Branch values in Ahlfors’ theory of covering surfaces

In the study of the constant in Ahlfors’second fundamental theorem involving a set Eq consisting of q points,branch values of covering surfaces outside Eq bring a lot of troubles.To avoid this situation,for a given surfaceΣ0,it is useful to construct a new surfaceΣ1,such that L(■Σ1)≤L(■Σ0),and H(Σ1,Eq)≥H(Σ0,Eq).and all branch values ofΣ1 are contained in Eq.The goal of this paper is to prove the existence of suchΣ1,which generalizes a result found by Zhang(2013).

Properties of Ahlfors constant in Ahlfors covering surface theory

This paper is a subsequent work of[Invent.Math.,2013,191:197-253].The second fundamental theorem in Ahlfors covering surface theory is that,for each set E_(q)of q(≥3)distinct points in the extended complex plane C,there is a minimal positive constant H_(0)(E_(q))(called Ahlfors constant with respect to E_(q)),such that the inequality(q-2)A(Σ)-4π#(f^(-1)(E_(q))∩U)≤H_(0)(E_(q))L(ЭΣ)holds for any simply-connected surfaceΣ=(f,U),where A(Σ)is the area ofΣ,L(ЭΣ)is the perimeter ofΣ,and#denotes the cardinality.It is difficult to compute H_(0)(E_(q))explicitly for general set E_(q),and only a few properties of H_(0)(E_(q))are known.The goals of this paper are to prove the continuity and differentiability of H_(0)(E_(q)),to estimate H_(0)(E_(q)),and to discuss the minimum of H_(0)(E_(q))for fixed q.

Relationship between spatio-temporal evolution of soil pH and geological environment/surface cover in the eastern Nenjiang River Basin of Northeast China during the past 30 years

To illuminate the spatio-temporal variation characteristics and geochemical driving mechanism of soil pH in the Nenjiang River Basin,the National Multi-objective Regional Geochemical Survey data of topsoil,the Second National Soil Survey data and Normalized Difference Vegetation Index(NDVI)were analyzed.The areas of neutral and alkaline soil decreased by 21100 km^(2)and 30500 km^(2),respectively,while that of strongly alkaline,extremely alkaline,and strongly acidic soil increased by 19600 km^(2),18200 km^(2),and 15500 km^(2),respectively,during the past 30 years.NDVI decreased with the increase of soil pH when soil pH>8.0,and it was reversed when soil pH<5.0.There were significant differences in soil pH with various surface cover types,which showed an ascending order:Arbor<reed<maize<rice<high and medium-covered meadow<low-covered meadow<Puccinellia.The weathering products of minerals rich in K_(2)O,Na_(2)O,CaO,and MgO entered into the low plain and were enriched in different parts by water transportation and lake deposition,while Fe and Al remained in the low hilly areas,which was the geochemical driving mechanism.The results of this study will provide scientific basis for making scientific and rational decisions on soil acidification and salinization.

DIAGONAL POINT BY POINT SURFACE DEVELOPMENT METHOD BASED ON NURBS SURFACE FOR BLANK SHAPE ESTIMATION OFCOVER PANEL

According to the characteristics of a complex cover panel, its geometry shape is described by the NURBS surface with great description capability. With the reference to the surface classification determined by Gauss curvature, the proportion of the mid-surface area between before and after being developed is derived from the displacement variation of the mid-surface in the normal vector direction of the sheet metal during the sheet metal forming process. Hereby, based on the curve development theory in differential geometry, a novel diagonal point by point surface development method is put forward to estimate a complex cover panel＇s blank contour efficiently. By comparing the sample＇s development result of diagonal point by point surface development method with that of available one-step method, the validity of the proposed surface development method is verified.

