Variational approach in weighted Sobolev spaces to scattering by unbounded rough surfaces

We consider the problem of scattering of time harmonic acoustic waves by an unbounded sound soft surface which is assumed to lie within a finite distance of some plane. The paper is concerned with the study of an equivalent variational formulation of this problem set in a scale of weighted Sobolev spaces. We prove well-posedness of this variational formulation in an energy space with weights which extends previous results in the unweighted setting [S. Chandler-Wilde and P. Monk, SIAM J. Math. Anal., 37 (2005), pp. 598–618] to more general inhomogeneous terms in the Helmholtz equation. In particular, in the two-dimensional case, our approach covers the problem of plane wave incidence, whereas in the three-dimensional case, incident spherical and cylindrical waves can be treated. As a further application of our results, we analyze a finite section type approximation, whereby the variational problem posed on an infinite layer is approximated by a variational problem on a bounded region.

Continental shift? An analysis of convergence trends in European real estate equities

European economic and political integration have been recognised as having implications for patterns of performance in national real estate and capital markets and have generated a wide body of research and commentary. In 1999, progress towards monetary integration within the European Union culminated in the introduction of a common currency and monetary policy. This paper investigates the effects of this ‘event’ on the behaviour of stock returns in European real estate companies. A range of statistical tests is applied to the performance of European property companies to test for changes in segmentation, co-movement and causality. The results suggest that, relative to the wider equity markets, the dispersion of performance is higher, correlations are lower, a common contemporaneous factor has much lower explanatory power whilst lead-lag relationships are stronger. Consequently, the evidence of transmission of monetary integration to real estate securities is less noticeable than to general securities. Less and slower integration is attributed to the relatively small size of the real estate securities market and the local and national nature of the majority of the companies’ portfolios.

Can carbon surface oxidation shift the pore size distribution curve calculated from Ar, N(2) and CO(2) adsorption isotherms? Simulation results for a realistic carbon model

Using the virtual porous carbon model proposed by Harris et al, we study the effect of carbon surface oxidation on the pore size distribution (PSD) curve determined from simulated Ar, N(2) and CO(2) isotherms. It is assumed that surface oxidation is not destructive for the carbon skeleton, and that all pores are accessible for studied molecules (i.e., only the effect of the change of surface chemical composition is studied). The results obtained show two important things, i.e., oxidation of the carbon surface very slightly changes the absolute porosity (calculated from the geometric method of Bhattacharya and Gubbins (BG)); however, PSD curves calculated from simulated isotherms are to a greater or lesser extent affected by the presence of surface oxides. The most reliable results are obtained from Ar adsorption data. Not only is adsorption of this adsorbate practically independent from the presence of surface oxides, but, more importantly, for this molecule one can apply the slit-like model of pores as the first approach to recover the average pore diameter of a real carbon structure. For nitrogen, the effect of carbon surface chemical composition is observed due to the quadrupole moment of this molecule, and this effect shifts the PSD curves compared to Ar. The largest differences are seen for CO2, and it is clearly demonstrated that the PSD curves obtained from adsorption isotherms of this molecule contain artificial peaks and the average pore diameter is strongly influenced by the presence of electrostatic adsorbate-adsorbate as well as adsorbate-adsorbent interactions.

Time weighted portfolio optimisation

In estimating the inputs into the Modern Portfolio Theory (MPT) portfolio optimisation problem, it is usual to use equal weighted historic data. Equal weighting of the data, however, does not take account of the current state of the market. Consequently this approach is unlikely to perform well in any subsequent period as the data is still reflecting market conditions that are no longer valid. The need for some return-weighting scheme that gives greater weight to the most recent data would seem desirable. Therefore, this study uses returns data which are weighted to give greater weight to the most recent observations to see if such a weighting scheme can offer improved ex-ante performance over that based on un-weighted data.

