Input-to-state stability of impulsive reaction–diffusion neural networks with infinite distributed delays

In this paper, we focus on the global existence–uniqueness and input-to-state stability of the mild solution of impulsive reaction–diffusion neural networks with infinite distributed delays. First, the model of the impulsive reaction–diffusion neural networks with infinite distributed delays is reformulated in terms of an abstract impulsive functional differential equation in Hilbert space and the local existence–uniqueness of the mild solution on impulsive time interval is proven by the Picard sequence and semigroup theory. Then, the diffusion–dependent conditions for the global existence–uniqueness and input-to-state stability are established by the vector Lyapunov function and M-matrix where the infinite distributed delays are handled by a novel vector inequality. It shows that the ISS properties can be retained for the destabilizing impulses if there are no too short intervals between the impulses. Finally, three numerical examples verify the effectiveness of the theoretical results and that the reaction–diffusion benefits the input-to-state stability of the neural-network system.

     

Conformality of a quasiconformal mapping at a point

Letf be a quasiconformal mapping with the complex dilation μ. A new condition on μ is introduced for the conformality off at a pointz. The result extends the classical Teichmüller-Wittich-Belinskiî regularity theorem.     

Dirichlet problem for the general Beltrami equation in Jordan domains

We study the Dirichlet problem for the general degenerate Beltrami equations $ \bar{\partial}f=\mu \partial f+\nu \overline{{\partial f}} $ in a Jordan domain. Some criteria for the existence of regular solutions are given.     

Mechanistic pathways for oxidative addition of aryl iodides to the low-ligated diethanolamine palladium(0) complex in phosphine-free Heck reactions

A set of reactions of different activated olefins and aryl iodides with the trans-dichlorobis(diethanolamine-N)palladium(II) complex (trans-[PdCl₂(DEA)₂]) as a precatalyst was performed, in the presence of diethanolamine (DEA) as a weak base, and NaOEt as a strong base. It was established that the presence of NaOEt slightly lowered the yields, but significantly accelerated the reactions. This experimental finding is in agreement with our computational investigation that shows that significantly higher activation barrier is required for the preactivation reaction in the presence of a weak base than in the presence of a strong base. The reaction between the catalytically active DEA-Pd(0)-Cl complex, formed in the preactivation reaction, and iodobenzene was investigated using density functional theory. Two mechanisms for the oxidative addition of the activated complex were found. The first mechanism is based on a nucleophilic attack of Pd on I of iodobenzene, and yields an intermediate tetracoordinated Pd complex (aI2). The second mechanism begins with a nucleophilic attack of Pd on the benzene ring, and yields a tricoordinated intermediate complex (bI4). It was concluded, on the basis of structural and energetical properties of aI2 and bI4, that the second mechanism is significantly more favorable. It was shown that the oxidative addition requires noticeable lower activation energy than that required for the preactivation process. Thus, our investigations indicate that oxidative addition is not the rate determining step for the Heck reactions investigated in this work, but preactivation step.     

Lanthanide-containing polymer nanoparticles for biological tagging applications: nonspecific endocytosis and cell adhesion

We describe the synthesis and characterization of element-encoded polystyrene nanoparticles with diameters on the order of 100 nm and a narrow size distribution. Individual particles contain ca. 10(3) chelated lanthanide ions, of either a single element or a mixture of elements. These particles were effectively internalized by nonspecific endocytosis into three cell lines associated with human leukemia. Using an assay based upon ICP-MS detection, we could monitor quantitatively cell adhesion induced by cell differentiation of THP-1 cells in response to phorbol ester stimulation (PMA) in single cell type or mixed cultures.     

Dissipative Evolution of the Qubit State in the Tomographic-Probability Representation

We consider the evolution of qubit states for the Demkov problem in the presence of dephasing processes in the spin tomographic-probability representation. We present an explicit solution of the spin tomogram in terms of the ₁ F ₂ hypergeometric function. We calculate the tomographic Shannon and q entropies through the solution of the master equation in the form of tomographic-probability distribution of the qubit states obtained.     

Langmuir-Blodgett monolayers of gold nanoparticles with amphiphilic shells from V-shaped binary polymer arms

Gold nanoparticles functionalized with amphiphilic polybutadiene-poly(ethylene glycol) (PB-PEG) V-shaped arms formed stable Langmuir monolayers at the air-water and the air-solid interfaces. At these interfaces, the binary arms vertically segregated into a dense polymer corona, which surrounded the gold nanoparticles, preventing their large-scale agglomeration and keeping individual nanoparticles well-separated from each other and forming flattened, pancake nanostructures. The presence of both PEG and PB chains in the close proximity to the gold core was confirmed by surface enhanced Raman spectroscopy, whereas the AFM phase contrast images revealed the presence of 2 nm gold cores surrounded by the polymer shell with the diameter of 11 nm. We suggest that the amphiphilic shell drives their spontaneous organization into discrete 2D pancake-like hybrid structures that measured up to 10 microm in diameter and had a high packing density of gold clusters.     

Regiodivergent metal-catalyzed rearrangement of 3-iminocyclopropenes into N-fused heterocycles

A highly efficient regiodivergent method for the synthesis of N-fused heterocycles via transition-metal-catalyzed rearrangement of 3-iminocyclopropenes has been developed.