Doppler Spectrum Analysis of Time-Evolving Sea Surface Covered by Oil Spills

Based on the model of a contaminated sea surface that was proposed by Lombardini et al., the influence of the damping effect of oil films on the sea surface roughness spectrum and the geometrical structure of the sea surface is examined in detail by comparing with a clean sea surface. Fhrthermore, based on a quasi-stationary algorithm, a time series of backscattered echoes from a time-evolving sea surface covered by oil slicks is obtained by utilizing the frequency-domain numerical method of the parallel fast multiple method. Then, the Doppler spectrum is evaluated by performing a standard spectral estimation technique. Finally, the influence of the oil film damping effect on the Doppler spectrum of the backscattered echoes from time-evolving sea surface is investigated in detail by making a comparison of the Doppler spectrum of an oil-covered sea surface with the Doppler spectrum of a dean sea surface. The numerical simulations show that the damping effect of oil films has an influence on the Doppler spectrum signature for both horizontal-to-horizontal and vertical-to-vertical polarizations.

Effect of ground cover changes on solar radiation absorption in Three Northeastern Provinces of China

Background,aim,and scope Solar radiation is the main source of energy for terrestrial ecosystems.Small changes in the absorption of solar radiation at the ground surface can have a significant impact on the climatic environment.Natural and anthropogenic changes in ground cover are important factors affecting the absorption of solar radiation at the ground surface.This phenomenon is particularly pronounced in the mid and high latitudes.In order to quantify the inf luence of surface cover change on the absorption of solar radiation at the surface and to provide a scientific basis for changes in the climatic environment,this paper analyzed ground cover change,ground absorbed solar radiation change and the effect of ground cover change on ground absorbed solar radiation in the Three Northeastern Provinces of China from 2001 to 2018.Materials and methods In this study,the Three Northeastern Provinces of China were used as the study area.Firstly,satellite remote sensing data were used to obtain land cover data and albedo data for Aug.1st of each year in 2001,2005,2010,2015 and 2018.The albedo data were further used to calculate the absorbed solar radiation data at the ground surface.Next,the land cover data were used to count the area changes and shifts of different land classes over the five-year period.The land cover data were overlaid with the surface absorbed solar radiation data to obtain the mean and standard deviation of radiation absorption for different ground classes.The surface absorbed solar radiation data were subtracted to obtain the changes in surface absorbed solar radiation for 2001-2005,2005-2010,2010-2015 and 2015-2018.Ultimately,we used a combination of shifted changes in ground classes and changes in surface absorbed solar radiation data,with unchanged ground classes as a baseline and data such as slope orientation as an aid.We analyzed the effect of ground cover change on surface absorbed solar radiation at regional and pixel point scales.Results(1)The area of woodland and waters in the Three Northeastern Provinces of China increased and then decreased from 2001 to 2018,with an overall increase of 3.96%and 10.51%respectively.Cropland decreased and then increased,with a total decrease of 1.22%.Grassland continued to decrease,with an overall decrease of 19.36%.Building sites increased all the time,with a total increase of 11.08%.The main types of ground cover shifted were woodland,cropland and grassland.The main factors for the change in ground cover were China’s woodland protection policy and the saturation of the total woodland stock.(2)The five ground types absorb solar radiation in the order of waters>building sites>woodland>grassland>cropland.The surface absorption of solar radiation in the Songnen Plain,the Sanjiang Plain and the Songhua River Basin flowing through the Songnen Plain and the Sanjiang Plain varies significantly,by more than 25 W·m^(-2).(3)Changes in the ground cover type affected the absorption of solar radiation energy by the ground surface.There was a clear trend of interconversion between waters and cropland/grassland,cropland and woodland/grassland.In particular,the conversion of waters to both cropland and grassland radiation absorption values decreased significantly,while the opposite increased.The absolute difference between waters and cropland was a maximum of -156.66 W·m^(-2)in 2010-2015,and between waters and grassland was a maximum of 102.36 W·m^(-2) in 2005-2010.The radiative absorption values of woodland and grassland reclamation declined and conversely increased.The absolute difference between woodland and cropland was a maximum of-13.94 W·m^(-2) in 2010-2015 when woodland converted to cropland,and between grassland and cropland was a maximum of 22.36 W·m^(-2) in 2001-2005 when cropland converted to grassland,respectively.Discussion Ground cover changes in the Three Northeastern Provinces of China from 2001-2018 were inextricably linked to natural factors and the inf luence of Chinese national policies.The main inf luencing factors were China’s woodland protection policy,restoration of woodland fire sites,saturation of total woodland,optimization of cropland patterns,sanding of grassland,expansion of water conservancy projects,and urbanization expansion.There were differences in the radiation absorption characteristics of different ground cover types.This was due to the nature of the ground type itself and the regional environment.When ground cover types changed,their ability to absorb solar radiation also changed.The degree of change could be inf luenced by different ground types and different environmental factors.Different spatial scales can also produce variability.We need to consider the effects of ground cover change on the absorption of solar radiation at the surface in an integrated and comprehensive way.Conclusions The Three Northeastern Provinces of China had frequent changes in ground cover from 2001-2018,with the area of grassland decreased by almost 20%.These changes were due to natural environmental change and policies issued by China since the 21st century.The extent to which solar radiation was absorbed by different ground cover types was different,with grassland being the strongest and cropland the least.In the past few years,the Songnen Plain and Sanjiang Plain regions were the most significant changes in the absorption of solar radiation by the ground cover.The change in ground cover type led to a change in solar radiation absorption at the ground surface,with the conversion of waters to cropland or grassland and the conversion of cropland to woodland or grassland showing the greatest change in radiation absorption values,and vice versa.Of these,the absolute difference in the conversion of waters to cropland amounts to-156.66 W·m^(-2) in 2010-2015.The variation in the absorption of solar radiation at the ground surface was related to the characteristics of the ground class itself,but was also limited by the regional environment.Recommendations and perspectives This study showed that surface cover change can affect the absorption of solar radiation at the surface to varying degrees.The unchanged land classes were used as a comparative analysis in this paper,and it was clear from the paper that some of the unchanged land classes showed significant changes in radiation absorption that should be of interest in future studies.

