Second Kind Representations of Sobolev Space Solutions to a First Order General Elliptic Linear System in a Simply Connected Plane Domain

Siberian Mathematical Journal - We consider a second kind representation for solutions to a first order general uniformly elliptic linear system in a simply connected...     

Specialty Yb fiber amplifier for microchip Nd laser: Towards ∼1-mJ/1-ns output at kHz-range repetition rate

We demonstrate and optimize, for a mJ/ns release at the wavelength 1.064 μm, the operation of a compact laser system designed in the form of a hybrid, active-passive, Q-switched Nd³⁺:YAG/Cr⁴⁺:YAG microchip laser seeding an Yb-doped specialty multi-port fiber amplifier. As the result of the amplifier optimization, ∼1 mJ, ∼1 ns, almost single-mode pulses at a 1-10-kHz repetition rate are achieved, given by a gain factor of ∼19 dB for an 11-μJ input from the microchip laser. Meanwhile, a lower pulse energy, ∼120 μJ, but a much higher gain (∼25 dB) are eligible for the less powerful (0.35 μJ) input pulses.     

Effect of low-threshold air breakdown on material ablation by short laser pulses

Ablative formation of channels in steel by picosecond and nanosecond pulses of Nd lasers was studied. It was found that significant screening of the incident energy (up to 80–90%) in this pulse duration range is caused by breakdown of air contaminated with ablated microparticles. The breakdown threshold, size of particles, and time of their settling down were estimated. It was shown that this kind of plasma screening results in a decrease in the ablation rate and significant channel widening. Practical approaches to eliminate the low-threshold breakdown induced by microparticles were proposed and implemented. These approaches are based on experimental results of the study of the dependences of laser ablation on the pressure and repetition rate. It was shown that a moderate decrease in the pressure below 300–400 mbar makes it possible to avoid screening. In high-repetition-rate ablation, it was found that values above several kilohertz correspond to quasi-vacuum conditions in the ablation spot.     

Extension of higher-order infinitesimal bendings of a simply connected surface of positive curvature with boundary conditions

We study continuous and infinitesimal bendings of orderk (k-bendings) of a simply connected surface of positive curvature with boundary conditions. We study the question of the extension ofk-bendings satisfying some boundary condition to continuous bendings satisfying an analogous boundary condition.Translated from Ukrainskií Geometricheskií Sbornik, No. 30, 1987, pp. 41–49.     

Some sufficient conditions for immersion in the large of metrics of positive curvature

It is proved that a regular Riemannian manifold diffeomorphic to a circle and having positive Gaussian curvature bounded from zero is immersible into a three-dimensional Euclidean space in the form of a regular surface if it has smallL _p (the norm of the gradient of Gaussian curvature), p > 2, or if it has a sufficiently small area (with any behavior of the geodesic boundary curvature).Translated from Ukrainskii Geometricheskii Sbornik, No. 34, pp. 51–59, 1991.