In this paper,we explicitly establish Poincaréinequality for 1≤p<∞ over simple geometric domains,such as segment,rectangle,triangle or tetrahedron.We obtain sharper bounds of the constant in Poincaré in...In this paper,we explicitly establish Poincaréinequality for 1≤p<∞ over simple geometric domains,such as segment,rectangle,triangle or tetrahedron.We obtain sharper bounds of the constant in Poincaré inequality and,in particular,the explicit relation between the constant and the geometric characters of the domain.展开更多
Plant species diversity is one of the most widely used indicators in ecosystem management.The relation of species diversity with the size of the sample plot has not been fully determined for Oriental beech forests(Fag...Plant species diversity is one of the most widely used indicators in ecosystem management.The relation of species diversity with the size of the sample plot has not been fully determined for Oriental beech forests(Fagus orientalis Lipsky),a widespread species in the Hyrcanian region.Assessing the impacts of plot size on species diversity is fundamental for an ecosystem-based approach to forest management.This study determined the relation of species diversity and plot size by investigating species richness and abundance of both canopy and forest floor.Two hundred and fifty-six sample plots of 625 m^(2) each were layout in a grid pattern across 16 ha.Base plots(25 m×25 m)were integrated in different scales to investigate the effect of plot size on species diversity.The total included nine plots of 0.063,0.125,0.188,0.250,0.375,0.500,0.563,0.750 and 1 ha.Ten biodiversity indices were calculated.The results show that species richness in the different plot sizes was less than the actual value.The estimated value of the Simpson species diversity index was not significantly different from actual values for both canopy and forest floor diversity.The coefficient of variation of this index for the 1-ha sample plot showed the lowest amount across different plot sizes.Inverse Hill species diversity was insignificant difference across different plot sizes with an area greater than 0.500 ha.The modified Hill evenness index for the 1-ha sample size was a correct estimation of the 16-ha for both canopy and forest floor;however,the precision estimation was higher for the canopy layer.All plots greater than 0.250-ha provided an accurate estimation of the Camargo evenness index for forest floor species,but was inaccurate across different plot sizes for the canopy layer.The results indicate that the same plot size did not have the same effect across species diversity measurements.Our results show that correct estimation of species diversity measurements is related to the selection of appropriate indicators and plot size to increase the accuracy of the estimate so that the cost and time of biodiversity management may be reduced.展开更多
The unique phase profile and polarization distribution of the vector vortex beam(VVB)have been a subject of increasing interest in classical and quantum optics.The development of higher-order Poincarésphere(HOPS)...The unique phase profile and polarization distribution of the vector vortex beam(VVB)have been a subject of increasing interest in classical and quantum optics.The development of higher-order Poincarésphere(HOPS)and hybrid-order Poincarésphere(HyOPS)has provided a systematic description of VVB.However,the generation of arbitrary VVBs on a HOPS and a HyOPS via a metasurface lacks a unified design framework,despite numerous reported approaches.We present a unified design framework incorporating all design parameters(e.g.,focal lengths and orders)of arbitrary HOPS and HyOPS beams into a single equation.In proof-of-concept experiments,we experimentally demonstrated four metasurfaces to generate arbitrary beams on the fifth-order HOPS(nonfocused and tightly focused,NA 0.89),0-2 order,and 0-1 order HyOPS.We showed HOPS beams’propagation and focusing properties,the superresolution focusing characteristics of the first-order cylindrical VVBs,and the different focusing properties of integerorder and fractional-order cylindrical VVBs.The simplicity and feasibility of the proposed design framework make it a potential catalyst for arbitrary VVBs using metasurfaces in applications of optical imaging,communication,and optical trapping.展开更多
Understanding local variation in forest biomass allows for a better evaluation of broad-scale patterns and interpretation of forest ecosystems’role in carbon dynamics.This study focuses on patterns of aboveground tre...Understanding local variation in forest biomass allows for a better evaluation of broad-scale patterns and interpretation of forest ecosystems’role in carbon dynamics.This study focuses on patterns of aboveground tree biomass within a fully censused 20 ha forest plot in a temperate forest of northern Alabama,USA.We evaluated the relationship between biomass and topography using ridge and valley landforms along with digitally derived moisture and solar radiation indices.Every live woody stem over 1 cm diameter at breast height within this plot was mapped,measured,and identified to species in 2019-2022,and diameter data were used along with speciesspecific wood density to map the aboveground biomass at the scale of 20 m×20 m