Sparse polynomial approximation in positive order Sobolev spaces with bounded mixed derivatives and applications to elliptic problems with random loading

In the present paper we study the approximation of functions with bounded mixed derivatives by sparse tensor product polynomials in positive order tensor product Sobolev spaces. We introduce a new sparse polynomial approximation operator which exhibits optimal convergence properties in L2 and tensorized View the MathML source simultaneously on a standard k-dimensional cube. In the special case k=2 the suggested approximation operator is also optimal in L2 and tensorized H1 (without essential boundary conditions). This allows to construct an optimal sparse p-version FEM with sparse piecewise continuous polynomial splines, reducing the number of unknowns from O(p2), needed for the full tensor product computation, to View the MathML source, required for the suggested sparse technique, preserving the same optimal convergence rate in terms of p. We apply this result to an elliptic differential equation and an elliptic integral equation with random loading and compute the covariances of the solutions with View the MathML source unknowns. Several numerical examples support the theoretical estimates.

Interpolation of Hilbert and Sobolev spaces: quantitative estimates and counterexamples

This paper provides an overview of interpolation of Banach and Hilbert spaces, with a focus on establishing when equivalence of norms is in fact equality of norms in the key results of the theory. (In brief, our conclusion for the Hilbert space case is that, with the right normalisations, all the key results hold with equality of norms.) In the final section we apply the Hilbert space results to the Sobolev spaces Hs(Ω) and tildeHs(Ω), for s in R and an open Ω in R^n. We exhibit examples in one and two dimensions of sets Ω for which these scales of Sobolev spaces are not interpolation scales. In the cases when they are interpolation scales (in particular, if Ω is Lipschitz) we exhibit examples that show that, in general, the interpolation norm does not coincide with the intrinsic Sobolev norm and, in fact, the ratio of these two norms can be arbitrarily large.

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.

Factors affecting the adoption of leguminous cover crops in Nigeria and a comparison with the adoption of new crop varieties

This paper presents the results of (a) On-farm trials (eight) over a two-year period designed to test the effectiveness of leguminous cover crops in terms of increasing maize yields in Igalaland, Nigeria. (b) A survey designed to monitor the extent of, and reasons behind, adoption of the leguminous cover crop technology in subsequent years by farmers involved, to varying degrees, in the trial programme. particular emphasis was placed on comparing adoption of leguminous cover crops with that of new crop varieties released by a non-governmental organization in the same area since the mid 1980s. While the leguminous cover crop technology boosted maize grain yields by 127 to 136% above an untreated control yield of between 141 and 171 kg ha(-1), the adoption rate (number of farmers adopting) was only 18%. By way of contrast, new crop varieties had a highly variable benefit in terms of yield advantage over local varieties, with the best average increase of around 20%. Adoption rates for new crop varieties, assessed as both the number of farmers growing the varieties and the number of plots planted to the varieties, were 40% on average. The paper discusses some key factors influencing adoption of the leguminous cover crop technology, including seed availability. Implications of these results for a local non-governmental organization, the Diocesan Development Services, concerned with promoting the leguminous cover crop technology are also discussed.

Designs for an adaptive tuned vibration absorber with variable shape stiffness element

An adaptive tuned vibration absorber (ATVA) with a smart variable stiffness element is capable of retuning itself in response to a time-varying excitation frequency., enabling effective vibration control over a range of frequencies. This paper discusses novel methods of achieving variable stiffness in an ATVA by changing shape, as inspired by biological paradigms. It is shown that considerable variation in the tuned frequency can be achieved by actuating a shape change, provided that this is within the limits of the actuator. A feasible design for such an ATVA is one in which the device offers low resistance to the required shape change actuation while not being restricted to low values of the effective stiffness of the vibration absorber. Three such original designs are identified: (i) A pinned-pinned arch beam with fixed profile of slight curvature and variable preload through an adjustable natural curvature; (ii) a vibration absorber with a stiffness element formed from parallel curved beams of adjustable curvature vibrating longitudinally; (iii) a vibration absorber with a variable geometry linkage as stiffness element. The experimental results from demonstrators based on two of these designs show good correlation with the theory.

