Compact operators without extended eigenvalues

A complex number lambda is called an extended eigenvalue of a bounded linear operator T on a Banach space B if there exists a non-zero bounded linear operator X acting on B such that XT = lambda TX. We show that there are compact quasinilpotent operators on a separable Hilbert space, for which the set of extended eigenvalues is the one-point set {1}.

The resonance spectrum of the cusp map in the space of analytic functions

We prove that the Frobenius-Perron operator $U$ of the cusp map $F:[-1,1]\to [-1,1]$, $F(x)=1-2 x^{1/2}$ (which is an approximation of the Poincare section of the Lorenz attractor) has no analytic eigenfunctions corresponding to eigenvalues different from 0 and 1. We also prove that for any $q\in (0,1)$ the spectrum of $U$ in the Hardy space in the disk $\{z\in C:|z-q|

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.

Extended spectral decompositions of the Renyi map

We present new general methods to obtain spectral decompositions of dynamical systems in rigged Hilbert spaces and investigate the existence of resonances and the completeness of the associated eigenfunctions. The results are illustrated explicitly for the simplest chaotic endomorphism, namely the Renyi map.

The spectrum of the Liouville-von Neumann operator in the Hilbert-Schmidt space

The singular continuous spectrum of the Liouville operator of quantum statistical physics is, in general, properly included in the difference of the spectral values of the singular continuous spectrum of the associated Hamiltonian. The absolutely continuous spectrum of the Liouvillian may arise from a purely singular continuous Hamiltonian. We provide the correct formulas for the spectrum of the Liouville operator and show that the decaying states of the singular continuous subspace of the Hamiltonian do not necessarily contribute to the absolutely continuous subspace of the Liouvillian.

Inter-phyla studies on neuropeptides: the potential for broad-spectrum anthelmintic and/or endectocide discovery

Flatworm, nematode and arthropod parasites have proven their ability to develop resistance to currently available chemotherapeutics. The heavy reliance on chemotherapy and the ability of target species to develop resistance has prompted the search for novel drug targets. In view of its importance to parasite/pest survival, the neuromusculature of parasitic helminths and pest arthropod species remains an attractive target for the discovery Of novel endectocide targets. Exploitation of the neuropeptidergic system in helminths and arthropods has been hampered by a limited Understanding of the functional roles of individual peptides and the structure of endogenous targets, such as receptors. Basic research into these systems has the potential to facilitate target characterization and its offshoots (screen development and drug identification). Of particular interest to parasitologists is the fact that selected neuropeptide families are common to metazoan pest species (nematodes, platyhelminths and arthropods) and fulfil specific roles in the modulation of muscle function in each of the three phyla. This article reviews the inter-phyla activity of two peptide families, the FMRFamide-like peptides and allatostatins, on motor function in helminths and arthropods and discusses the potential of neuropeptide signalling as a target system that could uncover novel endectocidal agents.

Extended electrochemical windows made accessible by room temperature ionic liquid/organic solvent electrolyte systems

The electrochemical windows of acetonitrile solutions doped with 0.1 m concentrations of several ionic liquids were examined by cyclic voltammetry at gold and platinum microelectrodes. These results were compared with those observed in the commonly used 0.1 m tetrabutylammonium perchlorate/acetonitrile system as well as with neat ionic liquids. The use of a trifluorotris(pentofluoroethyl)phosphate-based ionic liquid, specifically, as supporting electrolyte in acetonitrile solutions affords a wider anodic window, which is attributed to the high stability of the anionic component of these intrinsically conductive and thermally robust compounds.

Hoxa6 potentiates short-term hemopoietic cell proliferation and extended self-renewal.

Hemopoietic progenitor cells express clustered homeobox (Hox) genes in a pattern characteristic of their lineage and stage of differentiation. In general, HOX expression tends to be higher in more primitive and lower in lineage-committed cells. These trends have led to the hypothesis that self-renewal of hemopoietic stem/progenitor cells is HOX-dependent and that dysregulated HOX expression underlies maintenance of the leukemia-initiating cell. Gene expression profile studies support this hypothesis and specifically highlight the importance of the HOXA cluster in hemopoiesis and leukemogenesis. Within this cluster HOXA6 and HOXA9 are highly expressed in patients with acute myeloid leukemia and form part of the "Hox code" identified in murine models of this disease. We have examined endogenous expression of Hoxa6 and Hoxa9 in purified primary progenitors as well as four growth factor-dependent cell lines FDCP-Mix, EML, 32Dcl3, and Ba/F3, representative of early multipotential and later committed precursor cells respectively. Hoxa6 was consistently higher expressed than Hoxa9, preferentially expressed in primitive cells and was both growth-factor and cell-cycle regulated. Enforced overexpression of HOXA6 or HOXA9 in FDCP-Mix resulted in increased proliferation and colony formation but had negligible effect on differentiation. In both FDCP-Mix and the more committed Ba/F3 precursor cells overexpression of HOXA6 potentiated factor-independent proliferation. These findings demonstrate that Hoxa6 is directly involved in fundamental processes of hemopoietic progenitor cell development.

An extended framework for evidential reasoning systems.

Use of the Dempster-Shafer (D-S) theory of evidence to deal with uncertainty in knowledge-based systems has been widely addressed. Several AI implementations have been undertaken based on the D-S theory of evidence or the extended theory. But the representation of uncertain relationships between evidence and hypothesis groups (heuristic knowledge) is still a major problem. This paper presents an approach to representing such knowledge, in which Yen’s probabilistic multi-set mappings have been extended to evidential mappings, and Shafer’s partition technique is used to get the mass function in a complex evidence space. Then, a new graphic method for describing the knowledge is introduced which is an extension of the graphic model by Lowrance et al. Finally, an extended framework for evidential reasoning systems is specified.