New results and open problems on Toeplitz operators in Bergman spaces

We discuss some of the recent progress in the field of Toeplitz operators acting on Bergman spaces of the unit disk, formulate some new results, and describe a list of open problems -- concerning boundedness, compactness and Fredholm properties -- which was presented at the conference "Recent Advances in Function Related Operator Theory'' in Puerto Rico in March 2010.

Hankel operators on Fock spaces

We study Hankel operators on the weighted Fock spaces Fp. The boundedness and compactness of these operators are characterized in terms of BMO and VMO, respectively. Along the way, we also study Berezin transform and harmonic conjugates on the plane. Our results are analogous to Zhu's characterization of bounded and compact Hankel operators on Bergman spaces of the unit disk.

Universally reversible JC*-triples and operator spaces

Abstract. We prove that the vast majority of JC∗-triples satisfy the condition of universal reversibility. Our characterisation is that a JC∗-triple is universally reversible if and only if it has no triple homomorphisms onto Hilbert spaces of dimension greater than two nor onto spin factors of dimension greater than four. We establish corresponding characterisations in the cases of JW∗-triples and of TROs (regarded as JC∗-triples). We show that the distinct natural operator space structures on a universally reversible JC∗-triple E are in bijective correspondence with a distinguished class of ideals in its universal TRO, identify the Shilov boundaries of these operator spaces and prove that E has a unique natural operator space structure precisely when E contains no ideal isometric to a nonabelian TRO. We deduce some decomposition and completely contractive properties of triple homomorphisms on TROs.

Binding properties and adhesion-mediating regions of the major sheath protein of Treponema denticola ATCC 35405

There is growing evidence that a number of oral Treponema species, in particular Treponema denticola, are associated with the progression of human periodontal disease. The major sheath (or surface) protein (Msp) of T. denticola is implicated in adhesion of bacteria to host cells and tissue proteins and is likely to be an important virulence factor. However, the binding regions of the Msp are not known. We have purified from Escherichia coli recombinant Msp (rMsp) polypeptides corresponding to the following: full-length Msp (rMsp) minus 13 N-terminal amino acid (aa) residues, an amino-terminal fragment (rN-Msp, 189 aa residues), a 57-aa residue segment from the central region (rV-Msp), and a C-terminal fragment (rC-Msp, 272 aa residues). rMsp (530 aa residues) bound to immobilized fibronectin, keratin, laminin, collagen type 1, fibrinogen, hyaluronic acid, and heparin. The N- and V-region polypeptides, but not rC-Msp, also bound to these substrates. Binding of rMsp to fibronectin was targeted to the N-terminal heparin I/fibrin I domain. Antibodies to the N-region or V-region polypeptides, but not antibodies to the rC-Msp fragment, blocked adhesion of T. denticola ATCC 35405 cells to a range of host protein molecules. These results suggest that the N-terminal half of Msp carries epitopes that are surface exposed and that are involved in mediating adhesion. Binding of rMsp onto the cell surface of low-level fibronectin-binding Treponema isolates conferred a 10-fold increase in fibronectin binding. This confirms that Msp functions autonomously as an adhesin and raises the possibility that phenotypic complementation of virulence functions might occur within mixed populations of Treponema species.

NLO QCD Corrections to the Polarized Photo- and Hadroproduction of Heavy Quarks

The complete details of our calculation of the NLO QCD corrections to heavy flavor photo- and hadroproduction with longitudinally polarized initial states are presented. The main motivation for investigating these processes is the determination of the polarized gluon density at the COMPASS and RHIC experiments, respectively, in the near future. All methods used in the computation are extensively documented, providing a self-contained introduction to this type of calculations. Some employed tools also may be of general interest, e.g., the series expansion of hypergeometric functions. The relevant parton level results are collected and plotted in the form of scaling functions. However, the simplification of the obtained gluon-gluon virtual contributions has not been completed yet. Thus NLO phenomenological predictions are only given in the case of photoproduction. The theoretical uncertainties of these predictions, in particular with respect to the heavy quark mass, are carefully considered. Also it is shown that transverse momentum cuts can considerably enhance the measured production asymmetries. Finally unpolarized heavy quark production is reviewed in order to derive conditions for a successful interpretation of future spin-dependent experimental data.

