Spatial Differentiation and Convergence Trend of High-quality Development Level of China’s Tourism Economy

This paper aims to interpret the connotation of high-quality development of tourism economy(HQTE)from the perspective of the new development concepts of innovation,coordination,green,openness and sharing,and then to evaluate the spatial differenti-ation of China’s HQTE based on provincial panel data from 2009 to 2018.Specifically,we employ the spatial convergence model to ex-plore the absolute and conditionalβconvergence trends of HQTE in the whole country and the eastern,central and western regions of China.Our empirical results reveal that:1)within the decade,from 2009 to 2018,regions of China with the highest HQTE index is its eastern region followed by the central region and then the western region,but the fastest growing one is the western region of China fol-lowed by the central region and then the eastern region.2)Whether or not the spatial effect is included,there are absolute and condition-alβconvergence in HQTE in the whole country and aforementioned three regions.3)The degree of government attention as well as the level of economic development and location accessibility are the positive driving factors for the convergence of HQTE in the whole country and the three regions.The degree of marketization and human capital have not passed the significance test either in the whole country or in the three regions.The above conclusions could deepen the understanding of the regional imbalance and spatial conver-gence characteristics of HQTE,clarify the primary development objects,and accomplish the goal of China’s HQTE.

The Convergence Rate of Fréchet Distribution under the Second-Order Regular Variation Condition

In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.

Strong Convergence Rates of Double Kernel Estimates of Conditional Desity Under Stationary Sequences

In the paper,we study the strong convergence rates of double kernel estimates of conditional density under stationary sequences.

GLOBAL CONVERGENCE OF A CLASS OF OPTIMALLY CONDITIONED SSVM METHODS

This paper explores the convergence of a class of optimally conditioned self scaling variable metric (OCSSVM) methods for unconstrained optimization. We show that this class of methods with Wolfe line search are globally convergent for general convex functions.

Probabilistic assessment of tunnel convergence considering spatial variability in rock mass properties using interpolated autocorrelation and response surface method

This study aims at the probabilistic assessment of tunnel convergence considering the spatial variability in rock mass properties. The method of interpolated autocorrelation combined with finite difference analysis is adopted to model the spatial variability of rock mass properties. An iterative procedure using the first-order reliability method(FORM) and response surface method(RSM) is employed to compute the reliability index and its corresponding design point. The results indicate that the spatial variability considerably affects the computed reliability index. The probability of failure could be noticeably overestimated in the case where the spatial variability is neglected. The vertical scale of fluctuation has a much higher effect on the probabilistic result with respect to the tunnel convergence than the horizontal scale of fluctuation. And the influence of different spacing of control points on the computational accuracy is investigated.

Agricultural Non-point Source Pollution in China:Evaluation,Convergence Characteristics and Spatial Effects

In this study,an inventory analysis approach was used to investigate the intensity of agricultural non-point source pollution(ANSP)and its spatial convergence at national and provincial levels in China from 1999 to 2017.On this basis,spatial factors affecting ANSP were explored by constructing a spatial econometric model.The results indicate that:1)The intensity of China's ANSP emission showed an overall upward trend and an obvious spatial difference,with the values being high in the eastern and central regions and relatively low in the western region.2)Significant spatial agglomeration was shown in China's ANSP intensity,and the agglomeration effect was increasing gradually.3)In the convergence analysis,a spatial lag model was found applicable for interpretation of the ANSP intensity,with the convergence rate being accelerated after considering the spatial factors but slower than that of regional economic growth.4)The spatial factors affecting the ANSP intensity are shown to be reduced by improving agricultural infrastructure investment,labor-force quality,and crop production ratio,while the expansion of agricultural economy scale and precipitation and runoff have positive impact on ANSP in the study region.However,agricultural research and development(R&D)investment showed no direct significant effect on the ANSP intensity.Meanwhile,improving the quality of the labor force would significantly reduce the ANSP intensity in the surrounding areas,while the precipitation and runoff would significantly increase the pollution of neighboring regions.This research has laid a theoretical basis for formulation and optimization of ANSP prevention strategies in China and related regions.

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.

