Boundary integral equations on unbounded rough surfaces: Fredholmness and the finite section method

We consider a class of boundary integral equations that arise in the study of strongly elliptic BVPs in unbounded domains of the form $D = \{(x, z)\in \mathbb{R}^{n+1} : x\in \mathbb{R}^n, z > f(x)\}$ where $f : \mathbb{R}^n \to\mathbb{R}$ is a sufficiently smooth bounded and continuous function. A number of specific problems of this type, for example acoustic scattering problems, problems involving elastic waves, and problems in potential theory, have been reformulated as second kind integral equations $u+Ku = v$ in the space $BC$ of bounded, continuous functions. Having recourse to the so-called limit operator method, we address two questions for the operator $A = I + K$ under consideration, with an emphasis on the function space setting $BC$. Firstly, under which conditions is $A$ a Fredholm operator, and, secondly, when is the finite section method applicable to $A$?

Unification of the probe and singular sources methods for the inverse boundary value problem by the no-response test

In this article, we use the no-response test idea, introduced in Luke and Potthast (2003) and Potthast (Preprint) and the inverse obstacle problem, to identify the interface of the discontinuity of the coefficient gamma of the equation del (.) gamma(x)del + c(x) with piecewise regular gamma and bounded function c(x). We use infinitely many Cauchy data as measurement and give a reconstructive method to localize the interface. We will base this multiwave version of the no-response test on two different proofs. The first one contains a pointwise estimate as used by the singular sources method. The second one is built on an energy (or an integral) estimate which is the basis of the probe method. As a conclusion of this, the probe and the singular sources methods are equivalent regarding their convergence and the no-response test can be seen as a unified framework for these methods. As a further contribution, we provide a formula to reconstruct the values of the jump of gamma(x), x is an element of partial derivative D at the boundary. A second consequence of this formula is that the blow-up rate of the indicator functions of the probe and singular sources methods at the interface is given by the order of the singularity of the fundamental solution.

On integral equation and least squares methods for scattering by diffraction gratings

In this paper we consider the scattering of a plane acoustic or electromagnetic wave by a one-dimensional, periodic rough surface. We restrict the discussion to the case when the boundary is sound soft in the acoustic case, perfectly reflecting with TE polarization in the EM case, so that the total field vanishes on the boundary. We propose a uniquely solvable first kind integral equation formulation of the problem, which amounts to a requirement that the normal derivative of the Green's representation formula for the total field vanish on a horizontal line below the scattering surface. We then discuss the numerical solution by Galerkin's method of this (ill-posed) integral equation. We point out that, with two particular choices of the trial and test spaces, we recover the so-called SC (spectral-coordinate) and SS (spectral-spectral) numerical schemes of DeSanto et al., Waves Random Media, 8, 315-414 1998. We next propose a new Galerkin scheme, a modification of the SS method that we term the SS* method, which is an instance of the well-known dual least squares Galerkin method. We show that the SS* method is always well-defined and is optimally convergent as the size of the approximation space increases. Moreover, we make a connection with the classical least squares method, in which the coefficients in the Rayleigh expansion of the solution are determined by enforcing the boundary condition in a least squares sense, pointing out that the linear system to be solved in the SS* method is identical to that in the least squares method. Using this connection we show that (reflecting the ill-posed nature of the integral equation solved) the condition number of the linear system in the SS* and least squares methods approaches infinity as the approximation space increases in size. We also provide theoretical error bounds on the condition number and on the errors induced in the numerical solution computed as a result of ill-conditioning. Numerical results confirm the convergence of the SS* method and illustrate the ill-conditioning that arises.

