Copper(II)-acid co-catalyzed intermolecular substitution of electron-rich aromatics with diazoesters

The intermolecular aromatic substitution of N,N-dialkylanilines and alkoxybenzenes with diazoesters is shown to proceed in the presence of catalytic amounts of both copper(II) salt and acid (Lewis or Brønsted). This method is a mild and rare metal-free C-C bond formation reaction between aromatic (sp²) and aliphatic (sp³) carbons.     

Convergence of Anisotropically Decaying Solutions of a Supercritical Semilinear Heat Equation

We consider the Cauchy problem for a semilinear heat equation with a supercritical power nonlinearity. It is known that the asymptotic behavior of solutions in time is determined by the decay rate of their initial values in space. In particular, if an initial value decays like a radial steady state, then the corresponding solution converges to that steady state. In this paper we consider solutions whose initial values decay in an anisotropic way. We show that each such solution converges to a steady state which is explicitly determined by an average formula. For a proof, we first consider the linearized equation around a singular steady state, and find a self-similar solution with a specific asymptotic behavior. Then we construct suitable comparison functions by using the self-similar solution, and apply our previous results on global stability and quasi-convergence of solutions.     

In situ fuel concentration measurement near a spark plug in a spray-guided direct-injection spark-ignition engine using infrared absorption method

Vaporized fuel concentration in a spray-guided direct-injection spark-ignition (SG-DISI) engine was measured using an optical sensor installed in a spark plug. A laser infrared absorption method was applied to quantify the instantaneous gasoline concentration near the spark plug. This paper discusses the feasibility of obtaining in situ air–fuel ratio measurements with this sensor installed inside an SG-DISI engine cylinder. First, the effects of the spray plume from a multi-hole injector on the vaporized fuel concentration measurements near the spark-plug sensor were examined using a visible laser. We determined the best position for the sensor in the engine, which was critical due to the spray and vapor plume formation. Then, a 3.392-μm He–Ne laser that coincided with the absorption line of the hydrocarbons was used as a light source to examine the stratified mixture found during ultra-lean engine operation. A combustible mixture existed around the spark plug during the injection period when a preset air–fuel ratio of 45.0 was used with different fuel injection timings and net mean effect pressure conditions. The effects of the orientation of the spark plug on the measured results and ignitability of the SG-DISI engine were examined. Orienting the spark plug vertically to one of the spray plumes provided more accurate results and better engine reliability. The study demonstrated that it was possible to qualify the air–fuel ratio near the spark plug during the injection period using the developed spark-plug sensor in an SG-DISI engine.     

Giant motion of La atom inside C82 cage

An anomalous charge density distribution of La atom encapsulated in a C₈₂ cage has been revealed for La@C₈₂ by the maximum entropy method (MEM)/Rietveld analysis using synchrotron powder diffraction data. The obtained La atom charge density shows a feature almost like a bowl or a hemisphere, suggesting that the La atom has a giant motion (large amplitude motion) inside the C₈₂ cage at room temperature. From the obtained MEM charge density, the main results are (1) the cage structure of La@C₈₂ (I) has C_2V symmetry; (2) La atom locates at an off-centered position adjacent to a six-membered ring of the carbon cage; (3) the nearest La–C distance is 2.55(8) and (4) the amount of charge transfer from the La atom to the carbon cage is about 3.2 e, which corresponds to the nominal electronic structure, La³⁺@C₈₂³⁻.     

Similarities and Differences between Crystal and Enzyme Environmental Effects on the Electron Density of Drug Molecules

The crystal interaction density is generally assumed to be a suitable measure of the polarization of a low-molecular weight ligand inside an enzyme, but this approximation has seldomly been tested and has never been quantified before. In this study, we compare the crystal interaction density and the interaction electrostatic potential for a model compound of loxistatin acid (E64c) with those inside cathepsin B, in solution, and in vacuum. We apply QM/MM calculations and experimental quantum crystallography to show that the crystal interaction density is indeed very similar to the enzyme interaction density. Less than 0.1 e are shifted between these two environments in total. However, this difference has non-negligible consequences for derived properties.     

Ring-forming reaction via regioselective intramolecular insertion by (phenylthio) carbene into α c-h bond of alkoxides

ω-(Phenylthio)-ω-chloroalkyl acetates were allowed to react with MeLi (3.2 equiv) to give 2-(phenylthio) cycloalkanols which were produced by the regioselective intramolecular insertion by (phenylthio) carbenes.     

Effect of calcination temperature during preparation of Ru?Sn-alumina catalysts on the hydrogenation of carboxylic acid

The conversion of a carboxylic acid was increased to 90% with 100% selectivity to the corresponding alcohol by calcination of the catalyst precursor, Sn/alumina, of Ru–Sn/alumina in the hydrogenation of the carboxylic acid.     

A remark on stable subharmonic solutions of time-periodic reaction-diffusion equations

This paper is concerned with a time-periodic reaction-diffusion equation. It is known that typical trajectories approach periodic solutions with possibly longer period than that of the equation. Such solutions are called subharmonic solutions. In this paper, for any domain Ω, time-period τ>0 and integer n?2, we construct an example of a time-periodic reaction-diffusion equation on Ω with a minimal period τ which possesses a stable solution of minimal period nτ.     

Helicity induction on a poly(phenylacetylene) bearing a phosphonate residue by chiral dendrons

A series of optically active dendrons with a primary amino group at the terminal were prepared from L - or D -glutamic acid, and their helicity induction abilities for a poly(phenylacetylene) bearing a phosphonate pendant were characterized with ultraviolet–visible and circular dichroism spectroscopy. The magnitude of the Cotton effects of the polymer induced by the dendrons significantly increased upon complexation with a higher generation dendron. The effect of the chirality of the glutamate residues (L and D ) on the helicity induction was also studied. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4580–4586, 2004     

Krein's formula for indefinite multipliers in linear periodic Hamiltonian systems

This paper is concerned with Hamiltonian systems of linear differential equations with periodic coefficients under a small perturbation. It is well known that Krein's formula determines the behavior of definite multipliers on the unit circle and is quite useful in studying the (strong) stability of Hamiltonian system. Our aim is to give a simple formula that determines the behavior of indefinite multipliers with two multiplicity, which is generic case. The result does not require analyticity and is proved directly. Applying this formula, we obtain instability criteria for solutions with periodic structure in nonlinear dissipative systems such as the Swift-Hohenberg equation and reaction-diffusion systems of activator-inhibitor type.