Radius Of Convergence Research Articles

Synergy of pollution control and carbon reduction in China: Spatial–temporal characteristics, regional differences, and convergence

Promoting the synergy of pollution control (PC) and carbon reduction (CR) is an important strategy for ecological civilization construction in China. Based on constructing a measuring system for PC and CR respectively, we employ the coupling coordination model to determine the coupling coordination degree (CCD) between PC and CR in 30 Chinese provinces during 2006–2019, and analyze the spatial–temporal characteristics, regional differences, and convergence of the CCD between PC and CR from a dual perspective of east–west and south–north regional divisions. The results show that the average CCD between PC and CR increases from 0.8339 in 2006 to 0.8904 in 2019, suggesting that the two subsystems are in a well-coordinated stage. Moreover, China's CCD shows a “high in the east and low in the west, high in the south and low in the north” layout and exhibits a prominent spatial positive autocorrelation characteristic. Furthermore, the overall regional differences in the CCD of each province show an increasing trend initially, followed by a decreasing trend. The overall differences in east–west and south–north originate primarily from the cross-regional and within-regional difference, respectively. The results of the convergence model show that there is no σ convergence of China's CCD, while there exists β convergence in China and different regions. These findings provide empirical evidence and policy implications for facilitating the synergistic effect of PC and CR.

ϵ-expansion of multivariable hypergeometric functions appearing in Feynman integral calculus

We present a new methodology, suitable for implementation on computer, to perform the $\epsilon$-expansion of hypergeometric functions with linear $\epsilon$ dependent Pochhammer parameters in any number of variables. Our approach allows one to perform Taylor as well as Laurent series expansion of multivariable hypergeometric functions. Each of the coefficients of $\epsilon$ in the series expansion is expressed as a linear combination of multivariable hypergeometric functions with the same domain of convergence as that of the original hypergeometric function. We present illustrative examples of hypergeometric functions in one, two and three variables which are typical of Feynman integral calculus.

Pulse convergence analysis and pulse information calculation of NOLM fiber mode-locked lasers based on machine learning method

Nowadays, mode-locked fiber laser has been extensively applied in various fields such as communication, biomedical, nuclear physics and material processing. By controlling the parameters of cavity elements, people can realize the output of ultrafast pulse with different states. Utilizing the traditional numerical method, the influence of different cavity parameters on the pulses can be computed accurately, which provides the simulation basis for the fabrication of mode-locked fiber lasers. However, with the development of the practical application demand, the performance requirements of the mode-locked pulse are also increasing. The traditional numerical methods have shown some defects in the calculation speed and analysis ability at this time. To improve the shortcomings of the existing numerical methods, in this work, we propose using the machine learning method to analyze the mode-locked pulse convergence of the nonlinear loop mirror (NOLM) fiber mode-locked laser and calculated its pulse information. Firstly, the mapping between cavity parameters and convergence region is established by the support vector machine (SVM) model, and utilizing it, the influence of different cavity parameters on mode-locking is investigated. Then, we train two artificial neural networks (ANN) for calculating the pulse shape and spectral shape in the mode-locked state and find out the cavity parameters under which.the spectral shape approximates to a parabola based on genetic algorithm and the ability of ANN in rapid computing. Finally, we construct the laser cavity according to the numerical result and obtain the mode-locked pulse with a parabolic shape spectrum. The authors believe that the model presented in this work will show widely application prospects in the numerical calculation of fiber lasers.

Hyper-power series and generalized real analytic functions

This article is a natural continuation of the paper Tiwari, D., Giordano, P., Hyperseries in the non-Archimedean ring of Colombeau generalized numbers in this journal. We study one variable hyper-power series by analyzing the notion of radius of convergence and proving classical results such as algebraic operations, composition and reciprocal of hyper-power series. We then define and study one variable generalized real analytic functions, considering their derivation, integration, a suitable formulation of the identity theorem and the characterization by local uniform upper bounds of derivatives. On the contrary with respect to the classical use of series in the theory of Colombeau real analytic functions, we can recover several classical examples in a non-infinitesimal set of convergence. The notion of generalized real analytic function reveals to be less rigid both with respect to the classical one and to Colombeau theory, e.g. including classical non-analytic smooth functions with flat points and several distributions such as the Dirac delta. On the other hand, each Colombeau real analytic function is also a generalized real analytic function.

