The Discounted Limit Theorems

The large deviation theorems, exponential inequalities and a non-uniform estimate of the Berry–Esséen theorem in a discounted version are proved.Dedicated to Professor Vytautas Statulevičius on the occasion of his 75th birthday.     

Bimodal fission in binary and ternary spontaneous fission of 252Cf

The hot bimodal fission of ²⁵²Cf is reexamined with new high-statistics data. We constructed a γ-γ-γ coincidence cube for binary fission and LCP-gated γ-γ matrix for ternary fission. By identifying the secondary fission fragments from their γ-ray transitions, we measured the yields for various fission splits. The normal neutron yield distribution is found to be Gaussian for Xe-Ru. However, the binary fission split of Ba-Mo is found to exhibit a bimodal neutron distribution with the “hot mode” corresponding to ≈3.1% of the total yield. In α ternary fission, the first measurements of yields for specific fission splits are presented. The Te-α-Ru and Xe-α-Mo neutron yields fit well with a single mode, but the Ba-α-Zr split shows evidence for an enhanced hot mode with an intensity of ≈13.8% of the normal mode. The text was submitted by the authors in English.     

Effect of the electric field on “incommensurate-commensurate” magnetic phase transitions in BiFeO3-type multiferroics

The specific features of the “incommensurate-commensurate” phase transitions induced by a magnetic field in multiferroics (materials with coexisting magnetic and electric ordering) are considered. These materials are ferroelectromagnets, for example, bismuth ferrite BiFeO₃ and BiFeO₃-based compounds, which have spatially modulated spin structures. It is shown that the interaction between the electric and magnetic subsystems of the multiferroic material can lead to an electric-field-induced shift of the critical magnetic field corresponding to the transition from a spatially modulated state to a homogeneous antiferromagnetic state. According to the theoretical estimates obtained for material parameters characteristic of the bismuth ferrite, this shift is of the order of 0.5 T in an electric field of 50 kV/cm. The phase diagrams are constructed in the “electric field-magnetic field” coordinates. The results of calculations performed in the harmonic incommensurate structure approximation are compared with the exact soliton solution.     

Effects of trapped electrons on the line shape in emission Mössbauer spectra

To explain line broadening in emission Mössbauer spectra as compared to the corresponding absorber measurements, the model of trapped electrons has been proposed. Auger electrons (emitted, e.g. after electron capture by ⁵⁷Co or after the converted isomeric transition of ^119mSn), as well as secondary electrons, may be trapped in the proximity to the nucleogenic ion. Electrons captured by lattice traps at different distances from the daughter ion induce an asymmetric distribution of quadrupole splitting in the resulting emission spectra, as shown in a few examples. This model is supported by estimates of quadrupole splitting values which may be caused by such trapped electrons located at specified distances from the nucleogenic atom.     

Thermal desorption of interacting molecules from mixed adlayers

A Monte Carlo simulation method is used to study thermal desorption of gas molecules from mixed adlayers containing two species. The effects of lateral interactions among adatoms and initial surface coverage on the desorption spectra are examined. It is shown that attractive lateral interactions lead to sharper peaks and that desorption occurs at high temperatures, whereas repulsive interactions lead to multiple peak spectra. It is found that interactions between unlike molecules affect the spectra for species with lower desorption energy only, and that the two species desorb together only in certain cases. Lateral interactions also affect the desorption kinetics significantly and very different behavior for the two species may be obtained.     

Hilbert Space of Probability Density Functions Based on Aitchison Geometry

The set of probability functions is a convex subset of L1 and it does not have a linear space structure when using ordinary sum and multiplication by real constants. Moreover, difficulties arise when dealing with distances between densities. The crucial point is that usual distances are not invariant under relevant transformations of densities. To overcome these limitations, Aitchison＇s ideas on compositional data analysis are used, generalizing perturbation and power transformation, as well as the Aitchison inner product, to operations on probability density functions with support on a finite interval. With these operations at hand, it is shown that the set of bounded probability density functions on finite intervals is a pre-Hilbert space. A Hilbert space of densities, whose logarithm is square-integrable, is obtained as the natural completion of the pre-Hilbert space.     

Relaxation processes in glasses of the Ge-As-S system

The internal friction in Ge _x As_{40 ? x} S₆₀ glasses is investigated in the temperature range 100 K-T _g at infralow frequencies (10^?3?10^?1 Hz). It is shown that the concentration dependence of the internal friction of these materials changes as a result of the transformation of the dominant kinetic unit in dissipative processes of the relaxation and nonrelaxation types. It is established tha the change in the mechanism of internal friction in the Ge _x As_{40 ? x} S₆₀ glasses leads to a jump in the activation energy of the α relaxation and to a local minimum in the frequency factor τ₀.     

Category with a natural cone

Generally, in homotopy theory a cylinder object (or, its dual, a path object) is used to define homotopy between morphisms, and a cone object is used to build exact sequences of homotopy groups. Here, an axiomatic theory based on a cone functor is given. Suspension objects are associated to based objects and cofibrations, obtaining homotopy groups referred to an object and relative to a cofibration, respectively. Exact sequences of these groups are built. Algebraic and particular examples are given. We point out that the main results of this paper were already stated in [3], and the purpose of this article is to give full details of the foregoing.