Conditions For Convergence Research Articles

Testing the Solow Hypothesis for Fiscal Convergence: a Dynamic Spatial Analysis

The study of regional fiscal convergence is a recent extension of the neoclassical growth theory. Various studies have shown the existence of fiscal convergence across countries or states in federally governed countries. This paper tests the growth theory on income and fiscal variables differently in a centrally ruled country. Therefore, we estimate spatial and non-spatial panel models from 2004 to 2022 for Türkiye. A general-to-specific methodology is applied for selecting an appropriate model to determine spatial interactions of the variables by using the panel data at the level of 81 Turkish provinces. The Ordinary Least Squares (OLS) estimation results from the non-spatial model partially validate the growth theory as the study does not find evidence of absolute convergence for government expenditures. The results, however, confirm the conditional convergence for all variables. The Maximum Likelihood (ML) method is applied for the estimation of the dynamic and static spatial panel models to explain their spatial interactions. The ML findings are consistent with the OLS results. Moreover, unlike direct and total effects, it is not possible to define indirect effects explaining spatial spillover effects in the short and long terms.

Aging and Pathological Conditions Similarity Revealed by Meta-Analysis of Metabolomics Studies Suggests the Existence of the Health and Age-Related Metapathway

Background: The incidence of many diseases increases with age and leads to multimorbidity, characterized by the presence of multiple diseases in old age. This phenomenon is closely related to systemic metabolic changes; the most suitable way to study it is through metabolomics. The use of accumulated metabolomic data to characterize this phenomenon at the system level may provide additional insight into the nature and strength of aging–disease relationships. Methods: For this purpose, metabolic changes associated with human aging and metabolic alterations under different pathological conditions were compared. To do this, the published results of metabolomic studies on human aging were compared with data on metabolite alterations collected in the human metabolome database through metabolite set enrichment analysis (MSEA) and combinatorial analysis. Results: It was found that human aging and pathological conditions involve the set of the same metabolic pathways with a probability of 99.96%. These data show the high identity of the aging process and the development of diseases at the metabolic level and allow to identify the set of metabolic pathways reflecting age-related changes closely associated with health. Based on these pathways, a metapathway was compiled, changes in which are simultaneously associated with health and age. Conclusions: The knowledge about the strength of the convergence of aging and pathological conditions has been supplemented by the rigor evidence at the metabolome level, which also made it possible to outline the age and health-relevant place in the human metabolism.

Adaptive Path-Tracking Control Algorithm for Autonomous Mobility Based on Recursive Least Squares with External Condition and Covariance Self-Tuning

This paper introduces an adaptive path-tracking control algorithm for autonomous mobility based on recursive least squares (RLS) with external conditions and covariance self-tuning. The advancement and commercialization of autonomous driving necessitate universal path-tracking control technologies. In this study, we propose a path-tracking control algorithm that does not rely on vehicle parameters and leverages RLS with self-tuning mechanisms for external conditions and covariance. We designed an integrated error for effective path tracking that combines the lateral preview distance and yaw angle errors. The controller design employs a first-order derivative error dynamics model with the coefficients of the error dynamics estimated through the RLS using a forgetting factor. To ensure stability, we applied the Lyapunov direct method with injection terms and finite convergence conditions. Each regression process incorporates external conditions, and the self-tuning of the injection terms utilizes residuals. The performance of the proposed control algorithm was evaluated using MATLAB®/Simulink® and CarMaker under various path-tracking scenarios. The evaluation demonstrated that the algorithm effectively controlled the front steering angle for autonomous path tracking without vehicle-specific parameters. This controller is expected to provide a versatile and robust path-tracking solution in diverse autonomous driving applications.

Lippmann-Schwinger equation representation of Green's function and its preconditioned generalized over-relaxation iterative solution in wavelet domain

The calculation of Green's function is the core of seismic forward and inverse methods based on integral operators. When the Lippmann-Schwinger (L-S) equation is used to calculate Green's function in strongly scattering media, both the Born scattering series and the numerical iterative method encounter issues of slow convergence or divergence. Although the renormalization method derived from quantum mechanics can effectively address the convergence problem of Born scattering series in strong scattering problems, it is acknowledgeed that the convergence conditions and rates of convergence of different reformulation series may vary, and no universal convergence reformulation scattering series exists. Numerical methods for solving integral equations tend to be more general and mathematically robust. In this work, we focus on the numerical solution method of L-S equations. By using a wavelet-domain preconditioner to a reformulated or equivalent Lippmann-Schwinger (L-S) equation, we present an iterative method for numerically solving the equivalent L-S equation aimed at improving the rate of convergence and iteration efficiency in strongly inhomogeneous media. Following Jakobsen et al. (2020), we first introduce a small imaginary component into the background wave number，then rewrite the L-S equation to derive the equivalent complex wave number L-S equation. This reformulation ensures that the coefficient matrix exhibits a banded structure after numerical discretization, allowing the wavelet coefficient matrix to maintain good sparsity. We employ a multi-level fill-in incomplete LU (ILU) factorization method along with a block ILU-based algebraic recursive multilevel solve (ARMS) method in the wavelet domain to generate sparse approximate inverses as preconditioning operators, thereby accelerating the convergence of the generalized successive over-relaxation (GSOR) iterative method. This method is applied to compute numerical Green's functions in strongly inhomogeneous media. Numerical results demonstrate that our method yields simulation outcomes consistent with those obtained from the direct method for solving the original real wave number L-S equation. By testing various preconditioners, we find that the ARMS preconditioner offers significant advantages in operator generation efficiency and non-zero element filling ratio, effectively accelerating the convergence of the GSOR iterative method while achieving higher computational efficiency.

