On the solvability of second kind integral equations on the real line

This paper considers general second kind integral equations of the form(in operator form φ − kφ = ψ), where the functions k and ψ are assumed known, with ψ ∈ Y, the space of bounded continuous functions on R, and k such that the mapping s → k(s, · ), from R to L1(R), is bounded and continuous. The function φ ∈ Y is the solution to be determined. Conditions on a set W ⊂ BC(R, L1(R)) are obtained such that a generalised Fredholm alternative holds: If W satisfies these conditions and I − k is injective for all k ∈ W then I − k is also surjective for all k ∈ W and, moreover, the inverse operators (I − k) − 1 on Y are uniformly bounded for k ∈ W. The approximation of the kernel in the integral equation by a sequence (kn) converging in a weak sense to k is also considered and results on stability and convergence are obtained. These general theorems are used to establish results for two special classes of kernels: k(s, t) = κ(s − t)z(t) and k(s, t) = κ(s − t)λ(s − t, t), where κ ∈ L1(R), z ∈ L∞(R), and λ ∈ BC((R\{0}) × R). Kernels of both classes arise in problems of time harmonic wave scattering by unbounded surfaces. The general integral equation results are here applied to prove the existence of a solution for a boundary integral equation formulation of scattering by an infinite rough surface and to consider the stability and convergence of approximation of the rough surface problem by a sequence of diffraction grating problems of increasingly large period.

Preparation and properties of gallaborane, GaBH6: structure of the gaseous molecule H2Ga(μ-H)2BH2 as determined by vibrational, electron diffraction, and ab initio studies, and structure of the crystalline solid at 110 K as determined by x-ray diffraction``

Gallaborane (GaBH6, 1), synthesized by the metathesis of LiBH4 with [H2GaCl]n at ca. 250 K, has been characterized by chemical analysis and by its IR and 1H and 11B NMR spectra. The IR spectrum of the vapor at low pressure implies the presence of only one species, viz. H2Ga(μ-H)2BH2, with a diborane-like structure conforming to C2v symmetry. The structure of this molecule has been determined by gas-phase electron diffraction (GED) measurements afforced by the results of ab initio molecular orbital calculations. Hence the principal distances (rα in Å) and angles ( α in deg) are as follows: r(Ga•••B), 2.197(3); r(Ga−Ht), 1.555(6); r(Ga−Hb), 1.800(6); r(B−Ht), 1.189(7); r(B−Hb), 1.286(7); Hb−Ga−Hb, 71.6(4); and Hb−B−Hb, 110.0(5) (t = terminal, b = bridging). Aggregation of the molecules occurs in the condensed phases. X-ray crystallographic studies of a single crystal at 110 K reveal a polymeric network with helical chains made up of alternating pseudotetrahedral GaH4 and BH4 units linked through single hydrogen bridges; the average Ga•••B distance is now 2.473(7) Å. The compound decomposes in the condensed phases at temperatures exceeding ca. 240 K with the formation of elemental Ga and H2 and B2H6. The reactions with NH3, Me3N, and Me3P are also described.

Aggregation of parasitism risk in an aphid-parasitoid system: Effects of plant patch size and aphid density

Few studies have linked density dependence of parasitism and the tritrophic environment within which a parasitoid forages. In the non-crop plant-aphid, Centaurea nigra-Uroleucon jaceae system, mixed patterns of density-dependent parasitism by the parasitoids Aphidius funebris and Trioxys centaureae were observed in a survey of a natural population. Breakdown of density-dependent parasitism revealed that density dependence was inverse in smaller colonies but direct in large colonies (>20 aphids), suggesting there is a threshold effect in parasitoid response to aphid density. The CV2 of searching parasitoids was estimated from parasitism data using a hierarchical generalized linear model, and CV2>1 for A. funebris between plant patches, while for T. centaureae CV2>1 within plant patches. In both cases, density independent heterogeneity was more important than density-dependent heterogeneity in parasitism. Parasitism by T. centaureae increased with increasing plant patch size. Manipulation of aphid colony size and plant patch size revealed that parasitism by A. funebris was directly density dependent at the range of colony sizes tested (50-200 initial aphids), and had a strong positive relationship with plant patch size. The effects of plant patch size detected for both species indicate that the tritrophic environment provides a source of host density independent heterogeneity in parasitism, and can modify density-dependent responses. (c) 2007 Gessellschaft fur Okologie. Published by Elsevier GmbH. All rights reserved.

