Unique ergodicity of some flows related to axiom a diffeomorphisms

Continuous flows, whose orbits are the unstable manifolds of certain Axiom A attractors, are shown to be uniquely ergodic. The approach used is symbolic dynamics. Equicontinuity (and lack of it) for these flows is also discussed.     

Boundary value problems for nonuniformly elliptic equations with measurable coefficients

Summary Let A be a symmetric N × N real-matrix-valued function on a connected region in Rⁿ, with A positive definite a.e. and A, A⁻¹ locally integrable. Let b and c be locally integrable, non-negative, real-valued functions on Ω, with c positive a.e. Put a(u, v) = = ((A∇u, ∇v) + buv) dx. We consider in X the weak boundary value problem a(u, v) = = fvcdx, all v ε X; where X is a suitable Hilbert space contained in H _loc ^1,1 (Ω). Criteria are given in order that the Green's operator for this problem have an integral representation and bounded eigenfunctions; in addition, criteria for compactness are given. Entrata in Redazione il 21 giugno 1975. Research was partially supported by the National Science Foundation under Grant GP-28377A2.     

A Smart Access to the Dinitramide Anion – The Use of Dinitraminic Acid for the Preparation of Nitrogen-Rich Energetic Copper(II) Complexes

Dinitraminic acid (HN(NO₂)₂, HDN) was prepared by ion exchange chromatography and acid-base reaction with basic copper(II) carbonate allowed the in situ preparation of copper(II) dinitramide, which was reacted with twelve nitrogen-rich ligands, for example, 4-amino-1,2,4-triazole, 1-methyl-5H-tetrazole, di(5H-tetrazolyl)-methane/-ethane/-propane/-butane. Nine of the complexes were investigated by low-temperature X-ray diffraction. In addition, all compounds were investigated by infrared spectroscopy (IR), differential thermal analysis (DTA), elemental analysis (EA) and thermogravimetric analysis (TGA) for selected compounds. Furthermore, investigations of the materials were carried out regarding their sensitivity toward impact (IS), friction (FS), ball drop impact (BDIS) and electrostatic discharge (ESD). In addition, hot plate and hot needle tests were performed. Complex [Cu(AMT)₄(H₂O)](DN)₂, based on 1-amino-5-methyltetrazole (AMT), is most outstanding for its detonative behavior and thus also capable of initiating PETN in classical initiation experiments. Laser ignition experiments at a wavelength of 915 nm were performed for all substances and solid-state UV-Vis spectra were recorded to apprehend the ignition mechanism.     

Development and validation of a rapid RP‐HPLC method for analysis of (−)‐copalic acid in copaíba oleoresin

The Copaifera species (Leguminoseae) are popularly known as ‘copaíba’ or ‘copaíva’ and are grown in the states of Amazonas, Pará and Ceará in northern Brazil. The oleoresins obtained from these species have been extensively used owing to their pharmacological potential and their application in cosmetic and pharmaceutical preparations. In the present study, the development and validation of a novel, rapid and efficient RP‐HPLC methodology for the analysis of the diterpene (?)‐copalic acid (CA), pointed out as the only chemical marker of the Copaifera genus, are described. The regression equation (Y = 26,707x ? 29,498) was obtained with good linearity (r² = 0.9993) and the limits of quantification and detection were 9.182 and 3.032 µg/mL, respectively. The precision and the accuracy of the method were adequate (lower than 4%). Finally, the validation parameters evaluated were satisfactorily met, so the developed method represents a suitable tool for application in the quality control of such natural products. Further studies aiming to develop analytical methodologies for each Copaifera species using a more representative number of chemical markers should be performed. Copyright © 2012 John Wiley & Sons, Ltd.