Product Gauss quadrature rules vs. cubature rules in the meshless local Petrov–Galerkin method

A crucial point in the implementation of meshless methods such as the meshless local Petrov–Galerkin (MLPG) method is the evaluation of the domain integrals arising over circles in the discrete local weak form of the governing partial differential equation. In this paper we make a comparison between the product Gauss numerical quadrature rules, which are very popular in the MLPG literature, with cubature formulas specifically constructed for the approximation of an integral over the unit disk, but not yet applied in the MLPG method, namely the spherical, the circularly symmetrical and the symmetric cubature formulas. The same accuracy obtained with 64×64 points in the product Gauss rules may be obtained with symmetric quadrature formulas with very few points.     

Second‐Sphere Biomimetic Multipoint Hydrogen‐Bonding Patterns to Boost CO2 Reduction of Iron Porphyrins

Inspired by nature's orchestra of chemical subtleties to activate and reduce CO₂, we have developed a family of iron porphyrin derivatives in to which we have introduced urea groups functioning as multipoint hydrogen‐bonding pillars on the periphery of the porphyrinic ring. This structure closely resembles the hydrogen‐bond stabilization scheme of the carbon dioxide (CO₂) adduct in the carbon monoxide dehydrogenase (CODH). We found that such changes to the second coordination sphere significantly lowered the overpotential for CO₂ reduction in this family of molecular catalysts and importantly increased the CO₂ binding rate while maintaining high turnover frequency (TOF) and selectivity. Entrapped water molecules within the molecular clefts were found to be the source of protons for the CO₂ reduction.     

A new synthesis of butadienyl- and styrylboronic esters: highly reactive intermediates for Suzuki cross-coupling

Alkoxy-functionalized butadienyl- and styrylboronic esters have been synthesized starting from alpha,beta-unsaturated acetals. These derivatives readily cross-couple with aryl substrates, and the obtained products can be transformed under mild conditions into aromatic ketones, achieving the same result as an acylation reaction. [reaction: see text]     

Pseudoconvex fully nonlinear partial differential operators: strong comparison theorems

We introduce a new class of curvature PDOs describing relevant properties of real hypersurfaces of . In our setting, the pseudoconvexity and the Levi form play the same role as the convexity and the real Hessian matrix play in the real Euclidean one. Our curvature operators are second-order fully nonlinear PDOs not elliptic at any point. However, when computed on generalized s-pseudoconvex functions, we shall show that their characteristic form is nonnegative definite with kernel of dimension one. Moreover, we shall show that the missing ellipticity direction can be recovered by taking into account the CR structure of the hypersurfaces. These properties allow us to prove a strong comparison principle, leading to symmetry theorems for domains with constant curvatures and to identification results for domains with comparable curvatures.     

On the subRiemannian cut locus in a model of free two-step Carnot group

We characterize the subRiemannian cut locus of the origin in the free Carnot group of step two with three generators, giving a new, independent proof of a result by Myasnichenko (J Dyn Control Syst 8(4):573-597, 2002). We also calculate explicitly the cut time of any extremal path and the distance from the origin of all points of the cut locus. Furthermore, by using the Hamiltonian approach, we show that the cut time of strictly normal extremal paths is a smooth explicit function of the initial velocity covector. Finally, using our previous results, we show that at any cut point the distance has a corner-like singularity.     

A comparison of the extraction of clove buds with supercritical carbon dioxide and superheated water

Supercritical carbon dioxide and superheated water (subcritical water above 100 °C under pressure) have both been used to extract the buds of cloves (Syzygium aromaticum). The yields of eugenol and eugenyl acetate obtained by these methods and also by steam distillation and liquid solvent (Soxhlet) extraction are similar, but the yields of caryophyllene were lower for the methods using water. Received: 23 December 1998 / Revised: 26 March 1999 / Accepted: 31 March 1999     

Effect of a dipolar self-assembly monolayer formation on indium-tin oxide on the performance of single-layer polymer-based light-emitting diodes

We report on the use of indium-tin oxide surface modification, by grafting of highly polar p-disubstituted benzenes, in the fabrication of light-emitting diodes. The polar compounds possess COCl or SO₂Cl grafting groups and CF₃ or NO₂ as highly electronegative groups, leading to the formation of a dipolar monolayer, which brings about an increase in ITO work function, thereby reducing the barrier for hole injection into luminescent polymers. We observe that the effect of this self-assembled monolayer, in terms of light-onset voltage, efficiency and luminance, is at least comparable to the use of a hole injection layer of doped poly[(3,4-ethylenedioxy)thiophene] for LEDs using poly({2-[(2-ethylhexyl)oxy]-5-methoxy-1,4-phenylene}vinylene) (MEH-PPV) and polyfluorene blends as active layers.     

High-Efficiency FRET Processes in BODIPY-Functionalized Quantum Dot Architectures

Efficient FRET systems are developed combining colloidal CdSe quantum dots (QDs) donors and BODIPY acceptors. To promote effective energy transfer in FRET architectures, the distance between the organic fluorophore and the QDs needs to be optimized by a careful system engineering. In this context, BODIPY dyes bearing amino-terminated functionalities are used in virtue of the high affinity of amine groups in coordinating the QD surface. A preliminary QD surface treatment with a short amine ligand is performed to favor the interaction with the organic fluorophores in solution. The successful coordination of the dye to the QD surface, accomplishing a short donor–acceptor distance, provides effective energy transfer already in solution, with efficiency of 76 %. The efficiency further increases in the solid state where the QDs and the dye are deposited as single coordinated units from solution, with a distance between the fluorophores down to 2.2 nm, demonstrating the effectiveness of the coupling strategy.     

Evolutionary Variational Formulation for Oligopolistic Market Equilibrium Problems with Production Excesses

The paper is devoted to generalize a previous model of the dynamic oligopolistic market equilibrium problem allowing the presence of production excesses and assuming, in a more reasonable way that the total amounts of commodity shipments from a firm to all the demand markets be upper bounded. First, we give equilibrium conditions in terms of the well-known dynamic Cournot–Nash equilibrium principle. Then we show that such conditions can be expressed in terms of Lagrange multipliers; namely, by means of an utility function, prove that both equilibrium conditions can be equivalently expressed by a variational inequality. The variational formulation allows us to provide existence theorems and qualitative properties for equilibrium solutions. At last, a numerical example illustrates the results obtained.     

Superbase promoted synthesis of dienamides as useful intermediates for the synthesis of α-ketoamides, γ-lactams and cyclic imino ethers

Alkoxydienamides 2 have been synthesized exploiting the reactivity of α,β-unsaturated acetals 1 with isocyanates in the presence of Schlosser's superbase LIC-KOR. In a mild acidic medium, 2 can then be promptly converted both into α-ketoamides 3 and into substituted 2-pyrrolidinones 4 or imino ethers 5 by choosing the appropriate experimental conditions.