Some Results on Stability of Retarded Functional Differential Equations Using Dichotomic Map Techniques

This paper deals with the study of the stability of nonautonomous retarded functional differential equations using the theory of dichotomic maps. After some preliminaries, we prove the theorems on simple and asymptotic stability. Some examples are given to illustrate the application of the method. Main results about asymptotic stability of the equation and of itsnonlinear generalization are established.     

The rate function of hypoelliptic diffusions

Let be a hypoelliptic diffusion operator on a compact manifold M. Given an a priori smooth reference measure λ on M, we can then rewrite L as the sum of a λ-symmetric part L⁰ and a first-order drift part Y. The paper investigates the effect of the drift Y on the Donsker-Varadhan rate function corresponding to the large deviations of the empirical measure of the diffusion. When Y is in the linear span of the first and second-order Lie brackets of the X_i's, we derive an affine bound relating the rate functions associated with L and L⁰. As soon as one point exists where Y is not in the linear span of the first and second-order Lie brackets of the X_i's, we show that such an affine bound is impossible. © 1994 John Wiley & Sons, Inc.     

Determination of 1,4-dioxane impurity levels in Triton X-100 raw material by gas chromatography with mass spectrometric detection

Triton X-100 (octoxynol 9) is a commercially available surfactant used as a solvent detergent in numerous pharmaceutical applications including virus inactivation. A byproduct formed during its synthesis is 1,4-dioxane, the cyclic dimer of ethylene oxide and a possible carcinogen to humans. The United States Pharmacopoeia (USP) contains a labor-intensive 1,4-dioxane test for Triton X-100. The method couples vacuum distillation to extract the 1,4-dioxane from the Triton X-100 matrix followed by gas chromatography (GC) using a packed column with flame-ionization detection. In order to provide a more automated and specific test methodology, a headspace GC-mass spectrometry (MS) method has been developed for this application. Analyte quantitation is accomplished by the method of standard additions. The automated sample preparation, coupled with the specificity inherent in high-efficiency capillary column separations together with single-ion MS detection, results in an assay that is more efficient, accurate, and precise than the USP procedure. Performance characteristics of the headspace GC-MS method are contrasted with those characteristics of the USP methodology.     

The oxygen-rich carboxide series: COn (n = 3, 4, 5, 6, 7, or 8)

The lowest-energy isomers of the high-order carboxide series, COn (n = 3-8), have been elucidated via ab initio quantum chemical calculations. The structures of the lowest order of these (3 and 4) are in close agreement with previous calculations and with experimental data. The structures of the higher-order species are elucidated and correlated to the previous structures, showing similarities in structure and reactivity pathways. The reaction energies of the formation of all products are shown to be related. Exothermic pathways of formation often involve a C2v form of CO2, which was shown to be metastable. The newly identified species could be intermediates in atmospheric reactions. The calculated vibrational frequencies and IR intensities may be used to identify these metastable species.     

Synthesis and application in asymmetric C-C bond formation of solution phase ligand libraries of monodentate phosphoramidites

A library of 96 unique monodentate phosphoramidite ligands has been synthesized in solution and used in the asymmetric conjugate addition of potassium vinyltrifluoroborate to enones resulting in up to 88% ee.     

Constant transformation rate thermal analysis of HGdP<Subscript>2</Subscript>O<Subscript>7</Subscript>·3H<Subscript>2</Subscript>O

Summary The aim of this work is the optimization of the preparation of anhydrous gadolinium hydrogen phosphate with good fluorescence properties. The products obtained by dehydration of gadolinium hydrogen phosphate trihydrate depend on the conditions chosen for the thermal treatment. For this reason, the dehydration was followed by Constant Rate Thermal Analysis whilst strictly controlling the water vapour pressure above the sample. Intermediate samples, obtained during dehydration were characterised by IR spectroscopy and X-ray diffraction. It has thus been shown that the thermal pathway taken for the dehydration depends on the water vapour pressure above the sample in the region from 10^-2to 5 mbar. Under the lowest water vapour pressure (5·10^-3mbar), the elimination of the crystallization water is carried out in a continuous way and produces a quasi-amorphous intermediate. Under higher water vapour pressure (5 mbar), well crystallized intermediate products are obtained. The results obtained suggest that the trihydrate contains zeolitic water which confirms a prior structural study.     

Immunochemical-based method for detection of hazelnut proteins in processed foods

A competitive enzyme-linked immunosorbent assay (ELISA) was developed to detect hazelnut by using polyclonal antibodies generated against a protein extract of roasted hazelnut. No cross-reactivity was observed in tests against 39 commodities, including many common allergens, tree nuts, and legumes. Hazelnut protein standard solutions at 0.45 ng/mL [inhibition concentration (IC80) of the competitive test] were clearly identified by the ELISA. An extraction and quantification method was developed and optimized for chocolate, cookies, breakfast cereals, and ice cream, major food commodities likely to be cross-contaminated with undeclared hazelnut during food processing. No sample cleanup was required when extracts were diluted 10-fold. Recovery results were generated with blank matrixes spiked at 4 levels from 1 to 10 microg/g hazelnut protein. With the developed extraction and sample handling procedure, hazelnut proteins were recovered at 64-83% from chocolate and at 78-97% from other matrixes. A confirmatory technique was developed with sodium dodecyl sulfate-polyacrylamide gel electrophoresis and Western transfer. The developed methods were applied to a small market survey of chocolate products and allowed the identification of undeclared hazelnut in these products.     

Crystal structure and thermal study of the new hydrated cadmium-cerium(III) chloride CeCd4Cl11·13H2O

The new double-salt CeCd₄Cl₁₁·13H₂O in the ternary system CeCl₃-CdCl₂-H₂O has been prepared from aqueous solution upon evaporation at 5°C and characterized based on elemental analysis, spectroscopic data, thermal studies and X-ray powder and single-crystal diffraction. CeCd₄Cl₁₁·13H₂O crystallizes in the monoclinic space group P2₁ with a=7.667(2), b=17.351(3), c=11.970(2)Å, β=101.61(3)° and Z=2. After refinement of the structure the reliability factor R in the final cycle is 0.064. The structure can be regarded as consisting of endless double chains of CdCl₆ and CdOCl₅ octahedra and isolated tricapped triangular prisms surrounding the cerium cations. Differential scanning calorimetry showed that the title compound exhibits five endothermic anomalies interpreted from thermogravimetry. A comparison with the structure of SrCd₂Cl₆·8H₂O is proposed.     

First examples of improved catalytic asymmetric C-C bond formation using the monodentate ligand combination approach

[reaction: see text] Using a combination of chiral monodentate phosphoramidite ligands in the rhodium-catalyzed conjugate addition of boronic acids to three different substrates, we have shown for the first time that the ligand combination approach is applicable for C-C bond formation. Chiral catalysts based on hetero-combinations of ligands are found to be more effective than the homo-combinations. (31)P NMR experiments show that the hetero-combinations are formed in excess over the homo-combinations.