The elliptic sine-Gordon equation in a half plane

We consider boundary value problems for the elliptic sine-Gordon equation posed in the half plane y > 0. This problem was considered in Gutshabash and Lipovskii (1994 J. Math. Sci. 68 197–201) using the classical inverse scattering transform approach. Given the limitations of this approach, the results obtained rely on a nonlinear constraint on the spectral data derived heuristically by analogy with the linearized case. We revisit the analysis of such problems using a recent generalization of the inverse scattering transform known as the Fokas method, and show that the nonlinear constraint of Gutshabash and Lipovskii (1994 J. Math. Sci. 68 197–201) is a consequence of the so-called global relation. We also show that this relation implies a stronger constraint on the spectral data, and in particular that no choice of boundary conditions can be associated with a decaying (possibly mod 2π) solution analogous to the pure soliton solutions of the usual, time-dependent sine-Gordon equation. We also briefly indicate how, in contrast to the evolutionary case, the elliptic sine-Gordon equation posed in the half plane does not admit linearisable boundary conditions.

Moving boundary value problems for the wave equation

We study certain boundary value problems for the one-dimensional wave equation posed in a time-dependent domain. The approach we propose is based on a general transform method for solving boundary value problems for integrable nonlinear PDE in two variables, that has been applied extensively to the study of linear parabolic and elliptic equations. Here we analyse the wave equation as a simple illustrative example to discuss the particular features of this method in the context of linear hyperbolic PDEs, which have not been studied before in this framework.

The Klein-Gordon equation on the half line: a Riemann-Hilbert approach

We solve an initial-boundary problem for the Klein-Gordon equation on the half line using the Riemann-Hilbert approach to solving linear boundary value problems advocated by Fokas. The approach we present can be also used to solve more complicated boundary value problems for this equation, such as problems posed on time-dependent domains. Furthermore, it can be extended to treat integrable nonlinearisations of the Klein-Gordon equation. In this respect, we briefly discuss how our results could motivate a novel treatment of the sine-Gordon equation.

Initial boundary value problems for the nonlinear Schrödinger equation

A new spectral method for solving initial boundary value problems for linear and integrable nonlinear partial differential equations in two independent variables is applied to the nonlinear Schrödinger equation and to its linearized version in the domain {x≥l(t), t≥0}. We show that there exist two cases: (a) if l″(t)<0, then the solution of the linear or nonlinear equations can be obtained by solving the respective scalar or matrix Riemann-Hilbert problem, which is defined on a time-dependent contour; (b) if l″(t)>0, then the Riemann-Hilbert problem is replaced by a respective scalar or matrix problem on a time-independent domain. In both cases, the solution is expressed in a spectrally decomposed form.

Examination of the persistency of milk fatty acid composition responses to fish oil and sunflower oil in the diet of dairy cows

Based on the potential benefits of cis-9, trans-11 conjugated linoleic acid (CLA) for human health, there is a need to develop effective strategies for enhancing milk fat CLA concentrations. Levels of cis-9, trans-11 CLA in milk can be increased by supplements of fish oil (FO) and sunflower oil (SO), but there is considerable variation in the response. Part of this variance may reflect time-dependent ruminal adaptations to high levels of lipid in the diet, which lead to alterations in the formation of specific biohydrogenation intermediates. To test this hypothesis, 16 late lactation Holstein-British Friesian cows were used in a repeated measures randomized block design to examine milk fatty acid composition responses to FO and SO in the diet over a 28-d period. Cows were allocated at random to corn silage-based rations (8 per treatment) containing 0 (control) or 45 g of oil supplement/ kg of dry matter consisting (1:2; wt/wt) of FO and SO (FSO), and milk composition was determined on alternate days from d 1. Compared with the control, the FSO diet decreased mean dry matter intake (21.1 vs. 17.9 kg/d), milk fat (47.7 vs. 32.6 g/kg), and protein content (36.1 vs. 33.3 g/kg), but had no effect on milk yield (27.1 vs. 26.4 kg/d). Reductions in milk fat content relative to the FSO diet were associated with increases in milk trans-10 18: 1, trans-10, cis-12 CLA, and trans-9, cis-11 CLA concentrations (r(2) = 0.74, 0.57, and 0.80, respectively). Compared with the control, the FSO diet reduced milk 4: 0 to 18: 0 and cis 18:1 content and increased trans 18:1, trans 18:2, cis-9, trans-11 CLA, 20: 5 n-3, and 22: 6 n-3 concentrations. The FSO diet caused a rapid elevation in milk cis-9, trans-11 CLA content, reaching a maximum of 5.37 g/100 g of fatty acids on d 5, but these increases were transient, declining to 2.35 g/100 g of fatty acids by d 15. They remained relatively constant thereafter. Even though concentrations of trans-11 18: 1 followed the same pattern of temporal changes as cis-9, trans-11 CLA, the total trans 18:1 content of FSO milk was unchanged because of the concomitant increases in the concentration of other isomers (Delta(4-10) and Delta(12-15)), predominantely trans-10 18:1. In conclusion, supplementing diets with FSO enhances milk fat cis-9, trans-11 CLA content, but the high level of enrichment declines because of changes in ruminal biohydrogenation that result in trans-10 replacing trans-11 as the major 18:1 biohydrogenation intermediate formed in the rumen.

