Mapping and measuring urban-rural inequalities in accessibility to social infrastructures

Equal access to social infrastructures is a fundamental prerequisite for sustainable development,but has long been a great challenge worldwide.Previous studies have primarily focused on the accessibility to social infras-tructures in urban areas across various scales,with less attention to rural areas,where inequality can be more severe.Particularly,few have investigated the disparities of accessibility to social infrastructures between urban and rural areas.Here,using the Changsha-Zhuzhou-Xiangtan urban agglomeration,China,as an example,we investigated the inequality of accessibility in both urban and rural areas,and further compared the urban-rural difference.Accessibility was measured by travel time of residents to infrastructures.We selected four types of social infrastructures including supermarkets,bus stops,primary schools,and health care,which were funda-mentally important to both urban and rural residents.We found large disparities in accessibility between urban and rural areas,ranging from 20 min to 2 h.Rural residents had to spend one to two more hours to bus stops than urban residents,and 20 min more to the other three types of infrastructures.Furthermore,accessibility to multiple infrastructures showed greater urban-rural differences.Rural residents in more than half of the towns had no access to any infrastructure within 15 min,while more than 60%of the urban residents could access to all infrastructures within 15 min.Our results revealed quantitative accessibility gap between urban and rural areas and underscored the necessity of social infrastructures planning to address such disparities.

Inequality of rural residents'income in China since the targeted poverty alleviation strategy:New trends,causes,and policy implications

Poverty and income inequality are problems faced by many countries including China.Since the implementation of Targeted Poverty Alleviation(TPA),absolute poverty has been eradicated,meanwhile,Chinese rural residents'income and inequality have experienced unprecedented new dynamics,but still,very few studies have focused on them.Hence,we attempt to examine the new trends in Chinese farmers'income inequality and to understand its causes during this period.We observe that China's urban-rural income ratio has been shrinking and the urban-rural inequality has been decreasing from 2014 to 2021.The reduction in the Theil index indicates a decrease in the regional inequality of farmers'income as well,and the decline in inter-regional inequality among eight economic zones contributes about 80%to increased equality.These new trends are caused by the fact that,with the TPA,the incomes of rural residents especially that in destitute areas,grew faster than that of urban residents and farmers in prosperous areas.The higher share of non-agricultural industry and agricultural mechanization level have significant positive impact on regional equality of farmers'income,while urban-rural dual structure has significant negative inhibitory effects.The lowest farmers'income and the highest inequality in the Northwest,and the slowest growth in the Northeast deserve more attention in rural Revitalization.From these findings,we propose four policy implications that would be applied to improve Chinese farmers'income equality,govern relative poverty,and achieve common prosperity in the post-poverty era.

Fermions: Spin, Hidden Variables, Violation of Bell’s Inequality and Quantum Entanglement

Using real fields instead of complex ones, it was recently claimed, that all fermions are made of pairs of coupled fields (strings) with an internal tension related to mutual attraction forces, related to Planck’s constant. Quantum mechanics is described with real fields and real operators. Schrodinger and Dirac equations then are solved. The solution to Dirac equation gives four, real, 2-vectors solutions ψ1=(U1D1)ψ2=(U2D2)ψ3=(U3D3)ψ4=(U4D4)where (ψ1,ψ4) are coupled via linear combinations to yield spin-up and spin-down fermions. Likewise, (ψ2,ψ3) are coupled via linear combinations to represent spin-up and spin-down anti-fermions. For an incoming entangled pair of fermions, the combined solution is Ψin=c1ψ1+c4ψ4where c1and c4are some hidden variables. By applying a magnetic field in +Z and +x the theoretical results of a triple Stern-Gerlach experiment are predicted correctly. Then, by repeating Bell’s and Mermin Gedanken experiment with three magnetic filters σθ, at three different inclination angles θ, the violation of Bell’s inequality is proven. It is shown that all fermions are in a mixed state of spins and the ratio between spin-up to spin-down depends on the hidden variables.

