Diagonals of separately pointwise Lipschitz mappings

It is proved that, for a metric space X and a normed space Z, the diagonals of pointwise Lipschitz mappings f : X ²? →?Z are exactly stable pointwise limits of pointwise Lipschitz mappings. The joint Lipschitz property of separately pointwise Lipschitz mappings f : X?×?Y?→?Z, where X, Y, and Z are metric spaces, is investigated.     

Kinetics of the reaction of the heaviest hydrogen atom with H2, the 4Heμ + H2 → 4HeμH + H reaction: experiments, accurate quantal calculations, and variational transition state theory, including kinetic isotope effects for a factor of 36.1 in isotopic mass

The neutral muonic helium atom (4)Heμ, in which one of the electrons of He is replaced by a negative muon, may be effectively regarded as the heaviest isotope of the hydrogen atom, with a mass of 4.115 amu. We report details of the first muon spin rotation (μSR) measurements of the chemical reaction rate constant of (4)Heμ with molecular hydrogen, (4)Heμ + H(2) → (4)HeμH + H, at temperatures of 295.5, 405, and 500 K, as well as a μSR measurement of the hyperfine coupling constant of muonic He at high pressures. The experimental rate constants, k(Heμ), are compared with the predictions of accurate quantum mechanical (QM) dynamics calculations carried out on a well converged Born-Huang (BH) potential energy surface, based on complete configuration interaction calculations and including a Born-Oppenheimer diagonal correction. At the two highest measured temperatures the agreement between the quantum theory and experiment is good to excellent, well within experimental uncertainties that include an estimate of possible systematic error, but at 295.5 K the quantum calculations for k(Heμ) are below the experimental value by 2.1 times the experimental uncertainty estimates. Possible reasons for this discrepancy are discussed. Variational transition state theory calculations with multidimensional tunneling have also been carried out for k(Heμ) on the BH surface, and they agree with the accurate QM rate constants to within 30% over a wider temperature range of 200-1000 K. Comparisons between theory and experiment are also presented for the rate constants for both the D + H(2) and Mu + H(2) reactions in a novel study of kinetic isotope effects for the H + H(2) reactions over a factor of 36.1 in isotopic mass of the atomic reactant.     

Improved Synthesis of Monoprotected 5- and 6-Amino-2-azanorbornanes

An improved synthesis of Boc-monoprotected 5- and 6-amino-2-azanorbornanes is reported. The synthetic scheme consists of five steps and allows multigram quantities of the title compounds to be obtained. The regio- and stereochemistries of the products are established by two-dimensional NMR experiments.

Hetero-Diels–Alder reactions of perfluoroalkyl thioamides with electron-rich 1,3-dienes: synthesis of new 2-aminosubstituted-3,6-dihydro-2H-thiopyrans and related compounds

Hetero-Diels–Alder reactions of perfluoroalkyl thioamides with electron-rich 1,3-dienes such as 2,3-dimethylbutadiene, isoprene or penta-1,3-diene gave a simple and efficient access to new 2-aminosubstituted-3,6-dihydro-2H-thiopyrans. Three different procedures were used depending on the nature of the polyfluoroalkyl chains (R_F=CF₃, (CF₂)_nCF₃, (CF₂)₄H) and on the nitrogen substituents of the thioamides (R¹, R²=H, p-Tol, morpholino, Ac). Moreover, cycloadditions of silyloxydienes (1- or 2-trimethylsilyloxy-1,3-butadiene and Danishefsky's diene) with N-acyl,N-tolyl trifluoromethylthioamides afforded in almost all cases the corresponding 3,6-dihydro-2H-thiopyrans or 3-oxo-tetrahydrothiopyrans. For non-symmetrical 1,3-dienes, the regio- and stereochemistry of the reactions were studied (especially using X-ray diffraction analysis) indicating a strong similarity with those reported for fluorinated thiocarboxyl derivatives. Finally, two silylated 3,6-dihydro-2H-thiopyrans underwent an unexpected base-induced ring contraction to give new 1,3-thiazolidin-4-ones.     

Synthesis of Boc-protected 4,5-methano-β-proline

An efficient method for the preparation of Boc-protected 4,5-methano-β-proline—a novel bicyclic cyclopropane-containing β-amino acid—was developed, starting from readily available itaconic acid. A modified Simmons–Smith reaction was used for the construction of the cyclopropane ring. The method allowed for the synthesis of both cis and trans isomers of the title compound in 49% total yield and can be employed for gram-scale preparations. An approach to the preparation of methyl 5-oxopyrrolidine-3-carboxylate, which is one of the key intermediates in the synthetic scheme, on a multigram scale was also developed.     

Simulation of Cox Processes Driven by Random Gaussian Field

In this paper we consider the Cox processes directed by random log Gaussian homogeneous field. We construct models for such processes with some accuracy and reliability.     

A Case of Strong Metal–Support Interactions: Combining Advanced Microscopy and Model Systems to Elucidate the Atomic Structure of Interfaces

A symbiosis of advanced scanning probe and electron microscopy and a well‐defined model system may provide a detailed picture of interfaces on nanostructured catalytic systems. This was demonstrated for Pt nanoparticles supported on iron oxide thin films which undergo encapsulation by supporting oxide as a result of strong metal–support interactions.     

Protecting Group Free Synthesis of Carboxyl‐substituted Dihydropyrimidines Through Biginelli Reaction

Chlorotrimethylsilane‐promoted Biginelli‐type reaction of benzaldehyde, acetoacetic acid derivatives, and various carboxyl‐containing ureas was explored. It was found that the steric load of the urea substituents influenced strongly the reaction outcome; in particular, the method was efficient only in the case of unbranched mono‐substituted ureas bearing either aliphatic or aromatic groups. The method allows performing a one‐pot, protecting group free synthesis of dihydropyrimidines possessing carboxylic functionality.     

Pontryagin’s maximum principle for dynamic systems on time scales

In this work, an analogue of Pontryagin’s maximum principle for dynamic equations on time scales is given, combining the continuous and the discrete Pontryagin maximum principles and extending them to other cases ‘in between’. We generalize known results to the case when a certain set of admissible values of the control is not necessarily closed (but convex) and the attainable set is not necessarily convex. At the same time, we impose an additional condition on the graininess of the time scale. For linear systems, sufficient conditions in the form of the maximum principle are obtained.     

Chiral Catalysts for Pd0-Catalyzed Enantioselective C−H Activation

In the past few decades, processes that involve transition-metal catalysis have represented a major part of the synthetic chemist′s toolbox. Recently, the interest has shifted from the well-established cross-coupling reactions to C−H bond functionalization, thus making it a current frontier of transition-metal-catalyzed reactions. Constant progress in this field has led to the discovery of enantioselective methods to generate and control various types of stereogenic elements, thereby demonstrating its high value to generate scalemic chiral molecules. The present review is dedicated to enantioselective Pd⁰-catalyzed C−H activation, which may be considered as an evolution of Pd⁰-catalyzed cross-couplings, with a focus on the different chiral ligands and catalysts that enable these transformations.