Orbits of operators commuting with the Volterra operator

Asymptotic estimates of the norms of orbits of certain operators that commute with the classical Volterra operator V acting on L-P[0,1], with 1 0, but also to operators of the form phi (V), where phi is a holomorphic function at zero. The method to obtain the estimates is based on the fact that the Riemann-Liouville operator as well as the Volterra operator can be related to the Levin-Pfluger theory of holomorphic functions of completely regular growth. Different methods, such as the Denjoy-Carleman theorem, are needed to analyze the behavior of the orbits of I - cV, where c > 0. The results are applied to the study of cyclic properties of phi (V), where phi is a holomorphic function at 0.

Analyticity of smooth eigenfunctions and spectral analysis of the Gauss map

We provide a sufficient condition of analyticity of infinitely differentiable eigenfunctions of operators of the form Uf(x) = integral a(x, y) f(b( x, y)) mu(dy) acting on functions f: [u, v] --> C ( evolution operators of one-dimensional dynamical systems and Markov processes have this form). We estimate from below the region of analyticity of the eigenfunctions and apply these results for studying the spectral properties of the Frobenius-Perron operator of the continuous fraction Gauss map. We prove that any infinitely differentiable eigenfunction f of this Frobenius-Perron operator, corresponding to a non-zero eigenvalue admits a (unique) analytic extension to the set C\(-infinity, 1]. Analyzing the spectrum of the Frobenius Perron operator in spaces of smooth functions, we extend significantly the domain of validity of the Mayer and Ropstorff asymptotic formula for the decay of correlations of the Gauss map.

Trans Governmentality: the production and regulation of gendered subjectivities

Feminist theorists have long critiqued the hierarchical gender division inherent in Western societies, with the inequalities resulting from this divide being widely decried and some progress made in reducing these. Despite increased efforts to theorise trans identification in recent times, gender is still largely understood, both culturally and theoretically, as adhering to the dualism of male/female. I argue within this paper that consideration of the narratives of transpeople and their partners could expand our conceptualisation of gender and offers possible points of resistance from which to challenge the gender binary, thereby destabilising hegemonic discourses of gender. As such I explore the narratives of transpeople and their partners in relation to the construction and reconstruction of gendered subjectivities. Transpeople’s intimate partnerships, considered here due to the critique of gender norms often evident within them, are examined through the theoretical lens of Foucault’s notion of governmentality. This paper offers an example of how governmentality can be a useful tool in the effort to understand gender regulation, not least for those apparently on the margins of ‘normality’.

Density-Enhanced Gas and Dust Shells in a New Chemical Model for IRC+10216

A new chemical model is presented for the carbon-rich circumstellar envelope (CSE) of the asymptotic giant branch star IRC+10216. The model includes shells of matter with densities that are enhanced relative to the surrounding circumstellar medium. The chemical model uses an updated reaction network including reactions from the RATE06 database and a more detailed anion chemistry. In particular, new mechanisms are considered for the formation of CN-, C3N-, and C2H-, and for the reactions of hydrocarbon anions with atomic nitrogen and with the most abundant cations in the CSE. New reactions involving H- are included which result in the production of significant amounts of C2H- and CN- in the inner envelope. The calculated radial molecular abundance profiles for the hydrocarbons C2H, C4H, and C6H and the cyanopolyynes HC3N and HC5N show narrow peaks which are in better agreement with observations than previous models. Thus, the narrow rings observed in molecular microwave emission surrounding IRC+10216 are interpreted as arising in regions of the envelope where the gas and dust densities are greater than the surrounding circumstellar medium. Our models show that CN- and C2H- may be detectable in IRC+10216 despite the very low theorized radiative electron attachment rates of their parent neutral species. We also show that magnesium isocyanide (MgNC) can be formed in the outer envelope through radiative association involving Mg+ and the cyanopolyyne species.

FARM_2DRMP: A version of FARM for use with 2DRMP

To complete the 2DRMP package an asymptotic program, such as FARM, is needed. The original version of FARM is designed to construct the physical R-matrix, R, from surface amplitudes contained in the H-file. However, in 2DRMP, R has already been constructed for each scattering energy during propagation. Therefore, this modified version of FARM, known as as FARM_2DRMP, has been developed solely for use with 2DRMP.

SN 2008S: an electron-capture SN from a super-AGB progenitor?

