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.

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.

Electrochemical ammonia gas sensing in nonaqueous systems: A comparison of propylene carbonate with room temperature ffonc liquids

First, the direct and indirect electrochemical oxidation of ammonia has been studied by cyclic voltammetry at glassy carbon electrodes in propylene carbonate. In the case of the indirect oxidation of ammonia, its analytical utility of indirect for ammonia sensing was examined in the range from 10 and 100 ppm by measuring the peak current of new wave resulting from reaction between ammonia and hydroquinone, as function of ammonia concentration, giving a sensitivity 1.29 x 10(-7) A ppm(-1) (r(2)=0.999) and limit-of-detection 5 ppm ammonia. Further, the direct oxidation of ammonia has been investigated in several room temperature ionic liquids (RTILs), namely 1-butyl-3-methylimidazolium tetrafluoroborate ([C(4)mim] [BF4]), 1-butyl-3-methylimiclazolium trifluoromethylsulfonate ([C4mim] [OTf]), 1-Ethyl -3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([C(2)mim] [NTf2]), 1-butyl-3-methylimidazolium bis(tritluoromethylsulfonyl)imide ([C4mim] [NTf2]) and 1-butyl-3-methylimidazolium hexafluorophosphate ([C4mim] [PF6]) on a 10 put diameter Pt microdisk electrode. In four of the RTILs studied, the cyclic voltammetric analysis suggests that ammonia is initially oxidized to nitrogen, N-2, and protons, which are transferred to an ammonia molecule, forming NH4+ via the protonation of the anion(s) (A(-)). However, in [C4mim] [PF6], the protonated anion was formed first, followed by NH4+. In all five RTILs, both HA and NH4+ are reduced at the electrode surface, forming hydrogen gas, which is then oxidized. The analytical ability of this work has also been explored further, giving a limit-of-detection close to 50 ppm in [C(2)mim] [NTf2], [C(4)mim] [OTf], [C(4)mim] [BF4], with a sensitivity of ca. 6 x 10(-7) A ppm(-1) (r(2) = 0.999) for all three ionic liquids, showing that the limit of detection was ca. ten times larger than that in propylene carbonate since ammonia in propylene carbonate might be more soluble in comparison with RTILs when considering the higher viscosity of RTILs.

Family functioning during the diagnosis process in families with children on the autism spectrum,

While the causes of autism spectrum disorder (ASD) still are not fully understood, increasingly research focuses on interventions and treatment of children diagnosed with ASD. Considerably less attention is paid to family systems, family functioning, and family needs. This paper takes a family system perspective exploring how families with children on the autism spectrum function during the particularly stressful period of the diagnosis process and thereafter. Recommendations made in this paper include the need for empirical studies that address in detail family systems, family needs, the assessment and diagnostic process, service provision, social support networks, and additional stressful life events. Furthermore, the development of a family functioning assessment tools is called for in order to promote child-family-centred assessment and intervention. Details of an ongoing comparative study are outlined that will make a contribution to family studies and autism research field with a specific focus on the diagnosis

Experiences of parents during diagnosis and forward planning for children with Autism Spectrum Disorder.

Background For families of children diagnosed with autism spectrum disorder (ASD) getting a diagnosis is a traumatic experience on which future care and education plans for the child depend. In this paper parental experiences of diagnosis and forward planning for children with ASD are reported. Method This paper is part of a large cross-sectional study conducted in Northern Ireland and the Republic of Ireland that assessed the needs and experiences of parents of children diagnosed with ASD. Questionnaires were designed and completed by 95 parents, reporting on 100 children, as well as 67 multi-disciplinary professionals. Results Findings confirm that diagnostic and planning processes are extremely stressful for parents, that statutory diagnosis takes a long time, that care and education plans do not include full parental participation, and that reviews of plans do not consistently include intervention data. Conclusion Policy and practice implications of these findings are important for future revisions of diagnostic tools and manuals.