Totally real surfaces in C

It has been shown that a totally real surface in CP2 with parallel mean curvature vector and constant Gaussian curvature is either flat or totally geodesic

Convergence of expansions in Schr\"odinger and Dirac eigenfunctions, with an application to the R-matrix theory

Expansion of a wave function in a basis of eigenfunctions of a differential eigenvalue problem lies at the heart of the R-matrix methods for both the Schr\"odinger and Dirac particles. A central issue that should be carefully analyzed when functional series are applied is their convergence. In the present paper, we study the properties of the eigenfunction expansions appearing in nonrelativistic and relativistic $R$-matrix theories. In particular, we confirm the findings of Rosenthal [J. Phys. G: Nucl. Phys. 13, 491 (1987)] and Szmytkowski and Hinze [J. Phys. B: At. Mol. Opt. Phys. 29, 761 (1996); J. Phys. A: Math. Gen. 29, 6125 (1996)] that in the most popular formulation of the R-matrix theory for Dirac particles, the functional series fails to converge to a claimed limit.Comment: Revised version, accepted for publication in Journal of Mathematical Physics, 21 pages, 1 figur

On the Implementation of Constraints through Projection Operators

Quantum constraints of the type Q \psi = 0 can be straightforwardly implemented in cases where Q is a self-adjoint operator for which zero is an eigenvalue. In that case, the physical Hilbert space is obtained by projecting onto the kernel of Q, i.e. H_phys = ker(Q) = ker(Q*). It is, however, nontrivial to identify and project onto H_phys when zero is not in the point spectrum but instead is in the continuous spectrum of Q, because in this case the kernel of Q is empty. Here, we observe that the topology of the underlying Hilbert space can be harmlessly modified in the direction perpendicular to the constraint surface in such a way that Q becomes non-self-adjoint. This procedure then allows us to conveniently obtain H_phys as the proper Hilbert subspace H_phys = ker(Q*), on which one can project as usual. In the simplest case, the necessary change of topology amounts to passing from an L^2 Hilbert space to a Sobolev space.Comment: 22 pages, LaTe

Keratinases Produced by Aspergillus stelliformis, Aspergillus sydowii, and Fusarium brachygibbosum Isolated from Human Hair: Yield and Activity

Twenty fungal strains belonging to 17 species and isolated from male scalp hair were tested for their capacity to hydrolyze keratinous material from chicken feather. The identification of the three most efficient species was confirmed by sequencing of the internal transcribed spacer (ITS) region of rDNA. Activities of fungal keratinases produced by Aspergillus stelliformis (strain AUMC 10920), A. sydowii (AUMC 10935), and Fusarium brachygibbosum (AUMC 10937) were 113, 120, and 130 IU mg−1 enzymes, respectively. The most favorable conditions were at pH 8.0 and 50 °C. Keratinase activity was markedly inhibited by EDTA and metal ions Ca+2, Co+2, Ni+2, Cu+2, Fe+2, Mg+2, and Zn+2, with differences between the fungal species. To the best of our knowledge, this is the first study on the activity of keratinase produced by A. stelliformis, A. sydowii, and F. brachygibbosum. F. brachygibbosum keratinase was the most active, but the species is not recommended because of its known phytopathogenicty. Aspergillus sydowii has many known biotechnological solutions and here we add another application of the species, as producer of keratinases. We introduce A. stelliformis as new producer of active fungal keratinases for biotechnological solutions, such as in the management of keratinous waste in poultry industry