Conditions For Convergence Research Articles

Parameter effects on performance of piezoelectric wind energy harvesters based on the interaction between vortex-induced vibration and galloping

Our previous research experimentally validated that the interaction between vortex-induced vibration and galloping is an effective method for enhancing the performance of piezoelectric wind energy harvesters under low wind speed conditions. We proposed a distributed-parameter electromechanical coupling model as well. This study aims to investigate the effects of various parameters and optimize the performance of VIV-galloping interactive piezoelectric wind energy harvesters. Initially, we assessed the applicability of the model under different circuit and aerodynamic force conditions and discussed boundary and convergence conditions by replicating previous results. Further, simulations were performed to analyze the effects of the structural parameters of the bluff body and piezoelectric beam. The width or depth of the bluff body significantly influenced the low critical wind speed, interactive occurrence, and electrical output. To achieve a balance between material cost and electrical benefit, we recommend positioning the electrode length from the fixed end with a coverage ratio of at least 60%. Additionally, the output power is highly sensitive to the piezoelectric beam length, but reducing it results in a higher natural frequency and critical wind speed. We fabricated and tested four prototypes, which have demonstrated significantly higher power densities compared with previously reported values at the same wind speed.

On some mixtures of the Kies distribution

The purpose of this paper is to explore some mixtures, discrete and continuous, based on the Kies distribution. Some conditions for convergence are established. We study the probabilistic properties of these mixtures. Special attention is taken to the so-called Hausdorff saturation. Several models are examined in detail – bimodal, multimodal, and mixtures based on binomial, geometric, exponential, gamma, and beta distributions. We provide some numerical experiments for real-life tasks – one for the Standard and Poor’s 500 financial index and another for unemployment insurance issues. In addition, we check the consistency of the proposed estimator using generated data of different sizes.

Physician’s prosodic behavior and the regulation of patient anxiety: A quantitative study within the communication accommodation theory framework

ObjectivesPatients commonly experience anxiety when visiting a medical provider. While regulating its level, the physician may adjust their own prosodic behavior to express different levels of affective empathy and shape the emotional outcome. The primary aim was to examine the impact of convergence and divergence with the patient’s prosodic emotional cues on the patient-perceived physician’s affective empathy and the emotion regulation process. MethodsAnalog patients (n = 132) made assessments after the exposure to an audio vignette of a physician – patient conversation in the prosodic convergence or divergence condition. ResultsConvergence with the prosodic cues of anxiety was associated with the physician experiencing the same as or a similar emotional state to the patient. The former type of emotional reaction was related to lower odds of anxiety alleviation. Prosodic convergence had a negative effect on anxiety alleviation through the mediation of experiencing the same emotional state as the patient. ConclusionsDivergence from the prosodic cues of anxiety and, therefore, a low patient-perceived level of this emotion may facilitate the anxiety regulation process. Practice implicationsA careful use of convergence and divergence with prosodic emotional cues and adequate control of prosody in general are strongly recommended for practitioners.

Aggregate Estimates of Reflexive Collective Behavior Dynamics in a Cournot Oligopoly Model

This paper considers an oligopoly model with an arbitrary number of Cournotreflexive agents under incomplete information in the classical case of linear cost and demand functions. Agents make decisions based on a collective behavior model. The problem of identifying convergence conditions to the model equilibrium is studied, with an emphasis placed on the trajectory of the sum of the action residuals of all agents. Aggregate estimates of this trajectory are obtained. They can be used to judge how the trajectory of each agent evolves towards the equilibrium.

