This paper presents a new proof of a charaterization of fractional (g, f)-factors of a graph in which multiple edges are allowed. From the proof a polynomial algorithm for finding the fractional (g, f)-factor can be i...This paper presents a new proof of a charaterization of fractional (g, f)-factors of a graph in which multiple edges are allowed. From the proof a polynomial algorithm for finding the fractional (g, f)-factor can be induced.展开更多
Let G be a bipartite graph with vertex set V(G) and edge set E(G), and let g and f be two positive integer-valued functions defined on V(G) such that g(x) ≤ f(x) for every vertex x of V(G). Then a (g, f)-factor of G ...Let G be a bipartite graph with vertex set V(G) and edge set E(G), and let g and f be two positive integer-valued functions defined on V(G) such that g(x) ≤ f(x) for every vertex x of V(G). Then a (g, f)-factor of G is a spanning subgraph H of G such that g(x) ≤ dH(x) 5 f(x) for each x ∈ V(H). A (g, f)-factorization of G is a partition of E(G) into edge-disjoint (g, f)-factors. Let F = {F1, F2,…… ， Fm } and H be a factorization and a subgraph of G, respectively. If F, 1 ≤ i ≤ m， has exactly one edge in common with H, then it is said that ■ is orthogonal to H. It is proved that every bipartite (mg + m - 1, mf - m + 1 )-graph G has a (g, f)-factorization orthogonal to k vertex disjoint m-subgraphs of G if 2-k ≤ g(x) for all x ∈ V(G). Furthermore, it is showed that the results in this paper are best possible.展开更多
Grassland is most important in China due to its multi-functions. However, about 90% of total usable grassland in China has been degraded and the degradation expands at a rate of 2 million ha per year. Western China co...Grassland is most important in China due to its multi-functions. However, about 90% of total usable grassland in China has been degraded and the degradation expands at a rate of 2 million ha per year. Western China covers 6.12 million square kilometers and 63.8% of the total national area with a distribution of 50 minority nationalities and 75% of the minority national population. Ecological environment there is very vulnerable with more than 90% areas of the annually increased degradation taking place. Under the current tenure arrangement, the individual herder households become the main and direct users of grassland, their decision-making on grassland management may have crucial impact on ecological environment as well as their livelihoods. Thus, it is necessary to examine the determinants of their grassland management behaviors. This study applies 231 household field data from 6 provinces of western China and uses econometric models to explore the major constraints for restricting the herd households' grassland management behaviors. Main results show that under the current tenure and other governance measures, institutional factors, market price and herder's farm and household's characteristics affect the grassland management behaviors.展开更多
Let G be a bipartite graph and g and f be two positive integer-valued functions defined on vertex set V(G) of G such that g(x)≤f(x).In this paper,some sufficient conditions related to the connectivity and edge-connec...Let G be a bipartite graph and g and f be two positive integer-valued functions defined on vertex set V(G) of G such that g(x)≤f(x).In this paper,some sufficient conditions related to the connectivity and edge-connectivity for a bipartite (mg,mf)-graph to have a (g,f)-factor with special properties are obtained and some previous results are generalized.Furthermore,the new results are proved to be the best possible.展开更多
In this paper the properties of some maximum fractional [0, k]-factors of graphs are presented. And consequently some results on fractional matchings and fractional 1-factors are generalized and a characterization of ...In this paper the properties of some maximum fractional [0, k]-factors of graphs are presented. And consequently some results on fractional matchings and fractional 1-factors are generalized and a characterization of fractional k-factors is obtained.展开更多
Vegetation is the main component of the terrestrial ecosystem and plays a key role in global climate change. Remotely sensed vegetation indices are widely used to detect vegetation trends at large scales. To understan...Vegetation is the main component of the terrestrial ecosystem and plays a key role in global climate change. Remotely sensed vegetation indices are widely used to detect vegetation trends at large scales. To understand the trends of vegetation cover, this research examined the spatial-temporal trends of global vegetation by employing the normalized difference vegetation index(NDVI) from the Advanced Very High Resolution Radiometer(AVHRR) Global Inventory Modeling and Mapping Studies(GIMMS) time series(1982–2015). Ten samples were selected to test the temporal trend of NDVI, and the results show that in arid and semi-arid regions, NDVI showed a deceasing trend, while it showed a growing trend in other regions. Mann-Kendal(MK) trend test results indicate that 83.37% of NDVI pixels exhibited positive trends and that only 16.63% showed negative trends(P < 0.05) during the period from 1982 to 2015. The increasing NDVI trends primarily occurred in tree-covered regions because of forest growth and re-growth and also because of vegetation succession after a forest disturbance. The increasing trend of the NDVI in cropland regions was primarily because of the increasing cropland area and the improvement in planting techniques. This research describes the spatial vegetation trends at a global scale over the past 30+ years, especially for different land cover types.展开更多
基金This work is supported by NNSF of ChinaRFDP of Higher Education
文摘This paper presents a new proof of a charaterization of fractional (g, f)-factors of a graph in which multiple edges are allowed. From the proof a polynomial algorithm for finding the fractional (g, f)-factor can be induced.