Fully asynchronous distributed optimization with linear convergence over directed networks

We study distributed optimization problems over a directed network,where nodes aim to minimize the sum of local objective functions via directed communications with neighbors.Many algorithms are designed to solve it for synchronized or randomly activated implementation,which may create deadlocks in practice.In sharp contrast,we propose a fully asynchronous push-pull gradient(APPG) algorithm,where each node updates without waiting for any other node by using possibly delayed information from neighbors.Then,we construct two novel augmented networks to analyze asynchrony and delays,and quantify its convergence rate from the worst-case point of view.Particularly,all nodes of APPG converge to the same optimal solution at a linear rate of O(λ^(k)) if local functions have Lipschitz-continuous gradients and their sum satisfies the Polyak-?ojasiewicz condition(convexity is not required),where λ ∈(0,1) is explicitly given and the virtual counter k increases by one when any node updates.Finally,the advantage of APPG over the synchronous counterpart and its linear speedup efficiency are numerically validated via a logistic regression problem.

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.

Dynamic analysis of spatial convergence of green total factor productivity in China's primary provinces along its Belt and Road Initiative

This paper focuses on China's primary provinces along its Belt and Road Initiative,measures and analyses the provincial green total factor productivity (GTFP) development by GML index based on SBM directional distance function,discusses the temporal evolution characteristics of spatial convergence of the provincial GTFP under multiple spatial weight matrices,and estimates the net effect of China's Belt and Road Initiative on the development gap of provincial GTFP by regression discontinuity.The research shows that the provincial GTFP is generally good while the internal gap is relatively large.There is spatial absolute βconvergence and condition βconvergence in provincial GTFP,and the convergence speed has been signifcantly accelerated since the construction of China's Belt and Road Initiative.The current low economy level and infrastructure allocation efficiency of primary provinces restrict the GTFP development,while government expenditure has promoted the GTFP development,trade between provinces and countries along China's Belt and Road Initiative is negative to GTFP.China's Belt and Road Initiative has significantly narrowed the gap of provincial GTFP development with the net effect of-0.016.

A SUFFICIENT CONDITION OF CONVERGENCE FOR CLIFFORD CONTINUED FRACTIONS

In this article, a sufficient condition for a Clifford continued fraction to be convergent is established, and some applications are given.

Analysis of convergence for initial condition estimation of coupled map lattices based on symbolic dynamics

A novel approach to the inverse problem of diffusively coupled map lattices is systematically investigated by utilizing the symbolic vector dynamics. The relationship between the performance of initial condition estimation and the structural feature of dynamical system is proved theoretically. It is found that any point in a spatiotemporal coupled system is not necessary to converge to its initial value with respect to sufficient backward iteration, which is directly relevant to the coupling strength and local mapping function. When the convergence is met, the error bound in estimating the initial condition is proposed in a noiseless environment, which is determined by the dimension of attractors and metric entropy of the system. Simulation results further confirm the theoretic analysis, and prove that the presented method provides the important theory and experimental results for better analysing and characterizing the spatiotemporal complex behaviours in an actual system.

LOCAL CONVERGENCE OF INEXACT NEWTON-LIKE METHOD UNDER WEAK LIPSCHITZ CONDITIONS

The paper develops the local convergence of Inexact Newton-Like Method(INLM)for approximating solutions of nonlinear equations in Banach space setting.We employ weak Lipschitz and center-weak Lipschitz conditions to perform the error analysis.The obtained results compare favorably with earlier ones such as[7,13,14,18,19].A numerical example is also provided.

The convergence rate and necessary-and-sufficient condition for the consistency of isogeometric collocation method

Although the isogeometric collocation(IGA-C)method has been successfully utilized in practical applications due to its simplicity and efficiency,only a little theoretical results have been established on the numerical analysis of the IGA-C method.In this paper,we deduce the convergence rate of the consistency of the IGA-C method.Moreover,based on the formula of the convergence rate,the necessary and sufficient condition for the consistency of the IGA-C method is developed.These results advance the numerical analysis of the IGA-C method.

On the convergence for PNQD sequences with general moment conditions

Let fX;Xn;n≥1g be a sequence of identically distributed pairwise negative quadrant dependent(PNQD)random variables and fan;n1g be a sequence of positive constants with an=f(n)and f(θ^k)=f(θ^k-1)for all large positive integers k,where 1<θ≤βand f(x)>0(x≥1)is a non-decreasing function on[b;+1)for some b≥1:In this paper,we obtain the strong law of large numbers and complete convergence for the sequence fX;Xn;n≥1g,which are equivalent to the general moment conditionΣ∞n=1P(|X|>an)<1.Our results extend and improve the related known works in Baum and Katz[1],Chen at al.[3],and Sung[14].