ON THE BOREL DIRECTION OF K-QUASIMEROMORPHIC MAPPINGS

For the K-quasimeromorphic mappings, a precise fundamental inequality for the angular domain is established. Prom this, the Borel direction of the K-quasimeromorphic mappings of zero order is derived.

ON A NEW SINGULAR DIRECTION OF QUASIMEROMORPHIC MAPPINGS

By applying Ahlfors＇ theory of covering surface, we establish a fundamental inequality for quasimeromorphic mapping in an angular domain. As an application, we prove the existence of a new singular direction for quasimeromorphic mapping f, namely, a precise S direction, for which the spherical characteristic function S（r, f） is used as a comparison function.

On Singularity of Function Family

We define a notion of singularity for a family or meromorphic functions. Some sufficient and necessary conditions for this singularity are estabilished.

NORMAL THEOREMS ON SEVERAL COMPLEX VARIABLES

For general quasimeromorphic mappings of several complex variables, their normal theorems are studied by the method of covering surface, and some important theorems on normality are obtained.

On the Normal Criterion of Quasimeromorphic Mappings

In this paper, we generalize an, inequality of meromorphic mappings to quasimeromorphic ones. Applying the results here, we can establish a normal criterion of quasimeromorphic mappings.

The Impact of Agricultural Practices in China on Land-Atmosphere Interactions

Human-induced land use changes and the resulting alterations in vegetation features are major but poorly recognized drivers of regional climatic patterns.In order to investigate the impacts of anthropogenically-induced seasonal vegetation cover changes on regional climate in China,harmonic analysis is applied to 1982-2000 National Oceanic and Atmospheric Administration（NOAA） Advanced Very High Resolution Radiometer（AVVHRR）-derived normalized difference vegetation index（NDVI） time series（ten day interval data）.For two climatic divisions of South China,it is shown that the first harmonic term is in phase with air temperature,while the second and third harmonics are in phase with agricultural cultivation.The Penman-Monteith Equation and the Complementary Relationship Areal Evapotranspiration（CRAE） model suggest that monthly mean evapotranspiration is out of phase with temperature and precipitation in regions with signiffcant second or third harmonics.Finally,seasonal vegetation cover changes associated with agricultural cultivation are identiffed：for cropped areas,the temperature and precipitation time series have a single maximum value,while the monthly evapotranspiration time series has a bimodal distribution.It is hypothesized that multi-cropping causes the land surface albedo to sharply increase during harvesting,thereby altering the energy distribution ratio and contributing to observed seasonal vegetation cover changes.

