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Disparities in tree mortality among plant functional types(PFTs)in a temperate forest:Insights into size-dependent and PFT-specific patterns
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作者 Man Hu Hang Shi +6 位作者 Rui He Bingbin Wen Haikun Liu Kerong Zhang Xiao Shu Haishan Dang Quanfa Zhang 《Forest Ecosystems》 SCIE CSCD 2024年第4期480-490,共11页
Tree mortality significantly influences forest structure and function,yet our understanding of its dynamic patterns among a range of tree sizes and among different plant functional types(PFTs)remains incomplete.This s... Tree mortality significantly influences forest structure and function,yet our understanding of its dynamic patterns among a range of tree sizes and among different plant functional types(PFTs)remains incomplete.This study analysed size-dependent tree mortality in a temperate forest,encompassing 46 tree species and 32,565 individuals across different PFTs(i.e.,evergreen conifer vs.deciduous broadleaf species,shade-tolerant vs.shade-intolerant species).By employing all-subset regression procedures and logistic generalized linear mixed-effects models,we identified distinct mortality patterns influenced by biotic and abiotic factors.Our results showed a stable mortality patte rn in eve rgreen conifer species,contrasted by a declining pattern in deciduous broadleaf and shadetolerant,as well as shade-intolerant species,across size classes.The contribution to tree mortality of evergreen conifer species shifted from abiotic to biotic factors with increasing size,while the mortality of deciduous broadleaf species was mainly influenced by biotic factors,such as initial diameter at breast height(DBH)and conspecific negative density.For shade-tolerant species,the mortality of small individuals was mainly determined by initial DBH and conspecific negative density dependence,whereas the mortality of large individuals was subjected to the combined effect of biotic(competition from neighbours)and abiotic factors(i.e.,convexity and pH).As for shade-intolerant species,competition from neighbours was found to be the main driver of tree mortality throughout their growth stages.Thus,these insights enhance our understanding of forest dynamics by revealing the size-dependent and PFT-specific tree mortality patterns,which may inform strategies for maintaining forest diversity and resilience in temperate forest ecosystems. 展开更多
关键词 Size-dependent tree mortality Plant functional type Neighbourhood competition Topography variables Soil properties
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Classification of plant functional types based on the nutrition traits: a case study on alpine meadow community in the Zoigê Plateau 被引量:6
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作者 SHEN Song-tao ZHANG Shu-jie +1 位作者 FAN Min WANG Qing 《Journal of Mountain Science》 SCIE CSCD 2017年第10期2003-2012,共10页
The ecological concept of Plant Functional Types(PFTs), which refers to the assemblage of plants with certain functional traits, has been introduced for the study of plant responses to the environment change and hum... The ecological concept of Plant Functional Types(PFTs), which refers to the assemblage of plants with certain functional traits, has been introduced for the study of plant responses to the environment change and human disturbance. Taking the alpine meadow community in the Zoigê Plateau as a study case, this paper classified PFTs in terms of plant nutrition traits. The sequential results are as follows.(1) The main herbages in the Zoigê Plateau included 16 species in 5 families. Among the five families, Cyperaceae vegetation accounted for 81.37%of herbage area in total, while the remaining 4families occupied less than 20%. As for the species,Kobresia setchwanensis Hand.-Maizz. was dominant,accounting for 48.74% of the total area; while the remaining 51.26% was comprised of Polygonum viviparum L., Anaphalis fiavescens Hand.-Mazz.,Stipa aliena Keng and other species.(2) By using the Principal Component Analysis(PCA), the assessment of herbages nutrition was carried out based on the comprehensive multi-index evaluation model.Polygonum viviparum L. had the highest nutritional value score(1.43), and Stipa aliena Keng had the lowest(-1.40). Nutritional value of herbage species had a significantly positive correlation with altitude(P&lt;0.01) in the Zoigê Plateau.(3) Based on the nutritional values, herbages in the Zoigê Plateau could be grouped into 3 nutrition PFTs(high, medium and low) by using the Natural Breaks(Jenks) method. 展开更多
关键词 Plant functional types Nutritional value Forage resource management the Zoigê Plateau
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Effect of Implementing Ecosystem Functional Type Data in a Mesoscale Climate Model
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作者 Seung-Jae LEE E. Hugo BERBERY Domingo ALCARAZ-SEGURA 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2013年第5期1373-1386,共14页