Ingestion of onion soup high in quercetin inhibits platelet aggregation and essential components of the collagen-stimulated platelet activation pathway in man: a pilot study

Epidemiological data suggest that those who consume a diet rich in quercetin-containing foods may have a reduced risk of CVD. Furthermore, in vitro and ex vivo studies have observed the inhibition of collagen-induced platelet activation by quercetin. The aim of the present study was to investigate the possible inhibitory effects of quercetin ingestion from a dietary source on collagen-stimulated platelet aggregation and signalling. A double-blind randomised cross-over pilot study was undertaken. Subjects ingested a soup containing either a high or a low amount of quercetin. Plasma quercetin concentrations and platelet aggregation and signalling were assessed after soup ingestion. The high-quercetin soup contained 69 mg total quercetin compared with the low-quercetin soup containing 5 mg total quercetin. Plasma quercetin concentrations were significantly higher after high-quercetin soup ingestion than after low-quercetin soup ingestion and peaked at 2.59 (SEM 0.42) mu mol/l. Collagen-stimulated (0.5 mu g/ml) platelet aggregation was inhibited after ingestion of the high-quercetin soup in a time-dependent manner. Collagen-stimulated tyrosine phosphorylation of a key component of the collagen-signalling pathway via glycoprotein VI, Syk, was significantly inhibited by ingestion of the high-quercetin soup. The inhibition of Syk tyrosine phosphorylation was correlated with the area under the curve for the high-quercetin plasma profile. In conclusion, the ingestion of quercetin from a dietary source of onion soup could inhibit some aspects of collagen-stimulated platelet aggregation and signalling ex vivo. This further substantiates the epidemiological data suggesting that those who preferentially consume high amounts of quercetin-containing foods have a reduced risk of thrombosis and potential CVD risk.

Platelet nitric oxide synthase is activated by tyrosine dephosphorylation: possible role for SHP-1 phosphatase

Background: Endothelial nitric oxide synthase (eNOS) activity in endothelial cells is regulated by post-translational phosphorylation of critical serine, threonine and tyrosine residues in response to a variety of stimuli. However, the post-translational regulation of eNOS in platelets is poorly defined. Objectives: We investigated the role of tyrosine phosphorylation in the regulation of platelet eNOS activity. Methods: Tyrosine phosphorylation of eNOS and interaction with the tyrosine phosphatase SHP-1 were investigated by coimmunoprecipitation and immunoblotting. An in vitro immunoassay was used to determine eNOS activity together with the contribution of protein tyrosine phosphorylation. Results: We found platelet eNOS was tyrosine phosphorylated under basal conditions. Thrombin induced a dose- and time-dependent increase in eNOS activity without altering overall level of tyrosine phosphorylation, although we did observe evidence of minor tyrosine dephosphorylation. In vitro tyrosine dephosphorylation of platelet eNOS using a recombinant protein tyrosine phosphatase enhanced thrombin-induced activity compared to thrombin alone, but had no effect on endothelial eNOS activity either at basal or after stimulation with bradykinin. Having shown that dephosphorylation could modulate platelet eNOS activity we examined the role of potential protein phosphatases important for platelet eNOS activity. We found SHP-1 protein tyrosine phosphatase, co-associated with platelet eNOS in resting platelets, but does not associate with eNOS in endothelial cells. Stimulation of platelets with thrombin increased SHP-1 association with eNOS, while inhibition of SHP-1 abolished the ability of thrombin to induce elevated eNOS activity. Conclusions: Our data suggest a novel role for tyrosine dephosphorylation in platelet eNOS activation, which may be mediated by SHP-1.

