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.     

Synthesis and Characterization of Ligand-Linked Pt Nanoparticles: Tunable,Three-Dimensional,Porous Networks for Catalytic Hydrogen Sensing

Porous networks of Pt nanoparticles interlinked by bifunctional organic ligands have shown high potential as catalysts in micro-machined hydrogen gas sensors. By varying the ligand among p-phenylenediamine, benzidine, 4,4‘‘-diamino-p-terphenyl, 1,5-diaminonaphthalene, and trans-1,4-diaminocyclohexane, new variants of such networks were synthesized. Inter-particle distances within the networks, determined via transmission electron microscopy tomography, varied from 0.8 to 1.4 nm in accordance with the nominal length of the respective ligand. While stable structures with intact and coordinatively bonded diamines were formed with all ligands, aromatic diamines showed superior thermal stability. The networks exhibited mesoporous structures depending on ligand and synthesis strategy and performed well as catalysts in hydrogen gas microsensors. They demonstrate the possibility of deliberately tuning micro- and mesoporosity and thereby transport properties and steric demands by choice of the right ligand also for other applications in heterogeneous catalysis.     

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.     

Hydrodechlorination of Dichloromethane by a Metal-Free Triazole-Porphyrin Electrocatalyst: Demonstration of Main-Group Element Electrocatalysis**

In this work, the electrocatalytic reduction of dichloromethane (CH₂Cl₂) into hydrocarbons involving a main group element-based molecular triazole-porphyrin electrocatalyst H2PorT8 is reported. This catalyst converted CH₂Cl₂ in acetonitrile to various hydrocarbons (methane, ethane, and ethylene) with a Faradaic efficiency of 70 % and current density of −13 mA cm⁻² at a potential of −2.2 V vs. Fc/Fc⁺ using water as a proton source. The findings of this study and its mechanistic interpretations demonstrated that H2PorT8 was an efficient and stable catalyst for the hydrodechlorination of CH₂Cl₂ and that main group catalysts could be potentially used for exploring new catalytic reaction mechanisms.