THE LOGARITHMIC SOBOLEV INEQUALITY FOR A SUBMANIFOLD IN MANIFOLDS WITH ASYMPTOTICALLY NONNEGATIVE SECTIONAL CURVATURE

In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality,this inequality contains a term involving the mean curvature.

Spatial Distribution Pattern and Influencing Factors of Bed-and-breakfasts(B&Bs)from the Perspective of Urban-rural Differences:A Case Study of Jiaodong Peninsula,China

There are significant differences between urban and rural bed-and-breakfasts(B&Bs)in terms of customer positioning,economic strength and spatial carrier.Accurately identifying the differences in spatial characteristics and influencing factors of each type,is essential for creating urban and rural B&B agglomeration areas.This study used density-based spatial clustering of applications with noise(DBSCAN)and the multi-scale geographically weighted regression(MGWR)model to explore similarities and differences in the spatial distribution patterns and influencing factors for urban and rural B&Bs on the Jiaodong Peninsula of China from 2010 to 2022.The results showed that:1)both urban and rural B&Bs in Jiaodong Peninsula went through three stages:a slow start from 2010 to 2015,rapid development from 2015 to 2019,and hindered development from 2019 to 2022.However,urban B&Bs demonstrated a higher development speed and agglomeration intensity,leading to an increasingly evident trend of uneven development between the two sectors.2)The clustering scale of both urban and rural B&Bs continued to expand in terms of quantity and volume.Urban B&B clusters characterized by a limited number,but a higher likelihood of transitioning from low-level to high-level clusters.While the number of rural B&B clusters steadily increased over time,their clustering scale was comparatively lower than that of urban B&Bs,and they lacked the presence of high-level clustering.3)In terms of development direction,urban B&B clusters exhibited a relatively stable pattern and evolved into high-level clustering centers within the main urban areas.Conversely,rural B&Bs exhibited a more pronounced spatial diffusion effect,with clusters showing a trend of multi-center development along the coastline.4)Transport emerged as a common influencing factor for both urban and rural B&Bs,with the density of road network having the strongest explanatory power for their spatial distribution.In terms of differences,population agglomeration had a positive impact on the distribution of urban B&Bs and a negative effect on the distribution of rural B&Bs.Rural B&Bs clustering was more influenced by tourism resources compared with urban B&Bs,but increasing tourist stay duration remains an urgent issue to be addressed.The findings of this study could provide a more precise basis for government planning and management of urban and rural B&B agglomeration areas.

Weak and Strong Convergence of Self Adaptive Inertial Subgradient Extragradient Algorithms for Solving Variational Inequality Problems

Many solutions of variational inequalities have been proposed,among which the subgradient extragradient method has obvious advantages.Two different algorithms are given for solving variational inequality problem in this paper.The problem we study is defined in a real Hilbert space and has L-Lipschitz and pseudomonotone condition.Two new algorithms adopt inertial technology and non-monotonic step size rule,and their convergence can still be proved when the value of L is not given in advance.Finally,some numerical results are designed to demonstrate the computational efficiency of our two new algorithms.

A Study of Triangle Inequality Violations in Social Network Clustering

Clustering a social network is a process of grouping social actors into clusters where intra-cluster similarities among actors are higher than inter-cluster similarities. Clustering approaches, i.e. , k-medoids or hierarchical, use the distance function to measure the dissimilarities among actors. These distance functions need to fulfill various properties, including the triangle inequality (TI). However, in some cases, the triangle inequality might be violated, impacting the quality of the resulting clusters. With experiments, this paper explains how TI violates while performing traditional clustering techniques: k-medoids, hierarchical, DENGRAPH, and spectral clustering on social networks and how the violation of TI affects the quality of the resulting clusters.