The competitive ability of pea-barley intercrops against weeds and the interactions with crop productivity and soil N availability

Grain legumes, such as peas (Pisum sativum L.), are known to be weak competitors against weeds when grown as the sole crop. In this study, the weed-suppression effect of pea–barley (Hordeum vulgare L.)intercropping compared to the respective sole crops was examined in organic field experiments across Western Europe (i.e., Denmark, the United Kingdom, France, Germany and Italy). Spring pea (P) and barley(B) were sown either as the sole crop, at the recommended plant density (P100 and B100, respectively), or in replacement (P50B50) or additive (P100B50)intercropping designs for three seasons (2003–2005). The weed biomass was three times higher under the pea sole crops than under both the intercrops and barley sole crops at maturity. The inclusion of joint experiments in several countries and various growing conditions showed that intercrops maintain a highly asymmetric competition over weeds, regardless of the particular weed infestation (species and productivity), the crop biomass or the soil nitrogen availability. The intercropping weed suppression was highly resilient, whereas the weed suppression in pea sole crops was lower and more variable. The pea–barley intercrops exhibited high levels of weed suppression, even with a low percentage of barley in the total biomass. Despite a reduced leaf area in the case of a low soil N availability, the barley sole crops and intercrops displayed high weed suppression, probably because of their strong competitive capability to absorb soil N. Higher soil N availabilities entailed increased leaf areas and competitive ability for light, which contributed to the overall competitive ability against weeds for all of the treatments. The contribution of the weeds in the total dry matter and soil N acquisition was higher in the pea sole crop than in the other treatments, in spite of the higher leaf areas in the pea crops.

Conceptualizing change in the Portuguese footwear industry: regional voices and cognitive spaces of agency

Expanding national services sectors and global competition aggravate current and perceived future market pressures on traditional manufacturing industries. These perceptions of change have provoked a growing intensification of geo-political discourses on technological innovation and ‘learning’, and calls for competency in design among other professional skills. However, these political discourses on innovation and learning have paralleled public concerns with the apparent ‘growth pains’ from factory closures and subsequent increases in unemployment, and its debilitating social and economic implications for local and regional development. In this respect the following investigation sets out to conceptualize change through the complementary and differing perceptions of industry and regional actors’ experiences or narratives, linking these perceptions to their structure-determined spheres of agent-environment interactivity. It aims to determine whether agents’ differing perceptions of industry transformation can have a role in the legitimization of their interests in, and in sustaining their organizational influence over the process of industry-regional transformation. It argues that industry and regional agent perceptions are among the cognitive aspects of agent-environment interactivity that permeate agency. It stresses agents’ ability to reason and manipulate their work environments to preserve their self-regulating interests in, and task representative influence over the multi-jurisdictional space of industry-regional transformation. The contributions of this investigation suggest that agents’ varied perceptions of industry and regional change inform or compete for influence over the redirection of regional, industry and business strategies. This claim offers a greater appreciation for the reflexive and complex institutional dimensions of industry planning and development, and the political responsibility to socially just forms of regional development. It positions the outcomes of this investigation at the nexus of intensifying geo-political discourses on the efficiency and equity of territorial development in Europe.

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,

Toeplitz operators on Bergman spaces with locally integrable symbols

We study the boundedness of Toeplitz operators $T_a$ with locally integrable symbols on Bergman spaces $A^p(\mathbb{D})$, $1 < p < \infty$. Our main result gives a sufficient condition for the boundedness of $T_a$ in terms of some ``averages'' (related to hyperbolic rectangles) of its symbol. If the averages satisfy an ${o}$-type condition on the boundary of $\mathbb{D}$, we show that the corresponding Toeplitz operator is compact on $A^p$. Both conditions coincide with the known necessary conditions in the case of nonnegative symbols and $p=2$. We also show that Toeplitz operators with symbols of vanishing mean oscillation are Fredholm on $A^p$ provided that the averages are bounded away from zero, and derive an index formula for these operators.