Probabilistic investigation of piezoelectric application for reliability enhancement of composite laminates under edge delamination

In this research a novel probabilistic numerical approach is developed to investigate the effectiveness of piezoelectric (PZT) materials to enhance the reliability of composite laminates under edge delamination onset (EDO). To achieve this, finite element (FE) modeling is employed as an implicit limit state function (LSF) based on a quadratic failure criterion and the concept of critical length. An interactive interface that integrates FE analysis and reliability analysis is then established to execute both processes simultaneously until the convergence condition of the reliability index is satisfied. To validate current FE analysis, the interlaminar stress peaks, and resulting edge delamination probability obtained in this study are compared with available data. Subsequently, the probability of EDO in angle-ply composite laminates under applied longitudinal strain and an applied electric field on the PZT layer is assessed using both the first-order reliability method (FORM) and the second-order reliability method (SORM). The Monte Carlo simulation (MCS) is employed to verify the numerical results. Findings reveal that employment of PZT reduces EDO probability. Moreover, as the applied voltage increases, the critical strain required for definitive EDO also increases, and the positive influence of PZT on enhancing reliability becomes more pronounced, particularly with increased thickness under higher applied strain.

Development and validation of a gas chromatography method for analysing polychlorinated biphenyls in fish roe

A method for determining polychlorinated biphenyls (PCBs) in fish roe by gas chromatography (GC) has been developed. The suitability (validation) of the process for the determination of 14 PCBs (PCB 18, PCB 31, PCB 28, PCB 52, PCB 44, PCB 101, PCB 149, PCB 118, PCB 153, PCB 138, PCB 180, PCB 170, PCB 194, PCB 209) in fish roe by GC using an electron capture detector (ECD) was evaluated according to the following criteria: selectivity, linearity, limits of detection (LOD), limits of quantification (LOQ), accuracy and precision. Automated Soxhlet extraction and sample clean-up by solid phase extraction (SPE) were proposed for extracting PCBs from fish roe. The results of the method selectivity study showed that the determination of PCBs in fish roe is not affected by other components in the sample. The correlation coefficients for fourteen PCBs ranged from 0.9962 to 0.9999 (R2 ≥0.995). The limits of detection (LOD) and limits of quantification (LOQ) of PCBs are below the maximum permissible levels set by the European Union (EU). The recovery percentage ranged from 81.5% to 107%, indicating the PCB extraction procedure's acceptability (R, 80 – 120%). The relative standard deviation (RSD, %) of the measurement results under convergence conditions ranged from 1.02% to 9.43% (RSD ≥15%). The obtained method suitability (validation) data meets the Commission Regulation (EU) No 589/2014 criteria.

UAdam: Unified Adam-Type Algorithmic Framework for Nonconvex Optimization.

Adam-type algorithms have become a preferred choice for optimization in the deep learning setting; however, despite their success, their convergence is still not well understood. To this end, we introduce a unified framework for Adam-type algorithms, termed UAdam. It is equipped with a general form of the second-order moment, which makes it possible to include Adam and its existing and future variants as special cases, such as NAdam, AMSGrad, AdaBound, AdaFom, and Adan. The approach is supported by a rigorous convergence analysis of UAdam in the general nonconvex stochastic setting, showing that UAdam converges to the neighborhood of stationary points with a rate of O(1/T). Furthermore, the size of the neighborhood decreases as the parameter β1 increases. Importantly, our analysis only requires the first-order momentum factor to be close enough to 1, without any restrictions on the second-order momentum factor. Theoretical results also reveal the convergence conditions of vanilla Adam, together with the selection of appropriate hyperparameters. This provides a theoretical guarantee for the analysis, applications, and further developments of the whole general class of Adam-type algorithms. Finally, several numerical experiments are provided to support our theoretical findings.

Assessment of Green Innovation Efficiency in Chinese Industrial Enterprises Based on an Improved Relational Two-Stage DEA Approach: Regional Disparities and Convergence Analysis

Industrial enterprises are characterized by significant energy consumption and high emissions. Therefore, the implementation of green innovation by these enterprises is beneficial for promoting sustainable economic development and safeguarding the ecological environment. In this study, a relational two-stage DEA model containing shared inputs and undesired outputs is constructed to evaluate and decompose the green innovation efficiency (GIE) of Chinese industrial enterprises across 30 provinces from 2012 to 2021. Since the objective function of this model is nonlinear, a heuristic search method is employed for its resolution. On the basis of efficiency evaluation, the Gini coefficient, kernel density estimation, and convergence analysis are further employed to investigate the regional disparities and convergence properties in the two-stage efficiency of green innovation. Our findings are as follows: (1) The average GIE of Chinese industrial enterprises demonstrates a fluctuating upward trajectory, with significant regional disparities observed between provinces. (2) Regional disparities in R&D efficiency (RDE) and achievement conversion efficiency (ACE) have diminished in all regions. Super-variable density and interregional differences serve as the primary sources of regional disparities in RDE and ACE, respectively. (3) The presence of absolute and conditional convergence in RDE and ACE is observed across all regions. To improve the GIE of Chinese industrial enterprises, it is imperative to emphasize the heterogeneous impact of economic levels, industrial structure, and the degree of openness across various regions and stages of green innovation.