A Newton-like Midpoint Method for Solving Equations in Banach Space

The present paper includes the local and semilocal convergence analysis of a fourth-order method based on the quadrature formula in Banach spaces. The weaker hypotheses used are based only on the first Fréchet derivative. The new approach provides the residual errors, number of iterations, convergence radii, expected order of convergence, and estimates of the uniqueness of the solution. Such estimates are not provided in the approaches using Taylor expansions involving higher-order derivatives, which may not exist or may be very expensive or impossible to compute. Numerical examples, including a nonlinear integral equation and a partial differential equation, are provided to validate the theoretical results.

Sliding mode control based on multi-node transmission hybrid scheduling for Markovian jump systems with constrained bandwidth

The sliding mode control (SMC) problem is investigated for Markovian jump systems (MJSs) under constrained communication bandwidth. A multi-node hybrid transmission strategy composed of an event-triggered protocol and the weight try-once-discard (WTOD) protocol is introduced into the sensor-to-controller (S/C) channel. Its key feature is that by using two dynamic thresholds, the number of the transmitted components may be dynamically regulated, not just the one with the largest difference as in the conventional WTOD protocol. That may greatly increase the flexibility of transmission under limited bandwidth, meanwhile, it is also beneficial to balance system performance and network burden. Then, a compensating strategy is proposed via the previous transmitted signals, and a scheduling signal-dependent sliding mode controller is designed. By using mode-dependent Lyapunov function, both the stochastic stability and the reachability are analyzed under different transmission cases, respectively. Moreover, an optimization problem on convergent domain is formulated and the binary-encoded genetic algorithm (GA) is utilized to search a desirable sliding gain. Finally, the proposed multi-node hybrid scheduling-based SMC scheme is illustrated via simulation results.

On the basins of convergence in the beyond-Newtonian spatial collinear circular restricted four-body problem with spinning primaries

In this paper, we present the analysis of the Newton–Raphson basins of convergence (NR-BoCs) linked with the relative equilibria (LPs) in the Eulerian configuration of a pseudo-Newtonian planar circular restricted problem of four bodies (SCCR4BP) with spinning primaries. In this configuration of the SCCR4BP, the primaries are laid out in a symmetrical collinear shape in which the two peripheral primaries are of equal mass. We derive the equations of motion by assuming that the system consists of three Kerr-like primaries to examine how the geometry of the basins of convergence (BoCs) associated with the LPs of SCCR4BP are affected by the first-order non-Newtonian contribution to the gravitational field. Additionally, we analyze the correlation among the regions of convergence, the required number of iterations, and the associated probability distributions. Finally, for the quantitative study of the basins of convergence, we measure the uncertainty of the respective basins via the basin entropy and the basin boundary entropy.

Toward a statistical validation of brain signatures as robust measures of behavioral substrates.

The "brain signature of cognition" concept has garnered interest as a data-driven, exploratory approach to better understand key brain regions involved in specific cognitive functions, with the potential to maximally characterize brain substrates of behavioral outcomes. Previously we presented a method for computing signatures of episodic memory. However, to be a robust brain measure, the signature approach requires a rigorous validation of model performance across a variety of cohorts. Here we report validation results and provide an example of extending it to a second behavioral domain. In each of two discovery data cohorts, we derived regional brain gray matter thickness associations for two domains: neuropsychological and everyday cognition memory. We computed regional association to outcome in 40 randomly selected discovery subsets of size 400 in each cohort. We generated spatial overlap frequency maps and defined high-frequency regions as "consensus" signature masks. Using separate validation datasets, we evaluated replicability of cohort-based consensus model fits and explanatory power by comparing signature model fits with each other and with competing theory-based models. Spatial replications produced convergent consensus signature regions. Consensus signature model fits were highly correlated in 50 random subsets of each validation cohort, indicating high replicability. In comparisons over each full cohort, signature models outperformed other models. In this validation study, we produced signature models that replicated model fits to outcome and outperformed other commonly used measures. Signatures in two memory domains suggested strongly shared brain substrates. Robust brain signatures may therefore be achievable, yielding reliable and useful measures for modeling substrates of behavioral domains.

