Spectral Estimates for Degenerate Critical Levels

We establish spectral estimates at a critical energy level for h-pseudo-differential operators. Via a trace formula, we compute the contribution of isolated (nonextremum) critical points under a condition of "real principal type." The main result holds for all dimensions, for a singularity of any finite order and can be invariantly expressed in terms of the geometry of the singularity. When the singularities are not integrable on the energy surface the results are significative since the order w.r.t. h of the spectral distributions are bigger than in the regular setting.     

Spectral Fluctuations of Schrödinger Operators Generated by Critical Points of the Potential

Starting from the spectrum of Schrödinger operators on ${\mathbb R}^nStarting from the spectrum of Schr?dinger operators on , we propose a method to detect critical points of the potential. We argue semi-classically on the basis of a mathematically rigorous version of Gutzwiller's trace formula which expresses spectral statistics in term of classical orbits. A critical point of the potential with zero momentum is an equilibrium of the flow and generates certain singularities in the spectrum. Via sharp spectral estimates, this fluctuation indicates the presence of a critical point and allows to reconstruct partially the local shape of the potential. Some generalizations of this approach are also proposed.     

Quantitative colorimetric analysis of aloe polysaccharides as a measure of Aloe vera quality in commercial products

Aloe vera inner leaf gel has been used as a medicinal remedy for many years. Yet some aloe products do not demonstrate beneficial effects, indicating that poor quality products are reaching the market. Therefore, an efficient and accurate method is needed to evaluate the quality of aloe products. This paper describes a quick, quantitative colorimetric assay that has been developed for the determination of glucomannan in aloe gel and products. With this method, interference by non-aloe polysaccharides or other extraneous components was absent or negligible. Data indicate that the glucomannan can be determined at parts per million (mg/L) in aqueous solutions with an accuracy of 100 +/- 5% at a 10 mg/L concentration. The correlation coefficient is 0.999, and linearity is from 0.9 to 72.7 mg/L in the test solution. The method is inexpensive, simple, sensitive, and reproducible. This method was applied to determine the polysaccharide content of commercial aloe products. Both qualitative and quantitative information can be obtained in about 5 min.     

Hepcidin in iron metabolism

Hepcidin, which has been recently identified both by biochemical and genomic approaches, is a 25 amino acid polypeptide synthesized mainly by hepatocytes and secreted into the plasma. Besides its potential activity in antimicrobial defense, hepcidin plays a major role in iron metabolism. It controls two key steps of iron bioavailability, likely through a hormonal action: digestive iron absorption by enterocytes and iron recycling by macrophages. In humans, this could explain that low levels of hepcidin found during juvenile haemochromatosis and HFE-1 genetic haemochromatosis are associated with an iron overload phenotype. Conversely, an increase of hepcidin expression is suspected to play a major role in the development of anemia of chronic inflammatory diseases. However, the regulatory mechanisms of hepcidin expression are multiple, including iron-related parameters, anemia, hypoxia, inflammation and hepatocyte function. Therefore, many physiological and pathological situations may modulate hepcidin expression and subsequently iron metabolism. A better knowledge of the biological effects of hepcidin and of its expression regulatory mechanisms will clarify the place of hepcidin in the diagnosis and treatment of iron-related diseases.     

Crystal chemistry and thermal behavior of metal salts and complexes of unsaturated dicarboxylic acids: aquabis(hydrogen itaconato)barium(II), [Ba(C5H5O4)2(OH2)]

[Ba(C₅H₅O₄)₂(OH₂)] is monoclinic, C2/c, with a = 4.472(1), b = 13.312(3), c = 22.236(5) Å, = 92.90(1)°, Z = 4, and D _m = 2.06 g cm^–3. The barium atom is 10-coordinate with Ba—O distances in the range 2.749(2)–2.989(2) Å. The material suffers a complex decomposition process upon heating at temperatures between 25 and 600°C in dynamic nitrogen and static air atmospheres. FT-IR and gas chromatography analyses indicate that water, CO, CO₂, methane, ethane, ethylene, propane, propylene, and butane, are evolved during the heating process, leaving a residue of BaCO₃. ¹H-NMR spectra of a sample heated at 200°C, showed isomerization of barium itaconate to barium methylmaleate.     