Differential effects of thyroid hormone manipulation and ß adrenoceptor agonist administration on uncoupling protein mRNA abundance in adipose tissue and thermoregulation in neonatal pigs

We have shown that there is significant disparity in the expression of uncoupling proteins (UCP) 2 and 3 between modern-commercial and ancient-Meishan porcine genotypes, commercial pigs also have higher plasma triiodothyronine (T(3)) in on the first day of life. T(3) and the sympathetic nervous system are both known to regulate UCPs in rodents and humans; their role in regulating these proteins in the pig is unknown. This study examined whether thyroid hormone manipulation or administration of a selective beta3 adrenoceptor agonist (ZD) influenced plasma hormones, colonic temperature and UCP expression in adipose tissue of two breeds of pig. To mimic the differences observed in thyroid hormone status, piglets from Meishan and commercial litters were randomly assigned to control (1 ml/kg water), T(3) (10 mg/kg) (Meishan only), methimazole (a commonly used antithyroid drug) (50 mg/kg) (commercial only) or ZD (10 mg/kg) oral administration for the first 4 days of postnatal life. Adipose tissue UCP2/3 mRNA abundance was measured on day 4 using PCR. T(3) administration raised plasma T(3) concentrations and increased colonic temperature on day 4. UCP3 mRNA abundance was higher in Meishan, than commercial piglets (p = 0.042) and was downregulated following T(3) administration (p = 0.014). Irrespective of genotype, ZD increased UCP2 mRNA abundance (Meishan p = 0.05, commercial p = 0.03). Expression of neither UCP2 nor 3 was related to colonic temperature, regardless of treatment. In conclusion, we have demonstrated a dissociation between thyroid hormones and the sympathetic nervous system in the regulation of UCPs in porcine adipose tissue. We have also suggested that expression of adipose tissue UCP2 and 3 are not related to body temperature in piglets.

Differential susceptibilities of peach-potato aphid, Myzus persicae (Homoptera: Aphididae) and its parasitoid, Aphidius matricariae (Hymenoptera: Aphidiidae) to foliar insecticides on partially resistant and susceptible potato cultivars

In a field experiment the effects of Sumicidin (super) 5EC (fenitrothion), Metasystox EC25 (oxydemeton-methyl) and Tamaron SL600 (methamidophos), applied at different dosages, were evaluated against peach-potato aphid, Myzus persicae (Sulzer) and its parasitoid Aphidius matricariae Haliday on Cardinal and Desiree (respectively partially resistant and susceptible potato cultivars to M. persicae). Sumicidin (super) 5EC was found about 30% more effective in reducing aphid populations than the other insecticides tested. The highest doses of each insecticide caused maximum aphid mortality; in general aphid mortality appeared dose dependent. Almost all the higher and lower doses of the tested insecticides were about 19% more effective on Cardinal than on Desiree. The most significant result was the synergistic interaction at the lower doses with plant resistance, so that the same level of control was recorded with second highest dose on Cardinal as with the highest dose on Desiree. Also the same control level was achieved at the lowest dosage rate on Cardinal compared with the next higher dose on the Desiree. Sumicidin (super) 5EC was found least toxic to the parasitoid, A. matricariae in terms of percent parasitism, emergence of parasitoids and number of mature eggs in the emerging female parasitoids; increase of about 22, 67 and 47% respectively were found in parasitoid performance with Tamaron SL600 which was found comparatively highly toxic. The highest doses of all insecticides were found clearly toxic to the parasitoid. In general, effects on the parasitoid were dose dependent. Maximum yield was obtained from the second highest dose of Sumicidin (super) 5EC.

Differential expression of mRNAs encoding co-receptor (betaglycan) and activin type-I preovulatory and prehierarchical follicles of the putative inhibin and type-II receptors in the laying hen ovary

