Multi-Fractal Formalism for Quasi-Self-Similar Functions

The study of multi-fractal functions has proved important in several domains of physics. Some physical phenomena such as fully developed turbulence or diffusion limited aggregates seem to exhibit some sort of self-similarity. The validity of the multi-fractal formalism has been proved to be valid for self-similar functions. But, multi-fractals encountered in physics or image processing are not exactly self-similar. For this reason, we extend the validity of the multi-fractal formalism for a class of some non-self-similar functions. Our functions are written as the superposition of similar structures at different scales, reminiscent of some possible modelization of turbulence or cascade models. Their expressions look also like wavelet decompositions. For the computation of their spectrum of singularities, it is unknown how to construct Gibbs measures. However, it suffices to use measures constructed according the Frostman's method. Besides, we compute the box dimension of the graphs.     

Synthesis and crystal structure of a new lithium cyclohexaphosphate hydrate: Li6P6O18·10H2O

The synthesis and crystal structure of a novel hydrate of lithium cyclohexaphosphate are reported. Li₆P₆O₁₈·10H₂O crystallizes in the space group C2/c with a = 15.113(5), b = 12.006(2), c = 15.892(2) Å, = 122.85(2)°, and Z = 4. The structure consists of P₆O₁₈ ring layers stacked along the c direction in between which are located the lithiumions and water molecules. Two LiO₄ tetrahedra share common edges with LiO₅ pseudosquare pyramids to form two independant Li₃O₉ units. About 50% of the water molecules have fractional occupancy rates and form fragments of molecules. A linear relationship is established between the relative cell volume V/Z and the hydration degree, n, for all the known hydrates: Li₆P₆O₁₈·nH₂O.     

Design and development of a fiber-optic immunosensor utilizing near-infrared fluorophores

The design and application of a fluorescent fiber-optic immunosensor (FFOI) are reported. The FFOI is utilized for the detection of antibody/antigen binding within the near-infrared (NIR) spectral region. The technique is developed through the combined use of fiber-optic, semiconductor laser-excitation, fluorescence detection, NIR dye, and immunochemical techniques. The antibody is immobilized on the FFOI and utilized as a recognition component for trace amounts of specific antigen. The FFOI is constructed to utilize an antibody sandwich technique. The assay involves the immobilization of the capture antibody on the sensing tip of the FFOI followed by the exposure of the immobilized sensing tip to the antigen. The antigen-coated FFOI is then introduced to a second antibody previously labeled with the NIR dye. Typical measurements are performed in about 15 min. A semiconductor laser provides the excitation (780 nm) of the immune complex. The resulting emission is detected by a silicon photodiode detector (820 nm). The intensity of the resulting fluorescence is directly proportional to the concentration of the antigen. The sensitivity of the analysis reaches 10 ng/ml and the response time is 10–15 min.     

Development of the analytical methods and reference materials program for dietary supplements at the National Institutes of Health

The need for validated analytical methods and reference materials to identify and measure constituents in dietary supplements is essential. Such methods allow for the documentation that products meet manufacturer's specifications and contain what their labels declare. In March 2003, the U.S. Food and Drug Administration issued a proposed rule that would establish specific current good manufacturing practices for dietary supplements. This proposed rule requires that companies create a quality control unit to set specifications and ensure compliance with these specifications using scientifically valid procedures. This report provides insights and lessons learned from 3 meetings the Office of Dietary Supplements (ODS) at the National Institutes of Health helped organize. These meetings were structured to (1) educate individuals about the importance and need for validated analytical methods and reference materials to identify and quantify constituents of dietary supplements; (2) identify resources required to fulfill this need; and (3) serve as a platform to obtain input from interested parties to help frame the research agenda for the Dietary Supplements Methods and Reference Materials Program within ODS. Stakeholder's opinions and views expressed at these 3 meetings are outlined in this report.     

A Calculation of the Culler-shalen Seminorms Associated to Small Seifert Dehn Fillings

We determine the relationship between the multiplicities ofthe zeros of certain rational functions defined on the SL₂(C)and PSL₂C character varieties of knot exteriors. This leadsto a formula for the Culler–Shalen seminorms associatedto small Seifert Dehn fillings of such manifolds. 2000 MathematicsSubject Classification: 57M05, 57M27, 57R65.     

Novel long chain unsaturated diisocyanate from fatty acid: Synthesis,characterization, and application in bio‐based polyurethane

A novel long chain linear unsaturated terminal diisocyanate, 1,16‐diisocyanatohexadec‐8‐ene (HDEDI) was synthesized from oleic acid via Curtius rearrangement. Its chemical structure was identified by FTIR, ¹H NMR, ¹³C NMR, and HRMS. This diisocyanate was used as a starting material for the preparation of entirely bio‐based polyurethanes (PUs) by reacting it with canola diol and canola polyol, respectively. The physical properties and crystalline structure of the PUs prepared from this diisocyanate were compared to their counterparts prepared from similar fatty acid‐derived diisocyanate, 1,7‐heptamethylene diisocyanate (HPMDI). The HDEDI based PUs demonstrated various different properties compared to those of HPMDI based PUs. For example, HDEDI based PUs exhibited a triclinic crystal form; whereas HPMDI based PUs exhibited a hexagonal crystal lattice. In addition, canola polyol‐HDEDI PU demonstrated a higher tensile strength at break than that of canola polyol‐HPMDI, attributed to the higher degree of hydrogen bonding associated with the former sample. Nevertheless, lower Young's modulus and higher elongation in canola polyol‐HDEDI PU were obtained because of the flexibility of the long chain introduced by the HDEDI diisocyanate. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 3302–3310, 2010