AGGREGATE SPECIAL FUNCTIONS TO APPROXIMATE PERMUTING TRI-HOMOMORPHISMS AND PERMUTING TRI-DERIVATIONS ASSOCIATED WITH A TRI-ADDITIVEψ-FUNCTIONAL INEQUALITY IN BANACH ALGEBRAS

In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.

Development of Sustainable Urban-Rural Integration:Dongtan Case Study

The environmental impact issues,such as global warming and expansion of the urban zone,seem more serious and have become the biggest defining challenges of the 21st century.Climate change can lead to water shortages,desertification,land degradation,air pollution,rising sea levels,accelerated deforestation,and exacerbated economic pressures.Global urban growth greatly impacts changes in sociability,humanity,and the environment of the Earth.The human presence,especially in cities,seriously affects resource use and waste disposal,and they are consuming natural resources faster than the planet can sustain during urbanization,changing how people live.China,with a population of 1.3 billion,has seen tens of millions of people living in the countryside migrate to cities,especially megacities,since the 1980s.As a result of its decision to industrialize and urbanize to boost the economy,China has become the world’s second-largest consumer of energy.In recent years,China’s government has quickly recognized the lessons of“limits to growth”and has taken action by initiating the construction process in Dongtan,Shanghai,China.They are making efforts to build urban-rural integration communities to promote sustainable development.Based on a literature review focusing on Dongtan,research questions are raised according to the research objective:(1)What are the challenges of sustainable development in urban-rural integration?(2)What practices has Dongtan implemented for sustainable development,or how is sustainable development being applied to Dongtan?(3)What are the social,political,environmental,and economic concerns regarding the sustainable development of Dongtan?The sustainable urban-rural integration concerns the ecological,economic,environmental,and psychological aspects of urban-rural integration design and management.The overall objective is to promote sustainable development in economic,social,ecological,and spatial dimensions.It will be a liveable,complete community that makes economic,environmental,and social sense locally while also contributing to national and global sustainable development.It will serve as a compelling model for how to build sustainable urban-rural integration worldwide.

Spatial pattern of urban-rural integration in China and the impact of geography

Urban-rural integration (URI) is a global challenge that is highly related to inequalities, poverty, economic growth, and other Sustainable Development Goals (SDGs). Existing research has evaluated the extent of URI and explored its influencing factors, but urban-rural linkages are seldom incorporated in evaluation systems, and geographical factors are rarely recognized as the influencing factors. We construct a URI framework including regional economy, rural development, urban-rural linkage, and urban-rural gap. Based on a dataset consisting of 1,669 counties in China in 2020, we reveal the spatial pattern of URI and find a high correlation between the spatial pattern of URI and the relief degree of land surface (RDLS). Using structural equation modeling, we discover that topography has direct ( − 0.18, p < 0.001) and indirect ( − 0.17, p < 0.001) effects on URI. The indirect negative effects are mediated through the infrastructure, and the combination of localized advantages and modern technical conditions could mitigate the negative impact of topography. Finally, we identify 742 counties as lagging regions in URI, which can be clustered into eight types. Our findings could facilitate policy designing for those countries striving for integrated and sustainable development of urban and rural areas.

THE FEKETE-SZEG?INEQUALITY AND SUCCESSIVE COEFFICIENTS DIFFERENCE FOR A SUBCLASS OF CLOSE-TO-STARLIKE MAPPINGS IN COMPLEX BANACH SPACES

Let C be the familiar class of normalized close-to-convex functions in the unit disk.In[17],Koepf demonstrated that,as to a function■in the class C,■By applying this inequality,it can be proven that‖a3|-|a2‖≤1 for close-to-convex functions.Now we generalized the above conclusions to a subclass of close-to-starlike mappings defined on the unit ball of a complex Banach space.

