Decay spectrum and decay subspace of normal operators

Let A be a self-adjoint operator on a Hilbert space. It is well known that A admits a unique decomposition into a direct sum of three self-adjoint operators A(p), A(ac) and A(sc) such that there exists an orthonormal basis of eigenvectors for the operator A(p) the operator A(ac) has purely absolutely continuous spectrum and the operator A(sc) has purely singular continuous spectrum. We show the existence of a natural further decomposition of the singular continuous component A c into a direct sum of two self-adjoint operators A(sc)(D) and A(sc)(ND). The corresponding subspaces and spectra are called decaying and purely non-decaying singular subspaces and spectra. Similar decompositions are also shown for unitary operators and for general normal operators.

A further investigation of the kinetic demixing/decomposition of La0.6Sr0.4Co0.2Fe0.8O3- δ oxygen separation membranes

Kinetic demixing and decomposition were studied on three La_0.6Sr_0.4Co_0.2Fe_0.8O_{3- δ} oxygen-separation hollow fibre membrane modules, which were operated under a 0.21/0.009bar oxygen partial pressure difference at 950°C for 1128, 3672 and 5512h, respectively. The post-operation membranes were characterized by Secondary Ion Mass Spectrometry, Scanning Electronic Microscope, Energy Dispersive Spectrum and X-ray Diffraction. The occurrence of kinetic demixing and decomposition was confirmed through the microstructural evolution of the membranes. Secondary-phase grains were found on the air-side surface of the membranes after the long-term operation and Co and Fe enrichment as well as La depletion was found on the surface and in the bulk at the air side. Cation diffusivities were found to be in the order Co>Fe>Sr>La. Kinetic demixing and decomposition rates of the membranes at the air side were found to be self-accelerating with time; the role of A-site deficiency in the perovskite lattice in the bulk near the air side surface is implicated in the mechanism. The oxygen permeability was not affected by the kinetic demixing and decomposition of the material during long-term operation (up to 5512h), however, we may expect permeability to be affected by secondary phase formation on the air-side surface at even longer operational times. © 2010 Elsevier B.V.

The spectrum of endogenous human chromogranin A-derived peptides identified using a modified proteomic strategy.

The hypothesis that chromogranin A (CgA), a protein of neuroendocrine cell secretory granules, may be a precursor of biologically active peptides, rests on observed activities of peptide fragments largely produced by exogenous protease digestion of the bovine protein. Here we have adopted a modified proteomic strategy to isolate and characterise human CgA-derived peptides produced by endogenous prohormone convertases. Initial focus was on an insulinoma as previous studies have shown that CgA is rapidly processed in pancreatic beta cells and that tumours arising from these express appropriate prohormone convertases. Eleven novel peptides were identified arising from processing at both monobasic and dibasic sites and processing was most evident in the C-terminal domain of the protein. Some of these peptides were identified in endocrine tumours, such as mid-gut carcinoid and phaeochromocytoma, which arise from endocrine cells of different phenotype and in different anatomical sites. Two of the most interesting peptides, GR-44 and ER-37, representing the C-terminal region of CgA, were found to be amidated. These data would imply that the intact protein is C-terminally amidated and that these peptides are probably biologically active. The spectrum of novel CgA-derived peptides, described in the present study, should provide a basis for biological evaluation of authentic entities.

Non-Markovian decoherence: complete positivity and decomposition

In this work, the non-Markovian decoherence is considered in two ways. Firstly, an effective Hamiltonian approach is demonstrated to investigate the decoherence of a quantum system in a non-Markovian environment, in which complete positivity of the reduced dynamics is achieved. This method uses the notion of an effective environment, that is a subsystem of the environment that causes the decoherence. Secondly, the evolution of the system and environment is decomposed, thus partially illuminating how they would interact given that memory effects are allowed. It should be noted that beam splitters and rotators are sufficient to explain this decomposition.

How optimal life history changes with the community size-spectrum

This paper derives optimal life histories for fishes or other animals in relation to the size spectrum of the ecological community in which they are both predators and prey. Assuming log-linear size-spectra and well known scaling laws for feeding and mortality, we first construct the energetics of the individual. From these we find, using dynamic programming, the optimal allocation of energy between growth and reproduction as well as the trade-off between offspring size and numbers. Optimal strategies were found to be strongly dependent on size spectrum slope. For steep size spectra (numbers declining rapidly with size), determinate growth was optimal and allocation to somatic growth increased rapidly with increasing slope. However, restricting reproduction to a fixed mating season changed optimal allocations to give indeterminate growth approximating a von Bertalanffy trajectory. The optimal offspring size was as small as possible given other restrictions such as newborn starvation mortality. For shallow size spectra, finite optimal maturity size required a decline in fitness for large size or age. All the results are compared with observed size spectra of fish communities to show their consistency and relevance.