quadrats.The aboveground tree biomass was 211 Mg·ha^(-1).Other than small stream areas that experienced recent natural disturbances,the total stand biomass was not associated with landform or topographic indices.Dominant species,in contrast,had strong associations with topography.American beech(Fagus grandifolia)and yellow-poplar(Liriodendron tulipfera)dominated the valley landform,with 37% and 54% greater biomass in the valley than their plot average,respectively.Three other dominant species,white oak(Quercus alba),southern shagbark hickory(Carya carolinaeseptentrionalis),and white ash(Fraxinus americana),were more abundant on slopes and benches,thus partitioning the site.Of the six dominant species,only sugar maple(Acer saccharum)was not associated with landform.Moreover,both topographic wetness and potential radiation indices were significant predictors of dominant species biomass within each of the landforms.The study highlights the need to consider species when examining forest productivity in a range of site conditions.展开更多
Poincare dispersed dot plot was an important method in studying heart nonlinear state and rate variability(HRV). Based on the shape of Poincare dispersed dot plot, we proposed four quantitative parameters, introduced ...Poincare dispersed dot plot was an important method in studying heart nonlinear state and rate variability(HRV). Based on the shape of Poincare dispersed dot plot, we proposed four quantitative parameters, introduced the method and algorithm how to get them, and tested them with clinical and animal experiment data. The result showed that these four parameters have certain idiosyncrasy with different heart diseases, and the animal experiment result also showed that these parameters were changed remarkably after coronary artery ligation compared with before, which indicated these parameters might be useful for clinical diagnosis. Because the algorithm we used was based only on the shape of the graph, one can apply this algorithm on any other type of graphs like Poincare dispersed dot plot.展开更多
In this paper,we focus on studying weighted Poincare inequalities on stratified Lie groups.We derive various Poincaréinequalities in the case 1<p=q<∞ in the high order Sobolev space Wm,p.We derive several ...In this paper,we focus on studying weighted Poincare inequalities on stratified Lie groups.We derive various Poincaréinequalities in the case 1<p=q<∞ in the high order Sobolev space Wm,p.We derive several Poincare inequalities that complement existing results,which have only been proved for the case 1<p<q<∞.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.12001170 and 11601124)Innovative Funds Plan of Henan University of Technology(Grant No.2021ZKCJ11).
文摘In this paper,we explicitly establish Poincaréinequality for 1≤p<∞ over simple geometric domains,such as segment,rectangle,triangle or tetrahedron.We obtain sharper bounds of the constant in Poincaré inequality and,in particular,the explicit relation between the constant and the geometric characters of the domain.
基金funded by Gorgan University of Agricultural Sciences and Natural Resources(grant number 9318124503).
文摘Plant species diversity is one of the most widely used indicators in ecosystem management.The relation of species diversity with the size of the sample plot has not been fully determined for Oriental beech forests(Fagus orientalis Lipsky),a widespread species in the Hyrcanian region.Assessing the impacts of plot size on species diversity is fundamental for an ecosystem-based approach to forest management.This study determined the relation of species diversity and plot size by investigating species richness and abundance of both canopy and forest floor.Two hundred and fifty-six sample plots of 625 m^(2) each were layout in a grid pattern across 16 ha.Base plots(25 m×25 m)were integrated in different scales to investigate the effect of plot size on species diversity.The total included nine plots of 0.063,0.125,0.188,0.250,0.375,0.500,0.563,0.750 and 1 ha.Ten biodiversity indices were calculated.The results show that species richness in the different plot sizes was less than the actual value.The estimated value of the Simpson species diversity index was not significantly different from actual values for both canopy and forest floor diversity.The coefficient of variation of this index for the 1-ha sample plot showed the lowest amount across different plot sizes.Inverse Hill species diversity was insignificant difference across different plot sizes with an area greater than 0.500 ha.The modified Hill evenness index for the 1-ha sample size was a correct estimation of the 16-ha for both canopy and forest floor;however,the precision estimation was higher for the canopy layer.All plots greater than 0.250-ha provided an accurate estimation of the Camargo evenness index for forest floor species,but was inaccurate across different plot sizes for the canopy layer.The results indicate that the same plot size did not have the same effect across species diversity measurements.Our results show that correct estimation of species diversity measurements is related to the selection of appropriate indicators and plot size to increase the accuracy of the estimate so that the cost and time of biodiversity management may be reduced.