Direct detection of dimethylstannylene and tetramethyldistannene in solution and the gas phase by laser flash photolysis of 1,1-dimethylstannacyclopent-3-enes

The photochemistry of 1,1-dimethyl- and 1,1,3,4-tetramethylstannacyclopent-3-ene (4a and 4b,respectively) has been studied in the gas phase and in hexane solution by steady-state and 193-nm laser flash photolysis methods. Photolysis of the two compounds results in the formation of 1,3-butadiene (from 4a) and 2,3-dimethyl-1,3-butadiene (from 4b) as the major products, suggesting that cycloreversion to yield dimethylstannylene (SnMe2) is the main photodecomposition pathway of these molecules. Indeed, the stannylene has been trapped as the Sn-H insertion product upon photolysis of 4a in hexane containing trimethylstannane. Flash photolysis of 4a in the gas phase affords a transient absorbing in the 450-520nm range that is assigned to SnMe2 by comparison of its spectrum and reactivity to those previously reported from other precursors. Flash photolysis of 4b in hexane solution affords results consistent with the initial formation of SnMe2 (lambda(max) approximate to 500 nm), which decays over similar to 10 mu s to form tetramethyldistannene (5b; lambda(max) approximate to 470 nm). The distannene decays over the next ca. 50 mu s to form at least two other longer-lived species, which are assigned to higher SnMe2 oligomers. Time-dependent DFT calculations support the spectral assignments for SnMe2 and Sn2Me4, and calculations examining the variation in bond dissociation energy with substituent (H, Me, and Ph) in disilenes, digermenes, and distannenes rule out the possibility that dimerization of SnMe2 proceeds reversibly. Addition of methanol leads to reversible reaction with SnMe2 to form a transient absorbing at lambda(max) approximate to 360 nm, which is assigned to the Lewis acid-base complex between SnMe2 and the alcohol.

Gas-solid reactions of single crystals: a study of the reaction of bromine with single crystals of trans-cinnamic acid and a range of its derivatives by infrared and Raman microspectroscopy

Single crystals of trans-cinnamic acid and of a range of derivatives of this compound containing halogen substituents on the aromatic ring have been reacted with 165 Torr pressure of bromine vapour in a sealed desiccator at 20 degrees C for 1 week. Infrared and Raman microspectroscopic examination of the crystals shows that bromination of the aliphatic double bond, but not of the aromatic ring, has occurred. It is demonstrated also that the reaction is truly gas-solid in nature. A time-dependent study of these reactions shows that they do not follow a smooth diffusion-controlled pathway. Rather the reactions appear to be inhomogeneous and to occur at defects within the crystal. The reaction products are seen to flake from the surface of the crystal. It is shown, therefore, that these are not single crystal to single crystal transitions, as have been observed previously for the photodimerisation of trans-cinnamic acid and several of its derivatives. It is shown that there are no by-products of the reaction and that finely ground samples react to form the same products as single crystals.

