On extending actions of groups

Problems of dense and closed extension of actions of compact transformation groups are solved. The method developed in the paper is applied to problems of extension of equivariant maps and of construction of equivariant compactifications

On the localization of discontinuities of the first kind for a function of bounded variation

Methods of the localization (detection of positions) of discontinuities of the first kind for a univariate function of bounded variation are constructed and investigated. Instead of an exact function, its approximation in L2(-∞,+∞) and the error level are known. We divide the discontinuities into two sets, one of which contains discontinuities with the absolute value of the jump greater than some positive Δmin; the other set contains discontinuities satisfying a smallness condition for the value of the jump. It is required to find the number of discontinuities in the former set and localize them using the approximately given function and the error level. Since the problem is ill-posed, regularizing algorithms should be used for its solution. Under additional conditions on the exact function, we construct regular methods for the localization of discontinuities and obtain estimates for the accuracy of localization and for the separability threshold, which is another important characteristic of the method. The (order) optimality of the constructed methods on the classes of functions with singularities is established. © 2013 Pleiades Publishing, Ltd

Budget Feasible Mechanisms for Experimental Design

In the classical experimental design setting, an experimenter E has access to a population of $n$ potential experiment subjects $i\in \{1,...,n\}$, each associated with a vector of features $x_i\in R^d$. Conducting an experiment with subject $i$ reveals an unknown value $y_i\in R$ to E. E typically assumes some hypothetical relationship between $x_i$'s and $y_i$'s, e.g., $y_i \approx \beta x_i$, and estimates $\beta$ from experiments, e.g., through linear regression. As a proxy for various practical constraints, E may select only a subset of subjects on which to conduct the experiment. We initiate the study of budgeted mechanisms for experimental design. In this setting, E has a budget $B$. Each subject $i$ declares an associated cost $c_i >0$ to be part of the experiment, and must be paid at least her cost. In particular, the Experimental Design Problem (EDP) is to find a set $S$ of subjects for the experiment that maximizes V(S) = \log\det(I_d+\sum_{i\in S}x_i\T{x_i}) under the constraint $\sum_{i\in S}c_i\leq B$; our objective function corresponds to the information gain in parameter $\beta$ that is learned through linear regression methods, and is related to the so-called $D$-optimality criterion. Further, the subjects are strategic and may lie about their costs. We present a deterministic, polynomial time, budget feasible mechanism scheme, that is approximately truthful and yields a constant factor approximation to EDP. In particular, for any small $\delta > 0$ and $\epsilon > 0$, we can construct a (12.98, $\epsilon$)-approximate mechanism that is $\delta$-truthful and runs in polynomial time in both $n$ and $\log\log\frac{B}{\epsilon\delta}$. We also establish that no truthful, budget-feasible algorithms is possible within a factor 2 approximation, and show how to generalize our approach to a wide class of learning problems, beyond linear regression

DEVELOPMENT OF A MODEL FOR THE PRODUCTION OF METAL-POWDER COMPOSITIONS BASED ON CO-CR ALLOYS BY ELECTROEROSIVE DISPERSION

Abstract. The main requirement for powders for additive 3d technologies is the spherical shape of theparticles. Such particles are most compactly packed into a certain volume and ensure the "fluidity" of the powder composition in the supply systems of the material with minimal resistance. The wide use of the EED method for processing metal waste into powders for the purpose of their reuse and application in additive technologies is hampered by the lack in the scientific and technical literature of full-fledged information on the effect of the initial composition, regimes and media on the properties of powders and technologies of practical application. Therefore, in order to develop technologies for the reuse of electroerosive powders and to evaluate the effectiveness of their use, complex theoretical and experimental studies are required. The aim of the work was to develop a model for the production of metal powder compositions on the basis of Co-Cr alloys by electroerosive dispersion. Based on the results of the conducted studies, it has been established that the optimum parameters for the process of obtaining powder materials by the method of electroerosive dispersion of butyl alcohol are: capacitance of discharge capacitors 48 μF, voltage on electrodes 100 V, repetition rate of pulses 120 Hz

Influence of the focused ion beam parameters on the etching of planar nanosized multigraphene/SiC field emitters

The equipment of the Collective Usage Center “Nanotechnologies” and the Research and Educational Center "Nanotechnologies" of Southern Federal University was used for this study. This work was funded by Internal grant of Southern Federal University No. VnGr-07/2017-26

Modeling of temperature fields in the working chamber of the process furnace for REE synthesis

