THE OPTIMAL GENERALIZED LOGARITHMIC MEAN BOUNDS FOR SEIFFERT'S MEAN

For p ∈ R, the generalized logarithmic mean Lp（a, b） and Seiffert＇s mean T（a, b） of two positive real numbers a and b are defined in （1.1） and （1.2） below respectively. In this paper, we find the greatest p and least q such that the double-inequality Lp（a, b） 〈 T（a,b） 〈 Lq（a,b） holds for all a,b 〉 0 and a ≠ b.

Refinement of an Inequality for the Generalized Logarithmic Mean

In this article, we show that the generalized logarithmic mean is strictly Schurconvex function for p 〉 2 and strictly Schur-concave function for p 〈 2 on R_＋^2. And then we give a refinement of an inequality for the generalized logarithmic mean inequality using a simple majoricotion relation of the vector.

NORM SUMMABILITY OF NRLUND LOGARITHMIC MEANS ON UNBOUNDED VILENKIN GROUPS

The （Noerlund） logarithmic means of the Fourier series is：tnf=1/ln ^n-1∑k=1 Skf/n-k, where ln=^n-1∑k=1 1/k In general, the Fej6r （C, 1） means have better properties than the logarithmic ones. We compare them and show that in the case of some unbounded Vilenkin systems the situation changes.

Uniform and L-convergence of Logarithmic Means of Walsh-Fourier Series

The （NSrlund） logarithmic means of the Fourier series of the integrable function f is：1/lnn-1∑k=1Sk（f）/n-k, where ln：=n-1∑k=11/k.In this paper we discuss some convergence and divergence properties of this logarithmic means of the Walsh-Fourier series of functions in the uniform, and in the L^1 Lebesgue norm. Among others, as an application of our divergence results we give a negative answer to a question of Móricz concerning the convergence of logarithmic means in norm.

On the Divergence of N(?)rlund Logarithmic Means of Walsh-Fourier Series

It is well known in the literature that the logarithmic means 1/logn ^n-1∑k=1 Sk（f）/k of Walsh or trigonometric Fourier series converge a.e. to the function for each integrable function on the unit interval. This is not the case if we take the partial sums. In this paper we prove that the behavior of the so-called NSrlund logarithmic means 1/logn ^n-1∑k=1 Sk（f）/n-k is closer to the properties of partial sums in this point of view.

京津冀地区碳排放时空格局变化及其驱动因子

人类对陆地生态系统的改变是碳排放增加的主要原因。在“双碳”目标背景下探索土地利用变化与碳排放的动态关系,有助于区域土地低碳可持续利用。研究基于土地利用转移视角,采用重心-标准差椭圆方法揭示了京津冀地区土地利用碳排放时空格局演化特征,评估了碳排放与生态环境、社会经济发展的协调程度,并借助改进的Kaya模型和LMDI分解模型定量分析了土地利用变化对碳排放的影响程度。结果表明:(1)建设用地的转入是土地利用碳排放增加的主要来源,引起碳排放量增加15844.36万t;耕地、草地向林地、水域的转变促进了地区固碳能力的提升。(2)土地利用碳排放空间分布格局呈现出东北-西南方向向中心进一步聚集的趋势,并且东-西向聚集趋势大于南-北向。(3)京津冀地区整体碳排放与生态环境的协调性呈向好趋势发展,但大部分地区碳排放与社会经济发展出现失衡现象,地区间碳生产力差异逐渐增大。(4)经济水平是促进碳排放增加的最显著因素,单位GDP用地强度是抑制碳排放增加的最主要因素。分析结果表明,严格控制建设用地的无序扩张是促进低碳土地利用的基础,低碳经济发展是促进地区减碳的重要途径。

Decomposition and decoupling effect of energy eco-footprint based on global net primary productivity in urban agglomerations

