Radius Of Convergence Research Articles (Page 1)

Enhancing the efficiency of value conversion of forest ecological products is a crucial strategy to implement the “Two Mountains” concept and foster Chinese-style modernization, promoting harmonious coexistence between humanity and nature. Using the southern collective forest region as the study sample, this paper employs the value equivalent method and the super-EBM model of unexpected outputs. The value conversion efficiency of forest ecological products in this region was calculated from 2012 to 2021, with 2011 as the base year. Additionally, Kernel density estimation, the Dagum Gini coefficient, and other analytical methods were utilized to examine the regional disparities, dynamic evolution, and convergence of value conversion efficiency in southern collective forest regions. Findings indicate that from 2012 to 2021, the value conversion efficiency demonstrated an overall upward trend with periodic fluctuations. Coastal provinces such as Fujian and Guangxi exhibited higher conversion efficiency, while inland provinces like Jiangxi and Guizhou lagged. Kernel density estimation revealed a gradual expansion of highly efficient areas and an overall improvement in efficiency levels. Convergence tests (σ-convergence and β-convergence) confirmed significant regional convergence in the value conversion efficiency of forest ecological products. Promoting regional coordination and cooperation is essential to developing a complementary advantage model, advancing the marketization of forest ecological products, and establishing differentiated ecological compensation standards. These measures aim to enhance overall transformation efficiency and ensure balanced regional development.

Solving nonlinear systems of equations is a central challenge in scientific computing, impacting a wide range of fields such as engineering, physics, and applied mathematics.Although the Newton-Raphson method is popular for its quadratic convergence near solutions, it faces notable difficulties, including reliance on the initial guess, potential failure with ill-conditioned Jacobians, and complications when multiple or closely situated roots are present. In this study, we investigate the creation of new iterative algorithms aimed at overcoming these obstacles by promoting better global convergence and improving numerical stability. The proposed approaches utilize adaptive step-size management, quasi-Newton techniques, and hybrid strategies that integrate trust-region and homotopy concepts. Results from numerical tests on standard benchmark problems show that these algorithms provide enhanced robustness for a wide array of nonlinear systems. Compared to Newton-Raphson, the new methods expand the convergence domain and frequently deliver equal or better accuracy and computational speed. This work paves the way for developing more trustworthy solvers for complex nonlinear systems in contemporary computational practice.

The performance of iterative schemes used to solve nonlinear operator equations is strongly influenced by the initial guess. Therefore, it is essential to accurately determine convergence radii and develop theoretical strategies to broaden the region where convergence is guaranteed in order to enhance the reliability and efficiency of these methods. A crucial tool for this purpose is local convergence analysis, which investigates behavior near the true solution to establish convergence criteria. This work is dedicated to extending the convergence region of a parameter-based iteration scheme of the fifth-order. We carry out a comprehensive local convergence study within the framework of Banach spaces and derive precise formulas for the convergence radius, error estimates, and convergence zones associated with the method. A notable advantage of our approach is that it relies solely on the first derivative and avoids the need for additional conditions, making it easier to apply and significantly expanding the convergence region relative to earlier approaches. The theoretical contributions are further validated through a series of numerical experiments applied to diverse classes of nonlinear equations. Furthermore, the examination of the basins of attraction and their symmetry provides a deeper understanding of the method’s dynamic characteristics, robustness, and effectiveness in tackling complex-valued polynomial equations.

Let P,Q:Rn→R be two polynomials. This paper studies the existence of the following Łojasiewicz inequality at infinity: |Q(x)|θ≥c|P(x)| for ∥x∥≫1, where c and θ are positive constants. We provide a condition under which the Łojasiewicz inequality holds, and the exponent is computed explicitly in terms of the Newton polyhedra of the two polynomials. On the way, we give some criteria for the convergence of some integrals of rational functions, and describe the domain of convergence of multidimensional Dirichlet series associated with polynomials in terms of Newton polyhedra of polynomials defining the series.

Data-driven co-design of event-triggered schemes and switching control for discrete-time switched affine systems with unknown disturbances.