An Optimal Strategy for Estimating Weibull distribution Parameters by Using Maximum Likelihood Method

Several methods have been used to estimate the Weibull parameters such as least square method (LSM), weighted least square method (WLSM), method of moments (MOM), and maximum likelihood (MLE). The maximum likelihood method is the most popular method (MLE). Newton-Raphson method has been applied to solve the normal equations of MLE’s in order to estimate the Weibull parameters. The method was used to find the optimal values of the Weibull distribution parameters for which the log-likelihood function is maximized. We tried to find the approximation solution to the normal equations of the MLE’s because there is no close form for get analytical solution. In this work, we tried to carry out a study that show the difference between two strategies to solve the MLE equations using Newton-Raphson algorithm. Both two strategies are provided an optimal solution to estimate the Weibull distribution parameters but which one more easer and which one converges faster. Therefore, we applied both strategies to estimate the Weibull’s shape and scale parameters using two different types of data (Real and simulation). We compared between the results that we got by applying the two strategies. Two studies have been done for comparing and selecting the optimal strategy to estimate Weibull distribution parameters using maximum likelihood method. We used some measurements to compare between the results such as number of steps for convergence (convergence condition), the estimated values for AIC, BIC and the RMSE value. The results show the numerical solution that we got by applying first strategy convergence faster than the solution that we got by applying second strategy. Moreover, the MRSE estimated by applying the first strategy is lower than the MRSE estimated by applying second strategy for the simulation study with different noise levels and different samples size.

Regional Difference and Spatial Convergence of Land Use Carbon Emissions in Three Urban Agglomerations of Yangtze River Economic Belt

It is of great significance to explore the regional differences of land use carbon emission （LUCE） in the Yangtze River Economic Belt and the path of coordinated emission reduction for regional sustainable development. Based on the LUCE estimation method, this study scientifically calculated the LUCE of the three major urban agglomerations of the Yangtze River Economic Belt （Yangtze River Delta, middle reaches of the Yangtze River, and Chengdu-Chongqing urban agglomeration） from 2010 to 2020. Kernel density estimation and the spatial convergence model were used to study the dynamic evolution, regional differences, and convergence characteristics of LUCE. The results showed that： ① The carbon absorption of forest land, water areas, grassland, and unused land were relatively small in terms of carbon emissions from cultivated land and construction land. The carbon emission of construction land increased gradually, whereas the carbon absorption of four carbon sinks fluctuated little during the study period. ② The core density curves of different urban agglomerations showed different distribution patterns, extensibility, and polarization characteristics but generally tended to be balanced. ③ From 2010 to 2020, the LUCE of the Yangtze River Economic Belt as a whole showed the spatio-temporal characteristics of increasing first and then decreasing and high in the east and low in the west. The LUCE of the central cities of the three urban agglomerations were at the highest level steadily, and stable coupling mechanisms had not been established between the economic development level and the ecological environment. ④ The LUCE of the three urban agglomerations in the Yangtze River Economic Belt all had absolute β convergence and also had conditional β convergence under the model control variables such as economic development level, urbanization level, industrial structure, population density, and environmental regulation, etc., and the conditional convergence speed was greater than the absolute convergence speed in each region. The convergence speed of the Yangtze River Delta urban agglomeration was the slowest. The above conclusions provide support for the coordinated emission reduction path of the three urban agglomerations in the Yangtze River Economic Belt and are also conducive to actively and steadily promoting the realization of the goals of carbon peak and carbon neutralization.