We present comprehensive photometric and spectroscopic observations of the faint transient SN 2008S discovered in the nearby galaxy NGC 6946. SN 2008S exhibited slow photometric evolution and almost no spectral variability during the first nine months, implying a long photon diffusion time and a high-density circumstellar medium. Its bolometric luminosity (similar or equal to 10(41) erg s(-1) at peak) is low with respect to most core-collapse supernovae but is comparable to the faintest Type II-P events. Our quasi-bolometric light curve extends to 300 d and shows a tail phase decay rate consistent with that of Co-56. We propose that this is evidence for an explosion and formation of Ni-56 (0.0014 +/- 0.0003 M-circle dot). Spectra of SN 2008S show intense emission lines of H alpha, [Ca II] doublet and Ca II near-infrared (NIR) triplet, all without obvious P-Cygni absorption troughs. The large mid-infrared (MIR) flux detected shortly after explosion can be explained by a light echo from pre-existing dust. The late NIR flux excess is plausibly due to a combination of warm newly formed ejecta dust together with shock-heated dust in the circumstellar environment. We reassess the progenitor object detected previously in Spitzer archive images, supplementing this discussion with a model of the MIR spectral energy distribution. This supports the idea of a dusty, optically thick shell around SN 2008S with an inner radius of nearly 90 AU and outer radius of 450 AU, and an inferred heating source of 3000 K. The luminosity of the central star is L similar or equal to 10(4.6) L-circle dot. All the nearby progenitor dust was likely evaporated in the explosion leaving only the much older dust lying further out in the circumstellar environment. The combination of our long-term multiwavelength monitoring data and the evidence from the progenitor analysis leads us to support the scenario of a weak electron-capture supernova explosion in a super-asymptotic giant branch progenitor star (of initial mass 6-8 M-circle dot) embedded within a thick circumstellar gaseous envelope. We suggest that all of main properties of the electron-capture SN phenomenon are observed in SN 2008S and future observations may allow a definitive answer.

Convergence acceleration of the doubly periodic Green's function for the analysis of thin wire arrays

A method is proposed to accelerate the evaluation of the Green's function of an infinite double periodic array of thin wire antennas. The method is based on the expansion of the Green's function into series corresponding to the propagating and evanescent waves and the use of Poisson and Kummer transformations enhanced with the analytic summation of the slowly convergent asymptotic terms. Unlike existing techniques the procedure reported here provides uniform convergence regardless of the geometrical parameters of the problem or plane wave excitation wavelength. In addition, it is numerically stable and does not require numerical integration or internal tuning parameters, since all necessary series are directly calculated in terms of analytical functions. This means that for nonlinear problem scenarios that the algorithm can be deployed without run time intervention or recursive adjustment within a harmonic balance engine. Numerical examples are provided to illustrate the efficiency and accuracy of the developed approach as compared with the Ewald method for which these classes of problems requires run time splitting parameter adaptation.

Surface plasmons in layered structures with semiconductor and metallic films

The complete spectrum of eigenwaves including surface plasmon polaritons (SPP), dynamic (bulk) and complex waves in the layered structures containing semiconductor and metallic films has been explored. The effects of loss, geometry and the parameters of dielectric layers on the eigenmode spectrum and, particularly, on the SPP modes have been analysed using both the asymptotic and rigorous numerical solutions of the full-wave dispersion equation. The field and Poynting vector distributions have been examined to identify the modes and elucidate their properties. It has been shown that losses and dispersion of permittivity qualitatively alter the spectral content and the eigenwave properties. The SPP counter-directional power fluxes in the film and surrounding dielectrics have been attributed to vortices of power flow, which are responsible for the distinctive features of SPP modes. It has been demonstrated for the first time that the maximal attainable slow-wave factor of the SPP modes guided by thin Au films at optical frequencies is capped not by losses but the frequency dispersion of the actual Au permittivity. © 2009 EDP Sciences.

Application of Jacobi algorithm for ISI channels

Here, the Jacobi iterative algorithm is applied to combat intersymbol interference (ISI) caused by frequency-selective channels. The performance bound of the equaliser is analysed in order to gain an insight into its asymptotic behaviour. Because of the error propagation problem, the potential of this algorithm is not reached in an uncoded system. However, its extension to a coded system with the application of the turbo-processing principle results in a new turbo equalisation algorithm, which demonstrates comparable performance with reduced complexity compared with some existing filter-based turbo equalisation schemes; and superior performance compared with some frequency domain solutions, such as orthogonal frequency division multiplexing and single-carrier frequency domain equalisation.

Convergence of partial-wave expansions for energies, scattering amplitudes and positron annihilation rates

We use many-body theory to find the asymptotic behaviour of second-order correlation corrections to the energies and positron annihilation rates in many- electron systems with respect to the angular momenta l of the single-particle orbitals included. The energy corrections decrease as 1/(l+1/2)4, in agreement with the result of Schwartz, whereas the positron annihilation rate has a slower 1/(l+1/2)2 convergence rate. We illustrate these results by numerical calculations of the energies of Ne and Kr and by examining results from extensive con?guration-interaction calculations of PsH binding and annihilation.

