(α, β, λ, δ, m, Ω)p−Neighborhood for some families of analytic and multivalent functions
Abstract In the present investigation, we give some interesting results related with neighborhoods of p−valent functions. Relevant connections with some other recent works are also pointed out.
Coefficient inequalities and inclusion relations for some families of analytic and multivalent functions
Abstract By means of the derivative operator of order m ( m ∈ N 0 ), we introduce and investigate two new subclasses of p -valently analytic functions of complex order. The various results obtained here for each of these two function classes include coefficient inequalities and inclusion relationships involving the ( n , δ ) -neighborhood of p -valently analytic functions. Relevant connections with some other recent investigations are also pointed out.
Silica in Soils1
Publisher Summary Silica in free and combined forms is a dominant component of the solid material of many soils, and dissolved silica is commonly a major solute of soil solutions. Breakdown of primary silicates, translocation of silica in solution, and deposition of secondary silica-containing substances are involved in the development of soils. Ions essential for the growth of plants are released to the soil solution as silicates weather, and these ions may be held against leaching at exchange sites on other silicates. Silica is absorbed in appreciable quantities by some plants and is returned to the surface of the soil as the plants decay. The nature and transformations of silica and silicates in soil are, thus, fundamental to an understanding of many aspects of soil and plant sciences.