Purpose The suspension of microorganisms in nanomaterials presents excellent thermal stability and impressive properties. The current analysis aims to investigate the significance of bioconvection associated with the time-dependent flow of a micropolar nanofluid governed by an oscillatory sheet. Design/methodology/approach The consequences of the porous medium and magnetohydrodynamics are examined. The heat transfer modeling is updated by using the Cattaneo-Christov hypothesis. The flow is further driven by external thermal sources and radiative impact. Under the assumed theoretical assumptions, the flow model is developed, further simplified into dimensionless equations. For computational simulations, the homotopy analysis scheme is implemented. After ensuring the convergence region, a graphical analysis is performed. The problem is further visualized in a 3D pattern. The proposed results may find significant applications in nano-biofuels and heat management systems. Findings After ensuring the convergence region, a graphical analysis is performed. The problem is further visualized in a 3D pattern. The proposed results may find significant applications in nano-biofuels and heat management systems. Originality/value The model is based on the amplification of the revised flux theories, namely, the Cattaneo-Christov model. Insight into the radiated phenomenon and the external thermal (heat) source is observed. The solution of the governing equations was treated with the homotopy analysis method. A physical analysis and 3D illustration of the problem are presented.

Abstract This paper constructs the first long‐run estimates of Irish regional gross domestic product (GDP) over the twentieth century and traces the relative economic performance of Ireland's regions since independence. Using an array of data sources available at a county level, output in agriculture, industry, and services in benchmark census years is estimated. Applying a variety of alternative measures, we find a reduction in regional inequality over the period that resembles the broader European pattern. Regional convergence over the period 1926–91 was driven by both within‐sector convergence in productivity and structural change. Our paper helps us understand the regional dimensions of Irish economic development from the birth of a newly independent state up to the eve of Ireland's growth ‘miracle’ in the 1990s, when the first official efforts were initiated to construct these figures. Finally, we connect our regional estimates to the first official figures to study the evolution of Irish regional development up to 2021.

Agricultural green development cannot be achieved without effective financial support. Based on panel data from 30 provinces in China from 2014 to 2023, this paper uses a coupling coordination model to measure and analyse the degree of coordination between digital inclusive finance and green finance; this further constructs a comprehensive evaluation system for agricultural green development, and on this basis uses a fixed-effect model and a threshold regression model to systematically examine the impact of the coordination between the two on agricultural green development. The findings are as follows: first, the coordination between digital inclusive finance and green finance shows an upward trend over time, shifting spatially from a high trend in the east to a low trend in the west to regional convergence; second, the coordination between the two has a substantial and favourable impact on green agricultural development, which is a conclusion that persists after robustness tests; third, the effect is heterogeneous, with more pronounced promotion effects in non-grain-producing regions, regions with high agricultural technology levels, and low levels of financial exclusion; fourth, the effect exhibits nonlinear characteristics, with coordination and agricultural industrial agglomeration each forming a single-threshold effect. This research lays down a foundational framework for financial coordination in supporting agricultural green development. It suggests promoting a dual-wheel coordination mechanism to effectively empower agricultural green development by strengthening technological empowerment, regional linkage, and designing differentiated policies.

Abstract. With the coming launch of the Climate Absolute Radiance and Refractivity Earth Observatory (CLARREO) Pathfinder (CPF) comes an opportunity to develop a new retrieval for warm, non-precipitating clouds from spectral reflectance measurements. With continuous coverage across the shortwave spectrum and a factor of 5 to 10 lower radiometric uncertainty than the Moderate Resolution Imaging Spectroradiometer (MODIS), CPF facilitates the retrieval of a vertical profile of droplet size, providing insight into the internal structure of a cloud. Measurements from MODIS coincident with in situ observations provide the foundation for developing an optimal estimation technique. Solution constraints were required to ensure consistency with forward model assumptions. The limited unique information in the MODIS bands used in this analysis resulted in a non-unique solution, with many droplet profiles leading to convergence. Droplet size at cloud bottom is difficult to constrain because visible and shortwave infrared reflectances have an average penetration depth near cloud top. The region of convergence within the solution space decreased along the cloud bottom radius dimension by 1 µm when increasing the number of wavelengths used in the retrieval from 7 to 35 and by 3.75 µm when reducing the total uncertainty from 3 % to 1 %. The enhanced accuracy and, to a lesser degree, the enhanced spectral sampling provided by CPF measurements are essential to extracting vertically resolved droplet size information from moderately thick, warm clouds.