Net primary productivity(NPP)is an important breakthrough point of current research on ecological footprint improvement.The energy eco-footprint(EEF)of the Four-City Area in Central China(FCACC)was measured by constructing an EEF-NPP model.This work has made the following efforts:(1)Gini coefficient was employed to analyze the degree of matching between the EEF and economic growth,population,and energy consumption.(2)LMDI decomposition method was used to explore the impacts of multiple factors on the EEF in the FCACC.(3)Tapio decoupling model was applied to verify the decoupling relationships between the above influencing factors and the EEF.(4)LMDI decomposition formula was embedded into the decoupling model to analyze the impacts of technical and non-technical factors on the decoupling elasticity of the above.The main findings show that from 2010 to 2020:(1)the degree of matching of EEF-GDP,EEF-population,and EEF-energy consumption increased.(2)energy intensity and per capita GDP were the main factors that affected the EEF.(3)the decoupling states between total energy consumption,energy consumption structure,energy intensity,per capita GDP,and population size with the EEF were expansive negative decoupling,expansive negative decoupling,strong negative decoupling,weak decoupling,and expansive negative decoupling,respectively.(4)the impact of non-technical factors was greater than that of technical factors,and their impacts were always in opposite directions.

Assessing the effects of vegetation and precipitation on soil erosion in the Three-River Headwaters Region of the Qinghai-Tibet Plateau,China

Soil erosion in the Three-River Headwaters Region(TRHR)of the Qinghai-Tibet Plateau in China has a significant impact on local economic development and ecological environment.Vegetation and precipitation are considered to be the main factors for the variation in soil erosion.However,it is a big challenge to analyze the impacts of precipitation and vegetation respectively as well as their combined effects on soil erosion from the pixel scale.To assess the influences of vegetation and precipitation on the variation of soil erosion from 2005 to 2015,we employed the Revised Universal Soil Loss Equation(RUSLE)model to evaluate soil erosion in the TRHR,and then developed a method using the Logarithmic Mean Divisia Index model(LMDI)which can exponentially decompose the influencing factors,to calculate the contribution values of the vegetation cover factor(C factor)and the rainfall erosivity factor(R factor)to the variation of soil erosion from the pixel scale.In general,soil erosion in the TRHR was alleviated from 2005 to 2015,of which about 54.95%of the area where soil erosion decreased was caused by the combined effects of the C factor and the R factor,and 41.31%was caused by the change in the R factor.There were relatively few areas with increased soil erosion modulus,of which 64.10%of the area where soil erosion increased was caused by the change in the C factor,and 23.88%was caused by the combined effects of the C factor and the R factor.Therefore,the combined effects of the C factor and the R factor were regarded as the main driving force for the decrease of soil erosion,while the C factor was the dominant factor for the increase of soil erosion.The area with decreased soil erosion caused by the C factor(12.10×10^3 km^2)was larger than the area with increased soil erosion caused by the C factor(8.30×10^3 km^2),which indicated that vegetation had a positive effect on soil erosion.This study generally put forward a new method for quantitative assessment of the impacts of the influencing factors on soil erosion,and also provided a scientific basis for the regional control of soil erosion.

Decomposition Analysis of Sectoral Energy Use in Beijing (1981-2005) Using the LMDI Method

This paper aims to identify the main driving force for changes of total primary energy consumption in Beijing during the period of 1981-2005.Sectoral energy use was investigated when regional economic structure changed significantly.The changes of total primary energy consumption in Beijing are decomposed into production effects,structural effects and intensity effects using the additive version of the logarithmic mean Divisia index (LMDI) method.Aggregate decomposition analysis showed that the major contributor of total effect was made by the production effect fol- lowed by the intensity effect,and the structural effect was rela- tively insignificant.The total and production effects were all posi- tive.In contrast,the structural effect and intensity effect were all negative.Sectoral decomposition investigation indicated that the most effective way to slow down the growth rate of total primary energy consumption (TPEC) was to reduce the production of the energy-intensive industrial sectors and improving industrial en- ergy intensity.The results show that in this period,Beijing's economy has undergone a transformation from an industrial to a service economy.However,the structures of sectoral energy use have not been changed yet,and energy demand should be in- creasing until the energy-intensive industrial production to be reduced and energy intensity of the region reaches a peak.As sequence energy consumption data of sub-sectors are not available, only the fundamental three sectors are considered:agriculture, industry and service.However,further decomposition into secon- dary and tertiary sectors is definitely needed for detailed investi- gations.

