Distribution dynamics,regional differences,and convergence of sustainable development of cities and communities in China

China is one of the most populated and rapidly urbanizing countries worldwide and was among the earliest countries to integrate sustainable development into urban construction.To achieve high-quality development and implement the objectives of“Transforming Our World:The 2030 Agenda for Sustainable Development”,it is crucial to measure and analyze the current level of sustainable development of cities in China.Following the principles of relevance,scientific rigor,universality,reliability,and timeliness,this study constructs an assessment index system for sustainable development,covering seven themes corresponding to the UN Sustainable Development Goal 11.Through detailed calculations,we obtained sustainable development indices for 139 Chinese cities from 2016 to 2022 and analyzed them in three dimensions:distribution dynamics,regional differences,and convergence.The key findings are as follows.First,the level of sustainable development showed improvement,with the average score of included cities increasing by 11.88%from 2016 to 2022.Second,the level of sustainable development was relatively balanced,maintaining low Gini coefficients between 0.05 and 0.06.Third,a weak overallσconvergence feature existed,with increased differentiation in 2021.From a regional perspective,aσconvergence feature was observed in the northeastern but not in the western region.Fourth,both overall absoluteβ-convergence and conditionalβeffects were significant.Regional absoluteβ-convergence and conditionalβ-convergence were also significant.This study contributes to the literature by providing evidence of China’s urban sustainable development,offering policy insights for deepening the implementation of development goals in the future,and providing experiential reference for other developing countries to achieve sustainable development.

Impact of the central Pacific zonal wind divergence and convergence on the central Pacific El Nio event

The central Pacific（CP） zonal wind divergence and convergence indices are defined, and the forming mechanism of CP El Nio（La Nia） events is discussed preliminarily. The results show that the divergence and convergence of the zonal wind anomaly（ZWA） are the key process in the forming of CP El Nio（La Nia） events. A correlation analysis between the central Pacific zonal wind divergence and convergence indices and central Pacific El Nio indices indicates that there is a remarkable lag correlation between them. The central Pacific zonal wind divergence and convergence indices can be used to predict the CP events. Based on these results, a linear regression equation is obtained to predict the CP El Nio（La Nia） events 5 months ahead.

Technology Convergence and Divergence in China’s Electronic Industries:Evidence from Patents

By thoroughly reviewing international studies on technology convergence and divergence, four kinds of hypothesis are proposed based on patent data Herfindhal index （HI） measurement. The main fmding is that technology convergence does exist, based on patent technology records in China, primarily driven by overseas companies＇ strategic behavior, such as field intensiveness, competition during technology maturity session, and patent technology growth.

THE DIVERGENCE-CONVERGENCE EFFECT OF SURFACE CURRENT AND ITS ACTION ON THE BOHAI SEA

The action of the wind field and the influence of topography can cause divergence or convergence of surface current. The existence of the divergence-convergence effect is proved and the dynamical significance of the divergent or convergent state and its link with many marine phenomena are pointed out. Divergence fields of surface current in the Bohai Sea in winter and summer are obtained by numerical modelling describing the divergence-convergence character of seasonally wind-driven current. The relation between the effect and seasonal marine phenomena is discussed. Study on the divergence-convergence effect of surface current (DCESC)can be an indirect method for testing the calculated results.

Regional Disparity and Convergence of China's Inbound Tourism Economy

Comprehending regional characteristics and influencing factors of China＇s inbound tourism economy is im- portant to make effective policies that will help inbound tourism develop harmoniously and shrink regional disparity. This paper studied the regional disparity and convergence of China＇s inbound tourism economy during 1996-2008 with the methods of a-convergence, club convergence and r-convergence. The results indicate that 1） inbound tourism receipts per capita （ITRPC） of the whole country, the eastern, central and western regions presented the rapid increasing trend; 2） ITRPC of the whole country was characterized by convergence; 3） the eastern region presented club con- vergence, but the central and western regions did not show this trend; 4） the star-hotel levels and investment in fixed assets for the tourism industry per capita had a same trend to growth rates of ITRPC, promoting inbound tourism de- velopment, and there was no difference among the 31 provinces （municipalities） in the mainland of China; 5） but the proportion of employed persons in the tourism industry accounting for total population and the proportion of the terti- ary industry accounting for GDP had a reversal trend to growth rates of ITRPC, shrinking the provincial disparity in inbound tourism economy, and there were differences between the developed provinces and the developing provinces. Based on these analyses, we put forward some suggestions for the developing provinces to speed up inbound tourism economy.