Ovarian follicle development is primarily regulated by an interplay between the pituitary gonadotrophins, LH and FSH, and ovary-derived steroids. Increasing evidence implicates regulatory roles of transforming growth factor-beta (TGF beta) superfamily members, including inhibins and activins. The aim of this study was to identify the expression of mRNAs encoding key receptors of the inhibin/activin system in ovarian follicles ranging from 4 mm in diameter to the dominant F1 follicle (similar to 40 turn). Ovaries were collected (n=16) from inid-sequence hens maintained on a long-day photoschedule (16h of light:8 h of darkness). All follicles removed were dissected into individual granulosa and thecal layers. RNA was extracted and cDNA synthesized. Real-time quantitative PCR was used to quantify the expression of niRNA encoding betaglycan, activin receptor (ActR) subtypes (type-I, -IIA and -IIB) and glyceraldehyde-3-phosphate dehydrogenase (GAPDH); receptor expression data were normalized to GAPDH expression. Detectable levels of ActRI, -IIA and -IIB and the inhibin co-receptor (betaglycan) expression were found in all granulosa and thecal layers analysed. Granulosa ActRI mRNA peaked (P < 0(.)05) in 8-9(.)9 mm follicles, whereas ActRIIA rose significantly from 6-7(.)9 mm to 8-9(.)9 nun, before filling to F3/2; levels then rose sharply (3-fold) to F1 levels. Granulosa betaglycan niRNA expression rose 3-fold from 4-5(.)9 min to 8-9(.)9 mm, before falling 4-fold to F3/2; levels then rose sharply (4-fold) to F1 levels. ActRIIB levels did not vary significantly during follicular development. Thecal ActRI mRNA expression was similar from 4-7(.)9 mm then decreased significantly to a nadir at the F4 position, before increasing 2-fold to the F1 (P < 0(.)05). Although thecal ActRIIB and -IIA expression did not vary significantly from 4 nim to F3, ActRIIB expression increased significantly (2-fold) from F3 to F1 and ActIIA, increased 22-fold from F2 to F1 (P < 0(.)05). Thecal betaglycan fell to a nadir at F6 after follicle selection; levels then increased significantly to F2, before filling similar to 50% in the F I. In all follicles studied expression of betaglycan and ActRI (granulosa: 1-0(.)65, P < 0-001, n=144/group; theca: r=0(.)49, P < 0-001, n=144/group) was well correlated. No significant correlations were identified between betaglycan and ActRIIA or -IIB. Considering all follicles analysed, granulosa mRNA expression of betaglycan, ActRI ActRIIA and ActRIIB were all significantly lower than in corresponding thecal tissue (betaglycan, 11(.)4-fold; ActRIIB, 5(.)1-fold; ActR(.) 3-8-fold: ActRIIA, 2(.)8-fold). The co-localization of type-I and -II activin receptors and betaglycan on granulosa and thecal cells are consistent with a local auto/paracrine role of inhibins and activins in modulating ovarian follicle development, selection and progression in the domestic fowl.

The effects of temperature and light integral on early vegetative growth and chlorophyll fluorescence of four contrasting genotypes of cacao (Theobroma cacao)

The effect of temperature on early vegetative growth, leaf chlorophyll fluorescence and chlorophyll content was examined on four genotypes of cacao (Amelonado, AMAZ 15–15, SCA 6 and SPEC 54/1). A controlled environment glasshouse was used to simulate the temperature conditions of three cacao-growing regions (Bahia, Brazil; Tafo, Ghana and Lower Perak, Malaysia) over the course of a year. Base temperatures calculated from increments in main stem growth varied from 18.6°C for AMAZ 15/15 to 20.8°C for SPEC 54/1. Temporal variation in Fv/Fm observed for two of the clones (SCA 6 and SPEC 54/1) in two of the compartments were correlated with temperature differences over time. Significant differences were also recorded between genotypes in leaf chlorophyll content. It was shown that variation over time in leaf chlorophyll content could be quantified accurately as a function of temperature and light integral. The results imply that genetic variability exists in cacao in response to temperature stress.