Carbon Emission of Regional Land Use and Its Decomposition Analysis: Case Study of Nanjing City, China

Through the matching relationship between land use types and carbon emission items, this paper estimated carbon emissions of different land use types in Nanjing City, China and analyzed the influencing factors of carbon emissions by Logarithmic Mean Divisia Index（LMDI） model. The main conclusions are as follows： 1） Total anthropogenic carbon emission of Nanjing increased from 1.22928 ×10^7 t in 2000 to 3.06939 × 10^7 t in 2009, in which the carbon emission of Inhabitation, mining ＆ manufacturing land accounted for 93% of the total. 2） The average land use carbon emission intensity of Nanjing in 2009 was 46.63 t/ha, in which carbon emission intensity of Inhabitation, mining ＆ manufacturing land was the highest（200.52 t/ha）, which was much higher than that of other land use types. 3） The average carbon source intensity in Nanjing was 16 times of the average carbon sink intensity（2.83 t/ha） in 2009, indicating that Nanjing was confronted with serious carbon deficit and huge carbon cycle pressure. 4） Land use area per unit GDP was an inhibitory factor for the increase of carbon emissions, while the other factors were all contributing factors. 5） Carbon emission effect evaluation should be introduced into land use activities to formulate low-carbon land use strategies in regional development.

Influencing factors and contribution analysis of CO_(2) emissions originating from final energy consumption in Sichuan Province,China

Within the context of CO_(2)emission peaking and carbon neutrality,the study of CO_(2)emissions at the provincial level is few.Sichuan Province in China has not only superior clean energy resources endowment but also great potential for the reduction of CO_(2)emissions.Therefore,using logarithmic mean Divisia index(LMDI)model to analysis the influence degree of different influencing factors on CO_(2)emissions from final energy consumption in Sichuan Province,so as to formulate corresponding emission reduction countermeasures from different paths according to the influencing factors.Based on the data of final energy consumption in Sichuan Province from 2010 to 2019,we calculated CO_(2)emission by the indirect emission calculation method.The influencing factors of CO_(2)emissions originating from final energy consumption in Sichuan Province were decomposed into population size,economic development,industrial structure,energy consumption intensity,and energy consumption structure by the Kaya-logarithmic mean Divisia index(LMDI)decomposition model.At the same time,grey correlation analysis was used to identify the correlation between CO_(2)emissions originating from final energy consumption and the influencing factors in Sichuan Province.The results showed that population size,economic development and energy consumption structure have positive contributions to CO_(2)emissions from final energy consumption in Sichuan Province,and economic development has a significant contribution to CO_(2)emissions from final energy consumption,with a contribution rate of 519.11%.The industrial structure and energy consumption intensity have negative contributions to CO_(2)emissions in Sichuan Province,and both of them have significant contributions,among which the contribution rate of energy consumption structure was 325.96%.From the perspective of industrial structure,secondary industry makes significant contributions and will maintain a restraining effect;from the perspective of energy consumption structure,industry sector has a significant contribution.The results of this paper are conducive to the implementation of carbon emission reduction policies in Sichuan Province.

An Integral Inequality and Polya-Szego Inequality

The paper brings an important integral inequality, which includes the famous Polya-Szego inequality and the logarithmical-arithmetic mean inequality as special cases.

The Measurement of Carbon Emission Effect of Construction Land Changes in Anhui Province Based on the Extended LMDI Model

In the context of ＂two-wheel drive＂ development mode, China＇s construction land shows significant expansion characteristics. The carbon emission effect of construction land changes is an important factor for the increase of carbon emissions in the atmosphere. In this study, the drivers of carbon emissions in Anhui Province from 1997 to 2011 were quantitatively measured using the improved Kaya identity and Logarithmic Mean Divisia Index. The results show that： economic growth, expansion of construction land and changes in population density have incremental effects on carbon emissions. The average contribution rate of economic growth as the first driver is 266.32 percent. The construction land expansion is an important driving factor with annual mean carbon effect of 6.4057 million tons and annual mean contribution rate of 187.30 percent. But the change in population density has little impact on carbon emission driving. Energy structure changes and energy intensity reduction have inhibitory effects on carbon emissions, of which the annual mean contribution rate is -212.06 percent and -158.115 percent respectively. The targeted policy approaches of carbon emission reduction were put forward based on the decomposition of carbon emission factors, laying a scientific basis to rationally use the land for the Government, which is conducive to build an ecological province for Anhui and achieve the purpose of emission reduction, providing a reference for the research on carbon emission effect of changes in provincial-scale construction land.

