Longest cycles in generalized Buckminsterfullerene graphs

It is shown that every regular 3-valent polyhedral graph whose faces are all 5-gons and 6-gons contains a cycle through at least 4/5 of its vertices.     

PERFIDI: parametrically enabled relaxation filters with double and multiple inversion

We present a novel approach to the nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) analysis of complex samples with nontrivial distribution of longitudinal relaxation rate R(1). Parametrically enabled relaxation filters with double and multiple inversion (PERFIDI) aim to separate signals arising from components with different R(1) values prior to actual data acquisition. Given any standard NMR/MRI pulse sequence, which, by itself, is insensitive to differences in R(1) values, it can be combined with a PERFIDI preamble, which functions as a preliminary R(1) filter and confers on the original technique sensitivity to the dimension R(1). This article states the principles of the approach, including the way to account for instrumental imperfections, and shows how PERFIDI with specific filter profile functions can be built. Using terms borrowed from electronics, these filters are classified as low-pass, high-pass and band-pass types. Also included are an experimental verification example and a discussion of potential applications of PERFIDI in various NMR areas.     

JRQ and JPA irradiated and annealed reactor pressure vessel steels studied by positron annihilation

The paper is focused on a comprehensive study of JRQ and JPA reactor pressure vessel steels from the positron annihilation lifetime spectroscopy (PALS) point of view. Based on our more than 20 years’ experience with characterization of irradiated reactor steels, we confirmed that defects after irradiation start to grow and/or merge into bigger clusters. Experimental results shown that JPA steel is more sensitive to the creation of irradiation-induced defects than JRQ steel. It is most probably due to high copper content (0.29?wt.% in JPA) and copper precipitation has a major impact on neutron-induced defect creation at the beginning of the irradiation. Based on current PALS results, no large vacancy clusters were formed during irradiation, which could cause dangerous embrittlement concerning operation safety of nuclear power plant. The combined PALS, small angle neutron scattering and atomic probe tomography studies support the model for JRQ and JPA steels describing the structure of irradiation-induced clusters as agglomerations of vacancy clusters (consisting of 2–6 vacancies each) and are separated from each other by a distribution of atoms.     

A study of Ga layers on Si(1 0 0)-(2 × 1) by SR-PES: Influence of adsorbed water

Results for deposition and thermal annealing of gallium on the Si(1 0 0)-(2 × 1) surface achieved by synchrotron radiation photoelectron spectroscopy (SR-PES) and low energy electron diffraction (LEED) are presented. In addition to deposition of Ga on a clean surface, the influence of water adsorption on the arrangement of gallium atoms was also studied. The results on Ga deposition at a higher temperature (490 °C) are consistent with a Ga ad-dimer model showing equivalent bond arrangement of all Ga atoms for coverages up to 0.5 ML. The deposition onto a surface with adsorbed water at room temperature led to a disordered gallium growth. In this case gallium atoms bind to silicon dimers already binding fragments of adsorbed water. A subsequent annealing of these layers leads to a surface structure similar to the Ga-(2 × 2), however, it is less ordered, probably due to the presence of silicon oxides formed from water fragments.     

Dynamical stability of an elastic column and the phenomenon of bifurcation

The article studies the stability of rectilinear equilibrium shapes of a non-linear elastic thin rod (column or Timoshenko's beam), the ends of which are pressed. Stability is studied by means of the Lyapunov direct method with respect to certain integral characteristics of the type of norms in Sobolev spaces. To obtain equations of motion, a model suggested in [16] is used. Furta [6] solved the problem of stability for all values of the parameter except bifurcational ones. When values of the system's parameter become bifurcational, the study of stability is more complicated already in a finite-dimensional case. To solve a problem like that, one often has to use a procedure of solving the singularities described in [1], for example. In this paper a change of variables is made which, in fact, is the first step of the procedure mentioned. To prove instability, we use a Chetaev function which can be considered as an infinite-dimensional analogue of functions suggested in [14, 9]. The article also investigates a linear problem on the stability of adjacent shapes of equilibrium when the parameter has supercritical values (post-buckling).     

Tensor train completion: Local recovery guarantees via Riemannian optimization

In this work, we estimate the number of randomly selected elements of a tensor that with high probability guarantees local convergence of Riemannian gradient descent for tensor train completion. We derive a new bound for the orthogonal projections onto the tangent spaces based on the harmonic mean of the unfoldings' singular values and introduce a notion of core coherence for tensor trains. We also extend the results to tensor train completion with auxiliary subspace information and obtain the corresponding local convergence guarantees.     

Controlling soliton refraction in optical lattices

We show in the framework of the 1D nonlinear Schr?dinger equation that the value of the refraction angle of a fundamental soliton beam passing through an optical lattice can be controlled by adjusting either the shape of an individual waveguide or the relative positions of the waveguides. In the case of the shallow refractive index modulation, we develop a general approach for the calculation of the refraction angle change. The shape of a single waveguide crucially affects the refraction direction due to the appearance of a structural form factor in the expression for the density of emitted waves. For a lattice of scatterers, wave-soliton interference inside the lattice leads to the appearance of an additional geometric form factor. As a result, the soliton refraction is more pronounced for the disordered lattices than for the periodic ones.