FPT-algorithms for some problems related to integer programming

In this paper, we present FPT-algorithms for special cases of the shortest lattice vector, integer linear programming, and simplex width computation problems, when matrices included in the problems' formulations are near square. The parameter is the maximum absolute value of rank minors of the corresponding matrices. Additionally, we present FPT-algorithms with respect to the same parameter for the problems, when the matrices have no singular rank sub-matrices.Comment: arXiv admin note: text overlap with arXiv:1710.00321 From author: some minor corrections has been don

Isoperiodic deformations of the acoustic operator and periodic solutions of the Harry Dym equation

We consider the problem of describing the possible spectra of an acoustic operator with a periodic finite-gap density. We construct flows on the moduli space of algebraic Riemann surfaces that preserve the periods of the corresponding operator. By a suitable extension of the phase space, these equations can be written with quadratic irrationalities.Comment: 15 page

Quantum discrete Dubrovin equations

The discrete equations of motion for the quantum mappings of KdV type are given in terms of the Sklyanin variables (which are also known as quantum separated variables). Both temporal (discrete-time) evolutions and spatial (along the lattice at a constant time-level) evolutions are considered. In the classical limit, the temporal equations reduce to the (classical) discrete Dubrovin equations as given in a previous publication. The reconstruction of the original dynamical variables in terms of the Sklyanin variables is also achieved.Comment: 25 page

Whittaker-Hill equation and semifinite-gap Schroedinger operators

A periodic one-dimensional Schroedinger operator is called semifinite-gap if every second gap in its spectrum is eventually closed. We construct explicit examples of semifinite-gap Schroedinger operators in trigonometric functions by applying Darboux transformations to the Whittaker-Hill equation. We give a criterion of the regularity of the corresponding potentials and investigate the spectral properties of the new operators.Comment: Revised versio

Faddeev eigenfunctions for two-dimensional Schrodinger operators via the Moutard transformation

We demonstrate how the Moutard transformation of two-dimensional Schrodinger operators acts on the Faddeev eigenfunctions on the zero energy level and present some explicitly computed examples of such eigenfunctions for smooth fast decaying potentials of operators with non-trivial kernel and for deformed potentials which correspond to blowing up solutions of the Novikov-Veselov equation.Comment: 11 pages, final remarks are adde

Heavy quark potential in lattice QCD at finite temperature

Results of the study of lattice QCD with two flavors of nonperturbatively improved Wilson fermions at finite temperature are presented. The transition temperature for m_{\pi}/m_{\rho} \sim 0.8 and lattice spacing a \sim 0.12 fm is determined. A two-exponent ansatz is successfully applied to describe the heavy quark potential in the confinement phase.Comment: 3 pages, 1 figure, talk given at the 5th International Conference on Quark Confinement and the Hadron Spectrum, Gargnano, Italy, 10-14 Sep 200

Sub-nanosecond Pulse Generation from a Two-section Laser-thyristor: Theoretical Analysis

We have developed a theoretical model of a two-section laser-thyristor. It is shown that using a 4 µm weakly doped p-base can increase blocking voltage up to 50 V, which makes it possible to generate 2 ns 10 A current pulses. It is demonstrated that the proposed device utilizes passive Q switching to generate high-power short optical pulses that account for up to 80% of output power. By picking the optimal passive section length, we have achieved optical pulses of ∼30 ps full width at half maximum (FWHM) and ∼100 W peak power.     Keywords: pulsed laser, semiconductor N-p-N-i-P heterostructure, laser-thyristor, dynamic model of pulsed lase