A new approach towards the synthesis of pyrrolo[2,1-a]isoquinolines

Reaction of 5-bromo-2-methyl-8-nitro-1,2,3,4-tetrahydroisoquinoline with activated alkynes affords stable tetrahydropyrrolo[2,1-a]isoquinolin-4-ium ylides. Further reactions of ylide 2 gives access to substituted dihydropyrrolo[2,1-a]isoquinolines in good yields.     

Examining Protein-Lipid Interactions in Model Systems with a New Squarylium Fluorescent Dye

The applicability of newly synthesized squarylium dye Sq to probing the changes in physical characteristics of lipid bilayer on the formation of protein-lipid complexes has been evaluated. Lipid vesicles composed of zwitterionic phospholipid phosphatidylcholine (PC) and its mixtures with positively charged detergent cetyltrimethylammonium bromide (CTAB), anionic phospholipid cardiolipin (CL), and cholesterol (Chol) were employed as lipid component of model membrane systems while protein constituent was represented by lysozyme (Lz). Fluorescence intensity of Sq was found to decrease on Lz association with lipid bilayer. This effect was observed in all kinds of model systems suggesting that Sq is sensitive to modification of lipid bilayer physical properties on hydrophobic protein-lipid interactions. It was found that Sq spectral response to variations in Chol content depends on relative contributions of electrostatic and hydrophobic components of Lz-membrane binding.     

Interaction-induced resonance in conductance and thermopower of quantum wires

We study the effect of electron-electron interaction on the transport properties of short clean quantum wires adiabatically connected to reservoirs. Interactions lead to resonances in a multichannel wire at particular values of the Fermi energy. We investigate in detail the resonance in a two-channel wire. The (negative) conductance correction peaks at the resonance, and decays exponentially as the Fermi energy is tuned away, the resonance width being given by the temperature. Likewise, the thermopower shows a characteristic structure, which is surprisingly well approximated by the so-called Mott formula. Finally, fourfold splitting of the resonance in a magnetic field provides a unique signature of the effect.     

Invertibility of Sobolev mappings under minimal hypotheses

We prove a version of the Inverse Function Theorem for continuous weakly differentiable mappings. Namely, a nonconstant W1,n$W^{1,n}$ mapping is a local homeomorphism if it has integrable inner distortion function and satisfies a certain differential inclusion. The integrability assumption is shown to be optimal.     

Boron Phosphorus Nitride at Extremes: PN6 Octahedra in the High‐Pressure Polymorph β‐BP3N6

The high‐pressure behavior of non‐metal nitrides is of special interest for inorganic and theoretical chemistry as well as materials science, as these compounds feature intriguing elastic properties. The double nitride α‐BP₃N₆ was investigated by in situ single‐crystal X‐ray diffraction (XRD) upon cold compression to a maximum pressure of about 42 GPa, and its isothermal bulk modulus at ambient conditions was determined to be 146(6) GPa. At maximum pressure the sample was laser‐heated, which resulted in the formation of an unprecedented high‐pressure polymorph, β‐BP₃N₆. Its structure was elucidated by single‐crystal XRD, and can be described as a decoration of a distorted hexagonal close packing of N with B in tetrahedral and P in octahedral voids. Hence, β‐BP₃N₆ is the first nitride to contain PN₆ octahedra, representing the much sought‐after proof of principle for sixfold N‐coordinated P that has been predicted for numerous high‐pressure phases of nitrides.     

Catalytic cyclopropanation of spiro[2.4]hepta-4,6-diene with diazomethane

Catalytic cyclopropanation of spiro[2.4]hepta-4,6-diene with diazomethane in the presence of copper or palladium compounds results in mono- and dicyclopropanation products, namely, spiro[bicyclo[3.1.0]hex-3-ene-2,1′-cyclopropane] and spiro[cyclopropane-1,5′-tricyclo[4.1.0.0^2,4]heptane], with different efficiency. The use of Pd compounds as catalysts allows the cyclopropanation to be performed under conditions of simultaneous generation and decomposition of diazomethane.     

Electrochemical reduction of 2,4‐dimethyl(diethyl)‐9‐oxo‐10‐(4‐heptoxyphenyl)‐9H‐thioxanthenium hexafluorophosphates and 2,4‐dimethyl(diethyl)‐9H‐thioxanthene‐9‐ones

Electrochemical reduction of 2,4‐dimethyl(diethyl)‐9‐oxo‐10‐(4‐heptoxyphenyl)‐9H‐thioxanthenium hexafluorophosphates in acetonitrile (MeCN) and N,N‐dimethylformamide is an irreversible 1‐electron process accompanied by the cleavage of the C(Ph)‐S bond in thioxanthenium cations with the formation of the corresponding 2,4‐dimethyl(diethyl)‐9H‐thioxanthene‐9‐ones. One‐electron reversible electrochemical reduction of the latter compounds occurs at more negative potentials and yields the corresponding radical anions, which have been characterized by electron paramagnetic resonance spectroscopy and density functional theory calculations at the (U)B3LYP/6‐31+G*/polarizable continuum model level of theory.     

Track Billiards

We study a class of planar billiards having the remarkable property that their phase space consists up to a set of zero measure of two invariant sets formed by orbits moving in opposite directions. The tables of these billiards are tubular neighborhoods of differentiable Jordan curves that are unions of finitely many segments and arcs of circles. We prove that under proper conditions on the segments and the arcs, the billiards considered have non-zero Lyapunov exponents almost everywhere. These results are then extended to a similar class of 3-dimensional billiards. Interestingly, we find that for some track billiards, the mechanism generating hyperbolicity is not the defocusing one, which requires every infinitesimal beam of parallel rays to defocus after every reflection off of the focusing boundary.     

Energy transfer in weakly coupled nonlinear oscillator chains: Transition from a wandering breather to nonlinear self-trapping

We present analytical and numerical studies of phase-coherent dynamics of intrinsically localized excitations (breathers) in a system of two weakly coupled nonlinear oscillator chains. We show that there are two qualitatively different dynamical regimes of the coupled breathers, either immovable or slowly moving: the periodic wandering of the low-amplitude breather between the chains, and the one-chain-localization of the high-amplitude breather. These two modes of coupled breathers can be mapped exactly onto two solutions of a pendulum equation, detached by a separatrix mode. We also show that these two regimes of the coupled breathers are similar, and are described by a similar pair of equations, to the two regimes in the nonlinear tunneling dynamics of two weakly coupled Bose-Einstein condensates. On the basis of this analogy, we predict a new tunneling mode of two weakly coupled Bose-Einstein condensates in which their relative phase oscillates around π/2 modulo π.