Event-triggered iterative learning containment control for one-sided Lipschitz nonlinear singular switched multi-agent systems with multiple leaders and error quantization

In this work, under a repeatable control environment, the iterative learning containment control issue for multi-agent systems with one-sided Lipschitz nonlinear singular switched dynamics is addressed. It focuses on the output containment for one-sided Lipschitz nonlinear singular switched multi-agent systems (SWMASs) with multiple leaders, for which an event-triggered containment quantized iterative learning control (QILC) scheme is designed. Due to the limited system resources, SWMASs are often restricted in their communication capabilities and the frequency of controller updates in many applications, the proposed event-triggering mechanism can greatly restrict the use of communication and computation resources throughout the iterative learning process. When the triggering requirement is met, the event-triggered QILC input is repeatedly updated; alternatively, the control input stays unchanged. To conquer the nonidentical initial states of followers, an initial state learning with error quantization and event-triggering is also utilized. By virtue of some appropriate learning gains and sufficient convergent conditions, the containment error convergence can be accomplished for one-sided Lipschitz SWMASs. Finally, some numerical examples via Matlab are provided to demonstrate the efficacy of the event-triggered QILC scheme, it indicates that followers’ outputs can converge to the convex hull formed by leaders and the containment errors gradually converge to the 10−3 - vicinity of the origin along the iteration axis, where the communication resources can save more than 50% in the transmission channel.

On compressive self-calibration with structural constraints via alternating minimization

This paper considers the compressive bilinear self-calibration problem with explicit low-dimensional structural constraints. The celebrated proximal alternating linearized minimization (PALM) framework is adapted to simultaneously allow general sub-sampling schemes and structure-promoting regularizers. For the first time in literature, we refine the conditional convergence guarantees of PALM and show that the parameter commonly adopted to remove the scaling ambiguity as well as the structural penalties can ensure the unconditional convergence independent of strict assumptions on the statistical properties of the measurements, subspaces, number of snapshots, or initial iterates. In particular, we impose sparse and small total variation structures on the target signals and provide detailed numerical procedures for efficient computations. The extension to the complex-valued case is also made and extensive numerical experiments are carried out to corroborate the theoretical claims. Different choices of sub-sampling schemes and compression rates are simulated to support the effectiveness of the proposed algorithm under various settings. We also make comparisons with the state-of-art competing methods and the superiority of our proposed algorithm is empirically verified.

Shaped pattern synthesis for hybrid analog–digital arrays via manifold optimization-enabled block coordinate descent

Hybrid analog–digital (HAD) architecture is a promising means to realize large-scale arrays owing to the judicious trade-off between system performance and hardware complexity. This paper investigates the beampattern shaping of HAD arrays through minimizing the beampattern matching error between desired and actual patterns. Due to the nonconvex constraints on analog and digital weights and the nonconvex nonsmooth objective function, the resultant codesign is NP-hard. To address this issue, we create an efficient algorithm by leveraging block coordinate descent (BCD) and Riemannian manifold optimization. We first equivalently represent the objective function as a smooth bi-quadratic function by introducing a uni-modulus auxiliary variable. Subsequently, we alternatingly optimize the scaling factor, digital weights, analog weights and auxiliary variable under the BCD framework, where the simultaneous update of analog weights and auxiliary variable is recast as uni-modular constrained quadratic programming which is efficiently solved by Riemannian Newton method, and the digital weights have a global optimal solution via Lagrangian multiplier method. We also derive an explicit convergence condition of this algorithm. Numerical results demonstrate that the proposed algorithm has superior performance and faster convergence speed than alternative algorithms, and produces nearly the same mainlobe gain as fully digital arrays with significantly fewer radio-frequency chains.

Two remarks on properties of functions of bounded variation

In terms of variations, a sufficient condition for the uniform convergence of sequences of continuous functions is proved. Using this result, we obtain an addition to the classical Helly theorem on the selection of convergent sequences of functions with uniformly bounded variations in the case when the limit function is continuous. Also, by using an example we show that the condition of continuous differentiability of a function, ensuring the differentiability of its variation with the variable upper limit, is in a certain sense sharp.