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.

Distinct clinical and neuropathological features of G51D SNCA mutation cases compared with SNCA duplication and H50Q mutation

Background: We and others have described the neurodegenerative disorder caused by G51D SNCA mutation which shares characteristics of Parkinson’s disease (PD) and multiple system atrophy (MSA). The objective of this investigation was to extend the description of the clinical and neuropathological hallmarks of G51D mutant SNCA-associated disease by the study of two additional cases from a further G51D SNCA kindred and to compare the features of this group with a SNCA duplication case and a H50Q SNCA mutation case. Results: All three G51D patients were clinically characterised by parkinsonism, dementia, visual hallucinations, autonomic dysfunction and pyramidal signs with variable age at disease onset and levodopa response. The H50Q SNCA mutation case had a clinical picture that mimicked late-onset idiopathic PD with a good and sustained levodopa response. The SNCA duplication case presented with a clinical phenotype of frontotemporal dementia with marked behavioural changes, pyramidal signs, postural hypotension and transiently levodopa responsive parkinsonism. Detailed post-mortem neuropathological analysis was performed in all cases. All three G51D cases had abundant α-synuclein pathology with characteristics of both PD and MSA. These included widespread cortical and subcortical neuronal α-synuclein inclusions together with small numbers of inclusions resembling glial cytoplasmic inclusions (GCIs) in oligodendrocytes. In contrast the H50Q and SNCA duplication cases, had α-synuclein pathology resembling idiopathic PD without GCIs. Phosphorylated α-synuclein was present in all inclusions types in G51D cases but was more restricted in SNCA duplication and H50Q mutation. Inclusions were also immunoreactive for the 5G4 antibody indicating their highly aggregated and likely fibrillar state. Conclusions: Our characterisation of the clinical and neuropathological features of the present small series of G51D SNCA mutation cases should aid the recognition of this clinico-pathological entity. The neuropathological features of these cases consistently share characteristics of PD and MSA and are distinct from PD patients carrying the H50Q or SNCA duplication.

Biodegradation of the herbicide mecoprop-p with soil depth and its relationship with class III tfdA genes

Mecoprop-p [(R)-2-(4-chloro-2-methylphenoxy) propanoic acid) is widely used in agriculture and poses an environmental concern because of its susceptibility to leach from soil to water. We investigated the effect of soil depth on mecoprop-p biodegradation and its relationship with the number and diversity of tfdA related genes, which are the most widely known genes involved in degradation of the phenoxyalkanoic acid group of herbicides by bacteria. Mecoprop-p half-life (DT50) was approximately 12 days in soil sampled from <30 cm depth, and increased progressively with soil depth, reaching over 84 days at 70–80 cm. In sub-soil there was a lag period of between 23 and 34 days prior to a phase of rapid degradation. No lag phase occurred in top-soil samples prior to the onset of degradation. The maximum degradation rate was the same in top-soil and sub-soil samples. Although diverse tfdAα and tfdA genes were present prior to mecoprop-p degradation, real time PCR revealed that degradation was associated with proliferation of tfdA genes. The number of tfdA genes and the most probable number of mecoprop-p degrading organisms in soil prior to mecoprop-p addition were below the limit of quantification and detection respectively. Melting curves from the real time PCR analysis showed that prior to mecoprop-p degradation both class I and class III tfdA genes were present in top- and sub-soil samples. However at all soil depths only tfdA class III genes proliferated during degradation. Denaturing gradient gel electrophoresis confirmed that class III tfdA genes were associated with mecoprop-p degradation. Degradation was not associated with the induction of novel tfdA genes in top- or sub-soil samples, and there were no apparent differences in tfdA gene diversity with soil depth prior to or following degradation.

