Inverse spectral problems for Sturm--Liouville operators with matrix-valued potentials

We give a complete description of the set of spectral data (eigenvalues and specially introduced norming constants) for Sturm--Liouville operators on the interval $[0,1]$ with matrix-valued potentials in the Sobolev space $W_2^{-1}$ and suggest an algorithm reconstructing the potential from the spectral data that is based on Krein's accelerant method.Comment: 39 pages, uses iopart.cls, iopams.sty and setstack.sty by IO

Inverse Spectral-Scattering Problem with Two Sets of Discrete Spectra for the Radial Schroedinger Equation

The Schroedinger equation on the half line is considered with a real-valued, integrable potential having a finite first moment. It is shown that the potential and the boundary conditions are uniquely determined by the data containing the discrete eigenvalues for a boundary condition at the origin, the continuous part of the spectral measure for that boundary condition, and a subset of the discrete eigenvalues for a different boundary condition. This result extends the celebrated two-spectrum uniqueness theorem of Borg and Marchenko to the case where there is also a continuous spectru

Bunching Transitions on Vicinal Surfaces and Quantum N-mers

We study vicinal crystal surfaces with the terrace-step-kink model on a discrete lattice. Including both a short-ranged attractive interaction and a long-ranged repulsive interaction arising from elastic forces, we discover a series of phases in which steps coalesce into bunches of n steps each. The value of n varies with temperature and the ratio of short to long range interaction strengths. We propose that the bunch phases have been observed in very recent experiments on Si surfaces. Within the context of a mapping of the model to a system of bosons on a 1D lattice, the bunch phases appear as quantum n-mers.Comment: 5 pages, RevTex; to appear in Phys. Rev. Let

On a systematic approach to defects in classical integrable field theories

We present an inverse scattering approach to defects in classical integrable field theories. Integrability is proved systematically by constructing the generating function of the infinite set of modified integrals of motion. The contribution of the defect to all orders is explicitely identified in terms of a defect matrix. The underlying geometric picture is that those defects correspond to Backlund transformations localized at a given point. A classification of defect matrices as well as the corresponding defect conditions is performed. The method is applied to a collection of well-known integrable models and previous results are recovered (and extended) directly as special cases. Finally, a brief discussion of the classical $r$-matrix approach in this context shows the relation to inhomogeneous lattice models and the need to resort to lattice regularizations of integrable field theories with defects.Comment: 27 pages, no figures. Final version accepted for publication. References added and section 5 amende

Explicit solutions to the Korteweg-de Vries equation on the half line

Certain explicit solutions to the Korteweg-de Vries equation in the first quadrant of the $xt$-plane are presented. Such solutions involve algebraic combinations of truly elementary functions, and their initial values correspond to rational reflection coefficients in the associated Schr\"odinger equation. In the reflectionless case such solutions reduce to pure $N$-soliton solutions. An illustrative example is provided.Comment: 17 pages, no figure

New Constraints on the Origin of the Short-Term Cyclical Variability of the Wolf-Rayet Star WR 46

The Wolf-Rayet star WR 46 is known to exhibit a very complex variability pattern on relatively short time scales of a few hours. Periodic but intermittent radial velocity shifts of optical lines as well as multiple photometric periods have been found in the past. Non-radial pulsations, rapid rotational modulation or the presence of a putative low-mass companion have been proposed to explain the short-term behaviour. In an effort to unveil its true nature, we observed WR 46 with FUSE (Far Ultraviolet Spectroscopic Explorer) over several short-term variability cycles. We found significant variations on a time scale of ~8 hours in the far-ultraviolet (FUV) continuum, in the blue edge of the absorption trough of the OVI {\lambda}{\lambda}1032, 1038 doublet P Cygni profile and in the SVI {\lambda}{\lambda}933, 944 P Cygni absorption profile. We complemented these observations with X-ray and UV light-curves and an X-ray spectrum from archival XMM-Newton (X-ray Multi-Mirror Mission - Newton Space Telescope) data. The X-ray and UV light-curves show variations on a time scale similar to the variability found in the FUV. We discuss our results in the context of the different scenarios suggested to explain the short-term variability of this object and reiterate that non-radial pulsations is the most likely to occur.Comment: 36 pages, 11 figures. Accepted for publication in Ap

Eigenvalue Distributions for a Class of Covariance Matrices with Applications to Bienenstock-Cooper-Munro Neurons Under Noisy Conditions

We analyze the effects of noise correlations in the input to, or among, BCM neurons using the Wigner semicircular law to construct random, positive-definite symmetric correlation matrices and compute their eigenvalue distributions. In the finite dimensional case, we compare our analytic results with numerical simulations and show the effects of correlations on the lifetimes of synaptic strengths in various visual environments. These correlations can be due either to correlations in the noise from the input LGN neurons, or correlations in the variability of lateral connections in a network of neurons. In particular, we find that for fixed dimensionality, a large noise variance can give rise to long lifetimes of synaptic strengths. This may be of physiological significance.Comment: 7 pages, 7 figure

Detailed analysis of shake structures in the KLL Auger spectrum of H2S

Shake processes of different origin are identified in the KLL Auger spectrum of H2S with unprecedented detail. The KLL Auger spectrum is presented together with the S 1s−1 photoelectron spectrum including the S 1s−1V−1nλ and S 1s−12p−1nλ shake-up satellites with V−1 and nλ indicating a hole in the valence shell and an unoccupied molecular orbital, respectively. By using different photon energies between 2476 and 4150 eV to record the KLL Auger spectra two different shake-up processes responsible for the satellite lines are identified. The first process is a shake-up during the Auger decay of the S 1s−1 core hole and can be described by S 1s−1→2p−2V−1nλ. The second process is the Auger decay of the shake-up satellite in the ionization process leading to S 1s−1V−1nλ→2p−2V−1nλ transitions. By combining the results of photoelectron and Auger spectra the involved V−1nλ levels are assigned

Optimal and heuristic algorithms of planning of low-rise residential buildings

The problem of the optimal layout of low-rise residential building is considered. Each apartment must be no less than the corresponding apartment from the proposed list. Also all requests must be made and excess of the total square over of the total square of apartment from the list must be minimized. The difference in the squares formed due to with the discreteness of distances between bearing walls and a number of other technological limitations. It shown, that this problem is NP-hard. The authors built a linear-integer model and conducted her qualitative analysis. As well, authors developed a heuristic algorithm for the solution tasks of a high dimension. The computational experiment was conducted which confirming the efficiency of the proposed approach. Practical recommendations on the use the proposed algorithms are given. © 2017 Author(s).Russian Foundation for Basic Research, RFBR: 16-01-00649The work was supported by Act 211 Government of the Russian Federation, contract No 02.A03.21.0006, and by the Russian Foundation for Basic Research, project No. 16-01-00649