In this paper, we introduce a new concept of land-surface state representation for southern South America, which is based on "functional" attributes of vegetation, and implement a new land-cover (Ecosystem Function... In this paper, we introduce a new concept of land-surface state representation for southern South America, which is based on "functional" attributes of vegetation, and implement a new land-cover (Ecosystem Functional Type, hereafter EFT) dataset in the Weather and Research Forecasting (WRF) model. We found that the EFT data enabled us to deal with functional attributes of vegetation and time-variant features more easily than the default land-cover data in the WRF. In order to explore the usefulness of the EFT data in simulations of surface and atmospheric variables, numerical simulations of the WRF model, using both the US Geological Survey (USGS) and the EFT data, were conducted over the La Plata Basin in South America for the austral spring of 1998 and compared with observations. Results showed that the model simulations were sensitive to the lower boundary conditions and that the use of the EFT data improved the climate simulation of 2-m temperature and precipitation, implying the need for this type of information to be included in numerical climate models. 展开更多
关键词 Ecosystem functional type WRF land cover climate simulation
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Effects of Plant Functional Types,Climate and Soil Nitrogen on Leaf Nitrogen along the North-South Transect of Eastern China 被引量:5
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作者 展小云 于贵瑞 何念鹏 《Journal of Resources and Ecology》 CSCD 2013年第2期125-131,共7页
We conducted a systematic census of leaf N for 102 plant species at 112 research sites along the North-South Transect of Eastern China (NSTEC) following the same protocol, to explore how plant functional types (PFT... We conducted a systematic census of leaf N for 102 plant species at 112 research sites along the North-South Transect of Eastern China (NSTEC) following the same protocol, to explore how plant functional types (PFTs) and environmental factors affect the spatial pattern of leaf N. The results showed that mean leaf N was 17.7 mg g^-1 for all plant species. The highest and lowest leaf N were found in deciduous-broadleaf and evergreen-conifer species, respectively, and the ranking of leaf N from high to low was: deciduous 〉 evergreen species, broadleaf 〉 coniferous species, shrubs ≈ trees 〉 grasses. For all data pooled, leaf N showed a convex quadratic response to mean annual temperature (MAT), and a negative linear relationship with mean annual precipitation (MAP), but a positive linear relationship with soil nitrogen concentration (Nsoil). These patterns were similar when PFTs were examined individually. Importantly, PFTs, climate and Nsoil, jointly explained 46.1% of the spatial variation in leaf N, of which the independent explanatory powers of PFTs, climate and Nsoil, were 15.6%, 2.3% and 4.7%, respectively. Our findings suggest that leaf N is regulated by climate and Nsoil, mainly via plant species composition. The wide scale empirical relationships developed here are useful for understanding and modeling of the effects of PFTs and environmental factors on leaf N. 展开更多
关键词 forest ecosystem plant functional type temperature PRECIPITATION soil nitrogen
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Predicting plant traits and functional types response to grazing in an alpine shrub meadow on the Qinghai-Tibet Plateau 被引量:15
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作者 ZHU ZhiHong WANG XiaoAn +2 位作者 LI YingNian WANG Gang GUO Hua 《Science China Earth Sciences》 SCIE EI CAS 2012年第5期837-851,共15页
The identification of easily measured plant functional types (PFTs) that consistently predict grazing response would be a major advance.The responses to grazing of individual traits and PFTs were analyzed along a graz... The identification of easily measured plant functional types (PFTs) that consistently predict grazing response would be a major advance.The responses to grazing of individual traits and PFTs were analyzed along a grazing gradient in an alpine shrub meadow on the Qinghai-Tibet Plateau,China.Three response types were identified;grazing increaser (GI),grazing decreaser (GD),and neutral (NE) for both traits and PFTs.Seven traits were measured:plant height,economic group,cotyledon type,plant inclination,growth form,life cycle,and vegetative structure.The first five were significantly affected by grazing.Ordinal regressions for grazing response of the seven traits showed that the best single predictors of response were growth form (including the attributes "Scattered","Bunched" or "Closely Bunched"),and plant inclination ("Rosette","Prostrate",or "Erect"),followed by economic group ("Shrub","Grass","Sedge","Legume","Forb",or "Harmful") and plant height ("Tall","Medium",or "Small").Within the four optimal traits,the summed dominance ratio (SDR) of small plants,forbs,rosette and bunched plants,invariably increased,while that of tall plants,shrubs,grasses,and erect plants decreased,when grazing pressure was enhanced.Canonical correspondence analysis (CCA) identified