Three-photon detachment of electrons from the fluorine negative ion

Absolute three-photon detachment cross sections are calculated for the fluorine negative ion within the lowest-order perturbation theory. The Dyson equation of the atomic many-body theory is used to obtain the ground-state 2p wavefunction with correct asymptotic behaviour, corresponding to the true (experimental) binding energy. We show that in accordance with the adiabatic theory this is crucial for obtaining absolute values of the multiphoton cross sections. Comparisons with other calculations and experimental data are presented.

Adsorption of sulfur dioxide on chemically modified natural clinoptilolite. Acid modification

Natural Bulgarian clinoptilolite from the south-eastern Rhodopes mountain was modified through treatment with hydrochloric acid with various normality, both single and repeatedly, as well as through a charring of a preliminary obtained NH4-form. The parameters concerning the uptake of the ion-exchangeable cations (Ca2+, Na+ and K+), as well as the uptake of aluminium from the natural material were calculated on the basis of the chemical contents. The highest extent of cations removal was attained in the case of the treatment with NH4Cl solution, while the highest aluminium deficiency was established in the samples treated by hydrochloric acid solutions with increasing concentration. Sulfur dioxide adsorption on the obtained decationised and dealuminised samples was studied according to the frontal-dynamic method. The parameters of the breakthrough curves, namely breakthrough time, saturation time and some of the statistical moments of the curve distribution, were determined. The dynamic adsorption capacities were also specified. Comparing the momentum values it was established that as a result of the natural zeolite treatment with NH4Cl and with low concentrated acid, the diffusion resistance decreases because of the dominant exchange of the presenting exchangeable cations in the samples with the smaller size protons and because of enlargement of the pores opening. Intensified dealuminisation was observed when more concentrated acid solutions are used. The capacity is enhanced, probably due to an increase in the total pore volume.

Differential modulation of angiogenesis by erythropoiesis-stimulating agents in a mouse model of ischaemic retinopathy

Background: Erythropoiesis stimulating agents (ESAs) are widely used to treat anaemia but concerns exist about their potential to promote pathological angiogenesis in some clinical scenarios. In the current study we have assessed the angiogenic potential of three ESAs; epoetin delta, darbepoetin alfa and epoetin beta using in vitro and in vivo models.

Methodology/Principal Findings: The epoetins induced angiogenesis in human microvascular endothelial cells at high doses, although darbepoetin alfa was pro-angiogenic at low-doses (1-20 IU/ml). ESA-induced angiogenesis was VEGF-mediated. In a mouse model of ischaemia-induced retinopathy, all ESAs induced generation of reticulocytes but only epoetin beta exacerbated pathological (pre-retinal) neovascularisation in comparison to controls (p<0.05). Only epoetin delta induced a significant revascularisation response which enhanced normality of the vasculature (p<0.05). This was associated with mobilisation of haematopoietic stem cells and their localisation to the retinal vasculature. Darbepoetin alfa also increased the number of active microglia in the ischaemic retina relative to other ESAs (p<0.05). Darbepoetin alfa induced retinal TNF alpha and VEGF mRNA expression which were up to 4 fold higher than with epoetin delta (p<0.001).

Conclusions: This study has implications for treatment of patients as there are clear differences in the angiogenic potential of the different ESAs.

Maximum likelihood estimation of higher-order integer-valued autoregressive processes

In this article, we extend the earlier work of Freeland and McCabe [Journal of time Series Analysis (2004) Vol. 25, pp. 701–722] and develop a general framework for maximum likelihood (ML) analysis of higher-order integer-valued autoregressive processes. Our exposition includes the case where the innovation sequence has a Poisson distribution and the thinning is binomial. A recursive representation of the transition probability of the model is proposed. Based on this transition probability, we derive expressions for the score function and the Fisher information matrix, which form the basis for ML estimation and inference. Similar to the results in Freeland and McCabe (2004), we show that the score function and the Fisher information matrix can be neatly represented as conditional expectations. Using the INAR(2) speci?cation with binomial thinning and Poisson innovations, we examine both the asymptotic e?ciency and ?nite sample properties of the ML estimator in relation to the widely used conditional least
squares (CLS) and Yule–Walker (YW) estimators. We conclude that, if the Poisson assumption can be justi?ed, there are substantial gains to be had from using ML especially when the thinning parameters are large.