Long-term monounsaturated fatty acid diets reduce platelet aggregation in healthy young subjects

The aim of the present study was to compare the response of a range of atherogenic and thrombogenic risk markers to two dietary levels of saturated fatty acid (SFA) substitution with monounsaturated fatty acids (MUFA) in students living in a university hall of residence. Although the benefits of such diets have been reported for plasma lipoproteins in high-risk groups, more needs to be known about effects of more modest SFA-MUFA substitutions over the long term and in young healthy adults. In a parallel design over 16 weeks, fifty-one healthy young subjects were randomised to one of two diets: (1) a moderate-MUFA diet in which 16 g dietary SFA/100 g total fatty acids were substituted with MUFA (n 25); (2) a high-MUFA diet in which 33 g dietary SFA/100 g total fatty acids were substituted with MUFA (n 26). All subjects followed an 8-week run-in diet (reference diet), with a fatty acid composition close to the UK average values. There were no differences in plasma lipid responses between the two diets over 16 weeks of the study with similar reductions in total cholesterol (P<0.001) and LDL-cholesterol (P<0.01) in both groups; a small but significant reduction in HDL-cholesterol was also observed in both groups (P<0.01). Platelet responses to ADP (P<0.01) and arachidonic acid (P<0.05) differed with time on the two diets; at 16 weeks, platelet aggregatory response to ADP was significantly lower on the high-MUFA than the moderate-MUFA (P<0.01) diet; ADP responses were also significantly lower within this group at 8 (P< 0.05) and 16 (P< 0.01) weeks compared with baseline. There were no differences in fasting factor VII activity (factors VIII and VIIag), fibrinogen concentration or tissue-type plasminogen activator activity between the diets. There were no differences in postprandial factor VIII responses to a standard meal (area under the curve) between the diets after 16 weeks, but postprandial factor VIII response was lower than on the high-MUFA diet compared with baseline (P<0.01). In conclusion, a high-MUFA diet sustains potentially beneficial effects on platelet aggregation and postprandial activation of factor VII. Moderate or high substitution of MUFA for SFA achieves similar reductions in fasting blood lipids in young healthy subjects.

Effect of polydextrose on intestinal microbes and immune functions in pigs

Dietary fibre has been proposed to decrease risk for colon cancer by altering the composition of intestinal microbes or their activity. In the present study, the changes in intestinal microbiota and its activity, and immunological characteristics, such as cyclo-oxygenase (COX)-2 gene expression in mucosa, in pigs fed with a high-energy-density diet, with and without supplementation of a soluble fibre (polydextrose; PDX) (30 g/d) were assessed in different intestinal compartments. PDX was gradually fermented throughout the intestine, and was still present in the distal colon. Irrespective of the diet throughout the intestine, of the four microbial groups determined by fluorescent in situ hybridisation, lactobacilli were found to be dominating, followed by clostridia and Bacteroides. Bifidobacteria represented a minority of the total intestinal microbiota. The numbers of bacteria increased approximately ten-fold from the distal small intestine to the distal colon. Concomitantly, also concentrations of SCFA and biogenic amines increased in the large intestine. In contrast, concentrations of luminal IgA decreased distally but the expression of mucosal COX-2 had a tendency to increase in the mucosa towards the distal colon. Addition of PDX to the diet significantly changed the fermentation endproducts, especially in the distal colon, whereas effects on bacteria] composition were rather minor. There was a reduction in concentrations of SCFA and tryptamine, and an increase in concentrations of spermidine in the colon upon PDX supplementation. Furthermore, PDX tended to decrease the expression of mucosal COX-2, therefore possibly reducing the risk of developing colon cancer-promoting conditions in the distal intestine.

Optimization of apodization functions in terahertz transient spectrometry

A quadratic programming optimization procedure for designing asymmetric apodization windows tailored to the shape of time-domain sample waveforms recorded using a terahertz transient spectrometer is proposed. By artificially degrading the waveforms, the performance of the designed window in both the time and the frequency domains is compared with that of conventional rectangular, triangular (Mertz), and Hamming windows. Examples of window optimization assuming Gaussian functions as the building elements of the apodization window are provided. The formulation is sufficiently general to accommodate other basis functions. (C) 2007 Optical Society of America

Efficient on the fly calculation of time correlation functions in computer simulations

Time correlation functions yield profound information about the dynamics of a physical system and hence are frequently calculated in computer simulations. For systems whose dynamics span a wide range of time, currently used methods require significant computer time and memory. In this paper, we discuss the multiple-tau correlator method for the efficient calculation of accurate time correlation functions on the fly during computer simulations. The multiple-tau correlator is efficacious in terms of computational requirements and can be tuned to the desired level of accuracy. Further, we derive estimates for the error arising from the use of the multiple-tau correlator and extend it for use in the calculation of mean-square particle displacements and dynamic structure factors. The method described here, in hardware implementation, is routinely used in light scattering experiments but has not yet found widespread use in computer simulations.