Verification of the Landau Equation and Hardy’s Inequality

We prove the L estimate for the isotropic version of the homogeneous landau problem, which was explored by M. Gualdani and N. Guillen. As shown in a region of the smooth potentials range under values of the interaction exponent (2), a weighted Poincaré inequality is a natural consequence of the traditional weighted Hardy inequality, which in turn implies that the norms of solutions propagate in the L1 space. Now, the L estimate is based on the work of De Giorgi, Nash, and Moser, as well as a few weighted Sobolev inequalities.

NOTES ON THE LOG-BRUNN-MINKOWSKI INEQUALITY

Böröczky-Lutwak-Yang-Zhang proved the log-Brunn-Minkowski inequality for two origin-symmetric convex bodies in the plane in a way that is stronger than for the classical Brunn-Minkowski inequality.In this paper,we investigate the relative positive center set of planar convex bodies.As an application of the relative positive center,we prove the log-Minkowski inequality and the log-Brunn-Minkowski inequality.

The Bell Inequality, Inviolable by Data Used Consistently with Its Derivation, Is Satisfied by Quantum Correlations Whose Probabilities Satisfy the Wigner Inequality

It is not generally known that the inequality that Bell derived using three random variables must be identically satisfied by any three corresponding data sets of ±1’s that are writable on paper. This surprising fact is not immediately obvious from Bell’s inequality derivation based on causal random variables, but follows immediately if the same mathematical operations are applied to finite data sets. For laboratory data, the inequality is identically satisfied as a fact of pure algebra, and its satisfaction is independent of whether the processes generating the data are local, non-local, deterministic, random, or nonsensical. It follows that if predicted correlations violate the inequality, they represent no three cross-correlated data sets that can exist, or can be generated from valid probability models. Reported data that violate the inequality consist of probabilistically independent data-pairs and are thus inconsistent with inequality derivation. In the case of random variables as Bell assumed, the correlations in the inequality may be expressed in terms of the probabilities that give rise to them. A new inequality is then produced: The Wigner inequality, that must be satisfied by quantum mechanical probabilities in the case of Bell experiments. If that were not the case, predicted quantum probabilities and correlations would be inconsistent with basic algebra.

Some Refinement of Holder’s and Its Reverse Inequality

Holder’s inequality, its refinement, and reverse have received considerable attention in the theory of mathematical analysis and differential equations. In this paper, we give some refinements of Holder’s inequality and its reverse using a simple analytical technique of algebra and calculus. Our results show many results related to holder’s inequality as special cases of the inequalities presented.

Spatiotemporal Evolution and Influencing Factors of Urban-rural Construction Land in Rural Industrialized Areas in China:Case Studies in Changyuan City and Xinxiang County of Henan Province

Since China’s reform and opening up in 1978,the acceleration of industrialization and urbanization in China had led to dramatic changes in the pattern of urban-rural land use.In this paper,we focused on the rural industrialized areas in central China(Xinxiang County and Changyuan City of Henan Province).We used the average nearest neighbor index,spatial statistical analysis,and a structural equation model to analyze the spatiotemporal evolution and influencing factors of urban-rural construction land based on multisource spatial data and survey data.The results showed that:1)from 1975 to 2019,the spatial distribution of urban-rural construction land in rural industrialized areas had evolved from homogeneous distribution to local agglomeration.In terms of comparative analysis of cases,the spatial distribution of urban-rural construction land in Changyuan City had shown a trend from diffusion to agglomeration,and Xinxiang County had overall shown a spatial change from homogenization to agglomeration and then to regional integration development.2)The hot spots with increased urban-rural construction land significantly expanded,and they had a high degree of spatial overlap with industrial development.Among them,Xinxiang County was concentrated in central and marginal areas,and Changyuan was mainly concentrated in central urban areas.3)From the evolution of spatial proximity of urban-rural construction land,rural industrialized areas generally decline,showing the characteristics of internal differentiation in the rate of change.4)Industrial development,social economy,the policy environment,and urban development played a positive role in promoting the expansion of urban-rural construction land in rural industrialized areas.To promote the optimal use of regional land and the integrated development of urban-rural areas,we should combine the advantages of regional endowment,formulate development strategies according to local conditions,and adjust the way that land is used in a timely manner.