Remote sensing-based artificial surface cover classification in Asia and spatial pattern analysis

Artificial surfaces, characterized with intensive land-use changes and complex landscape structures, are important indicators of human impacts on terrestrial ecosystems. Without high-resolution land-cover data at continental scale, it is hard to evaluate the impacts of urbanization on regional climate, ecosystem processes and global environment. This study constructed a hierarchical classification system for artificial surfaces, promoted a remote sensing method to retrieve subpixel components of artificial surfaces from 30-m resolution satellite imageries(Globe Land30) and developed a series of data products of high-precision urban built-up areas including impervious surface and vegetation cover in Asia in 2010. Our assessment, based on multisource data and expert knowledge, showed that the overall accuracy of classification was 90.79%. The mean relative error for the impervious surface components of cities was 0.87. The local error of the extracted information was closely related to the heterogeneity of urban buildings and vegetation in different climate zones. According to our results, the urban built-up area was 18.18×104 km2, accounting for 0.59% of the total land surface areas in Asia; urban impervious surfaces were 11.65×104 km2, accounting for 64.09% of the total urban built-up area in Asia. Vegetation and bare soils accounted for 34.56% of the urban built-up areas. There were three gradients: a concentrated distribution, a scattered distribution and an indeterminate distribution from east to west in terms of spatial pattern of urban impervious surfaces. China, India and Japan ranked as the top three countries with the largest impervious surface areas, which respectively accounted for 32.77%, 16.10% and 11.93% of the urban impervious surface area of Asia. We found the proportions of impervious surface and vegetation cover within urban built-up areas were closely related to the economic development degree of the country and regional climate environment. Built-up areas in developed countries had relatively low impervious surface and high public green vegetation cover, with 50–60% urban impervious surfaces in Japan, South Korea and Singapore. In comparison, the proportion of urban impervious surfaces in developing countries is approaching or exceeding 80% in Asia. In general, the composition and spatial patterns of built-up areas reflected population aggregation and economic development level as well as their impacts on the health of the environment in the sub-watershed.

Statistical Estimation of High-Resolution Surface Air Temperature from MODIS over the Yangtze River Delta,China

High-resolution surface air temperature data are critical to regional climate modeling in terms of energy balance,urban climate change,and so on.This study demonstrates the feasibility of using Moderate Resolution Imaging Spectroradiometer（MODIS）land surface temperature（LST）to estimate air temperature at a high resolution over the Yangtze River Delta region,China.It is found that daytime LST is highly correlated with maximum air temperature,and the linear regression coefficients vary with the type of land surface.The air temperature at a resolution of 1 km is estimated from the MODIS LST with linear regression models.The estimated air temperature shows a clear spatial structure of urban heat islands.Spatial patterns of LST and air temperature differences are detected,indicating maximum differences over urban and forest regions during summer.Validations are performed with independent data samples,demonstrating that the mean absolute error of the estimated air temperature is approximately 2.5°C,and the uncertainty is about 3.1°C,if using all valid LST data.The error is reduced by 0.4°C（15%）if using best-quality LST with errors of less than 1 K.The estimated high-resolution air temperature data have great potential to be used in validating high-resolution climate models and other regional applications.

