The construction of wavelets adapted to compact domains

A theoretical framework to construct wavelets adapted to compact domains has already been established, however technical considerations must be addressed to implement the construction on a larger variety of domains. In this article we generalize the theory further and provide a methodology to explicitly construct the wavelets. Examples of the construction for a rectangular surface, a triangular surface, and a smooth simplex in ?³ are given. An extension of the theory to triangulated manifolds of finite distortion in n dimensions is also explained.     

Positioning a Carbon–Fluorine Bond over the π Cloud of an Aromatic Ring: A Different Type of Arene Activation

It is known that the fluoro group has only a small effect on the rates of electrophilic aromatic substitutions. Imagine instead a carbon–fluorine (C?F) bond positioned tightly over the π cloud of an aryl ring—such an orthogonal, noncovalent arrangement could instead stabilize a positively charged arene intermediate or transition state, giving rise to novel electrophilic aromatic substitution chemistry. Herein, we report the synthesis and study of molecule 1 , containing a rigid C?F???Ar interaction that plays a prominent role in both its reaction chemistry and spectroscopy. For example, we established that the C?F???Ar interaction can bring about a >1500 fold increase in the relative rate of an aromatic nitration reaction, affording functionalization on the activated ring exclusively. Overall, these results establish fluoro as a through‐space directing/activating group that complements the traditional role of fluorine as a slightly deactivating aryl substituent in nitrations.     

Decay of the 21/2− isomer in211Bi and structure of thevg 9 2/2 πh 9/2 levels

Gamma rays and conversion electrons have been measured in²¹¹Bi populated by the²⁰⁹Bi(t,p) reaction, and the near yrast levels were observed up to 21/2^?. The 21/2^? state is isomeric withT _1/2=70(5) ns. No alpha decaying isomer was found in²¹¹Bi. ObservedM1 transitions reveal mixing of the²¹⁰Pb parent states in the levels of²¹¹Bi. The levels and transitions are well reproduced by the shell model with experimental matrix elements and pure configurations.     

Search for a Strong,Virtually “No‐Shift” Hydrogen Bond: A Cage Molecule with an Exceptional OH⋅⋅⋅F Interaction

Reported herein is the synthesis of a molecule containing an unusually strong hydrogen bond between an OH donor and a covalent F acceptor, a heretofore somewhat ill‐defined if not controversial interaction. This unique hydrogen bond is to a large extent a product of the tight framework of the rigid caged system. Remarkably, the interaction shows little to no perceptible shift in the OH stretch of the IR spectrum relative to appropriate nonhydrogen‐bound standards in fairly non‐interactive solvents. This fascinating example of what has been termed a virtual “no‐shift” hydrogen bond is investigated through NMR (coupling constants, isotopic chemical shift perturbations, proton exchange rates) and IR studies which all tell a consistent story.     

Highly enantioselective azadiene Diels-Alder reactions catalyzed by chiral N-heterocyclic carbenes

Highly enantioselective, N-heterocyclic carbene (NHC)-catalyzed aza-Diels-Alder reactions are described. A novel chiral triazolium salt based on the cis-1,2-aminoindanol platform serves as an efficient precatalyst for the NHC-catalyzed redox generation of enolate dienophiles that undergo LUMOdiene-controlled Diels-Alder reactions with N-sulfonyl-alpha,beta-unsaturated imines in good yields and with exceptional diastereo- and enantioselectivities (>99% ee). In contrast to uncatalyzed variants, this organocatalytic process proceeds at room temperature without stoichiometric reagents, producing synthetically valuable, enantiomerically pure cis-3,4-disubstituted dihydropyridinone products.