SPATIAL-TEMPORAL DYNAMICS OF REGIONAL CONVERGENCE AT COUNTY LEVEL IN JIANGSU

The dynamics of regional convergence include spatial and temporal dimensions. Spatial Markov chain can be used to explore how regions evolve by considering both individual regions and their geographic neighbors. Based on per capita GDP data set of 77 counties from 1978 to 2000, this paper attempts to investigate the spatial-temporal dynamics of regional convergence in Jiangsu. First, traditional Markov matrix for five per capita GDP classes is constructed for later comparison. Moreover, each region’s spatial lag is derived by averaging all its neighbors’ per capita GDP data. Conditioning on per capita GDP class of its spatial lag at the beginning of each year, spatial Markov transition probabilities of each region are calculated accordingly. Quantitatively, for a poor region, the probability of moving upward is 3.3% if it is surrounded by its poor neighbors, and even increases to 18.4% if it is surrounded by its rich neighbors, but it goes down to 6.2% on average if ignoring regional context. For a rich region, the probability of moving down ward is 1.2% if it is surrounded by its rich neighbors, but increases to 3.0% if it is surrounded by its poor neighbors, and averages 1.5% irrespective of regional context. Spatial analysis of regional GDP class transitions indicates those 10 upward moves of both regions and their neighbors are unexceptionally located in the southern Jiangsu, while downward moves of regions or their neighbors are almost in the northern Jiangsu. These empirical results provide a spatial explanation to the "convergence clubs" detected by traditional Markov chain.

GLOBAL CONVERGENCE OF A TRUST REGION ALGORITHM USING INEXACT GRADIENT FOR EQUALITY-CONSTRAINED OPTIMIZATION

A trust-region algorithm is presented for a nonlinear optimization problem of equality-constraints. The characterization of the algorithm is using inexact gradient information. Global convergence results are demonstrated where the gradient values are obeyed a simple relative error condition.

A CLASS OF TRUST REGION METHODS FOR LINEAR INEQUALITY CONSTRAINED OPTIMIZATION AND ITS THEORY ANALYSIS Ⅱ．LOCAL CONVERGENCE RATE AND NUMERICAL TESTS

In this paper we prove that a class of trust region methods presented in part I is superlinearly convergent. Numerical tests are reported thereafter. Results by solving a set of typical problems selected from literatures have demonstrated that our algorithm is effective.

A CLASS OF TRUST REGION METHODS FOR LINEAR INEQUALITY CONSTRAINED OPTIMIZATION AND ITS THEORY ANALYSIS:I.ALGORITHM AND GLOBAL CONVERGENCEXIU NAIHUA

A class of trust region methods for solving linear inequality constrained problems is proposed in this paper. It is shown that the algorithm is of global convergence.The algorithm uses a version of the two-sided projection and the strategy of the unconstrained trust region methods. It keeps the good convergence properties of the unconstrained case and has the merits of the projection method. In some sense, our algorithm can be regarded as an extension and improvement of the projected type algorithm.

China’s urban green innovation:Regional differences,distribution dynamics,and convergence

Urban green innovation(UGI)is essential to environmental protection,ecological conservation,and high quality economic growth.Using green patents,our study assessed the level of UGI of 287 Chinese cities at and above the prefecture level.Then,using the Dagum Gini coefficient,kernel density estimation(KDE),and con‐vergence models,we examined regional differences,distribution dynamics,and convergence of UGI across China.The study’s findings are as follows:(1)Overall,regional differences in UGI tended to narrow,and the main contributor to these differences was the difference between economic zones.(2)KDE showed that the level of UGI was rising,which was polarized within each economic zone.(3)The national UGI in economic zones other than the Northeast and Middle Yellow River Economic Zones featured significantσconvergence,while each economic zone showed absolute and conditionalβconvergence.

Assessment of Electricity Productivity in China:Regional Differences and Convergence

Electricity productivity is regarded as a major assessment indicator in the design of energy saving policies,given that China has entered a“New Normal”of economic development.In fact,enhancing electricity productivity in an all-round way,as is one of the binding indicators for energy and environmental issues,means that non-growth target of total electric energy consumption in the economic development is feasible.The Gini coefficient,Theil index,and Mean log deviation are utilized to measure regional differences in China’s electricity productivity from 1997 to 2016 in five regions,and conditionalβconvergence is empirically analyzed with the spatial Durbin model.The results show that:(1)China’s electricity productivity is improving,while the overall feature is that the eastern area has a higher efficiency than the western area.(2)The difference in electricity productivity is the smallest in the northeast and the largest in the northwest.Interregional difference plays an important role and is the main cause for the differences.(3)The electricity productivity in China exhibitsβconvergence,except for the northwest.The positive driving factor is urbanization level(0.0485%),and the negative driving factor is FDI(–0.0104%).Moreover,the urbanization rate(0.0669%),foreign direct investment(0.0960%),and the industrial structure(–0.0769%)have a spatial spillover effect on improving regional electricity productivity.Based on this conclusion,the study provides some recommendations for saving energy policy design in China’s power industry.