ISSUES OF FORMATION OF PROFESSIONAL FOREIGN LANGUAGE COMPETENCE OF STUDENTS IN THE CONTEXT OF CONVERGENCE OF FORMAL AND NON-FORMAL EDUCATION

This article considers the peculiarities of theformation of students' professional foreign language competence in the conditions of convergence of formal and non-formal education. The necessity of integration of formal and non-formal education in foreign language education is substantiated. The role and significance of formal education provided by educational institutions and non-formal education carried out outside educational institutions in the formation of students' professional foreign language competence is analyzed. Special attention is paid to the interaction of these two forms of education and their influence on the development of students' linguistic and communicative skills. One of the main objectives of the study is to identify the educational needs of students in the conditions of formation of their professional foreign language competence. As aresult of the study, the authors made conclusions that the majority of students consider it appropriate to integrate formal and non-formal education, as it will allow them to master additional competencies and increase their motivation for learning. Thus,in conclusion, the authors of the article summarise the results of the study and draw conclusions about the significance of theinteraction between formal and non-formal education for the formation and improvement of students' professional foreign language competence.

Robust Maximum Correntropy Kalman Filter

ABSTRACTThe Kalman filter provides an optimal estimation for a linear system with Gaussian noise. However, when the noises are non‐Gaussian in nature, its performance deteriorates rapidly. For non‐Gaussian noises, maximum correntropy Kalman filter (MCKF) is developed which provides a more accurate result. In a scenario, where the actual system model differs from nominal consideration, the performance of the MCKF degrades. For such cases, in this article, we have proposed a new robust filtering technique for a linear system which maximizes a cost function defined by exponential of weighted past and present errors weighted with the kernel bandwidth. During filtering, at each time step, the kernel bandwidth is selected by maximizing the correntropy function of error. Further, a convergence condition of the proposed algorithm is derived. Numerical examples are presented to show the usefulness of the proposed filtering technique.

A new error estimate of a finite difference scheme for a fractional transport-advection equation with zero order term

In this work, we propose a finite difference scheme for Caputo’s fractional derivative transport equation in time and space, with a zero-order term. A new error estimation of the approximate solution has been demonstrated. By introducing an approximation of the Caputo derivative, we proved that the convergence is of order 2-α in time, and 2-β in space, for 0<α;β<1. Results of conditional stability and convergence of the numerical method are discussed. Finally a numerical implementation was presented to show the conformity between the theoretical and numerical approach of the finite difference scheme.

Stability and regularization for ill-posed Cauchy problem of a stochastic parabolic differential equation

Abstract In this paper, we investigate an ill-posed Cauchy problem involving a stochastic parabolic equation. We first establish a Carleman estimate for this equation. Leveraging this estimate, we derive the conditional stability and convergence rate of the Tikhonov regularization method for the aforementioned ill-posed Cauchy problem. To complement our theoretical analysis, we employ kernel-based learning theory to implement the completed Tikhonov regularization method for several numerical examples.

A robust iterative learning control for linear system with variable initial state and trail length

AbstractTo address the variable initial state and trail length this paper first presents a robust PD‐type open‐closed‐loop iterative learning control (ILC) law for a multiple‐input‐multiple‐output (MIMO) linear discrete‐time system. It is demonstrated that the convergence condition is dependent on the PD‐type feed‐forward learning gains, while an appropriate feedback learning gain can improve the ILC convergence performance. As a special case of PD‐type open‐closed‐loop ILC law, P‐type and D‐type open‐closed‐loop ILC laws are deduced. The three developed ILC laws ensure that as the number of iterations approaches infinity, the expectation of ILC tracking error will be constrained within a limited range, where the boundary is proportional to the initial state variation. Through a numerical simulation, the effectiveness of the proposed ILC laws is illustrated.

On the existence and avoidance of singularity in [formula omitted] gravity using Raychaudhuri equation

The paper deals with the modified Raychaudhuri equation in the framework of homogeneous and isotropic f(Q) gravity model subject to the parametrization f(Q)=Q+F(Q). Focusing of a congruence of time-like geodesics has been studied via the convergence condition for two choices of F(Q) namely, a polynomial in Q and an exponential form of Q. Finally, possibilities for the avoidance of initial big-bang singularity in both the models have been examined via the signature of Raychaudhuri scalar.

An efficient Newton-type matrix splitting algorithm for solving generalized absolute value equations with application to ridge regression problems

A generalized Newton-based matrix splitting (GNMS) method is proposed for solving the generalized absolute value equations (GAVEs). Under mild conditions, the GNMS method converges to the unique solution of GAVEs. Moreover, we can obtain a few weaker convergence conditions for some existing methods. Numerical results verify the effectiveness of the proposed method.

