The Helmholtz–Weyl decomposition in weighted Sobolev spaces

Let f∈L_{2, ? µ}(?³), where where x = (x₁, x₂, x₃) is the Cartesian system in ?³, x′ = (x₁, x₂), , µ∈?₊\?. We prove the decomposition f = ? ?u + g, with g divergence free and u is a solution to the problem in ?³ Given f∈L_{2, ? µ}(?³) we show the existence of u∈H(?³) such that where Since f, u, g are defined in ?³ we need a sufficiently fast decay of these functions as |x|→∞. Copyright © 2010 John Wiley & Sons, Ltd.     

A multifaceted approach to hydrogen storage

The widespread adoption of hydrogen as an energy carrier could bring significant benefits, but only if a number of currently intractable problems can be overcome. Not the least of these is the problem of storage, particularly when aimed at use onboard light-vehicles. The aim of this overview is to look in depth at a number of areas linked by the recently concluded HYDROGEN research network, representing an intentionally multi-faceted selection with the goal of advancing the field on a number of fronts simultaneously. For the general reader we provide a concise outline of the main approaches to storing hydrogen before moving on to detailed reviews of recent research in the solid chemical storage of hydrogen, and so provide an entry point for the interested reader on these diverse topics. The subjects covered include: the mechanisms of Ti catalysis in alanates; the kinetics of the borohydrides and the resulting limitations; novel transition metal catalysts for use with complex hydrides; less common borohydrides; protic-hydridic stores; metal ammines and novel approaches to nano-confined metal hydrides.     

Scanning electrochemical microscopy in the 21st century. Update 1: Five years after

This Perspective is an update to our more extensive survey of scanning electrochemical microscopy (SECM) published in 2007. During this time, the SECM field retained its momentum by expanding into new areas and meeting the emerging scientific and technological challenges. Here we focus on most prominent developments such as high-resolution imaging, investigation of structures and processes on the nanoscale, alternative energy applications, and new approaches to solving "real world" problems. The fabrication of novel SECM probes and related theoretical advances are also discussed.     

Phase transition induced improvement in H2 desorption kinetics: the case of the high-temperature form of Y(BH4)3

The high-temperature (HT) phase of Y(BH(4))(3) has been prepared by heating of the as mechanochemically synthesised low-temperature (LT) phase of Y(BH(4))(3) to 194-216 °C and subsequent rapid cooling to ambient temperature. Although the differences in the crystal structure and vibrational spectra for these closely-related polymorphs are rather small, yet the NMR MAS (1)H and CP MAS (89)Y spectra reveal clear differences in the chemical shifts for both nuclei. The thermal decomposition process of both forms differs noticeably below 260 °C, decomposition being faster and more facile for the HT phase. The activation energy for thermal decomposition, calculated according to the Kissinger equation, is nearly three times lower for the HT than for the LT polymorph for the first step of the thermal decomposition signalling giant improvement of kinetics of H(2) desorption.     

Molecular clusters in aqueous solutions of pyridine and its methyl derivatives

Small-angle neutron scattering proved that molecules in aqueous solutions of pyridine, 2-methylpyridine and 2,6-dimethylpyridine form clusters. The clusters are dynamic aggregates consisting of hydrogen-bonded water-amine complexes. Strengthening of the hydrogen bonds between water and amine molecules due to the methyl groups in the ortho position in the pyridine ring makes the structures more stable, as was evidenced by relatively long times of the structural relaxation. The strong intermolecular forces affect the thermal expansion of the systems. No aggregates similar to those in aqueous systems are present in the methanolic ones. That points to the crucial role of water in the molecular clustering. A molecule of methanol, although capable of hydrogen bonding with the amines, cannot participate in larger structures because of the lack of protons that could form the enhanced network. Thus, even if the amine-methanol complexes occur, they are incapable of further association. It was shown that the co-operative nature of hydrogen bonds and the propensity of water to association are the main factors that determine the properties of aqueous systems.     

