Homogeneous spaces and invariant tensors

In the present survey a method is presented for the construction of invariant tensors (with respect to a given representation) called the inclusion principle and the possibility of applying the cited method to various problems of algebra, topology, geometry, and analysis.Translated from Itogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 18, pp. 105–142, 1986.     

Singular series of genus 2 for sums of squares

Let f₁, ..., f_h be representatives of classes in the genus of a positive quadratic form f, r_i(k) the number of representations of k by the form f_i, (k) the value of the singular Hardy-Littlewood series, E_i the number of integer automorphisms of f_i. We derive an expression for in terms of the values of singular series of genus 1 and 2. This expression is evaluated for the simplest model f(x)=x ₁ ² +...+x _m ² , m1 (mod 8), k is a prime in-integer, k=1(mod 8).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 151, pp. 26–39, 1986.     

Eine ErweiterungT(V′) des Ordinalzahlensystems 58-0158-0158-01(Λ0) von G. Jäger

Summary This paper gives a recursive generalization of a strong notation system of ordinals, which was devellopped by Jäger [3]. The generalized systemT(V) is based on a hierarchy of Veblen-functions for inaccessible ordinals. The definition ofT(V) assumes the existence of a weak Mahlo-ordinal. The wellordering ofT(V) is provable in a formal system of second order arithmetic with the axiom schema of ₂ ¹ -comprehension in a similar way, as it is proved in [6] for the weaker notation systemT(V).     

Ultra'soft X-ray diagnostics of short-living plasmas

Ultrasoft X-ray plasma diagnostics in IPP is realized by using X-ray diodes with Al photocathodes and submicrometer nitrocellulose filters. The X-ray detections system is suitable for measurements in a relatively broad range of radiation intensities in the spectral interval of (10–1000) eV with the time resolution of (1–10) ns under various plasma conditions. Construction, calibration and characteristic properties of the measuring apparatus are described. To illustrate its use, some results of the diagnostics of REB-heated plasma are presented.We would like to acknowledge Dr. P. unka for many helpful discussions and Dr. J. Ullschmied for cooperation in REB-heated plasma diagnostics interpretation.     

Influence of crystal-field on the thermal conductivity of PrNi5

The thermal conductivity of PrNi₅ in the temperature range 0·5 to 20 K is investigated. The analysis of crystalline electric field effect on the experimentally obtained temperature dependence of the thermal conductivity indicates that beside the main electronic component also other contributions (phonons, magnetic excitons) can take place in the heat transport in this intermetallic compound.The authors would like to thank Dr. G. Eska for lending the sample and Dr. . Jáno for his interest in the work and stimulating discussions.     

Periodic solutions of some infinite-dimensional Hamiltonian systems associated with non-linear partial difference equations. II

This is our second paper devoted to the study of some non-linear Schrödinger equations with random potential. We study the non-linear eigenvalue problems corresponding to these equations. We exhibit a countable family of eigenfunctions corresponding to simple eigenvalues densely embedded in the band tails. Contrary to our results in the first paper, the results established in the present paper hold for an arbitrary strength of the non-linear (cubic) term in the non-linear Schrödinger equation.     

Effects of small external magnetic fields on the hyperfine field of iron in iron metal above the curie temperature: A new method for studying critical phenomena

By applying magnetic fields up to 2 kG, the equation of state and the critical dynamics of a spin system near its critical point can be studied with the Mössbauer effect. As an example, the equation of state near the Curie temperature of iron is investigated yielding the critical exponent =4.84±0.15.     

Searching for optimal configurations by simulated tunneling

Optimization theory deals with algorithms finding the lowest cost (energy) configuration in a minimal number of steps. When the cost function has many local minima, the deterministic algorithms become easily trapped in suboptimal solutions. The simulated annealing method tries to overcome this difficulty by introducting thermal noise in the problem. Here we explore the possibility of implementing search procedures analogous to the quantum tunneling effect. The suggested dynamics is a guided diffusion process of an interactingpopulation of configurations. Different dynamical aspects of the search process are formulated first in a simple one-dimensional tight-binding model with a hierarchical potential. The new algorithm is then applied to the Traveling Salesman Problem. It is demonstrated that the use of interacting, evolving populations of tours representing our wave packet leads to systematic improvements and possibly, to the optimal tour. In addition, the structure of the cost function landscape for a given instance becomes locally accessible. The performance of the algorithm and its implications for parallel computing and genetic programming are briefly discussed.