeconomic reforms, introduction of innovative technologies, an increase in the competitiveness of regions and an increase in the level of employment of the population has been achieved. In developed countries, programs are being developed to improve energy infrastructure, which include the development of alternative energy, the introduction of energy-saving technologies, and the creation of new energy communications. It is determined that in regional development an important role is played by stimulation of medium and small businesses, which is implemented on the basis of support of such initiatives by providing them with simplified access to capital, activation of enterprises engaged in tourism activities. It is determined that, despite the different levels of regional development, the main vector is the creation of prerequisites for the balanced development of all territories through minimizing the impact of negative environmental factors. The main instruments for ensuring the convergence of regional development have been allocated. The policy of France in the direction of stimulating the convergence of regions, which consists in the State-controlled system of contracts for planning regional development, is substantiated. The regional development policy of the Netherlands and Austria is more focused on the development of instruments of influence. The peculiarity of the Danish system of regional development is the refusal to stimulate and support certain problem regions and the application of a market approach, which is aimed at creating the necessary conditions for their independent development. The features of the policy of regional convergence of the USA, China, Canada and Australia have been studied, which allowed to allocate the features of their policy of stimulating the development of territories. The main aspects of the formation of regional development policy in Ukraine are also examined and the priority tasks in this aspect are allocated.

For $ \mu \geq-\frac{1}{2} $, and under appropriate conditions on the sequence $ \{M_p\}_{p = 0}^{\infty} $ of weights, the elements, the (weakly, weakly*, strongly) bounded subsets, and the (weakly, weakly*, strongly) convergent sequences in the dual of a space $ \mathcal{K}_\mu $ of type Hankel-$ K\{M_p\} $ can be represented by distributional derivatives of functions and measures in terms of iterated adjoints of the differential operator $ x^{-1} D_x $ and the Bessel operator $ S_\mu = x^{-\mu-\frac{1}{2}} D_x x^{2 \mu+1} D_x x^{-\mu-\frac{1}{2}} $. In this paper, such representations are compiled, and new ones involving adjoints of suitable iterations of the Zemanian differential operator $ N_\mu = $ $ x^{\mu+\frac{1}{2}} D_x x^{-\mu-\frac{1}{2}} $ are proved. Prior to this, new descriptions of the topology of the space $ \mathcal{K}_\mu $ are given in terms of the latter iterations.

Picard's three step iteration algorithm was one of the iteration algorithms that was recently shown to be faster than some other iterative algorithms in the existing literature. The purpose of this paper was to study using this iteration algorithm for the solution of nonlinear Volterra integral equations. It was investigated that the sequences obtained from this iteration algorithm converged to the solution of nonlinear Volterra integral equations. Moreover, data dependence was obtained for nonlinear Volterra integral equations. An example was given that confirmed the applicability of the newly proven theorems.

Scientific inquiry into effective numerical methods for modelling complex physical processes has led to the investigation of fluid dynamics, mainly when non-Newtonian properties and complex heat sources are involved. This paper presents an enhanced exponential time integrator approach to dynamically simulate non-Newtonian boundary layer flow with spatially and temporally varying heat sources. We propose an explicit scheme with second-order accuracy in time, demonstrated to be stable through Fourier series analysis, for solving time-dependent partial differential equations (PDEs). Utilizing this scheme, we construct and solve dimensionless PDEs representing the flow of Williamson fluid under the influence of space- and temperature-dependent heat sources. The scheme discretizes the continuity equation of incompressible fluid and Navier–Stokes, energy, and concentration equations using the central difference in space. Our analysis illuminates how factors affect velocity, temperature, and concentration profiles. Specifically, we observe a rise in temperature profile with enhanced coefficients of space and temperature terms in the heat source. Non-Newtonian behaviours and geographical/temporal variations in heat sources are critical factors influencing overall dynamics. The novelty of our work lies in developing an explicit exponential integrator approach, offering stability and second-order accuracy, for solving time-dependent PDEs in non-Newtonian boundary layer flow with variable heat sources. Our results provide valuable quantitative insights for understanding and controlling complex fluid dynamics phenomena. By addressing these challenges, our study advances numerical techniques for modelling real-world systems with implications for various engineering and scientific applications.