Influence of Tunnel Excavation on the Deformation of a Frame Building

Tunnel excavation inevitably causes surface deformation. In urban areas, surface deformation could lead to the deformation of surrounding buildings, which may cause damage to communities when accumulated to a certain extent. However, the current construction organization and management mainly rely on on-site deformation measurements, and there is still a lack of reliable prediction methods. Here, we proposed an effective evaluation method for frame building deformation based on the stochastic medium theory and the equivalent beam theory. This method could effectively evaluate the surface and building deformation after a horseshoe tunnel excavation by considering the non-uniform convergence. Furthermore, its accuracy and practicability were verified using the Nanyan Fourth Circuit Transmission Reconstruction located in Dalian, China. The results show that the spatial distribution and characteristic values of the maximum tensile strains were closely related to the ratio of Young’s modulus to the shear modulus (E/G), the building height (h), the tunnel depth (H), the tangent of the tunnel influence angle (tan β) and the convergence radius (ΔR). These achievements can provide a theoretical basis and analytical ideas for investigating the influence of shallow buried tunnel excavation on frame structure buildings in cities.

Feasibility Analysis of Autonomous Orbit Determination and Gravity-Field Recovery around Asteroids Using Inter-Satellite Range Data

Autonomous navigation and orbit determination are key problems of asteroid exploration missions. Inter-satellite range link is a type of measurement widely used in the orbit determination of Earth satellites, but not so widely used in missions around small bodies. In our study, we assume that highly accurate inter-satellite range data can be obtained around small bodies between the chief spacecraft and some low-cost deputies, and study the feasibility of simultaneous autonomous orbit determination of the spacecraft and the gravity-field recovery without the support from ground stations. After the feasibility analysis, two modified methods are proposed. Both methods demonstrate obvious improvements in both the convergence region and the accuracy. One remark is that the inter-satellite range data can be also used together with various observation data from ground stations to enhance the accuracy of the determined orbits and the gravity field.

Classes of graphs embeddable in order-dependent surfaces

Given a function \(g=g(n)\) we let \(\mathcal{E}^g\) be the class of all graphs \(G\) such that if \(G\) has order \(n\) (that is, has \(n\) vertices) then it is embeddable in some surface of Euler genus at most \(g(n)\), and let \(\widetilde{\mathcal E}^g\) be the corresponding class of unlabelled graphs. We give estimates of the sizes of these classes. For example we show that if \(g(n)=o(n/\log^3n)\) then the class \(\mathcal{E}^{g}\) has growth constant \(\gamma_{\mathcal{P}}\), the (labelled) planar graph growth constant; and when \(g(n) = O(n)\) we estimate the number of n-vertex graphs in \(\mathcal{E}^{g}\) and \(\widetilde{\mathcal E}^g\) up to a factor exponential in \(n\). From these estimates we see that, if \(\mathcal{E}^g\) has growth constant \(\gamma_{\mathcal{P}}\) then we must have \(g(n)=o(n/\log n)\), and the generating functions for \(\mathcal{E}^g\) and \(\widetilde{\mathcal E}^g\) have strictly positive radius of convergence if and only if \(g(n)=O(n/\log n)\). Such results also hold when we consider orientable and non-orientable surfaces separately. We also investigate related classes of graphs where we insist that, as well as the graph itself, each subgraph is appropriately embeddable (according to its number of vertices); and classes of graphs where we insist that each minor is appropriately embeddable. In a companion paper, these results are used to investigate random \(n\)-vertex graphs sampled uniformly from \(\mathcal{E}^g\) or from similar classes.Mathematics Subject Classifications: 05C10, 05C30Keywords: Embeddable graphs, order-dependent surfaces, approximate counting, labelled graphs

The impact of village funds on rural welfare in Indonesia: A regression discontinuity in time (RDiT) and difference in difference (DiD) approach

ABSTRACT This study examines the impact of village fund (VF) transfers on rural welfare in Indonesia. We use the monthly night-time light (NTL) dataset as a proxy for rural welfare for around 75,000 villages from 2014 to 2019. Using Regression Discontinuity in Time (RDiT), we find that VF positively impacts rural welfare, as the value of Average Light Intensity (ALI) increases by almost 97% after the implementation of VF. The highest influence of VF transfers is revealed to be in underdeveloped villages. This indicates preliminary evidence of regional convergence, where poor villages grow faster than developed villages. In addition to the RDiT, the Difference in Difference (DiD) estimations show that the rural welfare of villages that received VF early in 2015 was 19% higher than those without VF in 2015.

