Ridge top ecosystems (RTEs) are considered to be more sensitive to global warming as they are characterized by uniform sunlight exposure and low human interferences and hence are perfect places for monitoring and comparing the effects of climate change in species composition. The present study was carried out on RTEs of four different mountain ranges, viz. (1) NarendranagarHindolakhal (2) Mussoorie-Dhanolti (3) ChaurangikhalHarunta and (4) Dayara-Gidara, along altitudinal gradient (situated below 2000 to above 3500 m), in Garhwal Himalaya to understand the variation in tree composition and distribution range. 0.1 ha-sized sample plot was used to analyze the tree species, whereas 5 m 9 5 m for saplings and 1 m 9 1 m for seedlings. The tree layers on RTEs were consisted of total 69 tree species, belonging to 55 genera and 39 families. Shorea robusta, Pinus roxburghii, Rhododendron arboreum, Quercus leucotrichophora, Q. floribunda, Q. semecarpifolia, Cedrus deodara, Pinus wallichiana and Abies spectabilis were found as the dominant and well-occupied tree species on the RTEs from lower to higher elevations. The mean stand density was recorded as 597 ± 29 trees ha -1 (ranged between 546 and 616 trees ha -1 ) with a mean basal cover of 77.25 ± 17.90 m 2 ha -1 (ranged between 54.43 and 102.83 m 2 ha -1). A traditional pattern for tree diversity was recorded which decreased with increasing altitude. The detrended correspondence analysis ordination plot clumped the species together which shared the same habitat and environmental conditions which revealed that elevation and geographic location were the dominant factors for regional differences in species composition among RTEs.

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We characterize the boundedness and compactness of a product-type operator, which, among others, includes all the products of the single composition, multiplication, and differentiation operators, from a general space to Bloch-type spaces. We also give some upper and lower bounds for the norm of the operator. MSC: Primary 47B38; secondary 46E15

The present study aimed to analyze the regeneration dynamics, population structure, and forest composition in some ridge forests of the Western Himalaya to elucidate the impact of climate change. The highest species richness (trees, 17; saplings, 16; seedlings, 16) was recorded in mixed Rhododendron arboreum forest. The maximum tree density (737 § 25.93 trees ha ¡1 ; mixed Quercus floribunda); sapling density (5342 § 587.54 saplings ha ¡1 ; mixed Quercus semecarpifolia), and seedling density (71,429 § 26,632.29 seedlings ha ¡1 ; mixed Cedrus deodara) were recorded in forests of higher altitudes. The mean basal cover values in these forests oscillated between 39.21 § 1.53 m 2 ha ¡1 (mixed Quercus leucotrichophora) to 87.65 § 15.45 m 2 ha ¡1 (mixed Abies pindrow). The highest Shannon index value (0.51 § 0.05) and species evenness (0.36 § 0.02) for trees were recorded in mixed Rhododendron arboreum forest. Some species like Betula utilis, Myrica esculenta, Ficus rumphii, Ilex dipyrena, Quercus floribunda, Litsea elongata, Symplocos paniculata, and Abies spectabilis were noticed as new recruiters (recent invaders) in new habitats, which may change the future forest composition. This study revealed that ridge forests of the Bhagirathi catchment area were in transition phase at middle altitudes. Mixed Quercus floribunda forest was observed to be the youngest regenerating forest; however, mixed Abies pindrow forest was the most mature old-growth forest.