DNA cleavage and antitumour activity of platinum(II) and copper(II) compounds derived from 4-methyl-2-N-(2-pyridylmethyl)aminophenol: spectroscopic, electrochemical and biological investigation

The reaction of the redox-active ligand, Hpyramol (4-methyl-2-N-(2-pyridylmethyl)aminophenol) with K2PtCl4 yields monofunctional square-planar [Pt(pyrimol)Cl], PtL-Cl, which was structurally characterised by single-crystal X-ray diffraction and NMR spectroscopy. This compound unexpectedly cleaves supercoiled double-stranded DNA stoichiometrically and oxidatively, in a non-specific manner without any external reductant added, under physiological conditions. Spectro-electrochemical investigations of PtL-Cl were carried out in comparison with the analogue CuL-Cl as a reference compound. The results support a phenolate oxidation, generating a phenoxyl radical responsible for the ligand-based DNA cleavage property of the title compounds. Time-dependent in vitro cytotoxicity assays were performed with both PtL-Cl and CuL-Cl in various cancer cell lines. The compound CuL-Cl overcomes cisplatin-resistance in ovarian carcinoma and mouse leukaemia cell lines, with additional activity in some other cells. The platinum analogue, PtL-Cl also inhibits cell-proliferation selectively. Additionally, cellular-uptake studies performed for both compounds in ovarian carcinoma cell lines showed that significant amounts of Pt and Cu were accumulated in the A2780 and A2780R cancer cells. The conformational and structural changes induced by PtL-Cl and CuL-Cl on calf thymus DNA and phi X174 supercoiled phage DNA at ambient conditions were followed by electrophoretic mobility assay and circular dichroism spectroscopy. The compounds induce extensive DNA degradation and unwinding, along with formation of a monoadduct at the DNA minor groove. Thus, hybrid effects of metal-centre variation, multiple DNA-binding modes and ligand-based redox activity towards cancer cell-growth inhibition have been demonstrated. Finally, reactions of PtL-Cl with DNA model bases (9-Ethylguanine and 5'-GMP) followed by NMR and MS showed slow binding at Guanine-N7 and for the double stranded self complimentary oligonucleotide d(GTCGAC)(2) in the minor groove.

Burn in policies for products having dormant states

Constructing a building is a long process which can take several years. Most building services products are installed while a building is constructed, but they are not operated until the building is commissioned. The warranty term for the building service systems may cover the time starting from their installation to the end of the warranty period. Prior to the commissioning of the building, the building services systems are protected by warranty although they are not operated. The bum in time for such systems is important when warranty costs is analyzed. In this paper, warranty cost models for products with burn in periods are presented. Two burn in policies are developed to optimize the total mean warranty cost. A special case on the relationship between the failure rates of the product at the dormant state and at the I operating state is presented.

Enzyme glycation influences product yields during oligosaccharide synthesis by reverse hydrolysis

Possible evidence is presented for Maillard glycation of enzymes during oligosaccharide synthesis by reverse hydrolysis. In 70% (w/v) mannose solutions, 1,2-alpha-mannosidase from Penicillium citrinum lost 40% and alpha-mannosidase from almonds lost 60% activity at 55 degreesC over 2 weeks. Oligosaccharide yields were 15 and 45% respectively. Higher molecular weight glycation adducts were formed in a time-dependent manner as seen by MALDI-TOF. Inhibitors of the Maillard. reaction were able to partially alleviate these effects resulting in reduced loss of enzyme activity and oligosaccharide yield increases of 27-53% relative to the control. (C) 2004 Elsevier B.V. All rights reserved.

G protein ss gamma subunits mediate presynaptic inhibition of transmitter release from rat superior cervical ganglion neurones in culture

The activation of presynaptic G protein-coupled receptors (GPCRs) is widely reported to inhibit transmitter release; however, the lack of accessibility of many presynaptic terminals has limited direct analysis of signalling mediators. We studied GPCR-mediated inhibition of fast cholinergic transmission between superior cervical ganglion neurones (SCGNs) in culture. The adrenoceptor agonist noradrenaline (NA) caused a dose-related reduction in evoked excitatory postsynaptic potentials (EPSPs). NA-induced EPSP decrease was accompanied by effects on the presynaptic action potential (AP), reducing AP duration and amplitude of the after-hyperpolarization (AHP), without affecting the pre- and postsynaptic membrane potential. All effects of NA were blocked by yohimbine and synaptic transmission was reduced by clonidine, consistent with an action at presynaptic alpha 2-adrenoceptors. NA-induced inhibition of transmission was sensitive to pre-incubation of SCGNs with pertussis toxin (PTX), implicating the involvement of G alpha(i)/(o)beta y subunits. Expression of G alpha transducin, an agent which sequesters G protein beta gamma (G beta y) subunits, in the presynaptic neurone caused a time-dependent attenuation of NA-induced inhibition. Injection of purified G beta gamma subunits into the presynaptic neurone inhibited transmission, and also reduced the AHP amplitude. Furthermore, NA-induced inhibition was occluded by pre-injection of G beta gamma subunits. The Ca2+ channel blocker Cd2+ mimicked NA effects on transmitter release. Cd2+, NA and G beta gamma subunits also inhibited somatic Ca2+ current. In contrast to effects on AP-evoked transmitter release, NA had no clear action on AP-independent EPSPs induced by hypertonic solutions. These results demonstrate that G beta gamma subunits functionally mediate inhibition of transmitter release by alpha 2-adrenoceptors and represent important regulators of synaptic transmission at mammalian presynaptic terminals.

