Holonomicity of relative characters and applications to multiplicity bounds for spherical pairs

We prove that any relative character (a.k.a. spherical character) of any admissible representation of a real reductive group with respect to any pair of spherical subgroups is a holonomic distribution on the group. This implies that the restriction of the relative character to an open dense subset is given by an analytic function. The proof is based on an argument from algebraic geometry and thus implies also analogous results in the p-adic case. As an application, we give a short proof of some results of Kobayashi-Oshima and Kroetz-Schlichtkrull on boundedness and finiteness of multiplicities of irreducible representations in the space of functions on a spherical space. To deduce this application we prove the relative and quantitative analogs of the Bernstein–Kashiwara theorem, which states that the space of solutions of a holonomic system of differential equations in the space of distributions is finite-dimensional. We also deduce that, for every algebraic group \({{G}}\) defined over \(\mathbb {R}\), the space of \({{G(\mathbb {R})}}\)-equivariant distributions on the manifold of real points of any algebraic \({{G}}\)-manifold \({{X}}\) is finite-dimensional if \({{G}}\) has finitely many orbits on \({{X}}\).     

Investigation of interface properties by nanoscale elastic modulus mapping

We present a method for investigating the spatial changes of elastic moduli in a nm-scale vicinity of interfaces. The method is demonstrated on twin walls in PbTiO(3) single crystals. It is revealed that the region near the twin wall is significantly softer than the two domains surrounding it. A comparison with finite element simulations relates this effect to an anelastic relaxation due to point defect accumulation around the twin wall. Local softening around the twin wall can affect the overall elastic modulus in thin films and nanostructured ferroelectric materials, in which the average distance between twin walls is smaller than the thickness of the softer region.     

On the extension of polysoaps: The Gaussian approximation

Polysoaps are linear hydrophilic chains that incorporate, at intervals, covalently bound amphiphilic monomers. In water, the amphiphilic monomers self assemble into intrachain micelles thus endowing the chain with a secondary structure. The relaxation of the secondary structure upon deformation qualitatively modifies the elastic behaviour of polysoaps in accordance with the LeChatelier principle. For long polysoaps a regime in which the tension in the chain, f, is independent of the end to end distance R, f ˜ R° is predicted. The extension of long polysoaps is analysed for the particularly simple case when the backbone obeys Gaussian statistics and excluded volume interactions are neglected.     

Osmotic backwash mechanism of reverse osmosis membranes

A new osmotic backwash (BW) model for reverse osmosis (RO) membranes was developed for conditions of no applied pressures across the membrane. This analytical model has one adjustable parameter representing the coefficient of a linearized convection term in the general convection–diffusion equation. An experimental RO/BW system was used for 12 data sets to verify the proposed BW model and illustrate its predictability. Results show deviations of the model from the data within a range of 5–15%. The described dilution mechanism of the feed concentration polarization (CP) layer is based on RO originated concentrated layer detachment from the membrane surface followed by its gradual dilution.The understanding gained in this research may be applied to automatic RO/BW cleaning cycles. A dominant RO parameter of the BW process is the RO initial driving force—the concentration difference across the membrane. Other RO process parameters – applied pressure and feed flow rate – have lesser effects. Both theoretical and experimental methods provide quantitative relationships between RO and BW variables that enable an understanding and control of the BW process.     

N‐Glycosyl‐N′‐[p‐(isoamyloxy)phenyl]‐thiourea Derivatives: Potential Anti‐TB Therapeutic Agents

Thiocarlide (THC; N,N′‐bis[p‐(isoamyloxy)phenyl]‐thiourea; also known as Isoxyl^®) has been used in the past as an anti‐tuberculosis agent. In an effort to improve the therapeutic value of THC, several N‐glycosyl‐N′‐[p‐(isoamyloxy)phenyl]‐thiourea derivatives were synthesized by coupling an aniline derivative and glycosyl isothiocyanates. The minimum inhibitory concentration (MIC) values of the new products against M. tuberculosis were determined.     

Thermospray mass spectrometry of N-methylcarbamates

The thermospray mass spectrometry (TSP/MS) of five N-methylcarbamates is presented. This is the first time that ions other than [M + H]⁺ and [M + NH₄]⁺ have been reported using positive TSP/MS. Protonation of ROCONHCH₃ yields the [CH₃NH₂CO]^+· ion, with formation of the ion–molecule adduct [ROCONHCH₃ · CH₃NH₂CO]^+· through elimination of CO^+· from [CH₃NH₂CO]^+·, and the adduct [M + 75]^+·, [ROCONHCH₃ · OCONH₂CH₃]^+·, is also obtained.     

Stereoselective syntheses of heptaprenylphosphoryl β-d-arabino-and β-d-ribo-furanoses

The stereoselective syntheses of heptaprenylphosphoryl β-d-arabinofuranose and heptaprenylphosphoryl β-d-ribofuranose are described. In the synthesis of the d-arabino product, the stereoselectivity was achieved by the coupling of a suitably protected β-d-arabinofuranosyl phosphate intermediate with an activated form of heptaprenol and subsequent deprotection. In the case of the ribo-analog, the desired β-anomer could be obtained by the more convenient phosphoramidite method. The products were successfully employed in the mycobacterial epimerase assay.     

Serum Levels of 25‐Hydroxy‐Vitamin D3 Among Sun‐protected Outdoor Workers in Israel

The objective of this study was to evaluate the effect of reduced sun exposure of outdoor workers on vitamin D status using different modalities of sun protection, for primary prevention of skin cancer. 25‐OH‐D3 measurements were performed in two successive winters, 8 (interim) and 20 months after initiation of the study, in three groups of male outdoor workers, enrolled in either a complete, partial or minimal sun protection program. Ambient solar UVB radiation was monitored simultaneously. No intragroup or intergroup differences were observed between the interim‐ and postintervention measurements of mean 25‐OH‐D3, which were close to 30 ng mL^?1. Significant risk factors for postintervention 25‐OH‐D3 levels >33.8 ng mL^?1 (a surrogate for reduced sun protection) were: previous sunburn episodes (OR 2.5; 95% CI 1.01–6.3; P = 0.05) and younger age (OR 0.92; 95 CI 0.86–0.98; P = 0.009). Outdoor workers of Western, compared with those of Eastern paternal origin had a borderline significant risk (OR 2.4; 95% CI 0.9–6.3; P = 0.07). A borderline significant effect (OR 2.9; 95% CI 0.97–10.1; P = 0.085) was also noted for those in the minimal intervention group. In conclusion, sun protection among outdoor workers following a successful intervention did not suppress mean winter 25‐OH‐D3.