Bone morphogenetic protein (BMP) ligands and receptors in bovine ovarian follicle cells: actions of BMP-4,-6 and-7 on granulosa cells and differential modulation of Smad-1 phosphorylation by follistatin

Given the paucity of information on the potential roles of bone morphogenetic proteins (BMPs) in the ruminant ovary we conducted immunolocalization and functional studies on cells isolated from bovine antral follicles. Immunocytochemistry revealed expression of BMP-4 and -7 in isolated theca cells whereas granulosa cells and oocytes selectively expressed RMP-6. All three cell types expressed a range of BMP-responsive type-I (BMPRIB, ActRI) and type-II (BMPRII, ActRII, ActRIIB) receptors supporting autocrine/paracrine roles within the follicle. This was reinforced by functional experiments on granulosa cells which showed that BMP-4, -6 and -7 promoted cellular accumulation of phosphorylated Smad-1 but not Smad-2 and enhanced 'basal' and IGF-stimulated secretion of oestradiol (E2), inhibin-A, activin-A and follistatin (FS). Concomitantly, each BMP suppressed 'basal' and IGF-stimulated progesterone secretion, consistent with an action to prevent or delay atresia and/or luteinization. BMPs also increased viable cell number under 'basal' (BMP-4 and -7) and IGF-stimulated (BMP-4, -6 and -7) conditions. Since FS, a product of bovine granulosa cells, has been shown to bind several BMPs, we used the Biacore technique to compare its binding affinities for activin-A (prototype FS ligand) and BMP-4, -6 and -7. Compared with activin-A (K-d 0.28 +/- 0.02 nM; 100%), the relative affinities of FS for BMP-4, -6 and -7 were 10, 5 and 1% respectively. Moreover, studies on granulosa cells showed that preincubation of ligand with excess FS abolished activin-A-induced phosphorylation of Smad-2 and BMP-4-induced phosphorylation of Smad-1. However, FS only partially reversed BMP-6-induced Smad-1 phosphorylation and had no inhibitory effect on BMP-7-induced Smad-1 phosphorylation. These findings support functional roles for BMP-4, -6 and -7 as paracrine/autocrine modulators of granulosa cell steroidogenesis, peptide secretion and proliferation in bovine antral follicles. The finding that FS can differentially modulate BMP-induced receptor activation and that this correlates with the relative binding affinity of FS for each BMP type implicates FS as a potential modulator of BMP action in the ovary.

Crystallization in poly(L-lactide)-b-poly(epsilon-caprolactone) double crystalline diblock copolymers: a study using X-ray scattering, differential scanning calorimetry, and polarized optical microscopy

The crystallization of well-defined poly(L-lactide)-b-poly(epsilon-caprolactone) diblock copolymers, PLLA-b-PCL, was investigated by time-resolved X-ray techniques, polarized optical microscopy (POM), and differential scanning calorimetry (DSC). Two compositions were studied that contained 44 and 60 wt % poly(L-lactide), PLLA (they are referred to as (L44C5614)-C-11 and (L60C409)-C-12, respectively, with the molecular weight of each block in kg/mol as superscript). The copolymers were found to be initially miscible in the melt according to small-angle X-ray scattering measurements (SAXS). Their thermal behavior was also indicative of samples whose crystallization proceeds from a mixed melt. Sequential isothermal crystallization from the melt at 100 degreesC (for 30 min) and then at 30 degreesC (for 15 min) was measured. At 100 degreesC only the PLLA block is capable of crystallization, and its crystallization kinetics was followed by both WAXS and DSC; comparable results were obtained that indicated an instantaneous nucleation with three-dimensional superstructures (Avrami index of approximately 3). The spherulitic nature of the superstructure was confirmed by POM. When the temperature was decreased to 30 degreesC, the PCL block was able to crystallize within the PLLA negative spherulites (with an Avrami index of 2, as opposed to 3 in homo-PCL), and its crystallization rate was much slower than an equivalent homo-PCL. Time-resolved SAXS experiments in (L60C409)-C-12 revealed an initial melt mixed morphology at 165 degreesC that upon cooling transformed into a transient microphase-separated lamellar structure prior to crystallization at 100 degreesC.