New flux systems for the LPE growth of thin garnet films

A new flux system is presented for the growth of bismuth substituted iron garnet thin films by liquid phase epitaxy. The fluxes do not contain lead and are based on the system Bi₂O₃, RO₂ where R = Si, Ge, Ti or Ce. Data is presented that shows the viscosities of these melts are below 16 cp at temperatures ∽800°C when the eutectic compositions are chosen and that they have low freezing points. The growth conditions and melt compositions are given for the growth of various rare-earth iron garnets with high bismuth substitutions. Results of measurements of optical and magnetic properties of some of the from Pb containing fluxes. Thus these materials are more promising for use in magnetic bubble displays. It is also shown that the uniaxial anisotropy was also less in the films grown from the new system than those grown from Pb containing fluxes.     

Crystal structure of triaquamaleatostrontium(II) monohydrate, [Sr(C4H2O4)(OH2)3]·H2O

[Sr(C₄H₂O₄)(OH₂)₃]·H₂O is monoclinic, P2₁/n, witha=11.476(2),b=7.027(1),c=12.344(2) Å, =115.74(3)°,V=896.67 ų,Z=4. The Sr atom is surrounded by nine oxygen atoms which come from four different maleate anions and three water molecules. The Sr–O distances range from 2.546(2) to 2.808(2) Å. The C–O distances are equal within the standard deviation 1.263(3) to 1.258(3) Å). In the maleate anion, the planes that contain the carboxylate groups form an angle of 74.44(9)°. Both carboxylate groups deviate significantly from planarity. The different coordination modes of the carboxylate group and the extensive hydrogen bonding present are responsible for the polymeric nature of the structure.     

Active control of strong plasmon–exciton coupling in biomimetic pigment–polymer antenna complexes grown by surface-initiated polymerisation from gold nanostructures

Plexcitonic antenna complexes, inspired by photosynthetic light-harvesting complexes, are formed by attachment of chlorophylls (Chl) to poly(cysteine methacrylate) (PCysMA) scaffolds grown by atom-transfer radical polymerisation from gold nanostructure arrays. In these pigment–polymer antenna complexes, localised surface plasmon resonances on gold nanostructures are strongly coupled to Chl excitons, yielding hybrid light–matter states (plexcitons) that are manifested in splitting of the plasmon band. Modelling of the extinction spectra of these systems using a simple coupled oscillator model indicates that their coupling energies are up to twice as large as those measured for LHCs from plants and bacteria. Coupling energies are correlated with the exciton density in the grafted polymer layer, consistent with the collective nature of strong plasmon–exciton coupling. Steric hindrance in fully-dense PCysMA brushes limits binding of bulky chlorophylls, but the chlorophyll concentration can be increased to ∼2 M, exceeding that in biological light-harvesting complexes, by controlling the grafting density and polymerisation time. Moreover, synthetic plexcitonic antenna complexes display pH- and temperature-responsiveness, facilitating active control of plasmon–exciton coupling. Because of the wide range of compatible polymer chemistries and the mild reaction conditions, plexcitonic antenna complexes may offer a versatile route to programmable molecular photonic materials.

Excitons in pigment–polymer antenna complexes formed by attachment of chlorophyll to surface grafted polymers are coupled strongly to plasmon modes, with coupling energies twice those for biological light-harvesting complexes and active control of plasmon–exciton coupling.     

Integral inequalities for the fundamental solutions of diffusions on manifolds with divergence-free drift

The main purpose of this article is to present uniform integral inequalities for the fundamental solutions of diffusions on compact manifolds with divergence free drift vector fields. The method relies on the fact that the heat flow depends on the isoperimetric function. The isoperimetric function is used to construct a suitable comparison manifold. The heat kernel of this comparison manifold gives uniform bounds for the fundamental solutions of the original diffusion problem. The results presented here can be used to solve some open problem of Bhattacharya and Götze about diffusions with periodic, divergence free drift vector fields (see [Bhagöt1] and [Bhagöt2]). Mathematics Subject Classification (2000): 58J35, 47D07This research was supported by the German Exchange Service DAAD     

Channel waveguides in Ca4GdO(BO3)3 fabricated by He+ implantation for blue-light generation

Blue light at 405 nm is generated by frequency doubling of a Ti:sapphire tunable laser in He(+)-implanted channel waveguides in gadolinium calcium oxoborate crystal. A conversion efficiency of approximately 2% W(-1) cm(-2) is achieved between TM00 fundamental and TE01 harmonic modes.