Decomposition and decoupling analysis of carbon dioxide emissions in African countries during 1984–2014

The potential for mitigating climate change is growing worldwide,with an increasing emphasis on reducing CO_(2)emissions and minimising the impact on the environment.African continent is faced with the unique challenge of climate change whilst coping with extreme poverty,explosive population growth and economic difficulties.CO_(2)emission patterns in Africa are analysed in this study to understand primary CO_(2)sources and underlying driving forces further.Data are examined using gravity model,logarithmic mean divisia index and Tapio's decoupling indicator of CO_(2)emissions from economic development in 20 selected African countries during 1984-2014.Results reveal that CO_(2)emissions increased by 2.11%(453.73 million ton)over the research period.Gravity centre for African CO_(2)emissions had shifted towards the northeast direction.Population and economic growth were primary driving forces of CO_(2)emissions.Industrial structure and emission efficiency effects partially offset the growth of CO_(2)emissions.The economic growth effect was an offset factor in central African countries and Zimbabwe due to political instability and economic mismanagement.Industrial structure and emission efficiency were insufficient to decouple economic development from CO_(2)emissions and relieve the pressure of population explosion on CO_(2)emissions in Africa.Thus,future efforts in reducing CO_(2)emissions should focus on scaleup energy-efficient technologies,renewable energy update,emission pricing and long-term green development towards sustainable development goals by 2030.

Impacts of household living consumption on energy use and carbon emissions in China based on the input–output model

China must urgently accelerate its decrease of energy use,optimize its energy structure,reduce CO2 emissions,and promote the early realization of an ecological civilization.Simultaneously,meeting the growing consumer demand is one of the reasons for the increase in energy use.This study investigates the impacts of household consumption on energy use and CO2 emissions from the perspective of the lifestyle of Chinese residents.On the basis of the input–output model of 30 provinces,we analyze the current situation of energy use and CO2 emissions in different regions(spatial scale)with economic development and income improvement(time scale),investigate the pulling effect of household consumption in different provinces on industrial sectors,examine the influencing factors of indirect CO2 emissions from food,clothing,housing,and transportation in key regions,and explore the policy implications of the transition to a low-carbon lifestyle in different provinces.Results show that the fuel structure of Chinese residents should be optimized further.Total household energy consumption and total CO2 emissions considerably increased.In 2012,total household energy consumption accounted for nearly 30%of total energy consumption,while indirect CO2 emissions accounted for 66.3%of total household emissions.With regard to the structures of indirect household energy consumption,the housing sector accounted for the largest proportion,reaching 23.4%in indirect energy consumption in 2012.The pulling effect of the housing sector on industrial sectors was also evident.The decomposition analysis showed that the rapid increase in indirect household CO2 emissions was primarily due to the increase in per capita living expenditure.The consumption structures in different provinces produced various impacts,and the energy intensity effect was identified as an important factor for reducing indirect household CO2 emissions.

Decomposition analysis of energy-related carbon dioxide emissions in the iron and steel industry in China

This work aims to identify the main factors influencing the energy-related carbon dioxide （CO2） emissions from the iron and steel industry in China during the period of 1995-2007. The logarithmic mean divisia index （LMDI） technique was applied with period-wise analysis and time-series analysis. Changes in energy- related CO2 emissions were decomposed into four factors： emission factor effect, energy structure effect, energy consumption effect, and the steel production effect. The results show that steel production is the major factor responsible for the rise in CO2 emissions during the sampling period; on the other hand the energy consump- tion is the largest contributor to the decrease in C02 emissions. To a lesser extent, the emission factor and energy structure effects have both negative and positive contributions to C02 emissions, respectively. Policy implications are provided regarding the reduction of C02 emissions from the iron and steel industry in China, such as controlling the overgrowth of steel production, improving energy-saving technologies, and introducing low-carbon energy sources into the iron and steel industry.