This article analyses the relation between spatial restructuring and spatial development, in the context of progressing regionalization of concept relations 2017-2022 in Morocco. First, a coupling coordination degree (CCD) model develops two new compound indexes, or a regional development index (RDI) and a spatial restructuring index (SRI), whereby structural maximum rate of identity entropy weights are selected. Local spatial structure and spatial type of marriage, using the index of dispersion Clark and Evans (1954) in determining spatial development impact on the spatial type of marriage. Results reveal strong heterogeneity amongst the twelve regions or Morocco, again implying that spatial structure is an important factor in determining intensity coordination. Development-structure consistency is higher in areas that are more aggregated and lower in dispersed areas with structural bottlenecks as space becomes congested. The study contributes to the literature by extending the application of CCD framework in Africa, integrating spatial structure analysis, and developing policy-relevant implications regarding territorial governance and regional convergence alternatives.

A rational layout of circulation node cities and the construction of an efficient and coordinated urban circulation network are crucial for promoting green urban development. Investigating the effect of urban circulation network development on urban carbon emission performance and its underlying mechanisms can offer a theoretical foundation and empirical evidence for the evaluation and refinement of policies in circulation node cities. Based on the quasi-natural experiment of circulation node cities, this study utilizes a difference-in-difference (DID) model to evaluate the influence of urban circulation network construction on urban carbon emission performance and examine its operative mechanisms. The findings reveal that the development of urban circulation networks markedly improves urban carbon emission performance, a result demonstrated to be robust. The enhancement effect of such development is more substantial in central and western regions, non-resource-based cities, as well as small and medium-sized cities. Analyses of underlying mechanisms indicate that the construction of urban circulation networks primarily operates through green technology innovation to indirectly elevate urban carbon emission efficiency. Extended analysis confirms the objective existence of regional convergence in carbon emission performance. Although the development of urban circulation networks facilitates the advancement of carbon emission performance, its influence on accelerating regional convergence remains limited. The research conclusion helps to expand the understanding of the modern circulation system construction from a green and low-carbon perspective and provides policy reference value for achieving high-quality development.

Abstract A vorticity river is defined as a near-ground vertical vorticity band often extending from the north side of a supercell toward an incipient or mature tornado. Three successive vorticity rivers in a numerical simulation of a supercell tornado are found after the tornado has fully formed. Air parcels that enter the vorticity rivers first ascend in the inflow region of the supercell south of the forward-flank convergence boundary (FFCB) while moving northwestward. Upon approaching the downdraft region north of the FFCB, the air parcels start to descend and turn westward and then southward toward the tornadic region, converting the crosswise vorticity that the parcels initially carry into the streamwise vorticity. The horizontal streamwise vorticity of the parcels is enhanced by horizontal stretching when the flow accelerates toward the tornadic region. Near-ground positive vertical vorticity develops via upward tilting of horizontal streamwise vorticity as the air parcels descend along a gradually decreasing slope. As the parcels enter the region of strong surface convergence generated by downdrafts of varying intensity on both sides of the vorticity river, their vertical vorticity is further intensified by upward tilting of horizontal vorticity and vertical stretching. The calculated influxes of horizontal and vertical vorticity into the tornadic region show that the contribution to the tornado vorticity by the vorticity rivers is minimal, given their narrow width and shallow depth. Backward trajectory analysis shows that only about 7% of total parcels entering the tornado originate from vorticity rivers, suggesting that their direct contribution to tornado intensification or maintenance is insignificant. Significance Statement A vorticity river is a narrow band of vertical vorticity extending from the north side of simulated supercell storms southward toward an intensifying or mature tornado. The source of vorticity in the vorticity river and its contribution to tornado formation and maintenance are examined based on a tornado simulation. Trajectory analyses show that the vertical vorticity in vorticity rivers is generated first by upward tilting of horizontal vorticity and then intensified rapidly by near-ground vertical stretching due to along-river convergence. Budget calculations of vorticity into the tornadic region show that the contribution of the narrow and shallow vorticity rivers to the intensification and maintenance of the tornado is limited. Only a very small fraction of air parcels entering the tornado passes through the rivers. The primary source of both vertical and horizontal vorticity inflow into the tornadic region comes from the occlusion zone on the northeast side of the tornado.