eleven explanatory PFTs based on 195 defined PFTs,by combining the different attributes of the four optimal traits.Among explanatory PFTs,the most valuable in predicting the community response to grazing were Tall×Shrub×Erect×Scattered and Small×Forb×Rosette,as these have the closest connections with grazing disturbance and include fewer species.Species richness,diversity,and community evenness,did not differ among grazing treatments because turnover occurred in component species and their relative abundances along the grazing gradient.We have demonstrated that a minimum set of PFTs resulting from optimal individual traits can provide consistent prediction of community responses to grazing in this region.This approach provides a more accurate indicator of change within a changing environment than do univariate measures of species diversity.We hope to provide a link between management practices and vegetation structure,forming a basis for future,large scale,plant trait comparisons. 展开更多
关键词 Alpine shrub meadow grazing response optimal traits plant functional types
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Projections of land use changes under the plant functional type classification in different SSP-RCP scenarios in China 被引量:16
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作者 Weilin Liao Xiaoping Liu +4 位作者 Xiyun Xu Guangzhao Chen Xun Liang Honghui Zhang Xia Li 《Science Bulletin》 SCIE EI CAS CSCD 2020年第22期1935-1947,M0004,共14页
Land use projections are crucial for climate models to forecast the impacts of land use changes on the Earth’s system.However,the spatial resolution of existing global land use projections(e.g.,0.25°×0.25&#... Land use projections are crucial for climate models to forecast the impacts of land use changes on the Earth’s system.However,the spatial resolution of existing global land use projections(e.g.,0.25°×0.25°in the Land-Use Harmonization(LUH2)datasets)is still too coarse to drive regional climate models and assess mitigation effectiveness at regional and local scales.To generate a high-resolution land use product with the newest integrated scenarios of the shared socioeconomic pathways and the representative concentration pathways(SSPs-RCPs)for various regional climate studies in China,here we first conduct land use simulations with a newly developed Future Land Uses Simulation(FLUS)model based on the trajectories of land use demands extracted from the LUH2 datasets.On this basis,a new set of land use projections under the plant functional type(PFT)classification,with a temporal resolution of 5 years and a spatial resolution of 5 km,in eight SSP-RCP scenarios from 2015 to 2100 in China is produced.The results show that differences in land use dynamics under different SSP-RCP scenarios are jointly affected by global assumptions and national policies.Furthermore,with improved spatial resolution,the data produced in this study can sufficiently describe the details of land use distribution and better capture the spatial heterogeneity of different land use types at the regional scale.We highlight that these new land use projections at the PFT level have a strong potential for reducing uncertainty in the simulation of regional climate models with finer spatial resolutions. 展开更多
关键词 Land use change Plant functional type Future Land Uses Simulation(FLUS) Land use simulation SSP-RCP scenarios
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Uniform persistence of multispecies ecological competition predator-pray system with Holling Ⅲ type functional response 被引量:1
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作者 LI Zhan LI Ling-xiao WANG Ke 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2008年第4期410-412,共3页
The main purpose of this paper is to study the persistence of the general multispecies competition predator-pray system with Holling Ⅲ type functional response. In this system, the competition among predator species ... The main purpose of this paper is to study the persistence of the general multispecies competition predator-pray system with Holling Ⅲ type functional response. In this system, the competition among predator species and among prey species are simultaneously considered. By using the comparison theory and qualitative analysis, the sufficient conditions for uniform strong persistence are obtained. 展开更多
关键词 competition predator-pray system Holling type functional response persistence
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Impulsive Predator-Prey Dynamic Systems with Beddington-DeAngelis Type Functional Response on the Unification of Discrete and Continuous Systems 被引量:1
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作者 Ayse Feza Güvenilir Billur Kaymakcalan Neslihan Nesliye Pelen 《Applied Mathematics》 2015年第9期1649-1664,共16页