Finite Abelian Groups of K3 Surfaces with Smooth Quotient

The quotient space of a K3 surface by a finite group is an Enriques surface or a rational surface if it is smooth.Finite groups where the quotient space are Enriques surfaces are known.In this paper,by analyzing effective divisors on smooth rational surfaces,the author will study finite groups which act faithfully on K3 surfaces such that the quotient space are smooth.In particular,he will completely determine effective divisors on Hirzebruch surfaces such that there is a finite Abelian cover from a K3 surface to a Hirzebrunch surface such that the branch divisor is that effective divisor.Furthermore,he will decide the Galois group and give the way to construct that Abelian cover from an effective divisor on a Hirzebruch surface.Subsequently,he studies the same theme for Enriques surfaces.

Normal family of algebroidal functions

The multivalue algebroidal functions are studied with geometric method. The difficulties of multivalue and branch points are overcome, and some theorems on normality are obtained.

Simulation of land-cover change in Jing-Jin-Ji region under different scenarios of SSP-RCP

How to simulate land-cover change,driven by climate change and human activity,is not only a hot issue in the field of land-cover research but also in the field of sustainable urbanization.A surface-modeling method of land cover scenario(SSMLC)driven by the coupling of natural and human factors was developed to overcome limitations in existing land-cover models.Based on the climatic scenario data of CMIP6 SSP1-2.6,SSP2-4.5,and SSP5-8.5 released by IPCC in 2020,which combines shared socioeconomic paths(SSPs)with typical concentration paths(RCPs),observation climatic data concerning meteorological stations,the population,GDP,transportation data,land-cover data from 2020,and related policy refences,are used to simulate scenarios of land-cover change in the Jing-Jin-Ji region using SSP1-2.6,SSP2-4.5,and SSP5-8.5 for the years 2040,2070 and 2100,respectively.The simulation results show that the total accuracy of SSMLC in the Jing-Jin-Ji region attains 93.52%.The change intensity of land cover in the Jing-Jin-Ji region is the highest(plus 3.12%per decade)between 2020 and 2040,gradually decreasing after 2040.Built-up land has the fastest increasing rate(plus 5.07%per decade),and wetland has the fastest decreasing rate(minus 3.10%per decade)between 2020 and 2100.The change intensity of land cover under scenario SSP5-8.5 is the highest among the abovementioned three scenarios in the Jing-Jin-Ji region between 2020 and 2100.The impacts of GDP,population,transportation,and policies on land-cover change are generally greater than those on other land-cover types.The results indicate that the SSMLC method can be used to project the change trend and intensity of land cover under the different scenarios.This will help to optimize the spatial allocation and planning of land cover,and could be used to obtain key data for carrying out eco-environmental conservation measures in the Jing-Jin-Ji region in the future.

Sub-pixel analysis to enhance the accuracy of evapotranspiration determined using MODIS images

A study was carried out to estimate the actual evapotranspiration(ET)over a 1074 km2 of the humid area of Perak State(Malaysia),where water and evaporation cycle deeply influences the climate,natural resources and human living aspects.Images from both Terra and Aqua platforms of the Moderate Resolution Imaging Spectroradiometer(MODIS)sensor were used for ET estimation by employing the Surface Energy Balance Algorithm for Land(SEBAL)model.As a part of the accuracy assessment process,in-situ measurements on soil temperature and reference ET(ET0)were recorded at the time of satellite overpass.In order to enhance the accuracy of the generated ET maps,MODIS images were subjected to sub-pixel analysis by assigning weights for different land surface cover(urban,agriculture and multi-surface areas)reflections.The weighting process was achieved by integrating ET from pure pixels with the respective site-specific ET0 of each land cover.The enhanced SEBAL model estimated ET exhibited a good correlation with the in-situ measured Penman-Montieth ET0,with R2 values for the Aqua and the Terra platforms of 0.67 and 0.73,respectively.However,the correlation of the non-enhanced ET maps resulted in R2 values of 0.61 and 0.68 for the Aqua and the Terra platforms,respectively.Hence,the results of this study revealed the feasibility of employing the sub-pixel analysis method for an accurate estimation of ET over large areas.