On the numerical solution to space fractional differential equations using meshless finite differences

We derive a discretization of the Caputo and Riemann–Liouville spatial derivatives by means of the meshless Generalized Finite Difference Method, which is based on moving least squares. The conditional convergence of the method is proved and several examples over one dimensional irregular meshes are given.

ANALYSIS OF CONVERGENCE BETWEEN PROVINCES IN INDONESIA

&lt;p&gt;Indonesia is one of the developing countries that is always trying to increase its economic growth. Indonesia has a large number of people with various ethnic backgrounds and diverse customs, so this situation has given rise to disparities between regions. This study aims to determine whether or not sigma convergence, to find out whether absolute and conditional convergence occurs or not, and to determine the speed of convergence. This study uses secondary data, namely Gross Regional Domestic Product (GRDP) per capita, poverty, and inequality for each province in Indonesia from 2017-2021. The method used in this study is panel data with a fixed effect approach. The results of the analysis using the sigma convergence (σ) approach show the occurrence of convergence. The results of the absolute convergence analysis explain the divergence of GRDP per capita in Indonesia with a divergence speed of 13.76% per year. The results of the conditional convergence analysis show that there is a divergence of GRDP per capita in Indonesia with a divergence speed of 13.62% per year.&lt;/p&gt;

Застосування методу двобічних наближень до розв’язання першої крайової задачі для одновимірного рівняння теплопровідності з експоненціально нелінійним коефіцієнтом теплопровідності

The problem of heat conduction in nonlinear media reduces to solving boundary value problems for nonlinear heat conduction equations, where the coefficients of the equation or the function of the power of heat sources depend on temperature according to some law. Among the numerical methods for solving problems for nonlinear equations of mathematical physics, one can distinguish finite difference methods, finite element methods, variational and projection methods, as well as iterative methods. Among the latter group, the two-sided approximation method is particularly attractive due to its ability to provide a convenient estimate for the error of the approximate solution and to prove the existence of a solution to the original problem. The theory of linear partially ordered spaces was developed by L. V. Kantorovich in the second half of the 1930s. Further development of this theory is associated with the works of M. A. Krasnosel’skii, H. Amann, V. I. Opojtsev, N. S. Kurpel, B. A. Shuvar, A. I. Kolosov etc. The aim of this article is to develop a two-sided approximation method based on the use of Green's functions for solving the first boundary value problem for a one-dimensional nonlinear heat conduction equation and to investigate its performance when solving test problems. To achieve this goal, the unknown function was replaced, and the boundary value problem was reduced to a Hammerstein integral equation, which was considered as a nonlinear operator equation in a partially ordered Banach space. Conditions for the existence of a unique positive solution to the problem and conditions for two-sided convergence of successive approximations to it were obtained. The developed method was implemented in software and tested on solving test problems. The results of the computational experiment are illustrated with graphical and tabular information

Speed‐sensorless control for SPMSM via novel exponential super‐twisting ADRC

AbstractAlthough the conventional super‐twisting reaching law (CSTRL) maintains the desired tracking performance for disturbed systems, its implementation is challenging due to its dependence on accurate system dynamics. To mitigate this dependence and reduce chattering of CSTRL, a novel exponential super‐twisting reaching law (NESTRL) is proposed, leveraging the dynamic adaptability of the exponential reaching law and eliminating chattering. By using NESTRL, the proposed controller can achieve a fast response without chattering. Additionally, a comprehensive procedure for finite convergence time analysis is provided. The convergence conditions of the system's state variables are determined using a Lyapunov function, and the stability of system is proven using an algebraic Lyapunov function. Finally, simulations and experimental results demonstrate that the proposed approach is valid and effective, showing improvements compared to the traditional super‐twisting active disturbance rejection control and linear active disturbance rejection control in sensorless control.

Direct torque control of bearingless induction motor based on super-twisting sliding mode control

A bearingless induction motor (BIM) is an innovative magnetic levitation motor that incorporates torque system and suspension systems. Aiming to improve the anti-interference and levitation performance of the BIM, a second-order super-twisting sliding mode direct torque control strategy (STSM-DTC) is proposed. Initially, the basic principles and convergence conditions of the super-twisting algorithm are analysed. Subsequently, corresponding sliding mode surfaces are constructed according to speed, torque, and stator flux error, and the corresponding super-twisting sliding mode controllers (STSMC) are designed in the torque system. The STSMCs are designed based on the rotor radial displacement error and further enhanced by incorporating a differential loop in the suspension system. The hyperbolic tangent function tanh(x) is used as the switching function. Simulation and experimental of the BIM STSM-DTC system show that the STSM-DTC strategy effectively improves the anti-interference ability and suspension performance of the BIM, and show better dynamic response.