Quadratic differentials in problems of the product of inner radii of nonoverlapping domains

We study applications of the theory of quadratic differentials to the solution of new extremal problems of nonoverlapping domains with free poles on rays and generalize known results to a certain class of open sets. __________ Translated from Neliniini Kolyvannya, Vol. 10, No. 4, pp. 435–442, October–December, 2007.     

Decompositions of continuity and complete continuity

We introduce the notions of δ-t-sets, δ_β-t-sets, δ-B-continuity and δ_β -B-continuity and obtain decompositions of continuity and complete continuity.     

Optical bistability of planar metal/dielectric nonlinear nanostructures

We study theoretically a nonlinear response of the planar metal/dielectric nanostructures constituted from periodical array of ultra thin silver layers and the layers of Kerr-like nonlinear dielectric. We predict hysteresis-type dependences of the components of the tensor of effective dielectric permittivity on the field intensity allowing the change in material transmission properties from transparent to opaque and back at extremely low intensities of the light. It makes possible to control the light by light in all-optical nanoscale devices and circuits.     

Thermodynamic study of a series lithium β-diketonates

Thermal behaviour of a series of lithium β-diketonates: Li(dpm) (dpm=dipivaloylmethanate (2,2,6,6-tetramethylheptane-3,5- dionate)), Li(pta) (pta=pivaloyltrifluoracetonate (2,2-dimethyl-6,6,6-trifluoro-3,5-hexanedionate)), Li(tfa) (tfa=trifluoracetylacetonate (1,1,1-trifluoro-2,4-pentandionate)), Li(hfa) (hfa=hexafluoracetylacetonate (1,1,1,5,5,5-hexafluoro-2,4-pentandionate)) has been investigated. Gas phase composition of these complexes has been established. Temperature dependences of vapor pressure of lithium compounds were obtained by static and dynamic methods, and thermodynamic parameters were calculated. Dependence of compound volatility on ligand structure is shown. For Li(dpm) detailed investigation has been done by differential scanning calorimetry (DSC).     

Surface morphology of electrolytic deposits of vanadium, cobalt, and manganese oxides

The surface morphology of V₂O₅, Co₂O₃, and MnO₂ electroplated under different electrolysis conditions was studied. The nature of the electrocrystallization of these materials was suggested on the basis of the analysis results.     

Changes in the supramolecular structure of heat-resistant polyimide fibers in the course of thermal treatment

Changes in the supramolecular structure of heat-resistant fibers based on polyimide PM were studied by X-ray diffraction analysis and NMR spectroscopy.     

Low sintering temperature MnZn-ferrites for power applications in the frequency region of 400 kHz

In this paper, the effect of cubic zinc metaborate Zn₄O(BO₂)₆ on the sintering of MnZn-ferrites for medium frequency power applications is investigated. Zinc metaborate is synthesized in the laboratory using zinc oxide and boric acid as metal precursors. As observed, when zinc metaborate is added to the MnZn-ferrites at an optimum amount of 0.02 wt%, it significantly enhances densification and therefore allows, for a given density, reduction of the firing temperature by almost 200 °C. MnZn-ferrites exhibiting power losses of 70 mW/cm³ (measured at a frequency of 400 kHz, magnetic field 50 mT and temperature of 90 °C) are synthesized from conventionally milled powders with average particle diameter 0.6 μm, compacted and fired at 1100 °C. Identical experiments conducted under the same conditions on specimens without zinc metaborate additions revealed power losses greater than 300 mW/cm³, because of insufficient densification.     

Melting of heterogeneous vortex matter: The vortex ‘nanoliquid’

Disorder and porosity are parameters that strongly influence the physical behavior of materials, including their mechanical, electrical, magnetic and optical properties. Vortices in superconductors can provide important insight into the effects of disorder because their size is comparable to characteristic sizes of nanofabricated structures. Here we present experimental evidence for a novel form of vortex matter that consists of inter-connected nanodroplets of vortex liquid caged in the pores of a solid vortex structure, like a liquid permeated into a nanoporous solid skeleton. Our nanoporous skeleton is formed by vortices pinned by correlated disorder created by high-energy heavy ion irradiation. By sweeping the applied magnetic field, the number of vortices in the nanodroplets is varied continuously from a few to several hundred. Upon cooling, the caged nanodroplets freeze into ordered nanocrystals through either a first-order or a continuous transition, whereas at high temperatures a uniform liquid phase is formed upon delocalization-induced melting of the solid skeleton. This new vortex nanoliquid displays unique properties and symmetries that are distinct from both solid and liquid phases.