On equivalent definitions of the correlation dimension for a probability measure

In mathematical physics, one sometimes has to deal with averages of the type $$M\mu (T) = \frac{1}{{T^n }}\int\limits_{|\xi | \leqslant T} { d\xi |\hat \mu (\xi )|^2 , T > 0}$$ where $\hat \mu$ is the Fourier transform of some probability Borel measure μ. We show that the asymptotic behavior ofMμ is governed by the usual (upper and lower) correlation dimension of the measure μ.     

Novel biodegradable copolyesters containing blocks of poly(3-hydroxyoctanoate) and poly(epsilon-caprolactone): synthesis and characterization

Novel biodegradable polyester block copolymers have been synthesized by using well-defined poly(3-hydroxyoctanoate) (PHO) oligomers having a hydroxyl end group and an ester end group with M(n) values of 800, 2,500, 5,300, 8,000, or 20,000 as an elastomeric soft segment and poly(epsilon-caprolactone) as a more crystalline segment. These PHO oligomers prepared by methanolysis were subjected to block copolymerization with epsilon-caprolactone. The chemical structure of the copolymers was confirmed by (1)H NMR and (13)C NMR spectroscopy. All the copolyesters are semi-crystalline and two T(g) were observed by differential scanning calorimetry when the molecular weight of the PHO block is about 20,000.     

(Z,Z)-6,9-nonadecadien-3-one and (Z,Z,Z)-3,6,9-nonadecatriene: identification and synthesis of sex pheromone components of peribatodes rhomboidaria.

(Z,Z)-6,9-Nonadecadien-3-one and (Z,Z,Z)-3,6,9-nonadecatriene were identified by GC-EAD and GC-MS in ovipositor extracts of $\text{P}$. $\text{rhomboidaria}$; the synthetic mixture is attractive to males of the species in the field.     

"One-pot" tandem C-H borylation/1,4-conjugate addition/reduction sequence

A microwave-assisted, one-pot, iridium-catalyzed aromatic C-H borylation/rhodium-catalyzed 1,4-conjugate addition sequence provides a highly robust protocol suitable for high-throughput array synthesis. Selective formation of either β-aryl-substituted ketones or the corresponding alcohols can be achieved in good overall yields by simple variation of the reaction conditions.     

Electron transport through rectifying self-assembled monolayer diodes on silicon: Fermi-level pinning at the molecule-metal interface

We report the synthesis and characterization of molecular rectifying diodes on silicon using sequential grafting of self-assembled monolayers of alkyl chains bearing a pi group at their outer end (Si/sigma-pi/metal junctions). We investigate the structure-performance relationships of these molecular devices, and we examine the extent to which the nature of the pi end group (change in the energy position of their molecular orbitals) drives the properties of these molecular diodes. Self-assembled monolayers of alkyl chains (different chain lengths from 6 to 15 methylene groups) functionalized by phenyl, anthracene, pyrene, ethylene dioxythiophene, ethylene dioxyphenyl, thiophene, terthiophene, and quaterthiophene were synthesized and characterized by contact angle measurements, ellipsometry, Fourier transform infrared spectroscopy, and atomic force microscopy. We demonstrate that reasonably well-packed monolayers are obtained in all cases. Their electrical properties were assessed by dc current-voltage characteristics and high-frequency (1-MHz) capacitance measurements. For all of the pi groups investigated here, we observed rectification behavior. These results extend our preliminary work using phenyl and thiophene groups (Lenfant et al., Nano Lett. 2003, 3, 741). The experimental current-voltage curves were analyzed with a simple analytical model, from which we extracted the energy position of the molecular orbital of the pi group in resonance with the Fermi energy of the electrodes. We report experimental studies of the band lineup in these silicon/alkyl pi-conjugated molecule/metal junctions. We conclude that Fermi-level pinning at the pi group/metal interface is mainly responsible for the observed absence of a dependence of the rectification effect on the nature of the pi groups, even though the groups examined were selected to have significant variations in their electronic molecular orbitals.     

High-throughput synthesis and screening of ternary metal alloys for electrocatalysis

We report the application of a new method for the high-throughput synthesis and screening of thin film materials and its application to the discovery of electrocatalysts. Results are presented for the PtPdAu ternary alloy system with respect to activity for oxygen reduction. The results reveal an enhancement in activity for a range of PtPd alloy compositions over either of the pure elements. An optimum composition range of ternary alloys with significant activity was also identified. A correlation was also investigated between the surface reduction potential and the activity for oxygen reduction in both binary and ternary alloys. The results demonstrate the potential of the methodology for the discovery and optimization of electrocatalysts for a wide range of applications.     

Amine-catalyzed addition of azide ion to alpha,beta-unsaturated carbonyl compounds

[formula: see text] A new protocol for the beta-azidation of alpha,beta-unsaturated carbonyl compounds is described. The method employs tertiary amines as catalysts for azide addition. The azide source is a 1:1 mixture of TMSN3 and AcOH. Tertiary amines, either in solution or bound to a solid support, are efficient catalysts for the reaction.     

Strong decays ofΨ(4.03) andΨ(4.16) as radial excitations of charmonium

Considering the signals detected at 4.03 and 4.16 GeV as radial excitations of charmonium, we study their relative decay rates intoD \(\bar D\) ,D \(\bar D^* \) ,D ^* \(\bar D\) ,D ^* \(\bar D^* \) . We point out that one can understand these two peaks as ac \(\bar c\) 3S?2D wave state system with a large mixing angle in a Coulomb+linear interquark potential. We also examine the possibility that these two signals are respectively 3S and 4S wave excitations by studying a logarithmic charmonium potential model. We show that both these interpretations lead to drastically different predictions for the Ψ (4.16) decay rates (eitherD \(\bar D^* \) +D ^* \(\bar D\) orD \(\bar D\) mode is strongly suppressed) which would be very instructive to test experimentally.     

Accounting for diffuse layer ions in triple-layer models

The triple-layer model is one of the most widely used surface complexation models for adsorption on mineral surfaces. In current implementations, the accounting of ions in the diffuse layer may be neglected, resulting in a charge imbalance in the modeled solution as well as errors in mass balance, particularly in low ionic strength solutions when mineral-specific surface area is large. This paper introduces an internally consistent scheme for modeling diffuse layer ions in the triple-layer model. Model calculations illustrate the difference between the proposed and previous implementations using an idealized example. The guarantee of charge balance on both sides of the interface assures that pH is accurately modeled. This may be important in reactive transport simulations, such as modeling adsorption in low ionic strength variable charge soil solutions.