In this article, a collocation technique based on quintic trigonometric B-spline (QTB-spline) functions was presented for homogeneous as well as the nonhomogeneous extended Fisher-Kolmogorov (F-K) equation. This technique was used for space integration, while the time-derivative was discretized by the usual finite difference method (FDM). To handle the nonlinear term, the process of Rubin-Graves (R-G) type linearization was employed. Three examples of the homogeneous extended F-K equation and one example of the nonhomogeneous extended F-K equation were considered for the analysis. Stability analysis and numerical convergence were also discussed. It was found that the discretized system of the extended F-K equation was unconditionally stable, and the projected technique was second order accurate in space. The consequences were portrayed graphically to verify the accuracy of the outcomes and performance of the projected technique, and a relative investigation was accomplished graphically. The figured results were found to be extremely similar to the existing results.

In addition to the negative effects generated by the pandemic period, nowadays, the digital and ecological transition exerts additional pressure on the economy and society, especially on the labor market. Digital transformation is changing people\’s live, offering new opportunities to increase productivity and to improve the well-being of the citizens. To get the desired results, the EU\’s policies and measures must put people at the center of the actions by ensuring an equitable transition. Gender equality is a key factor in promoting an inclusive and sustainable growth. The digital transformation provides new tools to increase the participation of women in the labor market and to close the gender gap. In this context, the main objective of this paper is to examine the evolution of gender disparities between Member States and to show how Europe\’s digital decade can contribute to remarkable progress towards gender convergence by improving the labor market conditions.

Abstract Skin cancer is one of the most life-threatening diseases caused by the abnormal growth of the skin cells, when exposed to ultraviolet radiation. Early detection seems to be more crucial for reducing aberrant cell proliferation because the mortality rate is rapidly rising. Although multiple researches are available based on the skin cancer detection, there still exists challenges in improving the accuracy, reducing the computational time and so on. In this research, a novel skin cancer detection is performed using a modified falcon finch deep Convolutional neural network classifier (Modified Falcon finch deep CNN) that efficiently detects the disease with higher efficiency. The usage of modified falcon finch deep CNN classifier effectively analyzed the information relevant to the skin cancer and the errors are also minimized. The inclusion of the falcon finch optimization in the deep CNN classifier is necessary for efficient parameter tuning. This tuning enhanced the robustness and boosted the convergence of the classifier that detects the skin cancer in less stipulated time. The modified falcon finch deep CNN classifier achieved accuracy, sensitivity, and specificity values of 93.59%, 92.14%, and 95.22% regarding k-fold and 96.52%, 96.69%, and 96.54% regarding training percentage, proving more effective than literary works.

This paper analyses the self-representations of Portuguese media professionals and their work practices. Utilizing data from a broader empirical study, this paper delves into the dynamics of influence among various actors within newsrooms. Based on journalists’ perceptions of the content, the methods they use to assess the quality of the news are also identified. To address these enquiries, a survey was conducted among professionals engaged in the news production process. This sample comprised 72 individuals from various sectors of newsrooms, including photographers, designers, IT professionals, social media managers, and videographers. The main results indicate that seven out of ten respondents acknowledged their reliance on colleagues in newsrooms for success. Furthermore, the data suggest that there are no significant disparities among different professionals, with personal satisfaction emerging as the primary criterion for assessing the work quality. It is notable that almost twice as many women tend to indicate the low impact of the journalist on their work compared to male respondents. Moreover, most respondents stated that there is space for hybrid professionals in newsrooms.

In this paper, we investigate the numerical solution of the Brusselator system using a meshless method. A numerical scheme is derived employing the formulas of the Generalized Finite Difference Method, and the convergence of the approximate solution to the exact solution is examined. In order to demonstrate the applicability and accuracy of the method, several examples are proposed.

