On the Lagrange Problem on the Optimal Form for Circular Columns

A new approach to the classical Lagrange problem on the form of the strongest circular column of fixed volume and height clamped at both ends is proposed. The existence of the optimal column is proved and an algorithm for finding its design is given.__________Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 10, Suzdal Conference-4, 2003.An erratum to this article can be found at .     

First synthesis of cyclic organogermanium peroxides, 1,2,4,5,7,8-hexaoxa-3-germonanes

First, previously unknown, cyclic organogermanium peroxides, 1,2,4,5,7,8-hexaoxa-3-germonanes, were synthesized by the reaction of 1,1′-dihydroperoxydi(cyclododecyl)peroxide with (di)alkyl(aryl)dihalogengermanes. The new compounds have a higher tendency to undergo hydrolysis compared to silicon-containing analogs.     

Specific features of the melting of poly(ethylene terephthalate) after its thermal and mechanical treatment

Specific features of the melting of PET samples with different molecular masses after their thermal and mechanical treatment (orientational drawing) are studied by the DSC method. Orientational drawing of the samples leads to the development of a supermolecular structure, which depends on the molecular mass and thermal prehistory of the initial samples.     

Optical Properties of Three-Dimensional InGaP(As) Islands Formed by Substitution of Fifth-Group Elements

Optics and Spectroscopy - The optical properties of three-dimensional quantum-size InGaPAs islands, which are formed by substitution of phosphorous by arsenic in an InGaPAs layer deposited on GaAs...     

Effect of nonequilibrium processes in the infrasonic and ultrasonic regions of a nozzle on population inversion in flow of CO2 - N - O2 - H2O gas mixtures

The processes of oscillatory relaxation in flow through nozzles of CO₂, N₂, O₂, H₂O gas mixtures are studied. The effect of various oscillatory-oscillatory and osciallatory-translational exchange channels between mixture components and CO₂ intermode energy-exchange Channels on population inversion is examined. The importance of considering nonequilibrium processes in the infrasonic region of the nozzle is noted. The effect of inclined shock waves on flow characteristics in the supersonic nozzle region and population inversion is studied.     

Spherical polymer brushes under good solvent conditions: molecular dynamics results compared to density functional theory

A coarse grained model for flexible polymers end-grafted to repulsive spherical nanoparticles is studied for various chain lengths and grafting densities under good solvent conditions by molecular dynamics methods and density functional theory. With increasing chain length, the monomer density profile exhibits a crossover to the star polymer limit. The distribution of polymer ends and the linear dimensions of individual polymer chains are obtained, while the inhomogeneous stretching of the chains is characterized by the local persistence lengths. The results on the structure factor of both single chain and full spherical brush as well as the range of applicability of the different theoretical tools are presented. Finally, a brief discussion of the experiment is given.     

Reaction of rhodium trichloride with oxyethylated calix[4]resorcinarene

Reaction of rhodium trichloride with a new ligand, oxyethylated calix[4]resorcinarene was examined in an inert atmosphere in different solvents (acetone, acetone + chloroform). The product was characterized by IR, Raman, ¹H NMR, ESR, ESCA spectroscopy, conductometry. Its composition was proved by the data of elemental and X-ray fluorescent analyses. The solvent used does not affect the composition of the product but only its yield. The structure of the coordination node and the type of coordination of the rhodium-containing fragment was investigated by calculating the model molecules of the ligand and the complex using the molecular mechanics method (MM+).