Regional convergence and catching up process in Africa: A tale of three clubs

AbstractThe aims of this article were twofold. First, to tackle the issue of convergence from an analytical point of view by presenting the mathematical developments of the main economic growth models, which emphasized that the convergence of African economies is conditional to the investment level in the early stages of physical capital accumulation. As the latter increases, the convergence of African economies is determined by other factors (investment in research and development (R&D) and human capital, etc.). Second, to verify the empirical validity of these models by confronting them with data from 33 African economies stratified by development level over the period 2004–2019. Empirical results using both spatial and nonspatial panel estimation methodology and the ‘beta‐convergence’ approach pointed to three ‘convergence clubs,’ as well as a conditional convergence for all these clubs. However, the determinants of convergence among African economies differ by development level. In low‐income economies, convergence is conditional to financial development and inflation level. For lower‐middle‐income economies, institutional quality and inflation level contribute to the convergence of this club. The convergence of upper‐middle‐income economies is conditioned by public spending and human capital. In terms of policy implications, countries should develop measures that strengthen institutional reforms to improve the functioning of financial systems, democratic accountability, control of corruption, business climate, economic growth, strengthening the legal environment, and improving competition by reducing public expenditures. This paper is original insofar as it advances the field from the current state of knowledge in several ways. First, to stand out from the existing literature, we conducted a comparative analysis of the institutional quality levels across 33 African countries by developing an institutional quality index through the use of a principal component analysis (PCA) method. Second, we tested the empirical validity of the convergence hypothesis beneath economic growth theories and in the African context; moreover, it has verified the possible existence of ‘convergence clubs,’ then, it brought to light the main determinants of the convergence of these clubs.

Overcoming the barriers: cross-border convergence in Portugal and Spain between 2000 and 2018

ABSTRACT Cross-border cooperation is a major instrument of European policy to overcome the barriers posed by national borders and correcting regional imbalances. But the question of whether it is leading to the convergence of cross-border regions (CBRs) is still open for debate, given the significant heterogeneity of borders and the localized and spatially bound nature of many border effects. This article analyses the beta and sigma convergences in GDP per capita growth for the NUTS-3 at the Portuguese-Spanish border between 2000 and 2018, also considering their population growth. The main finding is that, even if their population growth is below the national averages, the CBR is converging in economic terms. This convergence is visible in the reduced dispersion of the GDP in the border regions and is also confirmed by spatial models, which showed that being a border region increases the probability of having above-average growth rates and that the NUTS-3 with initially low GDP in the cross-border region were also growing above average. This convergence was found to be robust, considering different model specifications and important factors for convergence, such as population growth and spatial dependence. A negative relationship between population and GDP per capita growth was found.

Adaptive Fuzzy Output-Feedback Consensus Tracking Control of Nonlinear Multiagent Systems in Prescribed Performance.

This article addresses the finite-time consensus tracking control problem for nonlinear multiagent systems (MASs), in which state variables are unmeasured and nonlinear functions are totally unknown. An observer is designed to estimate state variables and fuzzy-logic systems are employed to approximate nonlinearities. Then, an observer-based adaptive fuzzy consensus tracking controller is developed by using the backstepping technique and constructing a novel barrier Lyapunov function with the consideration of the characteristics of MASs. The proposed control protocol can guarantee that: 1) all signals in the closed-loop system keep bounded and 2) the consensus tracking error converges to a prespecified region of the origin in the prescribed finite time. Compared with the existing observer-based finite/fixed-time control protocols, the settling time and the convergence region in our work can be both preassigned by the designer and not affected by the unknown positive constant, which lies in the Lyapunov derivative inequality. Finally, two comparison simulation examples, including a numerical example and a practical example, check the availability of the designed control scheme.

Is there regional convergence between Morocco and its OECD partner countries in terms of well-being?