Genetic relationships were examined for a total of 90 individuals of 90 species or species var. from 13 genera of Malawian cichlids based on the sequences of an amplified 991‐bp fragment of the mtDNA control region (mtDNA‐CR). In the network analysis, no exclusive clades were made by all the members of any genera in this study. However, congeneric clades were observed by genera Buccochromis, Copadichromis, Protomelas, and Sciaenochromis, whereas no congeneric clades were observed by genera Mylochromis, Nimbochromis, and Otopharynx. In non‐mbuna, an Aulonocara–Lethrinops group was divided into two groups, and the mean genetic distance of the larger group was much lower from mbuna than from other non‐mbuna. Overall mean genetic distance within a genus was generally low in mbuna, whereas it was relatively high in non‐mbuna. In the genetic tree of each genus, two or more large clades were observed, and some clades, such as those of Aulonocara hansbaenschi and Aulonocara nyassae in genus Aulonocara, Lethrinops micrentodon and Lethrinops sp. “gold harbor” in Lethrinops, and Otopharynx ovatus and Otopharynx brooksi in Otopharynx, were very deeply differentiated. Besides, a mbuna species, Pseudotropheus crabro, was extremely deeply differentiated from other members of this genus. These results suggest a widespread morphological convergence across the taxa in parallel with deep genetic differentiation in the long evolutionary story and some possibility of generation of the species of Aulonocara–Lethrinops group by hybridization of small non‐mbuna and mbuna species. Furthermore, taxonomical reexamination is necessary based on a strong support by genetic connection. [ABSTRACT FROM AUTHOR]

The impact of changes in global temperatures and precipitation on climate distribution remains unclear. Taking the annual global average temperatures and precipitation as the origin, this study determined the climate distribution with the distances of temperature and precipitation from their global averages as the X and Y axes. The results showed that during 1980–2019, the global temperature distribution converged toward the mean (convergence), while the precipitation distribution moved away from the mean (divergence). The combined effects of both led to a convergence in the global climate distribution. During 2025–2100, significant climate convergence is observed under two emission scenarios (SSP245 and SSP585). However, the climate convergence and the area of change in climate type remains insignificant only under SSP126, suggesting that the diversity of the global climate pattern can be maintained under a sustainable emission pathway (SSP126), whereas high emission pathways will lead to greater uniformity in global climate. Plain Language Summary: Global average temperatures and precipitation have increased significantly over recent decades. However, the distribution of affected areas remains unclear in comparison to the global mean. Taking annual temperature and precipitation averages as a reference point, this study measured temperature and precipitation anomalies from the global mean on the X and Y axes. The Euclidean distance of each grid cell represents its deviation (anomaly) from the global climate mean. These distances are termed the degree of deviation of temperature, precipitation, and climate from the global mean for each raster. The results reveal a discernible homogenization trend regarding the distribution of global climate. Among three distinct climate scenarios, climate diversity is effectively preserved under the low‐emission model (SSP126), whereas global climate distribution exhibits a substantial convergence toward the annual mean under the high‐emission models (SSP245 and SSP585). Key Points: Against the backdrop of global warming, the climate pattern is shifting toward convergenceTemperature is the primary driver behind climate convergence, while precipitation plays a central role in climate diversityLow‐level emissions are conducive to preserving the diversity of future global climate distribution [ABSTRACT FROM AUTHOR]

Energy transition, as a crucial aspect of the country's high-value-added economic development, involves the construction of an energy transition index system and empirical analysis using methods such as the entropy weighting method, kernel density estimation, Markov chain, Dagum Gini coefficient, σ-convergence, and β-convergence. This study measures the level of energy transition in 280 Chinese cities from 2010 to 2019 and analyzes their evolutionary trends, regional disparities, structural differences, and convergence. The findings reveal that China's energy transition generally exhibits characteristics of "improvement in development levels and reduction in absolute disparities". The disparities in energy transition primarily stem from developmental differences among the three major regions, displaying typical σ-convergence and β-convergence characteristics. This analysis contributes to understanding the real level and distribution features of China's energy transition, providing a basis for identifying focal points for enhancing energy transition in the current and future stages. [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]

