### Article

## Kinetic regimes in aggregating systems with spontaneous and collisional fragmentation

We analyze systems of clusters and interacting upon colliding—a collision

between two clusters may lead to merging or fragmentation—and we also

investigate the influence of additional spontaneous fragmentation events. We

consider both closed systems in which the total mass remains constant and

open systems driven by a source of small-mass clusters. In closed systems,

the size distribution of aggregates approaches a steady state. For these systems

the relaxation time and the steady state distribution are determined mostly by

spontaneous fragmentation while collisional fragmentation plays a minor role.

For open systems, in contrast, the collisional fragmentation dominates. In this

case, the system relaxes to a quasi-stationary state where cluster densities linearly

grow with time, while the functional form of the cluster size distribution persists

and coincides with the steady state size distribution of a system which has the

same aggregation and fragmentation rates and only collisional fragmentation.

For a personnel selection problem we define a new mathematical approach and make a computer tool that finds effective stable matching between the set of employers and candidates. A characterization, main components and application with its advantages are given.

File fragmentation proves to be a major challenge for the majority of file carving techniques. Following the works of Simson Garfinkel, Nasir Memon and other authors we seek to find a technique to identify digital fragments (clusters or sectors) of JPEG-files on the digital storage medium or at least sort all the fragments of the storage based on their probability of being the part of JPEG-file from the most probable to the least probable. This paper offers the technique of identifying clusters of JPEG-files on the storage medium based on binary patterns and the experimental results of an attempt to build a similar technique for sector identifying.

Enterprise assets as object of the financial analysis are considered. Questions of preparation of accounting information of assets for the analysis are investigated. Traditionally carrying out such preparatory procedures is explained by desire, first of all, to provide information in simplified, more evident look. In article the emphasis is placed on other, more significant reason of transformation of accounting reports - need of ensuring reliability of information which has to reflect the real cost of assets. The criteria which are cornerstone of creation of analytical balance are considered. The main methodical approaches to carrying out the horizontal and vertical analysis of assets, and also their separate elements are stated. The purposes and a technique of the analysis of assets are designated. Criteria of an assessment of dynamics and structure of assets are defined. Including "positive" and "negative" characteristics of separate groups of assets which need to be considered in the analysis of active operations are revealed.

The problem of axiomatic and algorithmic constructions of the threshold decision making is studied in the case when individual opinions are given as m-graded strict preferences (with m ≥ 3). It is shown that the only rule satisfying the introduced axioms is the threshold rule. Two explicit algorithms are presented: the ordering algorithm, under which the vector-grades of alternatives are successively written out, and an enumerating social decision function corresponding to the natural order of the weak order equivalence classes.

We provide a review of methods for studying economic data and building economic indices based on the generalized nonparametric method for computing Konus-Divisia indices, with the focus on the case when the observed behavior is not consistent with the classical Pareto's model of a single rational representative consumer, but may be consistent with the generalized model with two or more rational representative consumers. Computing economic indices allows one to aggregate economic prices and consumption data from the level of individual goods to the level of some general categories of goods.

Classical change-point detection procedures assume a change-point model to be known and a change consisting in establishing a new observations regime, i.e. the change lasts infinitely long. These modeling assumptions contradicts applied problems statements. Therefore, even theoretically optimal statistics in practice very often fail when detecting transient changes online. In this work in order to overcome limitations of classical change-point detection procedures we consider approaches to constructing ensembles of change-point detectors, i.e. algorithms that use many detectors to reliably identify a change-point. We propose a learning paradigm and specific implementations of ensembles for change detection of short-term (transient) changes in observed time series. We demonstrate by means of numerical experiments that the performance of an ensemble is superior to that of the conventional change-point detection procedures.

The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.

By using superconducting quantum interference device (SQUID) magnetometry, we investigated anisotropic high-field (H less than or similar to 7T) low-temperature (10 K) magnetization response of inhomogeneous nanoisland FeNi films grown by rf sputtering deposition on Sitall (TiO2) glass substrates. In the grown FeNi films, the FeNi layer nominal thickness varied from 0.6 to 2.5 nm, across the percolation transition at the d(c) similar or equal to 1.8 nm. We discovered that, beyond conventional spin-magnetism of Fe21Ni79 permalloy, the extracted out-of-plane magnetization response of the nanoisland FeNi films is not saturated in the range of investigated magnetic fields and exhibits paramagnetic-like behavior. We found that the anomalous out-of-plane magnetization response exhibits an escalating slope with increase in the nominal film thickness from 0.6 to 1.1 nm, however, it decreases with further increase in the film thickness, and then practically vanishes on approaching the FeNi film percolation threshold. At the same time, the in-plane response demonstrates saturation behavior above 1.5-2T, competing with anomalously large diamagnetic-like response, which becomes pronounced at high magnetic fields. It is possible that the supported-metal interaction leads to the creation of a thin charge-transfer (CT) layer and a Schottky barrier at the FeNi film/Sitall (TiO2) interface. Then, in the system with nanoscale circular domains, the observed anomalous paramagnetic-like magnetization response can be associated with a large orbital moment of the localized electrons. In addition, the inhomogeneous nanoisland FeNi films can possess spontaneous ordering of toroidal moments, which can be either of orbital or spin origin. The system with toroidal inhomogeneity can lead to anomalously strong diamagnetic-like response. The observed magnetization response is determined by the interplay between the paramagnetic-and diamagnetic-like contributions.

Radiation conditions are described for various space regions, radiation-induced effects in spacecraft materials and equipment components are considered and information on theoretical, computational, and experimental methods for studying radiation effects are presented. The peculiarities of radiation effects on nanostructures and some problems related to modeling and radiation testing of such structures are considered.

Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.

This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.

Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.