Synthesis of unsaturated organosilicon compounds from propargyl alcohol

Summary -Trialkylsilylpropargyl and allyl alcohols, and also propargyloxysilanes were synthesized from propargyl alcohol.     

Structural nonuniformity of detonation-produced diamond-containing material

Raman backscattering spectra (RBS), infrared spectra, and X-ray diffraction intensity curves for various fractions of ultradispersed diamond-containing material (UDDCM) were recorded. The RBS and XRD curves obtained suggest that UDDCM is characterized by sharp variations in the ratio between the diamond and nondiamond components, a factor that makes it possible to consider this phase as an individual product and determines the scale of variations in the main characteristics. Fine UDDCM fractions contain only small amounts diamond-like (sp ³ carbon) grains, if any. One possible reason for changes in the ratio between the phases is density fluctuations under nonequilibrium conditions of synthesis.     

Technology of polishing of titanium surface using the fiber-laser radiation

The effect of the radiation of the pulsed fiber laser on the surfaces of cylindrical samples made of the VT16 titanium alloy is studied. It is demonstrated that the irradiation at appropriate parameters of the laser radiation in the inert-gas (argon) atmosphere leads to an increase in the microhardness of the surface layer and a decrease in the surface roughness of the irradiated samples by a factor of five in comparison with the roughness of the original samples.     

Laser photoelectron projection microscopy of an organic conducting polymer

A conducting organic polymer is visualized on a laser photoelectron projection microscope, which is based on Letokhov’s concept and has a nanometer spatial resolution. Photoelectron images of polyaniline (which is the most promising representative of conducting polymers) with a magnification of ∼10⁵ have been obtained when a 100-nm quartz capillary coated with a film of this material was irradiated by femtosecond laser pulses. The projection photoelectron method using 400- and 800-nm laser radiation has made it possible to directly reveal the existence of the redox heterogeneity of the organic polymer, which is due to the contact of the sections of polyaniline with different oxidation degrees and strongly affects the electric conductivity of the sample.     

An energy functional for Lagrangian tori in $$\mathbb {C}P^2$$

A two-dimensional periodic Schrödingier operator is associated with every Lagrangian torus in the complex projective plane \({\mathbb C}P^2\). Using this operator, we introduce an energy functional on the set of Lagrangian tori. It turns out this energy functional coincides with the Willmore functional \(W^{-}\) introduced by Montiel and Urbano. We study the energy functional on a family of Hamiltonian-minimal Lagrangian tori and support the Montiel–Urbano conjecture that the minimum of the functional is achieved by the Clifford torus. We also study deformations of minimal Lagrangian tori and show that if a deformation preserves the conformal type of the torus, then it also preserves the area, i.e., preserves the value of the energy functional. In particular, the deformations generated by Novikov–Veselov equations preserve the area of minimal Lagrangian tori.     

Zero level of a purely magnetic two-dimensional nonrelativistic Pauli operator for SPIN-1/2 particles

We study the manifold of complex Bloch-Floquet eigenfunctions for the zero level of a two-dimensional nonrelativistic Pauli operator describing the propagation of a charged particle in a periodic magnetic field with zero flux through the elementary cell and a zero electric field. We study this manifold in full detail for a wide class of algebraic-geometric operators. In the nonzero flux case, the Pauli operator ground state was found by Aharonov and Casher for fields rapidly decreasing at infinity and by Dubrovin and Novikov for periodic fields. Algebraic-geometric operators were not previously known for fields with nonzero flux because the complex continuation of “magnetic” Bloch-Floquet eigenfunctions behaves wildly at infinity. We construct several nonsingular algebraic-geometric periodic fields (with zero flux through the elementary cell) corresponding to complex Riemann surfaces of genus zero. For higher genera, we construct periodic operators with interesting magnetic fields and with the Aharonov-Bohm phenomenon. Algebraic-geometric solutions of genus zero also generate soliton-like nonsingular magnetic fields whose flux through a disc of radius R is proportional to R (and diverges slowly as R → ∞). In this case, we find the most interesting ground states in the Hilbert space L ₂ (ℝ ² ).