Relationship of Ecological Well-being Performance and Sustainable Economic Development in Liaoning Province

Liaoning Province is in a critical period of economic transformation. The rational utilization of ecological resources and the balance of the relationship between the resource environment and economic growth have become the key factors affecting its sustainable economic development. This paper uses data from the Human Development Index and an ecological footprint to construct the ecological well-being performance of Liaoning Province from 2006 to 2016. It then examines the relationship of ecological well-being performance with economic growth, considers the factors influencing the well-being level effect, and analyzes the trends for sustainable economic development from the perspective of ecological well-being. There is a horizontal comparison of the current situation of ecological well-being performance in Liaoning Province and with other coastal provinces in China and clarification of the stage and development gap. The conclusions show that: 1) The trend of ecological well-being performance in Liaoning Province during this period first decreased and then rose, with this movement mainly affected by changes in the ecological footprint;2) There is a U-shaped relationship between ecological well-being performance and economic growth, and resource consumption contributes less to promote well-being;3) There are three stages to the sustainable development trend: inferior, medium and advanced. When compared with others coastal provinces, Liaoning Province belongs to the high consumption and low well-being type.

Dynamic features and driving mechanism of coal consumption for Guangdong province in China

Guangdong Province,as one of China’s fast-developing regions,an important manufacturing base,and one of the national first round low-carbon pilots,still faces many challenges in controlling its total energy consumption.Coal dominates Guangdong’s energy consumption and remains the major source of CO_(2).Previous research on factors influencing energy consumption has lacked a systematic analysis both from supply side(factors related to scale,structure,and technologies)and demand side(investment,consumption,and trade).This paper develops the logarithmic mean Divisia index(LMDI)method that focuses on the supply side and the structural decomposition analysis(SDA)method that focuses on the demand side to systematically identify the key factors driving coal consumption in Guangdong.Results are as follows:(1)Supply side analysis indicates that economic growth has always been the most important factor driving coal consumption growth,while energy intensity is the most important constraining factor.Industrial structure and energy structure have different impacts on coal consumption control during different development phases.(2)Demand side analysis indicates that coal is consumed mainly for international exports,inter-provincial exports,fixed capital formation,and urban household.(3)Industries with the fastest coal consumption growth driven by final demand have experienced significant shifts.Increments in industrial sectors were mainly driven by inter-provincial exports and urban household consumption in recent years.(4)Research on energy consumption in subnational regions under China’s new development pattern of“dual circulation”should not only focus on exports in the context of economic globalization but also pay more attention to inter-provincial exports on the background of strengthened interregional connections.

Almost Sure Central Limit Theorem for Partial Sums of Markov Chain

Abstract The authors prove an almost sure central limit theorem for partial sums based on an irreducible and positive recurrent Markov chain using logarithmic means, which realizes the extension of the almost sure central limit theorem for partial sums from an i.i.d, sequence of random variables to a Markov chain.

Trends and driving forces of low-carbon energy technology innovation in China’s industrial sectors from 1998 to 2017: from a regional perspective

Low-carbon energy technology(LC)innovation contributes to both environmental protection and economic development.Using the panel data of 30 provinces/autonomous regions/municipalities in China from 1998 to 2017,this paper constructs a two-layer logarithmic mean Divisia index(LMDI)model to uncover the factors influencing the variation of the innovation of LC in China’s industrial sectors,including the alternative energy production technology(AEPT)and the energy conversation technology(ECT).The results show that China’s industrial LC patent applications rapidly increased after 2005 and AEPT patent applications outweighed ECT patent applications all the time with a gradually narrowing gap.Low-carbon degree played the dominant role in promoting the increase in China’s industrial LC patent applications,followed by the economic scale,R&D(research and development)efficiency,and R&D share.Economic structure contributed to the increases in LC patent applications in the central and the western regions,while led to the decreases in the eastern region,the north-eastern region,and Chinese mainland.Low-carbon degree and economic scale were two main contributors to the growths of both industrial AEPT patent applications and ECT patent applications in Chinese mainland and the four regions.Several policy recommendations are made to further promote industrial innovation in China.