The number of edge covers of bipartite graphs or of shortest paths with fixed endpoints in the space of compact sets in <Emphasis Type="Italic">R</Emphasis> <Superscript> <Emphasis Type="Italic">n</Emphasis> </Superscript>

The possible number of shortest paths joining points in the metric space of compact sets in Euclidean space endowed with the Hausdorff metric is studied. For all n ≤ 1000, except eight values, it is checked whether n can equal the number of such shortest paths. In particular, new lacunas are found, namely 41, 59, and 67 (previously, only two such lacunas, 19 and 37, were known).     

The nature of sites of absorption of low-molecular-mass compounds by butadiene–acrylonitrile copolymers

The rotational mobilities of the paramagnetic probes TEMPO (2,2,6,6-tetramethylpiperidine-1-oxyl) and BZONO (4-benzoate-2,2,6,6-tetramethylpiperidine-1-oxyl) are studied via EPR spectroscopy and the equilibrium swelling of random and multiblock butadiene–acrylonitrile copolymers of various compositions and stereostructures of butadiene units in n-heptane, methyl acetate, and toluene are studied. The nature of defective regions sorbing low-molecular-mass compounds is ascertained. The rotational mobilities of the probes in defects of various structures are estimated. The sites of sorption are found to be identical in crosslinked and noncrosslinked elastomers. It is shown that the sorption of n-heptane and methyl acetate appears in the same defective regions as those of the TEMPO radical, while the sorption of toluene emerges in sorption sites where the value of free volume is sufficient for the sorption of the bulky radical BZONO. A decay in local molecular mobility in structural defects (“holes”) does not hinder the absorption of lowmolecular- mass compounds if the free volume is sufficient.     

Networking particles over distance using oligonucleotide-based devices

Microparticles covered with DNA-based computing elements that sense inputs and release oligonucleotides as outputs could be used to construct autonomous networks with increasingly complex functions. We demonstrate cascades of particles with up to three layers and a nonlinear network with an AND gate hub. In order to establish functional networks, particles do not have to be in direct physical contact.     

Insight into the permeation barrier of glued Langmuir-Blodgett bilayers

Permeation measurements have been made for He, CO2, and N2 across single Langmuir-Blodgett (LB) bilayers derived from 1,2,4,5-tetrakis[(N-(undecanoamidoethyl)-N,N-dimethyl ammonium) methyl]benzene tetrabromide (2) and 1,2,4,5-tetrakis[(N-(perfluoroundecanoamidoethyl)-N,N-dimethyl ammonium)methyl]benzene tetrabromide (3) in the absence and in the presence of entrapped poly(acrylic acid) (PAA). In the absence of PAA, single LB bilayers of 3 show a higher permeance for He and N2 but a lower permeation rate of CO2, as compared with analogous LB bilayers made from 2. The relatively low permeation rate of CO2 for the former has been attributed to reduced associative interactions with the fluorocarbon-rich bilayer. The same behavior has also been observed for LB bilayers containing PAA, formed under conditions that yield glued bilayers of 2 and 3 having similar diffusional pathways, as judged by He/N2 selectivities. These results, together with the fact that glued bilayers of 2 (having a thinner PAA layer as compared with those made from 3) exhibit lower He and N2 permeances, provide compelling evidence that the main barrier for gas transport is the combination of surfactant plus PAA and not simply a thin PAA layer that is encased within the surfactant bilayer.     

Third-order diamagnetic susceptibilities of hydrogenlike atoms

We develop a method for calculating diamagnetic susceptibilities based on higher-order perturbation theory for the wave function and energy of the excited states of the hydrogen atom with degeneracy of arbitrary multiplicity. We derive analytical expressions for third-order matrix elements in the spherical states |nlm〉 with fixed principal quantum number n and magnetic quantum number m. The formulas for the susceptibilities of doubly degenerate levels are represented in the form of radical-fractional relationships containing polynomials in the principal quantum number. We establish the existence of a monotonic interdependence between the absolute values of susceptibilities of the first three orders. We also present the results of numerical calculations for the states with n⩽6 and m⩽3 mixed by the field. Finally, for Rydberg states with large n and small m we detect the existence of a discontinuity in the interdependence of the susceptibilities at the boundary between the doublet and equidistant parts of the spectrum of diamagnetic sublevels with opposite parities. Zh. éksp. Teor. Fiz. 116, 838–857 (September 1999)     

