Linear-cavity fiber laser using subring-cavity incorporated saturable absorber for single-frequency operation

By using a subring cavity incorporated with a saturable absorber, a stable single-frequency selection is realized in a linear-cavity fiber laser, which is constructed using a broadband fiber mirror and a partial reflectance fiber Bragg grating as the cavity ends. At 1550.33 nm, the laser has an optical signal-to-noise-ratio of >53.28 dB and with linewidth less than 1 MHz. The pumping efficiency is 25% improved by recycling the residual pump power to gain medium. The power stability and wavelength stability have also been studied.     

Formation of nickel coatings by electrochemical deposition under X-ray irradiation

The influence of X-ray irradiation on the formation of nickel electroplating coatings is studied. The regularities of the nickel electrocrystallization kinetics under X-ray irradiation of different wavelengths, such as the increase in the deposition rate and metal output by the current, are revealed. The features of the structuring of the nickel electroplating coatings under irradiation are revealed. The influence of X-ray irradiation on microhardness, microdeformations, and dislocation structure is estimated. An increase in microhardness and a decrease in microdeformations of nickel coatings with the growth of the radiation energy are established.     

Bell-type inequalities and tomographic entropies of multiqudit states

Tomographic entropies of multiqudit systems are studied. A comparison of Shannon and von Neumann entropic inequalities with analogous inequalities for tomographic entropies is presented. An attempt to associate the violation of these and Bell-type inequalities of multipartite states is done within the framework of tomographic probability theory.     

Luminescence of aluminoborosilicate glasses doped with Gd3+ ions

The two-photon absorption that leads to the ultraviolet upconversion luminescence in the SiO₂-Al₂O₃-B₂O₃-Na₂O₃-Zr₂O: Cd³⁺ glass has been investigated. The inference has been made that no photon cascade emission takes place under excitation by monochromatic light corresponding to the maximum of the absorption band of the Cd³⁺ ion (204 nm). The mechanisms of concentration quenching and energy transfer between Cd³⁺ ions and optically active defects of the aluminoborosilicate glass have been discussed.     

A 2-approximation polynomial algorithm for a clustering problem

A 2-approximation algorithm is presented for some NP-hard data analysis problem that consists in partitioning a set of Euclidean vectors into two subsets (clusters) under the criterion of minimum sum-of-squares of distances from the elements of clusters to their centers. The center of the first cluster is the average value of vectors in the cluster, and the center of the second one is the origin.     

Δ-graphs of polytopes in Bruns and Gubeladze K-theory

W. Bruns and J. Gubeladze introduced a new version of algebraic K-theory where K-groups are additionally parameterized by polytopes of some type. In this paper we propose a concept of stable E-equivalence which can be used to calculate K-groups for high-dimensional polytopes. Polytopes which are stable E-equivalent have similar inner structures and isomorphic K-groups. In addition, for each polytope we define a Δ-graph which is an oriented graph being invariant under a stable E-equivalence.     

Essentially different distributions of current in the inverse problem for the Grad-Shafranov equation

The paper answers a question debated by physicists for many years. It is proved that, for almost equal gradients of the magnetic flux u at its zero-level curve ∂ω, which is the piecewise smooth boundary of a simply-connected domain ω ⋐ ℝ², the inverse problem for the Grad-Shafranov equation of plasma equilibrium in a tokamak (in the cylindrical approximation) admits essentially different profiles of distributions f _u : ω ∋ (x, y) ↦ f(u(x, y)) = u _xx (x, y) + u _yy (x, y) ⩾ 0 in the class of third-order polynomials f(u) = Σ _m=0³ a _m u ^m .     

Using components of mathematical ability for initial development and identification of mathematically promising students

Kruteskii's work on the mathematical abilities of school children is a seminal work on the nature of mathematical ability. However, the task of developing methods for the practical application of his work is still a significant problem in mathematics education. The authors have developed a practical application of Kruteskii's approach to the important problem of initially developing components of mathematical ability in student and thereafter identifying mathematically promising students. Examples of problems that were designed to develop ability to generalize, flexibility and reversibility of mental processes are presented. A practical guide for determining the level of development of components of mathematical abilities in individual students, in terms of specified observables, is presented as a set of structured reference tables. The authors set out a practical application protocol that combines use of the tables and sets of specially developed problems for initial development of mathematical abilities prior to identification of mathematically promising students in the general classroom. A significant motivation for this work is the desire to avoid time-consuming and resource intensive practices such as interviews and summer schools which therefore have been used successfully because these practices are now out of reach for all but very wealthy countries or highly ideologically driven systems. On the other hand, special examinations heavily depend on the level of preparedness of the students for the particular examination, and therefore some students with high abilities but with fewer opportunities to prepare could be overlooked.     

On protection against a bright-pulse attack in the two-pass quantum cryptography system

The security of keys in quantum cryptography systems, in contrast to mathematical cryptographic algorithms, is guaranteed by fundamental quantum-mechanical laws. However, the cryptographic resistance of such systems, which are distributed physical devices, fundamentally depends on the method of their implementation and particularly on the calibration and control of critical parameters. The most important parameter is the number of photons in quasi-single-photon information states in a communication channel. The sensitivity to a bright-pulse attack has been demonstrated in an explicit form for a number of systems. A method guaranteeing the resistance to such attacks has been proposed and implemented. Furthermore, the relation of physical observables used and obtained at the control of quantum states to the length of final secret keys has been obtained for the first time.