Electronic spectrum of the three-dimensional Penrose lattice

The electronic spectrum of the three-dimensional Penrose lattice with “central” decoration by atoms is investigated using the tight binding model with nearest-neighbor interaction. Inverse participation ratios, higher moments of density probabilities, and fractal dimensions of the system are determined. The WFs are critical (they have a power-law dependence on the distance) at all energies in the band and are multifractal measures leading to the entire spectrum of the exponents. The results show that the system is in the critical state of the metal-insulator transition. On critical WFs, the cubic root temperature dependence of the conductivity is obtained.     

Output-feedback control robust stabilization of nonlinear pulse systems

A nonlinear pulse systems with a time-variant continuous linear part is considered. A method for synthesizing an output-feedback robust stabilizing control is suggested.     

Effect of oxygen stoichiometry and microstructure on superconducting properties of YBaCuO films

Microstructure and oxygen stoichiometry of YBaCuO films manufactured by laser ablation are investigated. Dependence of the specific electrical resistivity and superconducting parameters of films on microstructure and oxygen stoichiometry is demonstrated. Conditions of deposition are determined, under which films with minimum microstructure defects and good conducting properties are formed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 41–45, February, 2007.     

New methods for proving the existence and stability of periodic solutions in singularly perturbed delay systems

We carry out a detailed analysis of the existence, asymptotics, and stability problems for periodic solutions that bifurcate from the zero equilibrium state in systems with large delay. The account is based on a specific meaningful example given by a certain scalar nonlinear second-order differential-difference equation that is a mathematical model of a single-circuit RCL oscillator with delay in a feedback loop.     

Nonlinear resistor based on a polymer-ceramic composition

The resistivity of composite nonlinear resistors (varistors) consisting of zinc oxide ceramic and high-density polyethylene, as well as IR spectra and X-ray diffraction patterns taken of the samples, are studied. The component composition of the resistor is shown to influence its resistivity and IR and X-ray spectra.     

Supramolecular Complexes of Diglycidyl Methylphosphonate with Calix[4]resorcinolarene

Various-composition supramolecular complexes of calix[4]resorcinolarene with diglycidyl methylphosphonate were synthesized in organic solvents. The products have well-defined melting points, they are cleaved by acetylation, but remain unchanged on treatment with triethylamine.     

Design of thin-walled viscoelastic shells with allowance for damage

Azerbaidzhan Institute of Construction Engineering, Baku. Translated from Prikladnaya Mekhanika, Vol. 27, No. 1, pp. 55–64, January, 1991.     

Attractors of the sine-Gordon equation in the field of a quasiperiodic external force

The well-known sine-Gordon equation, supplemented with small damping and small quasiperiodic external force, is studied under the zero Dirichlet boundary conditions at the endpoints of a finite interval. The main assumption is that all frequencies of the external force are in 1:1 resonance with certain eigenfrequencies of the unperturbed equation; i.e., the socalled fundamental multifrequency resonance is observed. It is shown that in this case, by an appropriate choice of the parameters of the external force, one can make it so that the boundary value problem has a stable invariant torus of any finite dimension that bifurcates from zero on any preassigned finite set of spatial modes. It is also shown (by numerical analysis) that in a number of cases the above-mentioned torus coexists with a chaotic attractor.