Global existence of solutions for a nonlinearly perturbed Keller–Segel system in \mathbbR2{\mathbb{R}}^2

We show the global existence of small solution to the perturbed Keller–Segel system of simplified version. Our system has a perturbed nonlinear term of worse sign, therefore the existence and uniqueness of solution is not really obvious. The local existence theorem is obtained by a variational observation for the elliptic part.     

Global existence of solutions for a nonlinearly perturbed Keller–Segel system in {\mathbb{R}}^2

We show the global existence of small solution to the perturbed Keller–Segel system of simplified version. Our system has a perturbed nonlinear term of worse sign, therefore the existence and uniqueness of solution is not really obvious. The local existence theorem is obtained by a variational observation for the elliptic part.      

Singularities of lightcone Gauss images of spacelike hypersurfaces in de Sitter space

We define the notions of lightcone Gauss images of spacelike hypersurfaces in de Sitter space. We investigate the relationships between singularities of these maps and geometric properties of spacelike hypersurfaces as an application of the theory of Legendrian singularities. We classify the singularities and give some examples in the generic case in de Sitter 3-space.     

Stationary solutions to the drift–diffusion model in the whole spaces

We study the stationary problem in the whole space ?ⁿ for the drift–diffusion model arising in semiconductor device simulation and plasma physics. We prove the existence and uniqueness of stationary solutions in the weighted L^p spaces. The proof is based on a fixed point theorem of the Leray–Schauder type. Copyright © 2008 John Wiley & Sons, Ltd.     

Klein–Gordon equations with homogeneous time-dependent electric fields

We consider a system associated to Klein–Gordon equations with homogeneous time-dependent electric fields. The upper and lower boundaries of a time-evolution propagator for this system were proven by Veseli? (J Oper Theory 25:319–330, 1991) for electric fields that are independent of time. We extend this result to time-dependent electric fields.     

Catalysis of Mononuclear Aquaruthenium Complexes in Oxygen Evolution from Water: A New Radical Coupling Path using Hydroxocerium(IV) Species

The mechanism of O₂ evolution from water catalyzed by a series of mononuclear aquaruthenium complexes, [Ru(terpy)(bpy)(OH₂)]²⁺, [Ru(tmtacn)(R₂bpy)(OH₂)]²⁺ (R=H, Me, and OMe; R₂bpy=4,4′‐disubstituted‐2,2′‐bipyridines), and [Ru(tpzm)(R₂bpy)(OH₂)]²⁺ (R=H, Me, and OMe), is investigated, where terpy=2,2′:6′,2′′‐terpyridine, bpy=2,2′‐bipyridine, tmtacn=1,4,7‐trimethyl‐1,4,7‐triazacyclononane, and tpzm=tris(1‐pyrazolyl)methane. The kinetics of O₂ evolution is investigated as a function of either the catalyst concentration or the oxidant concentration by employing Ce(NH₄)₂(NO₃)₆ as an oxidant; these catalysts can be classified into two groups that have different rate laws for O₂ evolution. In one class, the rate of O₂ evolution is linear to both the catalyst and Ce⁴⁺ concentrations, as briefly reported for [Ru(terpy)(bpy)(OH₂)]²⁺ (S. Masaoka, K. Sakai, Chem. Lett. 2009 , 38, 182). For the other class, [Ru(tmtacn)(R₂bpy)(OH₂)]²⁺, the rate of O₂ evolution is quadratic to the catalyst concentration and independent of the Ce⁴⁺ concentration. Moreover, the singlet biradical character of the hydroxocerium(IV) ion was realized by experimental and DFT investigations. These results indicate that the radical coupling between the oxygen atoms of a Ru^V?O species and a hydroxocerium(IV) ion is the key step for the catalysis of [Ru(terpy)(bpy)(OH₂)]²⁺ and [Ru(tpzm)(R₂bpy)(OH₂)]²⁺, while the well‐known oxo‐oxo radical coupling among two Ru^V?O species proceeds in the catalysis of [Ru(tmtacn)(R₂bpy)(OH₂)]²⁺. This is the first report demonstrating that the radical character provided by the hydroxocerium(IV) ion plays a crucial role in the catalysis of such ruthenium complexes in the evolution of O₂ from water.     

Identification of Glycyrrhiza species by direct analysis in real time mass spectrometry

DART (Direct Analysis in Real Time)-MS is a novel mass spectrometric ion source, and allows the analysis of most compounds at ambient pressure and ground potential by producing [M+H]+ molecular ion species. Using this method, we examined the compounds characteristic of several kinds of licorices. For the analysis of Glycyrrhiza inflata Batalin, the peak at m/z 339 originates mainly from [M+H]+ of licochalcone A (LA), a species-specific compound. This peak was hardly detected in G. glabra Linné and G. uralensis Fischer. These results indicate that G. inflata can be differentiated from the other two species by detection of LA peaks using DART-MS analysis.     

Rapid and Direct Conversion of Graphite Crystals into High‐Yielding,Good‐Quality Graphene by Supercritical Fluid Exfoliation

Graphene has attracted a great deal of attention in recent years due to its unusual electronic, mechanical, and thermal properties. Exploiting graphene properties in a variety of applications requires a chemical approach for the large‐scale production of high‐quality, processable graphene sheets (GS), which has remained an unanswered challenge. Herein, we report a rapid one‐pot supercritical fluid (SCF) exfoliation process for the production of high‐quality, large‐scale, and processable graphene for technological applications. Direct high‐yield conversion of graphite crystals to GS is possible under SCF conditions because of the high diffusivity and solvating power of SCFs, such as ethanol, N‐methyl‐pyrrolidone (NMP), and DMF. For the first time, we report a one‐pot direct conversion of graphite crystals to a high yield of graphene sheets in which about 90–95 % of the exfoliated sheets are <8 layers with approximately 6–10 % monolayers and the remaining 5–10 % are ≥10 layers.     

Infrared predissociation spectroscopy of ammonia cluster cations (NH3)n+ (n=2-4) produced by vacuum-ultraviolet photoionization

Infrared predissociation spectroscopy of vacuum ultraviolet-pumped ion (IRPDS-VUV-PI) is performed on ammonia cluster cations (NH3)n+ (n=2-4) that are produced by VUV photoionization in supersonic jets. The structures of (NH3)2+ and (NH3)4+ are determined through the observation of infrared spectra and vibrational calculations based on ab initio calculations at the MP2/6-31G** and 6-31++G** levels. (NH3)2+ is found to be of the "hydrogen-transferred" form having the (H3N+-...NH2) composition. In contrast, (NH3)4+ exhibits the "head-to-head" dimer cation (H3...NH3+ core structure, where the positive charge is shared between two ammonia molecules in the core, and two other molecules are hydrogen bonded onto the core. An unequivocal assignment of the infrared spectrum of (NH3)3+ has not been achieved, because the presence of two isomeric structures could be suggested by the observed spectrum and theoretical calculations.