This paper presents a multifidelity surrogate modeling architecture to estimate the aerodynamics of complete rotor systems. A novel adaptive sampling method, rCorSpa, is designed to achieve global aerodynamics estimation and avoid failure design space. It introduces the concepts of a safe ball domain and a compound shell region, which guide sampling near complex failure boundaries. These regions are sampled independently to balance global exploration and failure avoidance. The core design space for rotor aerodynamics is uncovered, which enables the complex domain to be reconstructed and simplified. As this core design space inherently represents a lower-dimensional subspace, the cost of failure estimation is significantly reduced via space projection. Building on this foundation, a sphere contraction technique and the concept of a convergent radius are introduced to further minimize the number of redundant sampling iterations. Overall, the new sampling method achieves substantial computational savings by both simplifying core formulations and reducing the total number of required sampling steps. The proposed surrogate aerodynamic model is applied to a multicopter rotor system modeling scenario. Compared with a conventional hierarchical kriging model, the rCorSpa-enhanced surrogate model achieves a 95% improvement in global prediction accuracy, reducing the error to 3.5% after convergence.

ABSTRACT This study examines bilingual practices and language shift (LS) in Tianzhu Tibetan Autonomous County, a multiethnic convergence region in northwestern China. Using questionnaires (n = 395), semi-structured interviews, and supplementary ethnographic observations, it investigates residents’ language use, proficiency, and attitudes toward Tibetan, Standard Mandarin, and the Tianzhu Chinese dialect. Results reveal a two-stage LS trajectory: first from Tibetan to the Tianzhu dialect, and subsequently from the Tianzhu dialect to Mandarin. Tibetan has largely retreated from everyday communication, surviving mainly in religious domains, while the Tianzhu dialect itself is eroding among younger generations. Urban–rural contrasts highlight spatial variation in LS, with Mandarin dominating more rapidly in semi-urban centres than in rural settlements. Positive attitudes toward Mandarin, reinforced by educational and economic opportunities and national policies, further accelerate this transition. While Tibetan retains cultural and symbolic value, its communicative role is diminishing. By situating Tianzhu within broader debates on language contact, multilingual sustainability, and minority language shift, this study shows how ethnic integration and state policies reshape bilingualism in multiethnic regions and provides insights for inclusive language planning.

Schizophrenia is a severe mental illness with high heritability, but its underlying mechanisms are poorly understood. We meta-analyzed large-scale brain transcriptomic data from mice harboring individual loss-of-function mutations in seven schizophrenia risk genes (Akap11, Dagla, Gria3, Grin2a, Sp4, Srrm2, Zmym2). While all studied brain regions were affected, the striatum and the thalamus emerged as key brain regions of convergence. Striatum showed downregulation of synapse- and oxidative phosphorylation-related gene sets in all models. In the thalamus, mutants separated into two groups based on transcriptomic phenotype: synapse-related gene sets were upregulated in mutants with only schizophrenia and bipolar association, and were downregulated in mutants that are associated with developmental delay/intellectual disability in addition to schizophrenia. Overall, our meta-analysis reveals convergence and divergence in brain transcriptomic phenotype in these schizophrenia genetic models, supports the involvement of striatal disturbance and synapse dysfunction in schizophrenia, and points to a key role of the thalamus.

