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In present work, we first establish the corresponding Sobolev inequality and Poincaré inequality on the cone Sobolev spaces, and then, as an application of such inequalities, we prove the existence of non-trivial weak solution for Dirichlet boundary value problem for a class of non-linear elliptic equation on manifolds with conical singularities. Mathematics Subject Classification (2000) 35J20 · 58J05

The northeastern forest region of China is an important component of total temperate and boreal forests in the northern hemisphere. But how carbon (C) pool size and distribution varies among tree, understory, forest floor and soil components, and across stand ages remains unclear. To address this knowledge gap, we selected three major temperate and two major boreal forest types in northeastern (NE) China. Within both forest zones, we focused on four stand age classes (young, mid-aged, mature and over-mature). Results showed that total C storage was greater in temperate than in boreal forests, and greater in older than in younger stands. Tree biomass C was the main C component, and its contribution to the total forest C storage increased with increasing stand age. It ranged from 27.7% in young to 62.8% in over-mature stands in boreal forests and from 26.5% in young to 72.8% in over-mature stands in temperate forests. Results from both forest zones thus confirm the large biomass C storage capacity of old-growth forests. Tree biomass C was influenced by forest zone, stand age, and forest type. Soil C contribution to total forest C storage ranged from 62.5% in young to 30.1% in over-mature stands in boreal and from 70.1% in young to 26.0% in over-mature in temperate forests. Thus soil C storage is a major C pool in forests of NE China. On the other hand, understory and forest floor C jointly contained less than 13% and <5%, in boreal and temperate forests respectively, and thus play a minor role in total forest C storage in NE China.

In this article, we use the cone Sobolev inequality and Poincaré inequality to prove the existence theorem for a class of semilinear degenerate elliptic equation with critical cone Sobolev exponents on manifolds with conical singularities.

Soil microorganisms play vital roles in recovering and maintaining the health of ecosystems, particularly in fragile Karst ecosystems that are easily degraded after cultivation. We investigated the composition and diversity of soil bacterial communities, based on RFLP and 16S rDNA sequencing, in a cropland, a naturally revegetated land with former cultivation disturbance and a primeval forest in the subtropical Karst of southwest China. Our results illustrated that Proteobacteria accounted for 44.8% of the 600 tested clones, making it the most dominant phylum observed. This phylum was followed by Acidobacteria and Planctomycetes for the three Karst soils analyzed. Compared with the primeval forest soil, the proportions of Proteobacteria were decreased by 30.2 and 37.9%, while Acidobacteria increased by 93.9 and 87.9%, and the Shannon-Wiener diversity indices and the physicochemical parameters declined in the cropland and the revegetated land, respectively. Among the three soils, the proportion of dominant bacterial phyla and the diversity indices in the revegetated land were similar to the cropland, implying the bacterial community in the cropland was relatively stable, and the after-effects of cultivation were difficult to eliminate. However, similar distributions of the four Proteobacteria subphyla were observed between the revegetated land and the primeval forest soil. Furthermore, the proportion of Rhizobiales belonging to α-Proteobacteria was sharply decreased with cultivation compared to the primeval forest soil, while a small cluster of Rhizobiales recurred with vegetation recovery. These results indicated that although the subphyla of the dominant bacterial phylum had some positive responses to 20 years of vegetation recovery, it is a slow process. Our results suggest that priority should be given to conserve the primeval forest and inoculation of functional microorganisms on the basis of vegetation recovery may be more effective for the restoration of Karst ecosystems after cultivation.

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