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.     

Modified relations for calculating the dielectric constant of barium–strontium titanate nanofilms

The results of measuring the capacitances of planar capacitors are used to calculate the dielectric constants of barium–strontium titanate nanofilms. An expression is derived to calculate an adjustable coefficient to obtain adequate dielectric constants for 20-nm-thick ferroelectric films. The field of applicability of the adjustable coefficient is determined.     

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).     

Specific features of the ferroelectric state in two-layer barium strontium titanate-based heterostructures

The structural properties of one- and two-layer heterostructures based on the barium–strontium titanate of various compositions deposited by the Frank–Van der Merve on a magnesium oxide substrate have been studied. The heterostructures have been prepared by the rf sputtering of the stoichiometric ceramic targets in a Plazma 50 SE deposition system. The principal difference of this method of deposition from known analogs is that the growth of single-crystal films occurs from a disperse oxide phase formed in the plasma of a high-current rf discharge during the ceramic target sputtering at the cluster level. The peculiarities of the manifestation of the ferroelectric state in the two-layer heterostructures when changing the sequence order of the films with various compositions of barium–strontium titanate.     

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.