Examining Sigma and Beta Convergence in Emerging Market Economies

This study examines convergence among the select emerging market economies (EMEs) over two decades, from 2000 to 2020. The coefficient of variation was used to measure sigma convergence. Cross-sectional and panel regression analyses were performed to examine unconditional and conditional beta convergence, respectively. The macroeconomic variables chosen for the panel regression analysis were gross fixed capital formation, current account balance, inflation, research and development expenditure, world governance index and life expectancy index. The results supported the presence of convergence (both sigma and beta) among the EMEs over the selected period. In addition, it was found that, except for the current account balance, all selected variables contributed significantly to the growth process of EMEs.

Robust optimized weights spectrum: Enhanced interpretable fault feature extraction method by solving frequency fluctuation problem

Machine condition monitoring (MCM) plays a pivotal role in ensuring the reliability, safety, and efficiency of a production and operation system. Fault feature extraction (FFE), as an important step within MCM, aims to filter out interference components (ICs) and extract fault components (FCs) from raw signals. Consequently, it facilitates incipient fault detection and performance degradation assessment. A recently proposed optimized weights spectrum (OWS) provided a data-driven FFE methodology with a strong theoretical foundation, but it was found that the OWS is highly sensitive to a frequency fluctuation problem caused by rotational speed fluctuations and sensor errors, which may result in fake fault signatures. Therefore, a robust optimized weights spectrum (ROWS) is proposed in this paper to solve the frequency fluctuation problem. The ROWS is inspired by an intuitive idea that employs functions with adaptive frequency bandwidths instead of isolated spectral lines to represent frequency components, thus mitigating the impact of the frequency fluctuation problem. To adaptively determine the optimal parameters for these functions and estimate the corresponding ROWS, an alternative optimization strategy is adopted. Then, the proposed ROWS can be obtained when convergence conditions of this strategy are satisfied. Finally, the effectiveness and superiority of the proposed ROWS are verified by three real-world cases, i.e., the proposed ROWS can solve the frequency fluctuation problem and provide robust results for interpretable FFE.

Spatial conditional convergence analysis of total factor energy efficiency based on industry transfer and technology diffusion

Measuring energy efficiency is important to achieve the goal of sustainable economic development. This paper adopts the Malmquist index to measure the trend of regional total factor energy efficiency. This paper analyses the spatial aggregation characteristics of TFEE and the impact mechanism of industrial transfer and technology diffusion on TFEE convergence from a dynamic perspective. The results of the study show that there is a large gap in TFEE between regions in China, with a spatial characteristic of “high in the south and low in the north”. In 2006–2021, the convergence rate of TFEE shows a slowing down trend. Industrial transfer has a negative effect on TFEE. The impact of technology diffusion on TFEE is different in different periods. The impact of researchers, technology market, technology introduction, and import-export on TFEE have significant differences. The convergence rate of the south is higher than that of the north. The impact of industrial transfer and technology diffusion on TFEE in the two parts is different. Policymakers should implement differentiated energy policies based on the characteristics of the industrial structure and technological development of each region. They should actively guide technological innovation, promote industrial diversification, and build a clean and efficient energy system.

Digital economy empowered entrepreneurship

PurposeAs an important engine of economic growth, the digital economy is bringing new opportunities for the promotion of entrepreneurship. However, key questions regarding the extent of the effect of the digital economy on entrepreneurship remain unanswered. This study examines how the digital economy influences entrepreneurship in China using provincial data from 2011–2020, applying convergence tests and spatial econometric models.Design/methodology/approachBased on theoretical analysis and using macro provincial data covering the period of 2011–2020, we adopt a diversified empirical analytical method and apply a combination of the convergence trend test, spatial auto correlation test, and spatial Durbin model to test the research hypotheses.FindingsFirst, there is spatial correlation between the digital economy and entrepreneurship. Second, the overall trend of China’s digital economy shows s convergence, with the whole country and the eastern region showing absolute β convergence and the whole country as well as the central and western regions showing β conditional convergence. Third, the digital economy can significantly promote entrepreneurship and has spatial spillover effects. Moreover, higher education has a negative moderating effect on the process of digital economy empowering entrepreneurship.Research limitations/implicationsStudying the spatially correlated impacts of the digital economy on entrepreneurship enhances our understanding of its contribution to economic growth. Policy-makers can use these findings to develop targeted digital infrastructure investments in lagging provinces, guide entrepreneurs to better grasp the opportunities of the digital economy, and provide support for innovation and entrepreneurship. The findings also could offer Chinese experience that can be used to guide developing countries in utilizing the digital economy to enable entrepreneurship.Originality/valueThis paper expands and enriches the analytical focus on digital economy-empowered entrepreneurship and complements the current theoretical research on the moderating effect of the digital economy in empowering entrepreneurship.