In this study, the impulsive predator-prey dynamic systems on time scales calculus are studied. When the system has periodic solution is investigated, and three different conditions have been found, which are necessar... In this study, the impulsive predator-prey dynamic systems on time scales calculus are studied. When the system has periodic solution is investigated, and three different conditions have been found, which are necessary for the periodic solution of the predator-prey dynamic systems with Beddington-DeAngelis type functional response. For this study the main tools are time scales calculus and coincidence degree theory. Also the findings are beneficial for continuous case, discrete case and the unification of both these cases. Additionally, unification of continuous and discrete case is a good example for the modeling of the life cycle of insects. 展开更多
关键词 Time Scales Calculus Predator-Prey Dynamic Systems Periodic Solutions Coincidence Degree Theory Beddington-DeAngelis type functional Response
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The unimodal latitudinal pattern of K,Ca and Mg concentration and its potential drivers in forest foliage in eastern China
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作者 Zhijuan Shi Sining Liu +2 位作者 Yahan Chen Dongdong Ding Wenxuan Han 《Forest Ecosystems》 SCIE CSCD 2024年第3期318-328,共11页
Potassium(K),calcium(Ca),and magnesium(Mg)are essential elements with important physiological functions in plants.Previous studies showed that leaf K,Ca,and Mg concentrations generally increase with increasing latitud... Potassium(K),calcium(Ca),and magnesium(Mg)are essential elements with important physiological functions in plants.Previous studies showed that leaf K,Ca,and Mg concentrations generally increase with increasing latitudes.However,recent meta-analyses suggested the possibility of a unimodal pattern in the concentrations of these elements along latitudinal gradients.The authenticity of this unimodal latitudinal pattern,however,requires validation through large-scale field experimental data,and exploration of the underlying mechanisms if the pattern is confirmed.Here,we collected leaves of common species of woody plants from 19 montane forests in the north-south transect of eastern China,including 322 species from 160 genera,67 families;and then determined leaf K,Ca,and Mg concentrations to explore their latitudinal patterns and driving mechanisms.Our results support unimodal latitudinal patterns for all three elements in woody plants across eastern China,with peak values at latitude 36.5±1.0°N.The shift of plant-functional-type compositions from evergreen broadleaves to deciduous broadleaves and to conifers along this latitudinal span was the key factor contributing to these patterns.Climatic factors,mainly temperature,and to a lesser extent solar radiation and precipitation,were the main environmental drivers.These factors,by altering the composition of plant communities and regulating plant physiological activities,influence the latitudinal patterns of plant nutrient concentrations.Our findings also suggest that high leaf K,Ca,and Mg concentrations may represent an adaptive strategy for plants to withstand water stress,which might be used to predict plant nutrient responses to climate changes at large scales,and broaden the understanding of biogeochemical cycling of K,Ca,and Mg. 展开更多
关键词 Potassium Calcium Magnesium Mid-latitudes Latitudinal pattern Plant functional type Water stress Woody plant
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Trait-based representation of hydrological functional properties of plants in weather and ecosystem models 被引量:2
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作者 Ashley M. Matheny Golnazalsadat Mirfenderesgi Gil Bohrer 《Plant Diversity》 SCIE CAS CSCD 北大核心 2017年第1期1-12,共12页
Land surface models and dynamic global vegetation models typically represent vegetation through coarse plant functional type groupings based on leaf form, phenology, and bioclimatic limits. Although these groupings we... Land surface models and dynamic global vegetation models typically represent vegetation through coarse plant functional type groupings based on leaf form, phenology, and bioclimatic limits. Although these groupings were both feasible and functional for early model generations, in light of the pace at which our knowledge of functional ecology, ecosystem demographics, and vegetation-climate feedbacks has advanced and the ever growing demand for enhanced model performance, these groupings have become antiquated and are identified as a key source of model uncertainty. The newest wave of model development is centered on shifting the vegetation paradigm away from plant functional types(PFTs)and towards flexible trait-based representations. These models seek to improve errors in ecosystem fluxes that result from information loss due to over-aggregation of dissimilar species into the same functional class. We advocate the importance of the inclusion of plant hydraulic trait representation within the new paradigm through a framework of the whole-plant hydraulic strategy. Plant hydraulic strategy is known to play a critical role in the regulation of stomatal conductance and thus transpiration and latent heat flux. It is typical that coexisting plants employ opposing hydraulic strategies, and therefore have disparate patterns of water acquisition and use. Hydraulic traits are deterministic of drought resilience, response to disturbance, and other demographic processes. The addition of plant hydraulic properties in models may not only improve the simulation of carbon and water fluxes but also vegetation population distributions. 展开更多