The Convergence Analysis of Chinese Regional Inequality

Based on the convergence theory, this paper discusses Chinese regional economic inequality among 30 provinces, which are divided into three groups, that is, Traditional Advanced Regions group, New Advanced Regions group and Less Developed Regions group. It is verified that regional income growth does not present absolute beta convergence or sigma convergence, but presents conditional beta convergence from 1978 to 2003. Those economic policies of reform and opening-up to the outside world are provided with regionally heterogeneous characteristics and are powerful enough to influence regional performance in growth.

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 in 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 by taking into account the existence of spatial heterogeneity according to five specifications of spatial models. Thus, apart from environmental domain, we found 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.

GLOBAL CONVERGENCE OF NONMONOTONIC TRUST REGION ALGORITHM FOR NONLINEAR OPTIMIZATION

A trust region algorithm for equality constrained optimization is given in this paper.The algorithm does not enforce strict monotonicity of the merit function for every iteration.Global convergence of the algorithm is proved under the same conditions of usual trust region method.

GLOBAL CONVERGENCE OF TRUST REGION ALGORITHM FOR EQUALITY AND BOUND CONSTRAINED NONLINEAR OPTIMIZATION

This paper presents a trust region two phase model algorithm for solving the equality and bound constrained nonlinear optimization problem. A concept of substationary point is given. Under suitable assumptions,the global convergence of this algorithm is proved without assuming the linear independence of the gradient of active constraints. A numerical example is also presented.

Using Converging Strategies to Reduce Divergence in Intercultural User Interface Design

This chapter starts with an introduction illuminating the theoretical back-ground necessary for taking culture into account in HCI design. Definitions of concepts used are provided followed by a historical overview on taking culture into account in HCI design. Subsequently, a glimpse of the current state of research in culture-centered HCI design is derived from secondary literature providing the gist of the structures, processes, methods, models and theoretic approaches concerning the relationship between culture and HCI design (“converging” strategies). After presenting controversies and challenges, a short discussion of results from empirical studies and design recommendations for culture-centered HCI design lead to implications and trends in future intercultural user interface design research to close the knowledge gap (the “divergence”) regarding the relationship between culture and Human-Computer Interaction (HCI), i.e. converging the divergence to reach the convergent divergence.

GENERALIZED MATRIX MULTISPLITTING RELAXATION METHODS AND THEIR CONVERGENCE

In this paper, we set up a general framework of parallel matrix mullisplitting relaxation methods for solving large scale system of linear equations. We investigate the convergence properties of this framework and give several sufficient conditions ensuring it to converge as well as diverge. At last, we conclude a necessary and sufficient condition for the convergence of this framework when the coefficient matrix is an L-matrix.

A SUPERLINEARLY CONVERGENT TRUST REGION ALGORITHM FOR LC^1 CONSTRAINED OPTIMIZATION PROBLEMS

In this paper, a new trust region algorithm for nonlinear equality constrained LC1 optimization problems is given. It obtains a search direction at each iteration not by solving a quadratic programming subprobiem with a trust region bound, but by solving a system of linear equations. Since the computational complexity of a QP-Problem is in general much larger than that of a system of linear equations, this method proposed in this paper may reduce the computational complexity and hence improve computational efficiency. Furthermore, it is proved under appropriate assumptions that this algorithm is globally and super-linearly convergent to a solution of the original problem. Some numerical examples are reported, showing the proposed algorithm can be beneficial from a computational point of view.

The Hyperspace of the Regions Below of Continuous Maps from the Converging Sequence

Let S = {1,1/2,1/2^2,…,1/∞ = 0} and I = [0, 1] be the unit interval. We use ↓USC（S） and ↓C（S） to denote the families of the regions below of all upper semi-continuous maps and of the regions below of all continuous maps from S to I and ↓C0（S） = {↓f∈↓C（S） ： f（0） = 0}. ↓USC（S） endowed with the Vietoris topology is a topological space. A pair of topological spaces （X, Y） means that X is a topological space and Y is its subspace. Two pairs of topological spaces （X, Y） and （A, B） are called pair-homeomorphic （≈） if there exists a homeomorphism h ： X→A from X onto A such that h（Y） = B. It is proved that, （↓USC（S）,↓C0（S）） ≈（Q, s） and （↓USC（S）,↓C（S）／ ↓C0（S））≈（Q, c0）, where Q = [-1,1]^ω is the Hilbert cube and s = （-1,1）^ω,c0= {（xn）∈Q ： limn→∞= 0}. But we do not know what （↓USC（S）,↓C（S））is.

A Superlinerly Convergent ODE-type Trust Region Algorithm for LC^1 Optimization Problems

In this paper, a new trust region algorithm for unconstrained LC1 optimization problems is given. Compare with those existing trust regiion methods, this algorithm has a different feature: it obtains a stepsize at each iteration not by soloving a quadratic subproblem with a trust region bound, but by solving a system of linear equations. Thus it reduces computational complexity and improves computation efficiency. It is proven that this algorithm is globally convergent and locally superlinear under some conditions.