Concurrent Covalent and Supramolecular Polymerization

Covalent and supramolecular polymerizations, both of which offer their own unique advantages, have emerged as popular strategies for making artificial materials. Herein, we describe a concurrent covalent and supramolecular polymerization strategy—namely, one which utilizes 1) a bis‐azide‐functionalized diazaperopyrenium dication that undergoes polymeriation covalently with a bis‐alkyne‐functionalized biphenyl derivative in one dimension as a result of a rapid and efficient β‐cyclodextrin(CD)‐accelerated, cucurbit[6]uril(CB)‐templated azide–alkyne cycloaddition, while 2) the aromatic core of the dication is able to dimerize in a criss‐cross fashion by dint of π–π interactions, enabling simultaneous supramolecular assembly, resulting in an extended polymer network in an orthogonal dimension.     

Expedient Strategy for the Synthesis of 5-Acylethynylpyrrole-2-carbaldehydes

5-Acylethynylpyrrole-2-carbaldehydes have been synthesized from the protected pyrrole-2-carbaldehydes by their transition-metal-free topochemical mechanoactivated ethynylation with acylbromoacetylenes in a solid Al₂O₃ medium (room temperature, 6 h, 41–54% yields).     

A Convenient Method for the Synthesis of α-Functionalized Chlorophosphonic Esters

α-Functionalized chlorophosphonic monoesters were easily prepared by a selective chlorination of the corresponding phosphonic diesters with phosphorus oxychloride.     

Quantum Hamiltonians with Weak Random Abstract Perturbation. I. Initial Length Scale Estimate

We study random Hamiltonians on finite-size cubes and waveguide segments of increasing diameter. The number of random parameters determining the operator is proportional to the volume of the cube. In the asymptotic regime where the cube size, and consequently the number of parameters as well, tends to infinity, we derive deterministic and probabilistic variational bounds on the lowest eigenvalue, i.e., the spectral minimum, as well as exponential off-diagonal decay of the Green function at energies above, but close to the overall spectral bottom.     

Koplienko Spectral Shift Function on the Unit Circle

The note shows that, for every pair of contractions, a trace formula of Koplienko holds with a summable spectral shift function, see Theorem 1 below. This answers a question by F. Gesztesy, A. Pushnitski, B. Simon (see Zh Mat Fiz Anal Geom 4(1):63–107, 202, 2008, Open Question 11.2).     

Mechanism of Hydrolysis of 1,1,1-Trisubstituted Hyposilatranes and Hypogermatranes

Russian Journal of Organic Chemistry - According to DFT calculations, hydrolysis of 1,1,1-trisubstituted hyposilatranes and hypogermatranes proceed in one stage and have lower activation energies...     

A Compact Cauchy-Kovalevskaya Extension Formula in Discrete Clifford Analysis

We prove a compact expression for the Cauchy-Kovalevskaya extension in the setting of discrete Clifford analysis; it seamlessly simplifies to the well-know exponential formula in the continuous setting when the discrete step size tends to zero.