Padé approximants for the acoustical properties of rigid frame porous media with pore size distributions

Expressions for the viscosity correction function, and hence bulk complex impedance, density, compressibility, and propagation constant, are obtained for a rigid frame porous medium whose pores are prismatic with fixed cross-sectional shape, but of variable pore size distribution. The lowand high-frequency behavior of the viscosity correction function is derived for the particular case of a log-normal pore size distribution, in terms of coefficients which can, in general, be computed numerically, and are given here explicitly for the particular cases of pores of equilateral triangular, circular, and slitlike cross-section. Simple approximate formulae, based on two-point Pade´ approximants for the viscosity correction function are obtained, which avoid a requirement for numerical integration or evaluation of special functions, and their accuracy is illustrated and investigated for the three pore shapes already mentioned

Padé approximants for the acoustical characteristics of rigid frame porous media

In this paper it is shown that a number of theoretical models of the acoustical properties of rigid frame porous media, especially those involving ratios of Bessel functions of complex argument, can be accurately approximated and greatly simplified by the use of Padé approximation techniques. In the case of the model of Attenborough [J. Acoust. Soc. Am. 81, 93–102 (1987)] rational approximations are produced for the characteristic impedance, propagation constant, dynamic compressibility, and dynamic density, as a function of frequency and the material parameters. The model proposed by Stinson and Champoux

On asymptotic behavior at infinity and the finite section method for integral equations on the half-line

e consider integral equations on the half-line of the form and the finite section approximation to x obtained by replacing the infinite limit of integration by the finite limit β. We establish conditions under which, if the finite section method is stable for the original integral equation (i.e. exists and is uniformly bounded in the space of bounded continuous functions for all sufficiently large β), then it is stable also for a perturbed equation in which the kernel k is replaced by k + h. The class of perturbations allowed includes all compact and some non-compact perturbations of the integral operator. Using this result we study the stability and convergence of the finite section method in the space of continuous functions x for which ()()()=−∫∞dttxt,sk)s(x0()syβxβx()sxsp+1 is bounded. With the additional assumption that ()(tskt,sk−≤ where ()()(),qsomefor,sassOskandRLkq11>+∞→=∈− we show that the finite-section method is stable in the weighted space for ,qp≤≤0 provided it is stable on the space of bounded continuous functions. With these results we establish error bounds in weighted spaces for x - xβ and precise information on the asymptotic behaviour at infinity of x. We consider in particular the case when the integral operator is a perturbation of a Wiener-Hopf operator and illustrate this case with a Wiener-Hopf integral equation arising in acoustics.

A Wiener-Hopf type factorization for the exponential functional of Levy processes

For a Lévy process ξ=(ξt)t≥0 drifting to −∞, we define the so-called exponential functional as follows: Formula Under mild conditions on ξ, we show that the following factorization of exponential functionals: Formula holds, where × stands for the product of independent random variables, H− is the descending ladder height process of ξ and Y is a spectrally positive Lévy process with a negative mean constructed from its ascending ladder height process. As a by-product, we generate an integral or power series representation for the law of Iξ for a large class of Lévy processes with two-sided jumps and also derive some new distributional properties. The proof of our main result relies on a fine Markovian study of a class of generalized Ornstein–Uhlenbeck processes, which is itself of independent interest. We use and refine an alternative approach of studying the stationary measure of a Markov process which avoids some technicalities and difficulties that appear in the classical method of employing the generator of the dual Markov process.

Complex-valued b-spline neural networks for modelling and inverse of wiener systems

Communication signal processing applications often involve complex-valued (CV) functional representations for signals and systems. CV artificial neural networks have been studied theoretically and applied widely in nonlinear signal and data processing [1–11]. Note that most artificial neural networks cannot be automatically extended from the real-valued (RV) domain to the CV domain because the resulting model would in general violate Cauchy-Riemann conditions, and this means that the training algorithms become unusable. A number of analytic functions were introduced for the fully CV multilayer perceptrons (MLP) [4]. A fully CV radial basis function (RBF) nework was introduced in [8] for regression and classification applications. Alternatively, the problem can be avoided by using two RV artificial neural networks, one processing the real part and the other processing the imaginary part of the CV signal/system. A even more challenging problem is the inverse of a CV

Death has a touch of class: society and space in Brookwood Cemetery, 1853-1903

Changes in the cultures and spaces of death during the Victorian era reveal the shifting conceptualisations and mobilisations of class in this period. Using the example of Brookwood Necropolis, established 1852 in response to the contemporary burial reform debate, the paper explores tensions within the sanitary reform movement, 1853–1903. Whilst reformist ideology grounded the cemetery's practices in a discourse of inclusion, one of the consequences of reform was to reinforce class distinctions. Combined with commercial imperatives and the modern impulse towards separation of living and dead, this aspect of reform enacted a counter-discourse of alienation. The presence of these conflicting strands in the spaces and practices of the Necropolis and their changes during the time period reflect wider urban trends.

Postmodernism, culture and feminism: the aesthetics of space and performance in Rock Follies and Rock Follies of '77

This article discusses the aesthetic and spatial representational strategies of the popular studio-based musical television drama serials Rock Follies and Rock Follies of ’77. It analyses how the texts’ themes relating to women and the entertainment industry are mediated through their postmodern ironic mode and representation of fantastic spaces. Rock Follies’ distinctive stylised aesthetic and mode of caricature are analysed with reference to the visual intentions and ‘voice’ of the writer, Howard Schuman. Through considering the programmes’ various spatial strategies, the article draws attention to the importance of visual and performance style in their postmodern discourse on culture, fantasy, gender and subjectivity. Analysis of the spaces of musical performance, characters’ domestic environments and simulated entertainment spaces reveals how a dialectic is established between the escapist imaginative pleasures of fantasy and the manipulative and exploitative practices of the culture industry. The shift from the optimism of the first series, when the LittleLadies first form, to the darker mood of the second series, in which they are increasingly divided by industry pressures, is traced through changes in the aesthetics of space and characterisation. As a space of artifice, performance and electronic visual manipulation that facilitates the texts’ reflexive representation of culture and feminised fantasy, the studio’s unique aesthetic strengths emerge through this case study.