An introduction to radial basis functions for system identification: a comparison with other neural network methods

A look is taken at the use of radial basis functions (RBFs), for nonlinear system identification. RBFs are firstly considered in detail themselves and are subsequently compared with a multi-layered perceptron (MLP), in terms of performance and usage.

Staphylococcal extracellular adherence protein induces platelet activation by stimulation of thiol isomerases

OBJECTIVE: Staphylococcus aureus can induce platelet aggregation. The rapidity and degree of this correlates with the severity of disseminated intravascular coagulation, and depends on platelet peptidoglycans. Surface-located thiol isomerases play an important role in platelet activation. The staphylococcal extracellular adherence protein (Eap) functions as an adhesin for host plasma proteins. Therefore we tested the effect of Eap on platelets. METHODS AND RESULTS: We found a strong stimulation of the platelet-surface thiol isomerases protein disulfide isomerase, endoplasmic reticulum stress proteins 57 and 72 by Eap. Eap induced thiol isomerase-dependent glycoprotein IIb/IIIa activation, granule secretion, and platelet aggregation. Treatment of platelets with thiol blockers, bacitracin, and anti-protein disulfide isomerase antibody inhibited Eap-induced platelet activation. The effect of Eap on platelets and protein disulfide isomerase activity was completely blocked by glycosaminoglycans. Inhibition by the hydrophobic probe bis(1-anilinonaphthalene 8-sulfonate) suggested the involvement of hydrophobic sites in protein disulfide isomerase and platelet activation by Eap. CONCLUSIONS: In the present study, we found an additional and yet unknown mechanism of platelet activation by a bacterial adhesin, involving stimulation of thiol isomerases. The thiol isomerase stimulatory and prothrombotic features of a microbial secreted protein are probably not restricted to S aureus and Eap. Because many microorganisms are coated with amyloidogenic proteins, it is likely that the observed mechanism is a more general one.

Rhinocetin, a venom-derived integrin-specific antagonist inhibits collagen-induced platelet and endothelial cell functions

Snaclecs are small non-enzymatic proteins present in viper venoms reported to modulate haemostasis of victims through effects on platelets, vascular endothelial and smooth muscle cells. In this study, we have isolated and functionally characterised a snaclec which we named rhinocetin from the venom of West African gaboon viper, Bitis gabonica rhinoceros. Rhinocetin was shown to comprise α and β chains with the molecular masses of 13.5 and 13kDa respectively. Sequence and immunoblot analysis of rhinocetin confirmed this to be a novel snaclec. Rhinocetin inhibited collagen-stimulated activation of human platelets in dose dependent manner, but displayed no inhibitory effects on glycoprotein VI (collagen receptor) selective agonist, CRP-XL-, ADP- or thrombin-induced platelet activation. Rhinocetin antagonised the binding of monoclonal antibodies against the α2 subunit of integrin α2β1 to platelets and coimmunoprecipitation analysis confirmed integrin α2β1 as a target for this venom protein. Rhinocetin inhibited a range of collagen induced platelet functions such as fibrinogen binding, calcium mobilisation, granule secretion, aggregation and thrombus formation. It also inhibited integrin α2β1 dependent functions of human endothelial cells. Together, our data suggest rhinocetin to be a modulator of integrin α2β1 function and thus may provide valuable insights into the role of this integrin in physiological and pathophysiological scenarios including haemostasis, thrombosis and envenomation.

Efficient calculation of two-dimensional periodic and waveguide acoustic Green’s functions

New representations and efficient calculation methods are derived for the problem of propagation from an infinite regularly spaced array of coherent line sources above a homogeneous impedance plane, and for the Green's function for sound propagation in the canyon formed by two infinitely high, parallel rigid or sound soft walls and an impedance ground surface. The infinite sum of source contributions is replaced by a finite sum and the remainder is expressed as a Laplace-type integral. A pole subtraction technique is used to remove poles in the integrand which lie near the path of integration, obtaining a smooth integrand, more suitable for numerical integration, and a specific numerical integration method is proposed. Numerical experiments show highly accurate results across the frequency spectrum for a range of ground surface types. It is expected that the methods proposed will prove useful in boundary element modeling of noise propagation in canyon streets and in ducts, and for problems of scattering by periodic surfaces.