Promoting the synergy of pollution and carbon reduction (PCR), as well as accelerating high-quality economic development (HQED), are the two major tasks of China's current economic development. Thus, it is crucial to achieve a deep integration between PCR and HQED. We first construct the indicator system of PCR and HQED, and use the entropy method to assign weights to the indicator system. The coupling coordination model often portrays the level of coordinated development between systems. We apply this model to measure the synergistic relationship between PCR and HQED in 108 cities of the Yangtze River Economic Belt (YREB) in China from 2006 to 2021.We further analyze its spatial-temporal characteristics, regional differences, and convergence. The results reveal that the coupling coordination degree (CCD) between PCR and HQED in the YREB increases from 0.4234 in 2006 to 0.5832 in 2021. A higher CCD reflects a better coordinated developmental relationship between the two subsystems, and the relationship between the PCR and HQED shifts from on the verge of being uncoordinated to barely coordinated. Meanwhile, the CCD of the YREB shows a trend of decreasing downstream, midstream, and upstream, with significant spatial positive autocorrelation characteristics. Moreover, the overall differences in the CCD of the YREB from 2006 to 2021 show a fluctuating trend, with larger contributions of inter-regional differences and intra-regional differences. The convergence model reflects whether there is a tendency for the coupling coordination differences to narrow. Finally, the model indicates that there is no σ convergence but exists β convergence in the CCD of the YREB. Convergence is fastest in the downstream, followed by the midstream, and slowest in the upstream. The study reveals that the CCD of the YREB is increasing and has significant positive spatial correlation characteristics. It could utilize inter-city synergies, implement integrated strategies, and promote synergies between PCR and HQED in accordance with local conditions. Our findings provide empirical evidence and policy references for effectively promoting the deep integration of PCR with HQED. [ABSTRACT FROM AUTHOR]

This article explores the existence of two main perspectives on the concept of convergence. The first view assumes convergence as an epistemological, methodological and heuristic issue resulting from the confluence of scientific disciplines and technological fields. The second view emphasizes the importance of technology management and industrial application development as strategies for analyzing the technical challenges and risks associated with convergence processes in the firm. To differentiate between the two visions, 59 specialized bibliographic works selected from a theoretical sample are analyzed. The main finding of this review is the characterization of these two perspectives that, although contradictory, are part of a common conceptualization of convergence as an umbrella notion. These findings provide relevant insights for a field of knowledge under construction: policy agendas focused on fostering technological convergence should start from the differentiation of these two analytical and conceptual levels. [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]

We develop a new Kantorovich-like convergence analysis of Newton-type methods to solve nonsingular and singular nonlinear equations in Banach spaces. The outer or generalized inverses are exchanged by a finite sum of linear operators making the implementation of these methods easier than in earlier studies. The analysis uses relaxed generalized continuity of the derivatives of operators involved required to control the derivative and on real majorizing sequences. The same approach can also be implemented on other iterative methods with inverses. The examples complement the theory by verifying the convergence conditions and demonstrating the performance of the methods. [ABSTRACT FROM AUTHOR]

Due to the considerable complexity of meshfree approximants, there still lacks a rational theoretical estimate on the frequency accuracy of lumped mass meshfree methods. In this study, a detailed theoretical analysis is presented for the lumped mass Galerkin meshfree formulation with particular reference to the frequency accuracy. The proposed accuracy analysis is quite general and is fully based upon the reproducing or consistency conditions of meshfree shape functions and their gradients. The theoretical findings reveal that there exists an important and interesting odd/even basis degree discrepancy feature for the frequency accuracy, i.e., (p + 2)th and (p + 1)th order accurate frequencies are attained by the lumped mass Galerkin meshfree formulation using even and odd degrees of basis functions, where p is the degree of basis function employed in the meshfree shape function construction. Furthermore, it is found that interpolatory meshfree shape functions are capable of not only circumventing the non-physical modes arising from the lumped mass Galerkin meshfree formulation using the standard non-interpolatory shape functions, but also elevating the frequency accuracy for meshfree structural vibration analysis. Numerical examples well replicate the theoretical frequency accuracy analysis results for lumped mass Galerkin meshfree methods. [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]