基金the Chinese Scholarship Council is acknowledged.This work was supported by the UK’s Engineering and Physical Sciences Research Council(Grant Nos.EP/V000624/1,EP/X03495X/1,EP/X041166/1,and EP/T02643X/1)the Royal Society(Grant No.RG\R2\232531).
文摘The unique phase profile and polarization distribution of the vector vortex beam(VVB)have been a subject of increasing interest in classical and quantum optics.The development of higher-order Poincarésphere(HOPS)and hybrid-order Poincarésphere(HyOPS)has provided a systematic description of VVB.However,the generation of arbitrary VVBs on a HOPS and a HyOPS via a metasurface lacks a unified design framework,despite numerous reported approaches.We present a unified design framework incorporating all design parameters(e.g.,focal lengths and orders)of arbitrary HOPS and HyOPS beams into a single equation.In proof-of-concept experiments,we experimentally demonstrated four metasurfaces to generate arbitrary beams on the fifth-order HOPS(nonfocused and tightly focused,NA 0.89),0-2 order,and 0-1 order HyOPS.We showed HOPS beams’propagation and focusing properties,the superresolution focusing characteristics of the first-order cylindrical VVBs,and the different focusing properties of integerorder and fractional-order cylindrical VVBs.The simplicity and feasibility of the proposed design framework make it a potential catalyst for arbitrary VVBs using metasurfaces in applications of optical imaging,communication,and optical trapping.
基金supported in part by the intramural research program of the US Department of Agriculture,National Institute of Food and Agriculture,Evans-Allen#1024525,and Capacity Building Grant#006531supported in part by the US National Science Foundation RII Track 2 FEC:Leveraging Intelligent Informatics and Smart Data for Improved Understanding of Northern Forest Ecosystem Resiliency(INSPIRES)#1920908by The Lyndhurst Foundation.
文摘Understanding local variation in forest biomass allows for a better evaluation of broad-scale patterns and interpretation of forest ecosystems’role in carbon dynamics.This study focuses on patterns of aboveground tree biomass within a fully censused 20 ha forest plot in a temperate forest of northern Alabama,USA.We evaluated the relationship between biomass and topography using ridge and valley landforms along with digitally derived moisture and solar radiation indices.Every live woody stem over 1 cm diameter at breast height within this plot was mapped,measured,and identified to species in 2019-2022,and diameter data were used along with speciesspecific wood density to map the aboveground biomass at the scale of 20 m×20 m quadrats.The aboveground tree biomass was 211 Mg·ha^(-1).Other than small stream areas that experienced recent natural disturbances,the total stand biomass was not associated with landform or topographic indices.Dominant species,in contrast,had strong associations with topography.American beech(Fagus grandifolia)and yellow-poplar(Liriodendron tulipfera)dominated the valley landform,with 37% and 54% greater biomass in the valley than their plot average,respectively.Three other dominant species,white oak(Quercus alba),southern shagbark hickory(Carya carolinaeseptentrionalis),and white ash(Fraxinus americana),were more abundant on slopes and benches,thus partitioning the site.Of the six dominant species,only sugar maple(Acer saccharum)was not associated with landform.Moreover,both topographic wetness and potential radiation indices were significant predictors of dominant species biomass within each of the landforms.The study highlights the need to consider species when examining forest productivity in a range of site conditions.
基金This project is supported by the National Natural Science Foundation of China(No.3 9970 2 0 5)
文摘Poincare dispersed dot plot was an important method in studying heart nonlinear state and rate variability(HRV). Based on the shape of Poincare dispersed dot plot, we proposed four quantitative parameters, introduced the method and algorithm how to get them, and tested them with clinical and animal experiment data. The result showed that these four parameters have certain idiosyncrasy with different heart diseases, and the animal experiment result also showed that these parameters were changed remarkably after coronary artery ligation compared with before, which indicated these parameters might be useful for clinical diagnosis. Because the algorithm we used was based only on the shape of the graph, one can apply this algorithm on any other type of graphs like Poincare dispersed dot plot.
文摘In this paper,we focus on studying weighted Poincare inequalities on stratified Lie groups.We derive various Poincaréinequalities in the case 1<p=q<∞ in the high order Sobolev space Wm,p.We derive several Poincare inequalities that complement existing results,which have only been proved for the case 1<p<q<∞.