关键词 Hydraulic traits Land-surface modeling Whole-plant hydraulic strategy Trait-based models Demographic models Plant functional type
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The biological function of type I receptors of bone morphogenetic protein in bone 被引量:11
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作者 Shuxian Lin Kathy KH Svoboda +1 位作者 Jian Q Feng Xinquan Jiang 《Bone Research》 SCIE CAS CSCD 2016年第2期63-71,共9页
Bone morphogenetic proteins (BMPs) have multiple roles in skeletal development, homeostasis and regeneration. BMPs signal via type I and type II serine/threonine kinase receptors (BMPRI and BMPRII). In recent deca... Bone morphogenetic proteins (BMPs) have multiple roles in skeletal development, homeostasis and regeneration. BMPs signal via type I and type II serine/threonine kinase receptors (BMPRI and BMPRII). In recent decades, genetic studies in humans and mice have demonstrated that perturbations in BMP signaling via BMPRI resulted in various diseases in bone, cartilage, and muscles. In this review, we focus on all three types of BMPRI, which consist of activin-like kinase 2 (ALK2, also called type IA activin receptor), activin- llke kinase 3 (ALK3, also called BMPRIA), and activin-like kinase 6 (ALK6, also called BMPRIB). The research areas covered include the current progress regarding the roles of these receptors during myogenesis, chondrogenesis, and osteogenesis. Understanding the physiological and pathological functions of these receptors at the cellular and molecular levels will advance drug development and tissue regeneration for treating musculoskeletal diseases and bone defects in the future. 展开更多
关键词 ALK The biological function of type I receptors of bone morphogenetic protein in bone type
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POSITIVE EQUILIBRIUM AND ITS STABILITY OF THE BEDDINGTON-DEANGELIS'TYPE PREDATOR-PREY DYNAMICAL SYSTEM 被引量:7
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作者 Xiao Haibin Department of Mathematics, Ningbo University, Zhejiang 315211,China Department of Mathematics, Nanjing University, Jiangsu 210093,China. 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2006年第4期429-436,共8页
A class of Beddington-DeAngelis' type predator-prey dynamic system with prey and predator both having linear density restriction is considered. By using the qualitative methods of ODE, the existence and uniqueness of... A class of Beddington-DeAngelis' type predator-prey dynamic system with prey and predator both having linear density restriction is considered. By using the qualitative methods of ODE, the existence and uniqueness of positive equilibrium and its global asymptotic stability are analyzed. The direct criterions for local stability of positive equilibrium and existence of limit cycle are also established when inference parameter of predator is small. 展开更多
关键词 density restriction Beddington-DeAngelis' type functional response global stability limit cycle.
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HIGHER RADIAL DERIVATIVE OF BLOCH TYPE FUNCTIONS 被引量:4
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作者 李波 欧阳才衡 《Acta Mathematica Scientia》 SCIE CSCD 2002年第4期433-445,共13页
In this paper, The integral characterizations of alpha-Bloch (little alpha-Bloch) axe given in terms of higher radial derivative, and their characterizations of Caxleson type measure are obtained.
关键词 Bloch type function higher radial derivative Carleson type measure
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SUFFICIENT CONDITION FOR FUNCTIONS TO BE IN A CLASS OF MEROMORPHIC MULTIVALENT SAKAGUCHI TYPE SPIRAL-LIKE FUNCTIONS 被引量:1
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作者 Muhammad ARIF Janusz SOK Muhammad AYAZ 《Acta Mathematica Scientia》 SCIE CSCD 2014年第2期575-578,共4页
In this article, we define a subclass of meromorphic multivalent Sakaguchi type functions and obtain certain sufficient conditions for functions to be in this class. The main result presented here includes a number of... In this article, we define a subclass of meromorphic multivalent Sakaguchi type functions and obtain certain sufficient conditions for functions to be in this class. The main result presented here includes a number of consequences as its special cases. 展开更多
关键词 Sakaguchi type functions spirallike functions meromorphic functions
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A MAXIMAL FUNCTION CHARACTERIZATION 0F HARDY SPACES ON SPACES OF HOMOGENEOUS TYPE 被引量:6
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作者 Li Wenming Zhongshan University, China 《Analysis in Theory and Applications》 1998年第2期12-27,共16页
A new maximal function is introduced in the dual spaces of test function spaces on spaces of homogeneous type. Using this maximal function, we get new characterization of atomic H^p spaces.
