Photo-Induced Dihydroxylation of Alkenes with Diacetyl,Oxygen, and Water

Herein reported is a photo-induced production of vicinal diols from alkenes under mild reaction conditions. The present dihydroxylation method using diacetyl (= butane-2,3-dione), oxygen, and water dispenses with toxic reagents and intractable waste generation.     

An efficient synthesis of 5-diethoxymethylimidazole-4-carboxylate,a potential precursor for various imidazole derivatives

Anionic cycloaddition of methyl isocyanoacetate to diethoxyacetonitrile afforded methyl 5-diethoxymethylimidazole-4-carboxylate, a useful imidazole nucleus with two different functional groups.     

Some Invariant Manifolds for Functional Difference Equations with Infinite Delay

For nonlinear autonomous functional difference equations, the existence of the local stable manifolds, together with the local unstable manifolds and the local center-unstable manifolds, is shown. As an application, the principle of linearization which states that stabilities and instabilities for the zero solution of nonlinear equations can be derived from those of the zero solution of the linearized equations under some circumstances is established for functional difference equations.     

On a certain move generating link-homology

Dedicated to Professor Kunio Murasugi on his sixtieth birthday     

A concrete example with multiple limit cycles for three dimensional Lotka–Volterra systems

The number of limit cycles for three dimensional Lotka–Volterra systems is an open problem. Recently, Yu et al. (2016) constructed some examples with the possibility of the existence of four limit cycles. Unfortunately, multiple limit cycles are not visible by numerical simulations, because all of them are very close to the interior equilibrium and extremely small. We present a concrete example with multiple limit cycles for three dimensional Lotka–Volterra systems which we can confirm them by numerical simulations. First we prepare the modified formula to compute coefficients of the normal form for the generalized Hopf bifurcation. Applying this formula to three dimensional Lotka–Volterra competitive systems with the aid of the computer algebra system, we derive the critical parameter values explicitly such that the interior equilibrium is exactly an unstable weak focus. Also we show that the heteroclinic cycle on the boundary of ${\mathbb{R}}_{+}^3$ is repelling. This implies that there exists a stable limit cycle by the Poincare–Bendixson theorem. Then, adding some suitable perturbations to parameters, we generate additional two limit cycles near the interior equilibrium by the generalized Hopf bifurcation. Finally we confirm that there exist three limit cycles by numerical simulations.     

Right Alternative Unital Bimodules over the Matrix Algebras of Order $ \geq 3 $

Siberian Mathematical Journal - We address the unital right alternative bimodules over the matrix algebras  $ {\mathrm{M}}_{n}(\Phi) $ of order $ n\geq 3 $ , prove that each of these...     

Oxidation activity of Au nanoparticles on aerogel supports

We have prepared titania aerogel and titania-coated silica aerogel incorporating thiol-capped Au nanoparticles. Both composite materials showed high CO oxidation activity after they were calcined at 673 K. Compositional and morphological changes driven by calcination were evaluated with thermogravimetry and X-ray diffractometry. From the results, it was suggested that the nanoparticles transformed from a faulted to a near-regular FCC structure presumably in concert with the formation of firm contacts between the nanoparticles and the gel substrates. While the diameters of the Au particles in the titania aerogel considerably increased upon calcination, those in the titania-coated silica aerogel were almost unchanged. As a consequence, the latter composite aerogel showed higher activity for oxidation of CO.     

Effect of energy dependent cross-section on flow velocity measurements with charge exchange spectroscopy in magnetized plasma

Charge exchange spectroscopy (CXS) is widely used to measure plasma flow velocity. Accurate measurement is heavily affected by energy dependent cross section between neutral atoms and impurity ions. One symmetric layout of poloidal CXS is applied on Large Helical Device. Correction velocity due to the cross section is exacted from total velocity when actual plasma flow velocity is acquired with the benefit of this layout. A linear relationship between correction velocity and ion temperature is observed. Abundant discharges with wide plasma conditions are investigated and the ratio of correction velocity to ion temperature with the same beam energy shows the normal distribution. The impact of beam energy on the ratio of correction velocity to ion temperature of the carbon system and the hydrogen system is discovered based upon the statistics. Effective emission coefficient (Q) from Atomic Data and Analysis Structure (ADAS) is utilized to study the dependence of correction velocity on Q. The relationship in which the ratio of correction velocity to ion temperature increases linearly with the increasing normalized effective emission coefficient ((1/Q)dQ/dv) is observed. Experimental (1/Q)dQ/dv is obtained according to this observation, and comparison with different fractions of n?=?2 excited state is also discussed. The influence of different receivers (carbon and hydrogen) is also presented. The experimental (1/Q)dQ/dv from the carbon system decreases with beam energy decreasing when beam energy is less than 30 keV/amu. This tendency of (1/Q)dQ/dv at low beam energy indicates the existence of the contribution of n?=?2 excited state donors to the cross section.     

Dynamics of Semiconductor Lasers with Optical Feedback from Photorefractive Phase Conjugate Mirror

The dynamics of semiconductor lasers with photorefractive phase conjugate optical feedback are experimentally studied. Photorefractive fringes considered here are rather static compared with time fluctuations of laser output power. Therefore, it is expected that a semiconductor laser with photorefractive feedback shows similar dynamics to those with conventional optical feedback. We examine relaxation oscillation and external cavity modes of laser output power in the presence of photorefractive phase conjugate feedback. It is proved that the dynamics of photorefractive phase conjugate feedback are fundamentally the same as those of conventional optical feedback.