基金This work was supported by NNSF. RFDP and NNSF of shandong province(Z2000A02 ).
文摘Let G be a bipartite graph with vertex set V(G) and edge set E(G), and let g and f be two positive integer-valued functions defined on V(G) such that g(x) ≤ f(x) for every vertex x of V(G). Then a (g, f)-factor of G is a spanning subgraph H of G such that g(x) ≤ dH(x) 5 f(x) for each x ∈ V(H). A (g, f)-factorization of G is a partition of E(G) into edge-disjoint (g, f)-factors. Let F = {F1, F2,…… ， Fm } and H be a factorization and a subgraph of G, respectively. If F, 1 ≤ i ≤ m， has exactly one edge in common with H, then it is said that ■ is orthogonal to H. It is proved that every bipartite (mg + m - 1, mf - m + 1 )-graph G has a (g, f)-factorization orthogonal to k vertex disjoint m-subgraphs of G if 2-k ≤ g(x) for all x ∈ V(G). Furthermore, it is showed that the results in this paper are best possible.
基金Ford Foundation (1105-1408)Natural Science Foundation of China (71273268) for providing funding supports
文摘Grassland is most important in China due to its multi-functions. However, about 90% of total usable grassland in China has been degraded and the degradation expands at a rate of 2 million ha per year. Western China covers 6.12 million square kilometers and 63.8% of the total national area with a distribution of 50 minority nationalities and 75% of the minority national population. Ecological environment there is very vulnerable with more than 90% areas of the annually increased degradation taking place. Under the current tenure arrangement, the individual herder households become the main and direct users of grassland, their decision-making on grassland management may have crucial impact on ecological environment as well as their livelihoods. Thus, it is necessary to examine the determinants of their grassland management behaviors. This study applies 231 household field data from 6 provinces of western China and uses econometric models to explore the major constraints for restricting the herd households' grassland management behaviors. Main results show that under the current tenure and other governance measures, institutional factors, market price and herder's farm and household's characteristics affect the grassland management behaviors.
基金Supported by the National Natural Science Foundation of China( 60 1 72 0 0 3) NSF of Shandongprovince ( Z2 0 0 0 A0 2 )
文摘Let G be a bipartite graph and g and f be two positive integer-valued functions defined on vertex set V(G) of G such that g(x)≤f(x).In this paper,some sufficient conditions related to the connectivity and edge-connectivity for a bipartite (mg,mf)-graph to have a (g,f)-factor with special properties are obtained and some previous results are generalized.Furthermore,the new results are proved to be the best possible.
基金This work is supported by NSFC (10471078.10201019)RSDP (20040422004) of China
文摘In this paper the properties of some maximum fractional [0, k]-factors of graphs are presented. And consequently some results on fractional matchings and fractional 1-factors are generalized and a characterization of fractional k-factors is obtained.
基金Under the auspices of National Natural Science Foundation of China(No.41771179,41871103,41771138)the National Key Research and Development Project(No.2016YFA0602301)
文摘Vegetation is the main component of the terrestrial ecosystem and plays a key role in global climate change. Remotely sensed vegetation indices are widely used to detect vegetation trends at large scales. To understand the trends of vegetation cover, this research examined the spatial-temporal trends of global vegetation by employing the normalized difference vegetation index(NDVI) from the Advanced Very High Resolution Radiometer(AVHRR) Global Inventory Modeling and Mapping Studies(GIMMS) time series(1982–2015). Ten samples were selected to test the temporal trend of NDVI, and the results show that in arid and semi-arid regions, NDVI showed a deceasing trend, while it showed a growing trend in other regions. Mann-Kendal(MK) trend test results indicate that 83.37% of NDVI pixels exhibited positive trends and that only 16.63% showed negative trends(P < 0.05) during the period from 1982 to 2015. The increasing NDVI trends primarily occurred in tree-covered regions because of forest growth and re-growth and also because of vegetation succession after a forest disturbance. The increasing trend of the NDVI in cropland regions was primarily because of the increasing cropland area and the improvement in planting techniques. This research describes the spatial vegetation trends at a global scale over the past 30+ years, especially for different land cover types.
