Influence of the central metal on the crystal structures and electronic structures of biferrocene trinuclear complexes

Five metal-bridged biferrocene complexes of the Schiff-base ligand (HL = S-benzyl-N-(ferrocenyl-1-methyl-methylidene)dithiocarbazate) have been studied by single crystal X-ray diffraction and ⁵⁷Fe Mössbauer spectroscopy. The crystal structures of the complexes show that the central metal ions are tetra-coordinated by two ligands in two modes: the central d⁸ transition metal ions (Ni²⁺, Pd²⁺, and Pt²⁺) are nearly square-planar coordinated and the d¹⁰ transition metal ions (Zn²⁺ and Cd²⁺) are tetrahedrally coordinated. Interestingly, the isomer shifts in ⁵⁷Fe Mössbauer spectroscopy are also of two kinds: d⁸ transition metal ions (0.097-0.247 mm/s) and d¹⁰ transition metal ions (0.416-0.435 mm/s).     

Convenient Synthesis of Terminal Alkynes from anti‐3‐Aryl‐2,3‐dibromopropanoic Acids Using a K2CO3/DMSO System

A convenient, efficient, and generally applicable method was developed for the synthesis of terminal alkynes from anti‐3‐aryl‐2,3‐dibromopropanoic acids in the presence of DMSO and K₂CO₃.     

Esterification of levulinic acid to n-butyl levulinate over heteropolyacid supported on acid-treated clay

Levulinic acid has been identified as a promising green, biomass-derived platform chemical. n-Butyl levulinate is used as an important intermediate having diverse applications. The present work focuses on the synthesis of n-butyl levulinate by esterification of levulinic acid with n-butanol using heteropolyacid (HPA) supported on acid-treated clay montmorillonite (K10). 20% (w/w) dodecatungestophosphoric acid (DTPA) supported on K10 was found to be the most efficient catalyst with 97% levulinic acid conversion and 100% selectivity towards n-butyl levulinate. Effects of various process parameters were studied to examine the efficacy of 20% (w/w) DTPA/K10 for optimization of the activity.     

Homogenization limit of a parabolic equation with nonlinear boundary conditions

Consider the parabolic equation

(E)     

Random attractors for stochastic lattice dynamical systems in weighted spaces

In this paper, we first provide some sufficient conditions for the existence of global compact random attractors for general random dynamical systems in weighted space (p?1) of infinite sequences. Then we consider the existence of global compact random attractors in weighted space for stochastic lattice dynamical systems with random coupled coefficients and multiplicative/additive white noises. Our results recover many existing ones on the existence of global random attractors for stochastic lattice dynamical systems with multiplicative/additive white noises in regular l² space of infinite sequences.     

Superstability and rigorous asymptotics in singularly perturbed state-dependent delay-differential equations

We study the singularly perturbed state-dependent delay-differential equation

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The asymptotic behaviour of the heat equation in a twisted Dirichlet-Neumann waveguide

We consider the heat equation in a straight strip, subject to a combination of Dirichlet and Neumann boundary conditions. We show that a switch of the respective boundary conditions leads to an improvement of the decay rate of the heat semigroup of the order of t−1/2. The proof employs similarity variables that lead to a non-autonomous parabolic equation in a thin strip contracting to the real line, that can be analysed on weighted Sobolev spaces in which the operators under consideration have discrete spectra. A careful analysis of its asymptotic behaviour shows that an added Dirichlet boundary condition emerges asymptotically at the switching point, breaking the real line in two half-lines, which leads asymptotically to the 1/2 gain on the spectral lower bound, and the t−1/2 gain on the decay rate in the original physical variables.This result is an adaptation to the case of strips with twisted boundary conditions of previous results by the authors on geometrically twisted Dirichlet tubes.     

Homogenization of a parabolic model of ferromagnetism

This work deals with the homogenization of hysteresis-free processes in ferromagnetic composites. A degenerate, quasilinear, parabolic equation is derived by coupling the Maxwell-Ohm system without displacement current with a nonlinear constitutive law:

     

Nonexistence of type II blowup solution for a semilinear heat equation

A solution u of a Cauchy problem for a semilinear heat equation