In this paper we show that harmonic compact operator-valued functions are characterized by having harmonic diagonal matrix coefficients in any choice of basis. We also give an example which shows… (More)

In this note we offer a short, constructive proof for Hilbert spaces of Lindenstrauss’ famous result on the denseness of norm attaining operators. Specifically, we show given any A ∈ L(H) there is a… (More)

We study regions where the populations do not fully reproduce themselves but depend on immigration to keep up the population size. We also study regions with a reproductive surplus that leads to… (More)

The effects of nutrients on algal productivity are not transferred directly to production at higher trophic levels and can not be modelled as if they were. Rates of processes and time scales at… (More)

Abstract: In this paper, we generalize the (V, ρ)-invexity defined for nonsmooth multiobjective fractional programming by Mishra, Rueda and Giorgi (2003) to variational programming problems by… (More)

We prove that if T is a strictly singular 1-1 operator defined on an infinite dimensional Banach space X, then for every infinite dimensional subspace Y of X there exists an infinite dimensional… (More)

A language L E Z* is said to be sparse if L contains a vanishingly small fraction of all possible strings of length n in Z*. C. Ponder asked if there exists a sparse language L such that LL = Z*. We… (More)