Improved modulus-based matrix splitting iteration methods for a class of horizontal implicit complementarity problems

Recently, the modulus-based matrix splitting (MMS) iteration method has been successfully extended to solve the horizontal implicit complementarity problem (HICP). However, due to the existence of two system matrices and one nonlinear term, in addition to an equivalent fixed-point equation of the HICP, a system of linear equations has to be solved at each iteration to satisfy both the nonnegative constraint and the orthogonal constraint. This costs very expensive. In this paper, by introducing an additional judgement criterion after obtaining the approximate solution, a class of improved MMS (IMMS) iteration methods are proposed. By suitably choosing the judgement criterion, the IMMS iteration methods do not need to solve such system of linear equations at each iteration and thus greatly improves the computing efficiency. Convergence conditions of the IMMS iteration methods are studied when the system matrices are positive definite matrices and H+-matrices, respectively. Finally, two numerical examples are presented to show the effectiveness of the proposed IMMS iteration methods and their advantages over the existing MMS iteration methods when solving the HICP.

Consensus of multi‐agent system with reaction‐diffusion terms and time delays via output‐feedback adaptive boundary control

SummaryMulti‐agent systems (MASs) are widely used in many necessary fields such as cybersecurity, precision agriculture, satellites, and smart grids. In many practical processes, a proportion of states cannot be obtained directly. Therefore, it is desired to design an observer. This article explores the utilization of output‐feedback adaptive control techniques to achieve consensus in MASs based on partial differential equations (PDEs) with reaction‐diffusion terms and time delays. First, in dealing with time‐invariant delays, an observer according to the Luenberger method is proposed to assess the state of agents. Convergence conditions of the estimated states are obtained by employing Lyapunov functions and Wirtinger inequality. Using the obtained estimated states, a boundary adaptive control strategy is proposed to make the error system consensus. The merit of this control method lies in the fact that communication between agents only occurs at the spatial boundary position, not throughout the entire spatial domain, and the parameters of the system can be constantly changed. Consensus criteria of MASs with time‐invariant delays are obtained by using the output‐feedback adaptive control, and the results are further generalized to the model with time‐varying delays. Lastly, two experimental scenarios are provided to show the practicality of the proposed theories.

Tipler naked singularities in N dimensions

Abstract A spacetime singularity, identified by the existence of incomplete causal geodesics in the spacetime, is called a (Tipler) strong curvature singularity if the volume form acting on independent Jacobi fields along causal geodesics vanishes in the approach of the singularity. It is called naked if at least one of these causal geodesics is past incomplete. Here, we study the formation of strong curvature naked singularities arising from spherically symmetric gravitational collapse of general type-I matter fields in an arbitrarily finite number of dimensions. In the spirit of Joshi and Dwivedi (1993 Phys. Rev. D 47 5357), and Goswami and Joshi (2007 Phys. Rev. D 76 084026), beginning with regular initial data, we derive two distinct (but not mutually exclusive) conditions, which we call the positive root condition (PRC) and the simple positive root condition (SPRC), that serve as necessary and sufficient conditions, respectively, for the existence of naked singularities. In doing so, we generalize the results of both the aforementioned works. We further restrict the PRC and the SPRC by imposing the curvature growth condition (CGC) of Clarke and Krolak (1985 J. Geom. Phys. 2(2) 127) on all causal curves that satisfy the causal convergence condition. The CGC then gives a sufficient condition ensuring that the naked singularities implying the PRC and implied by the SPRC, are of strong curvature type and hence correspond to the inextendibility of the spacetime. Using the CGC, we extend the results of Mosani et. al. (2020 Phys. Rev. D 101 044052) (that hold for dimension N=4) to the case N=5, showing that strong curvature naked singularities can occur in this case. However, for the case N≥6, we show that past-incomplete causal curves that identify naked singularities do not satisfy the CGC. These results shed light on the validity of the cosmic censorship conjectures in arbitrary dimensions.

