An indefinite weight eigenvalue problem characterizing the threshold condition for extinction of a population based on the single-species diffusive logistic model in a spatially heterogeneous environment is analyzed in a bounded two-dimensional domain with no-flux boundary conditions. In this eigenvalue problem, the spatial heterogeneity of the environment is reflected in the growth rate functi...

Perlmutter (1970) argued that the indefinite article is categorically different from the definite article and proposed that it is a clitic version of the numeral "one". But there are, as Perlmutter himself pointed out, instances of "a" as well as of "one" that don't seem to have the semantics of the numeral. Hence a divorce of "a" (and of "one") from "numeral"-hood is called for. Furthermore, t...

l(f)=(-l)“(Pof’“‘)‘“‘+(-l)“-‘(p,f’”-”)’”~”+ ... +p,f=A.rf (0.1) on a finite or infinite interval (a, b) with real, locally summable coefficients l/PO,Pl, ..-3 Pnv r under the assumptions that p0 >O and that the weight function r changes its sign on (a, b). If r is positive, problem (0.1) can be studied in the context of Hermitian and self-adjoint operators in the Hilbert space L*(r) with the in...

Perlmutter (1970) argued that the indefinite article is categorically different from the definite article and proposed that it is a clitic version of the numeral "one". But there are, as Perlmutter himself pointed out, instances of "a" as well as of "one" that don't seem to have the semantics of the numeral. Hence a divorce of "a" (and of "one") from "numeral"-hood is called for. Furthermore, t...

The adaptive cross approximation method generates low-rank approximations to suitablem×n sub-blocks of discrete integral formulations of elliptic boundary value problems. A characteristic property is that the approximation, which requires k(m+n), k ∼ | log ε|∗, units of storage, is generated in an adaptive and purely algebraic manner using only few of the matrix entries. In this article we pres...