Fine-structure effects in relativistic calculations of the static polarizability of the helium atom

We use the relativistic configuration-interaction method and the model potential method to calculate the scalar and tensor components of the dipole polarizabilities for the excited states 1s3p ³ P ₀ and 1s3p ³ P ₂ of the helium atom. The calculations of the reduced matrix elements for the resonant terms in the spectral expansion of the polarizabilities are derived using two-electron basis functions of the relativistic Hamiltonian of the atom, a Hamiltonian that incorporates the Coulomb and Breit electron-electron interactions. We formulate a new approach to determining the parameters of the Fuss model potential. Finally, we show that the polarizability values are sensitive to the choice of the wave functions used in the calculations. Zh. éksp. Teor. Fiz. 115, 494–504 (February 1999)     

Conversion Rate Prediction Based on Text Readability Analysis of Landing Pages

Digital marketing has been extensively researched and developed remarkably rapidly over the last decade. Within this field, hundreds of scientific publications and patents have been produced, but the accuracy of prediction technologies leaves much to be desired. Conversion prediction remains a problem for most marketing professionals. In this article, the authors, using a dataset containing landing pages content and their conversions, show that a detailed analysis of text readability is capable of predicting conversion rates. They identify specific features that directly affect conversion and show how marketing professionals can use the results of this work. In their experiments, the authors show that the applied machine learning approach can predict landing page conversion. They built five machine learning models. The accuracy of the built machine learning model using the SVM algorithm is promising for its implementation. Additionally, the interpretation of the results of this model was conducted using the SHAP package. Approximately 60% of purchases are made by nonmembers, and this paper may be suitable for the cold-start problem.     

Spin-filter tunneling in superconducting mesa structures with a ferromagnetic manganite interlayer

We have studied the current transport and magnetism in epitaxial hybrid superconducting mesa structures consisting of a cuprate superconductor and superconducting niobium with a manganite LaMnO₃ (LMO) interlayer. We have shown experimentally using magnetic resonance that the magnetization, magnetic anisotropy parameters, and transition temperature to the ferromagnetic state of the interlayer of the structures are analogous to those of an autonomous LMO film grown on a neodymium gallate substrate. The estimate of the barrier height obtained from the dependence of the characteristic resistance of mesa structures on the interlayer thickness has shown the barrier height variation with the thickness in the range of 5–30 mV. The temperature dependences of the conductivity of the mesa structure in the range between superconducting transition temperatures of the superconductors can be described in the theory taking into account the d-wave nature of the superconductivity for one of the electrodes and the spin-filtering of carriers passing through the tunnel interlayer. Spin-filtering is confirmed by the tunnel magnetoresistance and the high sensitivity of mesa structures to a weak external magnetic field in a voltage interval smaller than the gap of niobium.     

Proximity effect in the finite and incommensurate ferromagnet/superconductor systems

The original theory of a proximity effect is proposed for the bi- and tri-layered system ferromagnetic metal/superconductor (F/S) in dirty limit. The F₁/S/F₂ trilayer is examined more closely. The distinctions in materials, in thicknesses of F layers (d_f1 and d_f2), in parameters interfaces, and in local environments of layers are considered among the causes of incommensurability of trilayer. The peculiar T_c(d_f1, d_f2) interference pattern is predicted for the F₁/S/F₂ systems. The reentrant superconductivity and possibility of the better observability of the spin-valve regime are discussed.     

A Statistical Analysis of Cyclical Changes in the Time Series of Meteorological Parameters in the Southwest of the Valdai Hills

A statistical analysis of periodic and cyclical components of time series of meteorological parameters was conducted for the 40-year observation period in the southwest of the Valdai Hills by classic seasonal decomposition and Fourier analysis. The dependence of the obtained OLS estimates of linear-regression models of meteorological parameters on a length of the smoothing interval was analyzed. Cyclical fluctuations in the time series of temperature with periods of 8 and 3 years and those of rainfall with periods of 3.5 and 10.5 years were detected and analyzed.