A coupled FDEM-IBM-level set method for water entry of multiple flexible objects

In order to construct a versatile technique for water entry problems with structural deformations of multiple bodies, a novel hybrid algorithm, which couples the improved immersed boundary method (IBM) based fluid solver with the finite-discrete element method (FDEM) based structural solver, is proposed. The incompressible Navier-Stokes equations added with a virtual body force are employed for the hydrodynamic behaviors in the presence of elastic bodies. Representing the boundaries of solids by a set of immersed boundary points, the direct forcing IBM is enhanced to tackle the sharply moving objects of arbitrary geometries with inherent advantages. Such treatment enables the velocity boundary condition on the interface of the fluid and solid along with the divergence-free condition to be ensured simultaneously in the implicit computation of the added body force, which give rise to a more accurate depiction for fluid-solid interactions (FSI). Described by the finite element method (FEM), the deformable objects are allowed to deform and collide with each other during water entry which is seldom reported in literature. The contact interactions are calculated according to the distance potential function based discrete element method on the outermost layer of the finite elements. Furthermore, the improved conservative level set method is adopted to deal with the violently distorted free surface during hydroelastic impact. The strongly coupled FSI system is then resolved through a partitioned procedure, where sub-iterations are required in each time step to satisfy the convergence conditions exactly. The reliability of the present solver is validated by the classical cases of slamming of a flexible wedge and a free-falling cylindrical shell, along with dam break through an elastic gate and the settlement of two interactional circular cylinders. The accuracy and convergence rates of the proposed algorithm are also studied. Finally, a self-designed case, in which water entry of multiple compliant cylindrical shells is investigated, is performed to illustrate the effectiveness of the current approach, and a three-dimensional case study of multiple rocks impacting on the calm water surface demonstrates its great potential in practical applications.

Projection FxLMS framework of active noise control against impulsive noise environments

This paper focuses on active noise control in the presence of disturbance from an α-stable distribution. The filtered-x fractional lower-order covariance algorithm has been introduced to enhance the performance of traditional algorithms in impulsive noise environments. For minimal adjustment of the weight vector, another filtered-x normalized fractional lower-order covariance (FxNFLOC) algorithm is proposed. Furthermore, the projection approach of the filtered-x least mean square (FxLMS) algorithm is explored. Within this framework, a new algorithm called filtered-x least mean logarithmic square (FxLMLS), which employs a logarithmic function, is devised. The convergence conditions of the developed schemes are also derived. Numerical examples demonstrate the effectiveness and superior performance of the FxNFLOC and FxLMLS algorithms in handling impulsive noise over existing competitors in various scenarios.

Physics‐informed reinforcement learning for optimal control of nonlinear systems

AbstractThis article proposes a model‐free framework to solve the optimal control problem with an infinite‐horizon performance function for nonlinear systems with input constraints. Specifically, two Physics‐Informed Neural Networks (PINNs) that incorporate the knowledge of the Lyapunov stability theorem and the convergence conditions of the policy iteration algorithm are utilized to approximate the value function and control policy, respectively. Then, a Reinforcement Learning (RL) algorithm that does not require any first‐principles or data‐driven models of nonlinear systems is developed to iteratively learn a nearly optimal control policy. Furthermore, we provide a rigorous theoretical analysis showing the conditions that ensure the stability of closed‐loop systems with the control policy learned by RL and guarantee the convergence of the iteration algorithm. Finally, the proposed Physics‐Informed Reinforcement Learning (PIRL) method is applied to a chemical process example to demonstrate its effectiveness.