Differential effects of apolipoprotein E3 and E4 on markers of oxidative status in macrophages

ApoE is secreted by macrophages at the lesion site of the atherosclerotic plaque, where it is thought to play a protective role against atherosclerosis independently of its effects on lipid metabolism. Of the three common isoforms for apoE, apoE4 is associated with higher risk of cardiovascular disease (CVD). In vitro studies have shown that recombinant apoE may act as an antioxidant in an isoform-dependent manner (E2 > E3 > E4). The oxidative status of the macrophages plays a key role in the process of atherosclerosis. In the present study the possible differential actions of apoE3 and apoE4 on several parameters of oxidative status were determined in stably transfected murine macrophages (RAW 2647-apoE3 and apoE4). No differences between genotypes were observed after peroxide challenge in either protection against cytotoxicity or in cell membrane oxidation, and modest differences were observed in the non-enzymatic antioxidants (glutathione and a-tocopherol) in apoE3 v. apoE4 macrophages. Importantly, cells secreting apoE4 showed increased membrane oxidation under basal conditions, and produced more NO and superoxide anion radicals than the apoE3 macrophages after stimulation. The present data suggest that apoE genotype influences the oxidative status of macrophages, and this could partly contribute to the higher CVD risk observed in apoE4 carriers.

Plant- and marine-derived n-3 polyunsaturated fatty acids have differential effects on fasting and postprandial blood lipid concentrations and on the susceptibility of LDL to oxidative modification in moderately hyperlipidemic subjects

Background: Dietary a-linolenic acid (ALA) can be converted to long-chain n-3 polyunsaturated fatty acids (PUFAs) in humans and may reproduce some of the beneficial effects of eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA) on cardiovascular disease risk factors. Objective: This study aimed to compare the effects of increased dietary intakes of ALA and EPA+DHA on a range of atherogenic risk factors. Design: This was a placebo-controlled, parallel study involving 150 moderately hyperlipidemic subjects randomly assigned to 1 of 5 interventions: 0.8 or 1.7 g EPA+DHA/d, 4.5 or 9.5 g ALA/d, or an n-6 PUFA control for 6 mo. Fatty acids were incorporated into 25 g of fat spread and 3 capsules to be consumed daily. Results: The change in fasting or postprandial lipid, glucose, or insulin concentrations or in blood pressure was not significantly different after any of the n-3 PUFA interventions compared with the n-6 PUFA control. The mean (+/-SEM) change in fasting triacylglycerols after the 1.7-g/d EPA+DHA intervention (-7.7 +/- 4.99%) was significantly (P < 0.05) different from the change after the 9.5-g/d ALA intervention (10.9 +/- 4.5%). The ex vivo susceptibility of LDL to oxidation was higher after the 1.7-g/d EPA+DHA intervention than after the control and ALA interventions (P < 0.05). There was no significant change in plasma a-tocopherol concentrations or in whole plasma antioxidant status in any of the groups. Conclusion: At estimated biologically equivalent intakes, dietary ALA and EPA+DHA have different physiologic effects.

Differential induction of apoptosis in human colonic carcinoma cells (Caco-2) by Atopobium, and commensal, probiotic and enteropathogenic bacteria: mediation by the mitochondrial pathway

The induction of apoptosis in mammalian cells by bacteria is well reported. This process may assist infection by pathogens whereas for non-pathogens apoptosis induction within carcinoma cells protects against colon cancer. Here, apoptosis induction by a major new gut bacterium, Atopobium minutum, was compared with induction by commensal (Escherichia coli K-12 strains), probiotic (Lactobacillus rhamnosus, Bifidobacterium latis) and pathogenic (E. coli: EPEC and VTEC) gut bacteria within the colon cancer cell line, Caco-2. The results show a major apoptotic effect for the pathogens, mild effects for the probiotic strains and A. minutum, but no effect for commensal E. coli. The mild apoptotic effects observed are consistent with the beneficial roles of probotics in protection against colon cancer and suggest, for the first time, that A. minutum possesses similar advantageous, anti-cancerous activity. Although bacterial infection increased Caco-2 membrane FAS levels, caspase-8 was not activated indicating that apoptosis is FAS independent. Instead, in all cases, apoptosis was induced through the mitochondrial pathway as indicated by BAX translocation, cytorchrome c release, and caspase-9 and -3 cleavage. This suggests that an intracellular stimulus initiates the observed apoptosis responses.