The problem of optimal design of timber frame structures is addressed. A computational algorithm has been developed and tested for selecting the cross-sectional areas of structural elements to minimize material volume while satisfying code requirements for strength and stiffness. The mathematical model is formalized as a nonlinear programming problem and solved using a method based on a modified Lagrange function, which ensures a wide convergence region. The algorithm was implemented in the MathCAD software environment, ensuring clarity and making it accessible to design engineers. To verify the optimization results, validation calculations were performed using the Lira-Soft software (CAD system). The research results demonstrated the robust convergence of the developed algorithm and the high accuracy of the obtained solutions. A demonstration of its practical applicability is provided using an example of an actual frame structure.

The local convergence analysis of the m+1-step Newton-Jarratt composite scheme with order 2m+1 has been shown previously. But the convergence order 2m+1 is obtained using Taylor series and assumptions on the existence of at least the fifth derivative of the mapping involved, which is not present in the method. These assumptions limit the applicability of the method. A priori error estimates or the radius of convergence or uniqueness of the solution results have not been given either. These drawbacks are addressed in this paper. In particular, the convergence is based only on the operators on the method, which are the operator and its first derivative. Moreover, the radius of convergence is established, a priori estimates and the isolation of the solution is discussed using generalized continuity assumptions on the derivative. Furthermore, the more challenging semi-local convergence analysis, not previously studied, is presented using majorizing sequences. The convergence for both analyses depends on the generalized continuity of the Jacobian of the mapping involved, which is used to control it and sharpen the error distances. Numerical examples validate the sufficient convergence conditions presented in the theory.

In this article, we address the error estimation problem of quasi-synchronization for a class of multilayer dynamical networks. The proposed network model simultaneously accounts for interlayer and intralayer time-varying coupling structures, network directionality, and interlayer communication delays. To achieve synchronization in a cost-effective manner, we design a novel pinning impulsive control strategy that leverages large-scale impulse delay information together with the number of pinned nodes. By employing an iterative algorithm, we establish a new delay-dependent impulsive differential inequality, which precisely characterizes the convergence domain and provides flexibility in the choice of impulse delays. Then, some quasi-synchronization criteria are derived to guarantee convergence of multilayer networks within a prescribed error level, and explicit analytical expressions for the synchronization error bounds are obtained. Finally, to demonstrate the practical applicability, the proposed criteria are applied to the synchronization of multilayer single-link robot arm networks under error bounds, with numerical examples validating the effectiveness of the method.

Sliding mode control with power-type barrier function for autonomous aerial refueling based on disturbance observer.

The article offers a methodological framework for the comprehensive assessment of regional convergence and divergence processes in household energy efficiency based on multifactor modeling. The purpose of developing this model is to support the adoption of substantiated managerial decisions that will contribute to the formation of a fair and effective energy transition policy in post-war Ukraine. The model is based on the adapted Cobb-Douglas function, which takes into account a wide range of factors (socio-economic, behavioral, climatic, technical, and others) that directly influence energy consumption levels in the residential sector. The proposed approach enables not only the identification of key determinants of household energy efficiency across different regions but also the detection of common dynamic patterns (attractors) that outline regional development trajectories, considering the potential for convergence as well as the risks of divergence in energy efficiency levels among regions. The practical significance of the model lies in its application for simulating various policy scenarios and corresponding managerial decisions. This facilitates the planning and evaluation of the effectiveness of targeted subsidy programs for energy efficiency measures for households and communal enterprises, the development of comprehensive energy modernization plans for the housing stock, and the assessment of the impact of climate change on energy consumption in the residential sector. Additionally, the model supports substantiating the feasibility of creating educational programs on energy saving and the rational use of resources for households. The results of the simulation analysis within the model have enabled the formulation of scientifically grounded recommendations to improve the efficiency and fairness of resource allocation in the household energy supply sector. This, in turn, will contribute to the adoption of strategically balanced and adaptive decisions at the regional level, ensuring a sustainable and equitable energy transition for Ukraine in the post-war period.