The results of mathematical modeling of temperature fields in the working chamber of the process furnace for special purposes are shown. Studied laboratory furnace is test equipment, which is used for practicing the stages of the technological process of continuous solid-phase synthesis of nanopowders of various purpose, such as obtaining of luminophore powders with rare earth elements oxides in its composition. Mathematical model adequacy is tested empirically

Of combined electric arc coatings

The paper considers possibilities to increase the wear resistance for parts machines and mechanisms using combined electric arc coatings thanks to nitriding the coatings deposited. The possibility of controlling the properties of surfaces owing to choice with required characteristics electric arc coatings is shown. The influence of spray factors such as the flow rate and pressure of working gases, composition of combustion mixture, spraying distance, dispersion of the spray, properties of wire material, etc. on the properties of the coatings obtained has been investigated. The paper considers the use of pulse ion nitriding of arc-spray EAS (eelectric arc spraying) coatings from wire materials as one of the efficient ways to increase their performance characteristics.=В работе предложено повышать износостойкость деталей машин и механизмоа комбинированными ЭДН-покрытиями за счет азотирования напыленных покрытий. В работе исследование влияния факторов процесса элпектродугового напыления: расхода и давления рабочих газов, состава горючей смеси, дистанции напыления, дисперсности распыления, свойств материала проволоки и др. на свойства ЭДН-покрытий. В работе рассмотрен один из способов повышения эксплуатационных характеристик ЭДН-покрытий из проволочных материалов посредством использования импульсного ионного азотирования. В работе предложено повышать износостойкостьь и срок службы деталей машин и механизмоа при их упрочнении и реновации комбинированными ЭДН-покрытиями с высокой плотностью, прочностью сцепления и микротвердостью за счет управления параметрами электродугового напыления и процесса азотирования напыленных покрытий. В работе рассмотрена возможность обеспечивать необходимые свойства поверхностей с целью повышения ресурса деталей машин путем регулирования факторами ЭДН. В частности, регулируя скорость и температуру струи транспортирующего газа и частиц можно уменьшить диаметр капель, повысить плотность и снизить окисляемость покрытий. В работе исследование влияния факторов процесса напыления: расхода и давления рабочих газов, состава горючей смеси, дистанции напыления, дисперсности распыления, свойств материала проволоки и др. на свойства ЭДН-покрытий. В работе рассмотрен один из способов повышения эксплуатационных характеристик ЭДН-покрытий из проволочных материалов посредством использования ионного азотирования

Dijet production as a centrality trigger for p-p collisions at CERN LHC

We demonstrate that a trigger on hard dijet production at small rapidities allows to establish a quantitative distinction between central and peripheral collisions in pbar-p and p-p collisions at Tevatron and LHC energies. Such a trigger strongly reduces the effective impact parameters as compared to minimum bias events. This happens because the transverse spatial distribution of hard partons (x >~ 10^{-2}) in the proton is considerably narrower than that of soft partons, whose collisions dominate the total cross section. In the central collisions selected by the trigger, most of the partons with x >~ 10^{-2} interact with a gluon field whose strength rapidly increases with energy. At LHC (and to some extent already at Tevatron) energies the strength of this interaction approaches the unitarity ('black-body') limit. This leads to specific modifications of the final state, such as a higher probability of multijet events at small rapidities, a strong increase of the transverse momenta and depletion of the longitudinal momenta at large rapidities, and the appearance of long-range correlations in rapidity between the forward/backward fragmentation regions. The same pattern is expected for events with production of new heavy particles (Higgs, SUSY). Studies of these phenomena would be feasible with the CMS-TOTEM detector setup, and would have considerable impact on the exploration of the physics of strong gluon fields in QCD, as well as the search for new particles at LHC.Comment: 17 pages, Revtex 4, 14 EPS figures. Expanded discussion of some points, added 3 new figures and new references. Included comment on connection with cosmic ray physics near the GZK cutoff. To appear in Phys Rev

Vector Meson Production in Ultraperipheral Heavy Ion Collisions

The ultraperipheral heavy ion collisions (UPC's) are an important alternative to study the QCD dynamics until the next generation of $e^+e^-/ ep / eA$ colliders become reality. Due to the coherent action of all the protons in the nucleus, the electromagnetic field is very strong and the resulting flux of equivalent photons is large, which allows to study two-photon as well as photonuclear interactions at high energies. In this paper we present a brief review of the vector meson production in UPC's at high energies using the QCD color dipole approach to describe their photonuclear production and the perturbative QCD Pomeron (BFKL dynamics) to describe the double meson production in photon-photon process. Predictions for rates and integrated cross sections are presented for energies of RHIC and LHC.Comment: 16 pages, 1 figure. Version to be published in Journal of Physics G: Nuclear and Particle Physic