where an, bn > 0 and ∑ n an = ∞. Then there exist a threshold α, such that f( ) = ∞ for < α, while f( ) < ∞ for > α. The so-called precise asymptotics problem consists in finding, under appropriate moment conditions, an elementary function g( ) > 0, > α, such that lim ↓α g( ) = 0 and lim ↓α g( )f( ) = l = 0,∞, i.e., in establishing that f( ) ∼ l/g( ) as ↓ α. For almost exhaustive references on ...

This paper addresses bivariate orthogonal polynomials, which are a tensor product of two different orthogonal polynomials in one variable. These bivariate orthogonal polynomials are used to define several new types of continuous and discrete orthogonal moments. Some elementary properties of the proposed continuous Chebyshev–Gegenbauer moments (CGM), Gegenbauer–Legendre moments (GLM), and Chebys...

accurate and nondestructive methods to determine individual leaf areas of plants are useful tools in physiological and agronomic research. a determination of the individual leaf area (la) of such species in brassicaceae family as red cabbage (brassica oleracea var. cappitata l. f. rabra), cabbage (brassica oleracea var. cappitata l. f. alba) and broccoli (brassica oleracea var. italica l.) ...

For strategic traffic flow management, models are needed that allow NAS stakeholders to characterize the joint evolution of weather (and/or its impact on air traffic operating capabilities) in conjunction with the evolution of traffic flows. While queueing models show some promise for permitting meshed analysis of weather and traffic (including flow management initiatives), they are mathematica...