Weaning diet induces sustained metabolic phenotype shift in the pig and influences host response to Bifidobacterium lactis NCC2818

Background The process of weaning causes a major shift in intestinal microbiota and is a critical period for developing appropriate immune responses in young mammals.Objective To use a new systems approach to provide an overview of host metabolism and the developing immune system in response to nutritional intervention around the weaning period.Design Piglets (n=14) were weaned onto either an egg-based or soya-based diet at 3 weeks until 7 weeks, when all piglets were switched onto a fish-based diet. Half the animals on each weaning diet received Bifidobacterium lactis NCC2818 supplementation from weaning onwards. Immunoglobulin production from immunologically relevant intestinal sites was quantified and the urinary (1)H NMR metabolic profile was obtained from each animal at post mortem (11 weeks).Results Different weaning diets induced divergent and sustained shifts in the metabolic phenotype, which resulted in the alteration of urinary gut microbial co-metabolites, even after 4 weeks of dietary standardisation. B lactis NCC2818 supplementation affected the systemic metabolism of the different weaning diet groups over and above the effects of diet. Additionally, production of gut mucosa-associated IgA and IgM was found to depend upon the weaning diet and on B lactis NCC2818 supplementation.ConclusionThe correlation of urinary (1)H NMR metabolic profile with mucosal immunoglobulin production was demonstrated, thus confirming the value of this multi-platform approach in uncovering non-invasive biomarkers of immunity. This has clear potential for translation into human healthcare with the development of urine testing as a means of assessing mucosal immune status. This might lead to early diagnosis of intestinal dysbiosis and with subsequent intervention, arrest disease development. This system enhances our overall understanding of pathologies under supra-organismal control.

A note on the Fredholm properties of Toeplitz operators on weighted Bergman spaces with matrix-valued symbols

We characterize the essential spectra of Toeplitz operators Ta on weighted Bergman spaces with matrix-valued symbols; in particular we deal with two classes of symbols, the Douglas algebra C+H∞ and the Zhu class Q := L∞ ∩VMO∂ . In addition, for symbols in C+H∞ , we derive a formula for the index of Ta in terms of its symbol a in the scalar-valued case, while in the matrix-valued case we indicate that the standard reduction to the scalar-valued case fails to work analogously to the Hardy space case. Mathematics subject classification (2010): 47B35,

Borrowing and shift-induced interference: contrasting patterns in French-Germanic contact in Brussels and Strasbourg

The main aim of the present article is to test hypotheses derived from the model for contact- induced language change as formulated in Thomason and Kaufman (1988 et seq.). As the model correctly predicts the asymmetries between the mutual influences of the Germanic and the Romance varieties in Brussels and Strasbourg it is a very powerful tool for describing the contact patterns in these cities. The analysis shows that the contact patterns are very similar, both from a quantitative and from a qualitative point of view, despite important differences in the sociolinguistic situation of both cities. The striking similarities in the outcome of language contact seem to find a plausible explanation in the fact that the language contact situations in both cities are similar from a typological point of view: in each city a variety of French is in contact with a Germanic variety (Alsatian and Brussels Dutch). Thus, the claim of the present article is that the structure of the languages plays a more prominent role in the outcome of language contact than the sociolinguistic history of the speakers.

Atlantic Ocean influence on a shift in European climate in the 1990s

European climate exhibits variability on a wide range of timescales. Understanding the nature and drivers of this variability is an essential step in developing robust climate predictions and risk assessments. The Atlantic Ocean has been suggested as an important driver of variability in European climate on decadal timescales1, but the importance of this influence in recent decades has been unclear, partly because of difficulties in separating the influence of the Atlantic Ocean from other contributions, for example, from the tropical Pacific Ocean and the stratosphere. Here we analyse four data sets derived from observations to show that, during the 1990s, there was a substantial shift in European climate towards a pattern characterized by anomalously wet summers in northern Europe, and hot, dry, summers in southern Europe, with related shifts in spring and autumn. These changes in climate coincided with a substantial warming of the North Atlantic Ocean, towards a state last seen in the 1950s. The patterns of European climate change in the 1990s are consistent with earlier changes attributed to the influence of the North Atlantic Ocean, and provide compelling evidence that the Atlantic Ocean was the key driver. Our results suggest that the recent pattern of anomalies in European climate will persist as long as the North Atlantic Ocean remains anomalously warm.

Solvability and spectral properties of integral equations on the real line: I. Weighted spaces of continuous functions

We consider in this paper the solvability of linear integral equations on the real line, in operator form (λ−K)φ=ψ, where and K is an integral operator. We impose conditions on the kernel, k, of K which ensure that K is bounded as an operator on . Let Xa denote the weighted space as |s|→∞}. Our first result is that if, additionally, |k(s,t)|⩽κ(s−t), with and κ(s)=O(|s|−b) as |s|→∞, for some b>1, then the spectrum of K is the same on Xa as on X, for 01. As an example where kernels of this latter form occur we discuss a boundary integral equation formulation of an impedance boundary value problem for the Helmholtz equation in a half-plane.