Postpartum GAD is a risk factor for postpartum MDD: the course and longitudinal relationships of postpartum GAD and MDD

Background The objective was to examine the course and longitudinal associations of generalized anxiety disorder (GAD) and major depressive disorder (MDD) in mothers over the postpartum 2 years. Method Using a prospective naturalistic design, 296 mothers recruited from a large community pool were assessed for GAD and MDD at 3, 6, 10, 14, and 24 months postpartum. Structured clinical interviews were used for diagnoses, and symptoms were assessed using self-report questionnaires. Logistic regression analyses were used to examine diagnostic stability and longitudinal relations, and latent variable modeling was employed to examine change in symptoms. Results MDD without co-occurring GAD, GAD without co-occurring MDD, and co-occurring GAD and MDD, displayed significant stability during the postpartum period. Whereas MDD did not predict subsequent GAD, GAD predicted subsequent MDD (in the form of GAD + MDD). Those with GAD + MDD at 3 months postpartum were significantly less likely to be diagnosis free during the follow-up period than those in other diagnostic categories. At the symptom level, symptoms of GAD were more trait-like than those of depression. Conclusions Postpartum GAD and MDD are relatively stable conditions, and GAD is a risk factor for MDD but not vice versa. Given the tendency of MDD and GAD to be persistent, especially when comorbid, and the increased risk for MDD in mothers with GAD, as well as the potential negative effects of cumulative exposure to maternal depression and anxiety on child development, the present findings clearly highlight the need for screening and treatment of GAD in addition to MDD during the postpartum period.

The EU societal awareness of landscape indicator: a review of its meaning, utility and performance across different scales

There is increasing recognition that agricultural landscapes meet multiple societal needs and demands beyond provision of economic and environmental goods and services. Accordingly, there have been significant calls for the inclusion of societal, amenity and cultural values in agri-environmental landscape indicators to assist policy makers in monitoring the wider impacts of land-based policies. However, capturing the amenity and cultural values that rural agrarian areas provide, by use of such indicators, presents significant challenges. The EU social awareness of landscape indicator represents a new class of generalized social indicator using a top-down methodology to capture the social dimensions of landscape without reference to the specific structural and cultural characteristics of individual landscapes. This paper reviews this indicator in the context of existing agri-environmental indicators and their differing design concepts. Using a stakeholder consultation approach in five case study regions, the potential and limitations of the indicator are evaluated, with a particular focus on its perceived meaning, utility and performance in the context of different user groups and at different geographical scales. This analysis supplements previous EU-wide assessments, through regional scale assessment of the limitations and potentialities of the indicator and the need for further data collection. The evaluation finds that the perceived meaning of the indicator does not vary with scale, but in common with all mapped indicators, the usefulness of the indicator, to different user groups, does change with scale of presentation. This indicator is viewed as most useful when presented at the scale of governance at which end users operate. The relevance of the different sub-components of the indicator are also found to vary across regions.

MCP-1 induces migration of adult neural stem cells

As a model for brain inflammation we previously studied transcriptional profiles of tumor necrosis factor-alpha (TNF)treated U373 astroglioma cells. In previous work we were able to demonstrate that the chemokine monocyte chemoattractant protein-1 (MCP-1, SCYA2, CCL2, MCAF) expression in U373 cells was inducible by TNF-alpha treatment. Demonstrably MCP-1 mRNA and protein expression in U373 cells was sustainable over time and at the highest level of all genes analyzed (Schwamborn et al., BMC Genomics 4, 46, 2003). In the hematopoietic system MCP-1 is a CC chemokine that attracts monocytes, memory T lymphocytes, and natural killer cells. In search of further functions in brain inflammation we tested the hypothesis that MCP-1 acts as a chemokine on neural stem cells. Here we report that MCP-1 activates the migration capacity of rat-derived neural stem cells. The migration of stem cells in a Boyden chamber analysis was elevated after stimulation with MCP-1. Time-lapse video microscopy visualized the migration of single stem cells from neurospheres in MCP-1-treated cultures, whereas untreated cultures depicted no migration at all, but showed signs of sprouting. Expression of the MCP-1 receptor CCR2 in neurosphere cultures was verified by RT-PCR and immunofluorescence microscopy. Supernatants from TNF-treated U373 cells also induced migration of neural stem cells.