Some asymptotically optimal one-sided embeddings of trees of similar formulas into rectangular lattices

We consider the problem of optimally placing trees of formulas in rectangular lattices. We construct and study two types of these trees and corresponding ways of placing (embedding) them into such lattices. The first is based on perfect binary trees, while the second is based on special binary trees. For the second type of tree embeddings, we prove asymptotic optimality among the trees of all formulas similar to the initial formula of no greater depth.     

Application of numerical schemes with singling out the boundary layer for the computation of turbulent flows using eddy-resolving approaches on unstructured grids

The use of eddy-resolving approaches to solving problems on arbitrary unstructured grids is investigated. The applications of such approaches requires the use of low dissipation numerical schemes, which can lead to numerical oscillations of the solution on unstructured grids. Numerical oscillations typically occur in domains with large gradients of velocities, in particular, in the near-wall layer. It is proposed to single out the boundary layer and use a numerical scheme with increased numerical dissipation in it. The algorithm for singling out the boundary layer uses a switching function to change the parameters of the numerical scheme. This algorithm is formulated based on the BCD scheme from the family NVD. Its validity and advantages are investigated using the zonal RANS–LES approach for solving some problems of turbulent flow of incompressible fluids.     

Approximation algorithm for the problem of partitioning a sequence into clusters

We consider the problem of partitioning a finite sequence of Euclidean points into a given number of clusters (subsequences) using the criterion of the minimal sum (over all clusters) of intercluster sums of squared distances from the elements of the clusters to their centers. It is assumed that the center of one of the desired clusters is at the origin, while the center of each of the other clusters is unknown and determined as the mean value over all elements in this cluster. Additionally, the partition obeys two structural constraints on the indices of sequence elements contained in the clusters with unknown centers: (1) the concatenation of the indices of elements in these clusters is an increasing sequence, and (2) the difference between an index and the preceding one is bounded above and below by prescribed constants. It is shown that this problem is strongly NP-hard. A 2-approximation algorithm is constructed that is polynomial-time for a fixed number of clusters.     

The relationship between self-organization and membrane effects of aqueous dispersion systems of the thyroliberin oligopeptide

The relationship between rearrangement of the dispersed phase inducing considerable changes in the pH and nonmonotonic concentration dependences of membrane effects in aqueous systems of the endogenous regulatory peptide, thyroliberin (thyrotropin-releasing hormone), in 10^–3–10^–16 mol/L concentration range was demonstrated for the first time. The membrane structure modification in the 10^–13–10^–16 mol/L range was found to be due to accumulation of nanoassociates, while the oppositely directed pronounced structural changes in the 10^–6–10^–12 mol/L range may be associated with the coexistence and rearrangement of dispersed phases of various nature (domains and associates) whose action on membrane lipid components is regulated in this concentration range by the correlated changes in the dispersed phase parameters and pH.     

Electronic properties of achiral and chiral gold nanotubes

The band structure of ten single-walled gold nanotubes of different radius and chirality angle have been calculated by the linearized augmented cylindrical wave method. For all tubes, the Fermi level crosses the half-filled band; therefore, the tubes are characterized by a metallic electronic structure. The band structure of the nanotubes changes relatively weakly with a change in nanotube structure. The valence band width for all the tubes is 9.1 eV. The density of states at the Fermi level remains unaltered with a change in chirality angle and decreases by 30% with an increase in radius from 3 to 12 Å.     

Effect of 3<Emphasis Type="Italic">d</Emphasis>-metal dopants on the electronic properties of hexagonal titanium dioxide nanotubes

The electronic structure of hexagonal TiO₂ nanotubes doped with 3d transition metals from Sc to Zn was calculated by the linearized augmented cylindrical wave method. The calculated densities of states demonstrate that the substitution of Sc, V, Co, Cu, or Fe atoms for a part of Ti atoms leads to the decrease in the band gap width of the material from 4 to 2 eV. Such nanotubes are promising materials for creation of electrodes for electrochemical photolysis of water.     

Coprecipitation of calcium hydroxyapatite,graphene oxide,and chitosan from aqueous solutions

We determined the character of interactions between calcium hydroxyapatite Са₁₀(РO₄)₆(ОН)₂ (HA), graphene oxide (GO), and chitosan (С₆Н₁₁NO₄) _n (CHT) to yield HA/CHT/GO nanocomposites (NCs) in the СаС1₂–(NH₄)₂НРО₄–NH₃–Н₂О–(С₆Н₁₁NO₄) _n –GO system (25°С). A set of physicochemical methods helped us to elucidate composition–synthesis parameters–structure–particle size–properties correlations for the prepared NCs and to prove the feasibility to manufacture NCs with tailored HA, CHT, and GO contents, described by the bulk formula Са₁₀(РО₄)₆(ОН)₂ · х(С₆Н₁₁NO₄) _n · yGO · zН₂О, where х = 0.1, 0.2, 0.3; y = 0.6, 1.2, 2.4; and z = 6.0–7.4.     

Phase equilibria in the Cu–Cu<Subscript>2</Subscript>Se–As system

Phase equilibria in the Cu–Cu₂Se–As were investigated by differential thermal analysis and X-ray powder diffraction analysis. Informative plots describing this system were constructed, viz., the polythermal sections Cu_0.667Se_0.333–As, Cu_0.667Se_0.333–Cu_0.735As_0.265, and Cu_0.8Se_0.2–As, the isothermal section of the phase diagram at 300 K, and the projection of the liquidus surface. The obtained results differ from the published data in length of fields of primary crystallization of phases and in coordinates of a number of invariant equilibrium points.     

Copper(II), nickel(II), and zinc(II) complexes with <Emphasis Type="Italic">o</Emphasis>-tozylaminobenzaldehyde 4,6-dimethylpyrimidyl hydrazone

o-Tosylaminobenzaldehyde dimethylpyrimidyl hydrazone and its copper(II), nickel(II), and zinc(II) complexesare synthesized and studied. According to the X-ray diffraction data, the zinc(II) complex has the structure of a tetragonal pyramid with the N₃O donor ligand environment. According to EPR and magnetochemistry data, the copper(II) complex has a similar structure of the chelate core. In the nickel(II) complex, the solvent molecule completes the coordination core to an octahedron.