A generalized mean-value theorem

We give another proof of Seymour and Zaslavsky's theorem: For every familyf ₁,f ₂,...,f _n of continous functions defined on [0, 1], there exists a finite setF[0, 1] such that the average sum off _k overF coincides with the integral off _k for everyk=1, 2,...,n.     

Analysis of the 5p6p configuration of Xe V

The spectrum of four times ionized Xenon (XeV), has been observed in the 500–6800 Å range and 84 new lines have been identified as transitions between levels of 5s5p ³, 5s ²5p5d, 5s ²5p6s, 5s ²5p ², and 5s ²5p6p configurations. Nine new levels belonging to the configuration 5p6p have been determined. The results of this analysis are supported by Hartree-Fock calculations. The configurations are interpreted by fitting the theoretical energy parameters to the observed levels using least-squares techniques.     

Crowning Proteins: Modulating the Protein Surface Properties using Crown Ethers

Crown ethers are small, cyclic polyethers that have found wide‐spread use in phase‐transfer catalysis and, to a certain degree, in protein chemistry. Crown ethers readily bind metallic and organic cations, including positively charged amino acid side chains. We elucidated the crystal structures of several protein‐crown ether co‐crystals grown in the presence of 18‐crown‐6. We then employed biophysical methods and molecular dynamics simulations to compare these complexes with the corresponding apoproteins and with similar complexes with ring‐shaped low‐molecular‐weight polyethylene glycols. Our studies show that crown ethers can modify protein surface behavior dramatically by stabilizing either intra‐ or intermolecular interactions. Consequently, we propose that crown ethers can be used to modulate a wide variety of protein surface behaviors, such as oligomerization, domain–domain interactions, stabilization in organic solvents, and crystallization.     

Reversible and Selective CO2 to HCO2− Electrocatalysis near the Thermodynamic Potential

Reversible catalysis is a hallmark of energy‐efficient chemical transformations, but can only be achieved if the changes in free energy of intermediate steps are minimized and the catalytic cycle is devoid of high transition‐state barriers. Using these criteria, we demonstrate reversible CO₂/HCO₂^? conversion catalyzed by [Pt(depe)₂]²⁺ (depe=1,2‐bis(diethylphosphino)ethane). Direct measurement of the free energies associated with each catalytic step correctly predicts a slight bias towards CO₂ reduction. We demonstrate how the experimentally measured free energy of each step directly contributes to the <50 mV overpotential. We also find that for CO₂ reduction, H₂ evolution is negligible and the Faradaic efficiency for HCO₂^? production is nearly quantitative. A free‐energy analysis reveals H₂ evolution is endergonic, providing a thermodynamic basis for highly selective CO₂ reduction.     

Classified Lines in the Spectra of Xe II and Xe III

The spectra of singly and doubly ionized xenon emitted by pulsed light sources have been studied. 35 lines of XeII and 69 lines of XeIII are classified in the range 112 - 676 nm.     

Fuzzy processing in transitivity development

We review the literature on the development of transitive reasoning, and note three historical stages. Stage 1 was dominated by the Piagetian idea that transitive inference is logical reasoning in which relationships between adjacent terms figure as premises. Stage 2 was dominated by the information-processing view that memory for relationships between adjacent terms is determinative in transitivity performance. Stage 3 has produced data that are inconsistent with both the logic and memery positions, leading to a new theory that is designed to account for such findings, fuzzy-trace theory. The basic assumption of fuzzytrace theory is that reasoners rely on global patterns, or gist. We describe the tenets of fuzzytrace theory, and explore its implications for different theoretical conceptions of logical competence, concluding that young children possess transitivity competence. We discuss the connection between transitivity competence (cognition) and intransitive preferences (metacognition).     

Exo conformers of N‐(pyridin‐2‐yl)‐ and N‐(pyridin‐3‐yl)norbornene‐5,6‐dicarboximide crystals

Two isomeric pyridine‐substituted norbornenedicarboximide derivatives, namely N‐(pyridin‐2‐yl)‐exo‐norbornene‐5,6‐dicarboximide, (I), and N‐(pyridin‐3‐yl)‐exo‐norbornene‐5,6‐dicarboximide, (II), both C₁₄H₁₂N₂O₄, have been crystallized and their structures unequivocally determined by single‐crystal X‐ray diffraction. The molecules consist of norbornene moieties fused to a dicarboximide ring substituted at the N atom by either pyridin‐2‐yl or pyridin‐3‐yl in an anti configuration with respect to the double bond, thus affording exo isomers. In both compounds, the asymmetric unit consists of two independent molecules (Z′ = 2). In compound (I), the pyridine rings of the two independent molecules adopt different conformations, i.e. syn and anti, with respect to the methylene bridge. The intermolecular contacts of (I) are dominated by C—H...O interactions. In contrast, in compound (II), the pyridine rings of both molecules have an anti conformation and the two independent molecules are linked by carbonyl–carbonyl interactions, as well as by C—H...O and C—H...N contacts.     

Copper-free Sonogashira cross-coupling for functionalization of alkyne-encoded proteins in aqueous medium and in bacterial cells

Bioorthogonal reactions suitable for functionalization of genetically or metabolically encoded alkynes, for example, copper-catalyzed azide-alkyne cycloaddition reaction ("click chemistry"), have provided chemical tools to study biomolecular dynamics and function in living systems. Despite its prominence in organic synthesis, copper-free Sonogashira cross-coupling reaction suitable for biological applications has not been reported. In this work, we report the discovery of a robust aminopyrimidine-palladium(II) complex for copper-free Sonogashira cross-coupling that enables selective functionalization of a homopropargylglycine (HPG)-encoded ubiquitin protein in aqueous medium. A wide range of aromatic groups including fluorophores and fluorinated aromatic compounds can be readily introduced into the HPG-containing ubiquitin under mild conditions with good to excellent yields. The suitability of this reaction for functionalization of HPG-encoded ubiquitin in Escherichia coli was also demonstrated. The high efficiency of this new catalytic system should greatly enhance the utility of Sonogashira cross-coupling in bioorthogonal chemistry.