We study the existence and uniqueness of solutions to the inverse quasi-variational inequality problem. Motivated by the dynamical approach to solving optimization problems such as variational inequality, monotone inclusion, and inverse variational problems, we consider a dynamical system associated with the inverse quasi-variational inequality problem, and establish the existence and uniqueness of a solution to the proposed system. We prove that every trajectory of the proposed dynamical system converges to the unique solution of the inverse quasi-variational inequality problem and that the system is globally asymptotically stable at its equilibrium point. We also prove that if the function which governs the inverse quasi-variational inequality problem is strongly monotone and Lipschitz continuous, then the dynamical system is globally exponentially stable at its equilibrium point. We discretize the dynamical system and show that the sequence generated by the discretization of the system converges strongly to the unique solution of the inverse quasi-variational inequality problem under certain assumptions on the parameters involved. Finally, we provide numerical examples to support and illustrate our theoretical results. [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]

Patrick Chamoiseau's inter-generational fascination with the writing of Saint-John Perse (SJP) is sustained, intense, sentient, and highly generative. The focus on SJP amplifies the connective timbre of Chamoiseau's own writing, confirming the relation to the "pays natal" and to the "tout-monde" as central to both writers' poetics. Five moves constitute the high points of this particular realization of a Glissantian "poetics of Relation": the SJP intertext in Chamoiseau's childhood memoirs and fiction; the two-hander construction of SJP's poetic persona in Lettres créoles (1991); the sentimenthèque disseminated across Écrire en pays dominé (1997); and, most crucially, the "Méditations à Saint-John Perse", an oral presentation from 1995 which was eventually integrated into Chamoiseau's 2013 book-length account of his "Magnetic Liaisons" with Césaire, Saint-John Perse and Glissant. The Méditations articulate a critique of criticism in favor of a demiurgic poetics of self-reflexive magnification and esteem even as they perform a dance of ethno-social and intergenerational convergence. [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]

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]

We introduce an alternative closed-form objective function α-ELBO for improved parameter estimation in the Gaussian process ( G P ) based on the Rényi α-divergence. We use a decreasing temperature parameter α to iteratively deform the objective function during optimization. Ultimately, our objective function converges to the exact log-marginal likelihood function of G P. At early optimization stages, α-ELBO can be viewed as a regularizer that smoothes some unwanted critical points. At late stages, α-ELBO recovers the exact log-marginal likelihood function that guides the optimizer to solutions that best explain the observed data. Theoretically, we derive an upper bound of the Rényi divergence under the proposed objective and derive convergence rates for a class of smooth and non-smooth kernels. Case studies on a wide range of real-life engineering applications demonstrate that our proposed objective is a practical alternative that offers improved prediction performance over several state-of-the-art inference techniques. [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]

The co-infection of HIV and COVID-19 is a pressing health concern, carrying substantial potential consequences. This study focuses on the vital task of comprehending the dynamics of HIV-COVID-19 coinfection, a fundamental step in formulating efficacious control strategies and optimizing healthcare approaches. Here, we introduce an innovative mathematical model grounded in Caputo fractional order differential equations, specifically designed to encapsulate the intricate dynamics of co-infection. This model encompasses multiple critical facets: the transmission dynamics of both HIV and COVID-19, the host’s immune responses, and the influence of treatment interventions. Our approach embraces the complexity of these factors to offer an exhaustive portrayal of co-infection dynamics. To tackle the fractional order model, we employ the Laplace-Adomian decomposition method, a potent mathematical tool for approximating solutions in fractional order differential equations. Utilizing this technique, we simulate the intricate interactions between these variables, yielding profound insights into the propagation of co-infection. Notably, we identify pivotal contributors to its advancement. In addition, we conduct a meticulous analysis of the convergence properties inherent in the series solutions acquired through the Laplace-Adomian decomposition method. This examination assures the reliability and accuracy of our mathematical methodology in approximating solutions. Our findings hold significant implications for the formulation of effective control strategies. Policymakers, healthcare professionals, and public health authorities will benefit from this research as they endeavor to curtail the proliferation and impact of HIV-COVID-19 co-infection. [ABSTRACT FROM AUTHOR]