Morocco wants its 12 regions to play the role as the main lever of its public policies to initiate harmonized spatial multidimensional development. In the context of this goal and Morocco's openness over the past two decades to bilateral and multilateral cooperation in an effort toward regional integration, this article studies the convergence of 389 regions in 36 countries (Morocco and 35 of its partner member countries of the Organization for Economic Co-operation and Development (OECD)) between 2000 and 2019 in terms of well-being. To this end, we considered the territorial dimension of β-convergence models for well-being and its four domains (economic, social, environmental, and governance). Then, we adapted the absolute β-convergence model taking into account the existence of spatial heterogeneity according to five specifications of spatial models. Thus, apart from environmental domain, we showed that β-convergence of regions is significant for well-being and three of its domains (economic, social, and governance). These convergences are made by a spatially autocorrelated error model (SEM). However, the speed and period of convergence are relatively low for social domain, partly explaining the very exacerbated tensions at the territorial level. The fastest convergence was achieved in governance domain, followed by economic domain. This suggests that emerging countries must pay particular attention to national public action in favor of social cohesion at the territorial level. The lack of convergence in environmental domain calls for common actions for all countries at the supranational level to protect the commons at the territorial level.

Unified Convergence Criteria of Derivative-Free Iterative Methods for Solving Nonlinear Equations

A local and semi-local convergence is developed of a class of iterative methods without derivatives for solving nonlinear Banach space valued operator equations under the classical Lipschitz conditions for first-order divided differences. Special cases of this method are well-known iterative algorithms, in particular, the Secant, Kurchatov, and Steffensen methods as well as the Newton method. For the semi-local convergence analysis, we use a technique of recurrent functions and majorizing scalar sequences. First, the convergence of the scalar sequence is proved and its limit is determined. It is then shown that the sequence obtained by the proposed method is bounded by this scalar sequence. In the local convergence analysis, a computable radius of convergence is determined. Finally, the results of the numerical experiments are given that confirm obtained theoretical estimates.

Semilocal Convergence of a Multi-Step Parametric Family of Iterative Methods

In this paper, we deal with a new family of iterative methods for approximating the solution of nonlinear systems for non-differentiable operators. The novelty of this family is that it is a m-step generalization of the Steffensen-type method by updating the divided difference operator in the first two steps but not in the following ones. This procedure allows us to increase both the order of convergence and the efficiency index with respect to that obtained in the family that updates divided differences only in the first step. We perform a semilocal convergence study that allows us to fix the convergence domain and uniqueness for real applied problems, where the existence of a solution is not known a priori. After this study, some numerical tests are developed to apply the semilocal convergence theoretical results obtained. Finally, mediating the dynamic planes generated by the different numerical methods that compose the family, we study the symmetry of the basins of attraction generated by each solution, the shape of these basins, and the convergence to each root of a polynomial function.

Iran and Regional Convergence in Eurasia

AbstractRegional convergence in Eurasia has been evolving since the collapse of the Soviet Union. The Commonwealth of Independent States was Russia's initial attempt to forge a comprehensive regional integration. However, Russia gradually shifted its focus to economics, and this produced the Eurasian Economic Union (EEU). This organization has concluded numerous cooperation agreements, even with countries outside the borders of Eurasia, raising questions about regional convergence. In addition, with the expansion of China's influence in Central Asia, there has been a shift in the role and scope of the EEU. Iran has concluded a preferential trade agreement with the EEU, including non‐tariff measures and a list of commodities for which barriers have been reduced or cut to zero. The main question of this study is how Iran's presence in this organization will influence Eurasian convergence. We examine the opportunities for, and obstacles to, convergence through an analysis of the forces that can bind an institution like the EEU: cultural and ideological affinities; the hegemony of the most powerful actors; and the potential for solving common problems.

Distributed Intelligent Adaptive Controller for Disturbance Rejection in Multiagent Systems

A cooperative task consisting of multiple agents has the advantages of reducing cost, enhancing configurability, and increasing robustness in a large set of mission applications. A distributed strategy, applied using intelligence and adaptability characteristics, can provide the extended potential to achieve high levels of mission protection, especially under disturbances that might lead to operation degradation. This paper describes the design and development of a novel bioinspired distributed adaptive control architecture designed to increase the resilience of multiagent systems. The architecture is formulated using nonlinear bounded functions that characterize the immune system responses of living organisms. Numerical simulations are performed to evaluate the capabilities of this architecture to solve a consensus problem under bounded disturbances. Stability analysis is presented using the Lyapunov direct method to estimate the radius of convergence of the global tracking error under a time-varying disturbance. The proposed distributed controller successfully ensures that consensus is achieved among all agents while simultaneously mitigating the effect of disturbances.