Influence of birth weight on gene regulators of lipid metabolism and utilization in subcutaneous adipose tissue and skeletal muscle of neonatal pigs.

Epidemiological studies suggest that low-birth weight infants show poor neonatal growth and increased susceptibility to metabolic syndrome, in particular, obesity and diabetes. Adipose tissue development is regulated by many genes, including members of the peroxisome proliferator-activated receptor (PPAR) and the fatty acid-binding protein (FABP) families. The aim of this study was to determine the influence of birth weight on key adipose and skeletal muscle tissue regulating genes. Piglets from 11 litters were ranked according to birth weight and 3 from each litter assigned to small, normal, or large-birth weight groups. Tissue samples were collected on day 7 or 14. Plasma metabolite concentrations and the expression of PPARG2, PPARA, FABP3, and FABP4 genes were determined in subcutaneous adipose tissue and skeletal muscle. Adipocyte number and area were determined histologically. Expression of FABP3 and 4 was significantly reduced in small and large, compared with normal, piglets in adipose tissue on day 7 and in skeletal muscle on day 14. On day 7, PPARA and PPARG2 were significantly reduced in adipose tissue from small and large piglets. Adipose tissue from small piglets contained more adipocytes than normal or large piglets. Birth weight had no effect on adipose tissue and skeletal muscle lipid content. Low-birth weight is associated with tissue-specific and time-dependent effects on lipid-regulating genes as well as morphological changes in adipose tissue. It remains to be seen whether these developmental changes alter an individual's susceptibility to metabolic syndrome.

Numerical modeling of the propagation environment in the atmospheric boundary layer over the Persian Gulf

Strong vertical gradients at the top of the atmospheric boundary layer affect the propagation of electromagnetic waves and can produce radar ducts. A three-dimensional, time-dependent, nonhydrostatic numerical model was used to simulate the propagation environment in the atmosphere over the Persian Gulf when aircraft observations of ducting had been made. A division of the observations into high- and low-wind cases was used as a framework for the simulations. Three sets of simulations were conducted with initial conditions of varying degrees of idealization and were compared with the observations taken in the Ship Antisubmarine Warfare Readiness/Effectiveness Measuring (SHAREM-115) program. The best results occurred with the initialization based on a sounding taken over the coast modified by the inclusion of data on low-level atmospheric conditions over the Gulf waters. The development of moist, cool, stable marine internal boundary layers (MIBL) in air flowing from land over the waters of the Gulf was simulated. The MIBLs were capped by temperature inversions and associated lapses of humidity and refractivity. The low-wind MIBL was shallower and the gradients at its top were sharper than in the high-wind case, in agreement with the observations. Because it is also forced by land–sea contrasts, a sea-breeze circulation frequently occurs in association with the MIBL. The size, location, and internal structure of the sea-breeze circulation were realistically simulated. The gradients of temperature and humidity that bound the MIBL cause perturbations in the refractivity distribution that, in turn, lead to trapping layers and ducts. The existence, location, and surface character of the ducts were well captured. Horizontal variations in duct characteristics due to the sea-breeze circulation were also evident. The simulations successfully distinguished between high- and low-wind occasions, a notable feature of the SHAREM-115 observations. The modeled magnitudes of duct depth and strength, although leaving scope for improvement, were most encouraging.