let  be a hilbert space of functions analytic on a plane domain  such that for every  in  the functional of evaluation at  is bounded. assume further that  contains the constants and admits multiplication by the independent variable , , as a bounded operator. we give sufficient conditions for  to be reflexive for all positive integers .

quantitative structure-activity relationship (qsar) studies of a series of substituted 3-hydroxy-pyridine-4-ones and 3-hydroxy-pyran-4-ones as antibacterial and antifungal agents against a variety of microorganisms were performed. multiple linear regression approach was used as variable selection method. the antimicrobial activities of these compounds against staphylococcus aureus, aspergilus n...

As pointed out in the paper preceding this one, in the case of functionals whose independent variable must obey conditions of integral normalization, conventional functional differentiation, defined in terms of an arbitrary test function, is generally inapplicable and functional derivatives with respect to the density must be evaluated through the alternative and widely used limiting procedure ...

Given a function f0 defined on the unit square Ω with values in R, we construct a piecewise linear function f on a triangulation of Ω such that f agrees with f0 on the boundary nodes, and the image of f has minimal surface area. The problem is formulated as that of minimizing a discretization of a least squares functional whose critical points are uniformly parameterized minimal surfaces. The n...

in this paper, we solve the quadratic $alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f(alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-archimedean number with $alpha^{-2}neq 3$. using the fixed point method and the direct method, we prove the hyers-ulam stability of the quadratic $alpha$-functional equation (0.1) in non-archimedean banach spaces.