Complexation of [2.2]paracyclophane with β- and γ-cyclodextrins studied by HPLC and NMR

The NMR spectra of [2.2]paracyclophane with β- or γ-cyclodextrin in DMF-d₇ at room temperature do not show significant complexation, while HPLC of the complexes in mixed H₂O:alcohol solvents demonstrate complexation with different stoichiometries. At 243 K in DMF solution the H3 and H5 NMR signals of γ-cyclodextrin (but not β) exhibit complexation-induced chemical shifts denoting complex formation. According to HPLC, at room temperature the [2.2]paracyclophane complex with β-cyclodextrin in 20% H₂O:EtOH exhibits 1:2 stoichiometry with K ₁ = 1×10² ± 2, K ₂ = 9.0×10⁴ ± 2×10³ (K = 9×10⁶) while that with γ-cyclodextrin in 50% H₂O:MeOH exhibits 1:1 stoichiometry with K ₁ = 4×10³ ± 150 M⁻¹. Thermodynamic parameters for both complexes have been estimated from the retention time temperature dependence. For the β-cyclodextrin complexation at 25°C ΔG ⁰ _CD is −39.7 kJ mol⁻¹ while ΔH ⁰ _CD and ΔS ⁰ _CD are −88.2 kJ mol⁻¹ and −0.16 kJ mol⁻¹ K⁻¹. For γ-cyclodextrin, the corresponding values are ΔG ⁰ _CD = −20.5 kJ mol⁻¹, ΔH ⁰ _CD = −33.5 kJ mol⁻¹ and ΔS ⁰ _CD = −0.04 kJ mol⁻¹ K⁻¹.      

Asymmetry and structural information in preferential attachment graphs

Graph symmetries intervene in diverse applications, from enumeration, to graph structure compression, to the discovery of graph dynamics (e.g., node arrival order inference). Whereas Erd?s‐Rényi graphs are typically asymmetric, real networks are highly symmetric. So a natural question is whether preferential attachment graphs, where in each step a new node with m edges is added, exhibit any symmetry. In recent work it was proved that preferential attachment graphs are symmetric for m = 1, and there is some nonnegligible probability of symmetry for m = 2. It was conjectured that these graphs are asymmetric when m ≥ 3. We settle this conjecture in the affirmative, then use it to estimate the structural entropy of the model. To do this, we also give bounds on the number of ways that the given graph structure could have arisen by preferential attachment. These results have further implications for information theoretic problems of interest on preferential attachment graphs.     

The Occurrence and Biological Activity of Tormentic Acid—A Review

This review focuses on the natural sources and pharmacological activity of tormentic acid (TA; 2α,3β,19α-trihydroxyurs-2-en-28-oic acid). The current knowledge of its occurrence in various plant species and families is summarized. Biological activity (e.g., anti-inflammatory, antidiabetic, antihyperlipidemic, hepatoprotective, cardioprotective, neuroprotective, anti-cancer, anti-osteoarthritic, antinociceptive, antioxidative, anti-melanogenic, cytotoxic, antimicrobial, and antiparasitic) confirmed in in vitro and in vivo studies is compiled and described. Biochemical mechanisms affected by TA are indicated. Moreover, issues related to the biotechnological methods of production, effective eluents, and TA derivatives are presented.     

Equation of state of CaMnO3: a combined experimental and computational study

Elastic properties of CaMnO₃ are of primary importance in the science and technology of CaMnO₃-based perovskites. From X-ray diffraction experiments performed at pressures up to 100 kbar using a diamond-anvil cell to hydrostatically compress our sample, a bulk modulus, K ₀, of 1734(96) kbar was obtained after fitting parameters to the third-order Birch–Murnaghan equation of state. Mean field, semiclassical simulations predict, for the first time, the third-order equation-of-state parameters and show how the bulk modulus increases with pressure (the zero pressure value being 2062.1 kbar) and decreases with the extent of nonstoichiometry caused by the formation of oxygen vacancies. These trends are amplified for the shear modulus. A more accurate model that allows for the explicit reduction of Mn ions, or localization of excess electrons, yields qualitatively similar results. The experimental and calculated axial ratios show the same trends in their variation with rising pressure.