Field trials to assess the uptake of arsenic by vegetables from contaminated soils and soil remediation with iron oxides

The uptake of arsenic (As) by plants from contaminated soils presents a health hazard that may affect the use of agricultural and former industrial land. Methods for limiting the hazard are desirable. A proposed remediation treatment comprises the precipitation of iron (Fe) oxides in the contaminated soil by adding ferrous sulfate and lime. The effects on As bioavailability were assessed using a range of vegetable crops grown in the field. Four UK locations were used, where soil was contaminated by As from different sources. At the most contaminated site, a clay loam containing a mean of 748 mg As kg(-1) soil, beetroot, calabrese, cauliflower, lettuce, potato, radish and spinach were grown. For all crops except spinach, ferrous sulfate treatment caused a significant reduction in the bioavailability of As in some part of the crop. Application of ferrous sulfate in solution, providing 0.2% Fe oxides in the soil (0-10 cm), reduced As uptake by a mean of 22%. Solid ferrous sulfate was applied to give concentrations of 0.5% and 1% Fe oxides: the 0.5% concentration reduced As uptake by a mean of 32% and the 1% concentration gave no significant additional benefit. On a sandy loam containing 65 mg As kg(-1) soil, there was tentative evidence that ferrous sulfate treatment up to 2% Fe oxides caused a significant reduction in lettuce As, but calabrese did not respond. At the other two sites, the effects of ferrous sulfate treatment were not significant, but the uptake of soil As was low in treated and untreated soils. Differences between sites in the bioavailable fraction of soil As may be related to the soil texture or the source of As. The highest bioavailability was found on the soil which had been contaminated by aerial deposition and had a high sand content. (C) 2003 Elsevier Science B.V. All rights reserved.

Trends in aerosol optical depth in the Russian Arctic and their links with synoptic climatology

Temporal and spatial variability of aerosol optical depth (AOD) are examined using observations of direct solar radiation in the Eurasian Arctic for 1940-1990. AOD is estimated using empirical methods for 14 stations located between 66.2 degrees N and 80.6 degrees N, from the Kara Sea to the Chukchi Sea. While AOD exhibits a well-known springtime maximum and summertime minimum at all stations, atmospheric turbidity is higher in spring in the western (Kara-Laptev) part of the Eurasian Arctic. Between June and August, the eastern (East Siberian-Chukchi) sector experiences higher transparency than the western part. A statistically significant positive trend in AOD was observed in the Kara-Laptev sector between the late 1950s and the early 1930s predominantly in spring when pollution-derived aerosol dominates the Arctic atmosphere but not in the eastern sector. Although all stations are remote, those with positive trends are located closer to the anthropogenic sources of air pollution. By contrast, a widespread decline in AOD was observed between 1982 and 1990 in the eastern Arctic in spring but was limited to two sites in the western Arctic. These results suggest that the post-1982 decline in anthropogenic emissions in Europe and the former Soviet Union has had a limited effect on aerosol load in the Arctic. The post-1982 negative trends in AOD in summer, when marine aerosol is present in the atmosphere, were more common in the west. The relationships between AOD and atmospheric circulation are examined using a synoptic climatology approach. In spring, AOD depends primarily on the strength and direction of air flow. Thus strong westerly and northerly flows result in low AOD values in the East Siberian-Chukchi sector. By contrast, strong southerly flow associated with the passage of depressions results in high A OD in the Kara-Laptev sector and trajectory analysis points to the contribution of industrial regions of the sub-Arctic. In summer, low pressure gradient or anticyclonic conditions result in high atmospheric turbidity. The frequency of this weather type has declined significantly since the early 1980s in the Kara-Laptev sector, which partly explains the decline in summer AOD values. (c) 2004 Elsevier B.V. All rights reserved.