Complete Convergence Properties of the Sums for -mixing Sequences of Random Variables

This paper discusses complete convergence properties of the sums of -mixing random sequences.As a result,we improve the corresponding results of Wu Qunying(2001). And extended the Baum and Katz complete convergence to the case of -mixing random sequences by moment inequality and truncating without necessarily adding any extra conditions.

WEAK ORLICZ SPACE AND ITS CONVERGENCE THEOREMS

In this article, a class of weak Orlicz function spaces is defined and their basic properties are discused. In particular, for the sequences in weak Orlicz space, we establish several basic convergence theorems including bounded convergence theorem, control convergence theorem and Vitali-type convergence theorem and so on. Moreover, the conditional compactness of its subsets is also discussed.

Evaluating Spatial Heterogeneity of Land Surface Hydrothermal Conditions in the Heihe River Basin

Land surface hydrothermal conditions(LSHCs) reflect land surface moisture and heat conditions, and play an important role in energy and water cycles in soil-plant-atmosphere continuum. Based on comparison of four evaluation methods(namely, the classic statistical method, geostatistical method, information theory method, and fractal method), this study proposed a new scheme for evaluating the spatial heterogeneity of LSHCs. This scheme incorporates diverse remotely sensed surface parameters, e.g., leaf area index-LAI, the normalized difference vegetation index-NDVI, net radiation-Rn, and land surface temperature-LST. The LSHCs can be classified into three categories, namely homogeneous, moderately heterogeneous and highly heterogeneous based on the remotely sensed LAI data with a 30 m spatial resolution and the combination of normalized information entropy(S’) and coefficient of variation(CV). Based on the evaluation scheme, the spatial heterogeneity of land surface hydrothermal conditions at six typical flux observation stations in the Heihe River Basin during the vegetation growing season were evaluated. The evaluation results were consistent with the land surface type characteristics exhibited by Google Earth imagery and spatial heterogeneity assessed by high resolution remote sensing evapotranspiration data. Impact factors such as precipitation and irrigation events, spatial resolutions of remote sensing data, heterogeneity in the vertical direction, topography and sparse vegetation could also affect the evaluation results. For instance, short-term changes(precipitation and irrigation events) in the spatial heterogeneity of LSHCs can be diagnosed by energy factors, while long-term changes can be indicated by vegetation factors. The spatial heterogeneity of LSHCs decreases when decreasing the spatial resolution of remote sensing data. The proposed evaluation scheme would be useful for the quantification of spatial heterogeneity of LSHCs over flux observation stations toward the global scale, and also contribute to the improvement of the accuracy of estimation and validation for remotely sensed(or model simulated) evapotranspiration.

SOLUTION OF BACKWARD HEAT PROBLEM BY MOROZOV DISCREPANCY PRINCIPLE AND CONDITIONAL STABILITY

Consider a 1-D backward heat conduction problem with Robin boundary condition. We recover u(x, 0) and u(x, to) for to ∈ (0, T) from the measured data u(x, T)respectively. The first problem is solved by the Morozov discrepancy principle for which a 3-order iteration procedure is applied to determine the regularizing parameter. For the second one, we combine the conditional stability with the Tikhonov regularization together to construct the regularizing solution for which the convergence rate is also established. Numerical results are given to show the validity of our inversion

Fusion of Multi-Pinched Plasma Beams Converging with Spatial Symmetry

Fusion reactions can be achieved by using deuterium from sea water as the fuel.The amount of deuterium in one gallon of sea water contains energy equivalent to three hundred gallons of gasoline.Satisfactory conditions of plasma temperature and density necessary to initiate fusion have been achieved in various research facilities.However,the confinement time is not sufficient for ignition due to plasma instabilities.Here we show that fatal plasma instabilities could be suppressed by the ingenious arrangement of multi-pinched plasma beams converging symmetrically in space based on the minimization principle of plasma potential energy.Confirmation tests are proposed using tiny wires containing deuterium.If successful,the results could lead to a feasible approach to obtaining commercial fusion power from sea water,hence without the need to use expensive and radioactive tritium as the fuel.