关键词 A MAXIMAL FUNCTION CHARACTERIZATION 0F HARDY SPACES ON SPACES OF HOMOGENEOUS type APPI 尸气
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The X-ray Background (Deep Fields, Luminosity Functions and Type-Ⅱ Quasars)
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作者 Günther Hasinger 《天文研究与技术》 CSCD 北大核心 2003年第S1期136-146,共11页
Deep X ray surveys have shown that the cosmic X ray background (XRB) is largely due to the accretion onto supermassive black holes, integrated over the cosmic time. These surveys have resolved more than 80% of the 0.1... Deep X ray surveys have shown that the cosmic X ray background (XRB) is largely due to the accretion onto supermassive black holes, integrated over the cosmic time. These surveys have resolved more than 80% of the 0.1-10keV X ray background into discrete sources. Optical spectroscopic identifications show that the sources producing the bulk of the X ray background are a mixture of obscured (type 1) and unobscured (type 2) AGNs, as predicted by the XRB population synthesis models. A class of highly luminous type 2 AGN, so called QSO 2s, has been detected in the deepest Chandra and XMM Newton surveys. The new Chandra AGN redshift distribution peaks at much lower redshifts (z≈0.7) than that based on ROSAT data, indicating that Seyfert galaxies peak at significantly lower redshifts than QSOs. 展开更多
关键词 AGN The X-ray Background Figure Luminosity Functions and type QUASARS Deep Fields
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APPROXIMATION OF CONVEX TYPE FUNCTION BY PARTIAL SUMS OF FOURIER SERIES
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作者 YuGuohua 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2004年第1期67-76,共10页
The concept of convex type function is introduced in this paper,from which a kin d of convex decomposition approach is proposed.As one of applications of this a pproach,the approximation of the convex type function b... The concept of convex type function is introduced in this paper,from which a kin d of convex decomposition approach is proposed.As one of applications of this a pproach,the approximation of the convex type function by the partial sum of its Fourier series is inves tigated.Moreover,the order of approximation is describe d with the 2th continuous modulus. 展开更多
关键词 Fourier series convex type function CONVEX DECOMPOSITION Riemann deriv ative continuous modulus approximation.
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Global analysis of Ivlev's type predator-prey dynamic systems
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作者 肖海滨 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第4期461-470,共10页
Consider a class of Ivlev's type predator-prey dynamic systems with prey and predator both having linear density restricts. By using the qualitative methods of ODE, the global stability of positive equilibrium and ex... Consider a class of Ivlev's type predator-prey dynamic systems with prey and predator both having linear density restricts. By using the qualitative methods of ODE, the global stability of positive equilibrium and existence and uniqueness of non-small amplitude stable limit cycle are obtained. Especially under certain conditions, it shows that existence and uniqueness of non-small amplitude stable limit cycle is equivalent to the local un-stability of positive equilibrium and the local stability of positive equilibrium implies its global stability. That is to say, the global dynamic of the system is entirely determined by the local stability of the positive equilibrium. 展开更多
关键词 limit cycle global stability Ivlev's type functional response density restrict existence and uniqueness
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Algebraic Independence Measures for the Values of Mahler Type Functions
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作者 WANG Tian-qin LIU Hua-ke 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2006年第4期567-576,共10页
In this paper, we give the algebraic independence measures for the values ofMahler type functions in complex number field and p-adic number field, respectively.
关键词 algebraic independence measure Mahler type function p-adic number field
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Ulam-Hyers Stability of Trigonometric Functional Equation with Involution
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作者 Cheng Li-hua 《Communications in Mathematical Research》 CSCD 2018年第2期141-148,共8页
The present work aims to determine the solution of trigonometric functional equation f with involution from group to field by using the properties of involution function, and the solution and Ulam-Hyers stability of t... The present work aims to determine the solution of trigonometric functional equation f with involution from group to field by using the properties of involution function, and the solution and Ulam-Hyers stability of the trigonometric functional equation are also discussed. Furthermore, this method generalizes the main theorem and gives the supplement in some reference. 展开更多
关键词 exponential type functional equation multiplicative function STABILITY
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