Rigorous computation of smooth branches of equilibria for the three dimensional Cahn–Hilliard equation

In this paper, we propose a new general method to compute rigorously global smooth branches of equilibria of higher-dimensional partial differential equations. The theoretical framework is based on a combination of the theory introduced in Global smooth solution curves using rigorous branch following (van den Berg et al., Math. Comput. 79(271):1565–1584, 2010) and in Analytic estimates and rigorous continuation for equilibria of higher-dimensional PDEs (Gameiro and Lessard, J. Diff. Equ. 249(9):2237–2268, 2010). Using this method, one can obtain proofs of existence of global smooth solution curves of equilibria for large (continuous) parameter ranges and about local uniqueness of the solutions on the curve. As an application, we compute several smooth branches of equilibria for the three-dimensional Cahn–Hilliard equation.     

High fidelity neuronal networks formed by plasma masking with a bilayer membrane: analysis of neurodegenerative and neuroprotective processes

Spatially defined neuronal networks have great potential to be used in a wide spectrum of neurobiology assays. We present an original technique for the precise and reproducible formation of neuronal networks. A PDMS membrane comprising through-holes aligned with interconnecting microchannels was used during oxygen plasma etching to dry mask a protein rejecting poly(ethylene glycol) (PEG) adlayer. Patterns were faithfully replicated to produce an oxidized interconnected array pattern which supported protein adsorption. Differentiated human SH-SY5Y neuron-like cells adhered to the array nodes with the micron-scale interconnecting tracks guiding neurite outgrowth to produce neuronal connections and establish a network. A 2.0 μm track width was optimal for high-level network formation and node compliance. These spatially standardized neuronal networks were used to analyse the dynamics of acrylamide-induced neurite degeneration and the protective effects of co-treatment with calpeptin or brain derived neurotrophic factor (BDNF).     

First total synthesis of (−)-8-epi-9-deoxygoniopypyrone

The structure and absolute configuration of natural 8-epi-9-deoxygoniopypyrone have been confirmed by an efficient and highly diastereoselective synthesis in 15 steps from (S)-mandelic acid with an overall yield of 43%.     

Cytotoxic Agents in the Treatment of Laryngeal Sarcoidosis: A Case Report and Review of the Literature

SUMMARY: Sarcoidosis is a multisystem disease with various clinical manifestations. It is characterized primarily on a histopathologic basis by the presence of noncaseating granulomata. Laryngeal involvement reportedly occurs in 3-5% of cases, and it is typically localized to the supraglottic region. Patients often present with hoarseness, dysphagia, stridor, or dyspnea. Laryngoscopy typically demonstrates a pale, edematous epiglottis studded with nodules. Tissue biopsy reveals the classic noncaseating granuloma; however, the finding is not diagnostic. Sarcoidosis remains a diagnosis of exclusion to be entertained once other verifiable etiologies for granulomatous disease of the larynx, such as TB, syphilis, fungal infection, berylliosis, or Wegener's granulomatosis, have been ruled out. Systemic corticosteroids remain the mainstay of treatment; however, new steroid-sparing therapies that target the inflammatory response of sarcoidosis are currently being investigated. The case history of a patient with laryngeal sarcoidosis who was managed with the immunosuppressant azathioprine (Imuran) is summarized along with a discussion of other treatment options.     

Conservation laws for cosmological perturbations

We briefly recall the problem of defining conserved quantities such as energy in general relativity, and the solution given by introducing a symmetric background. We apply the general formalism to perturbed Robertson-Walker spacetimes with de Sitter geometry as background. We relate the obtained conserved quantities to Traschen's integral constraints and mention a few applications in cosmology.     

A Discrete Phenomenon in the C and Analytic Regularity of the Blow-Up Curve of Solutions to the Liouville Equation in One Space Dimension

We give a complete discussion of the C^∞ or analytic regularity of blow-up curves for Cauchy problems or some mixed problems for the Liouville equation in one space dimension. In the case of mixed problems, the regularity results depend on the boundary condition: actually, we show the existence of a sequence of boundary conditions for which the regularity of the blow-up curve is better than in the general case.     

Simultaneous analysis of 13C‐glutathione as its dimeric form GSSG and its precursor [1‐13C]glycine using liquid chromatography/isotope ratio mass spectrometry

Determination of glutathione kinetics using stable isotopes requires accurate measurement of the tracers and tracees. Previously, the precursor and synthesized product were measured with two separate techniques, liquid chromatography/isotope ratio mass spectrometry (LC/IRMS) and gas chromatography/combustion/isotope ratio mass spectrometry (GC/C/IRMS). In order to reduce sample volume and minimize analytical effort we developed a method to simultaneously determine ¹³C‐glutathione as its dimeric form (GSSG) and its precursor [1‐¹³C]glycine in a small volume of erythrocytes in one single analysis. After having transformed ¹³C‐glutathione into its dimeric form GSSG, we determined both the intra‐erythrocytic concentrations and the ¹³C‐isotopic enrichment of GSSG and glycine in 150 µL of whole blood using liquid chromatography coupled to LC/IRMS. The results show that the concentration (range of µmol/mL) was reliably measured using cycloleucine as internal standard, i.e. with a precision better than 0.1 µmol/mL. The ¹³C‐isotopic enrichment of GSSG and glycine measured in the same run gave reliable values with excellent precision (standard deviation (sd) <0.3‰) and accuracy (measured between 0 and 5 APE). This novel method opens up a variety of kinetic studies with relatively low dose administration of tracers, reducing the total cost of the study design. In addition, only a minimal sample volume is required, enabling studies even in very small subjects, such as preterm infants. Copyright © 2009 John Wiley & Sons, Ltd.     

Synthese et isomerisation de methoxycarbonyl-5 dihydropyrannones-2

Condensation of dimethyl 3-methylglutaconate with ketones provides a one pot route for the preparation of 5-methoxycarbonyl-4-methyldihydropyran-2-ones. The experimental conditions to give selectively pyran-2-ones isomers are discussed. The structure of the different products was established on the basis of ¹H and ¹³C nmr spectral data.     

Are defect models consistent with the entropy and specific heat of glass formers?

We show that pointlike defect model of glasses cannot explain the thermodynamic properties of glass formers, as for example, the excess specific heat close to the glass transition, contrary to the claim of Garrahan and Chandler [Proc. Natl. Acad. Sci. U.S.A. 100, 9710 (2003)]. More general models and approaches in terms of extended defects are also discussed.