A new approach towards the sustainability of urban-rural integration:The development strategy for central villages in the Abbasiya District of Iraq using GIS techniques

The development of rural areas usually has a positive impact on the urban-rural integration. This study explores an innovative approach to stimulate rural development by proposing qualified villages as central villages that can provide basic urban services for their residents and residents of neighboring villages. This approach can contribute to overcoming the various problems that rural areas faced at the social, economic, and environmental levels. It seeks to achieve spatial sustainability of rural areas, representing a new approach by integrating urban development methods to revitalize rural villages. The study analyzed 15 villages belonging to Abbasiya District of AL Kufa City in the Najaf Governorate of Iraq. Based on the GIS techniques and the analysis of urban service indicators(village population, percentage of urban building materials used in villages, distance between village and health centers, distance between village and main roads, nature of economic activity, distance between village and educational institutions, distance between village and drinking water sources, number of communication towers, and distance between village and urban administrative center), this study proposed that Abu Gharb and Albu Ghraib can served as central villages in Abbasiya District in the future. This study establishes a new rural spatial structure to achieve rural sustainable development, improves the development status of rural areas, and provides a theoretical basis for the government and relevant institutions to use urban service indicators, achieving rural sustainable development and formulating relevant development policies in Abbasiya District.

TRANSPORTATION COST-INFORMATION INEQUALITY FOR A STOCHASTIC HEAT EQUATION DRIVEN BY FRACTIONAL-COLORED NOISE

In this paper,we prove Talagrand’s T2 transportation cost-information inequality for the law of stochastic heat equation driven by Gaussian noise,which is fractional for a time variable with the Hurst index H∈(1/2,1),and is correlated for the spatial variable.The Girsanov theorem for fractional-colored Gaussian noise plays an important role in the proof.

Does digitalization mitigate regional inequalities?Evidence from China

Regional inequality significantly influences sustainable development and human well-being.In China,there exists pronounced regional disparities in economic and digital advancements;however,scant research delves into the interplay between them.By analyzing the economic development and digitalization gaps at regional and city levels in China,extending the original Cobb-Douglas production function,this study aims to evaluate the impact of digitalization on China's regional inequality using seemingly unrelated regression.The results indicate a greater emphasis on digital inequality compared to economic disparity,with variable coefficients of 0.59 for GDP per capita and 0.92 for the digitalization index over the past four years.However,GDP per capita demonstrates higher spatial concentration than digitalization.Notably,both disparities have shown a gradual reduction in recent years.The southeastern region of the Hu Huanyong Line exhibits superior levels and rates of economic and digital advancement in contrast to the northwestern region.While digitalization propels economic growth,it yields a nuanced impact on achieving balanced regional development,encompassing both positive and negative facets.Our study highlights that the marginal utility of advancing digitalization is more pronounced in less developed regions,but only if the government invests in the digital infrastructure and education in these areas.This study's methodology can be utilized for subsequent research,and our findings hold the potential to the government's regional investment and policy-making.

Thinking about Value Realization of Ecological Products under the Background of Urban-rural Integration in Chengdu“Western Control”Area

Chengdu's development strategy of“western control”has laid a solid ecological background for 8 western districts,cities and counties and cultivated good ecological resources.The integrated urban-rural development in the new era will realize the balanced development of urban and rural areas and give full play to the value of rural ecological resources through the“powerful combination”of urban and rural areas.To realize the urban-rural integration and high-quality rural development in Chengdu“western control”area,it is necessary to enhance the awareness of ecological resources and ecological products,and carry out unified planning of ecological infrastructure,ecological material products and ecological service products in the whole“western control”area.Meantime,ecological restoration must be carried out scientifically,and scene design for value transformation of ecological products should be implemented innovatively.