Kazan Federal University Science Tatarstan / Каза́нский федера́льный университе́т Science Tatarstan (E-Journal)
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Simulation of toroidal shell with local defect
No full textThin-walled toroidal shells are widely used in the construction and facilities of present-day design. During operation, various defects arise on the surface of the shells, in particular local deepenings. The article describes a model of a fragment of the toroidal shell with a local deepening based on three-dimensional nite elements with cubic approximation of the original variables. The inuence of the defect depth on the stress distribution is investigated
The oblique fall of an acoustic wave on the boundary of a multifractional gas suspension with polydisperse inclusions
No full textThis article is devoted to the study of the oblique fall of an acoustic wave from a pure gas to the boundary of a multifraction gas suspension with polydisperse inclusions of different sizes and materials. A mathematical model that allows to determine the reflection coefficient when an acoustic wave falls obliquely on the interface between two media is presented. Dependencies of the reflection coefficient on the disturbance frequency were calculated. Influence of the oblique angle of acoustic wave on the dependence of the reflection coefficient was established
Generation of Amorphous Silicon Dioxide Structures via Melting-quenching Density Functional Modeling
No full textAb initio quantum molecular dynamics simulation is used to transform a silicon dioxide crystal into silica amorphous states. Two type of amorphous states are obtained from the melts stabilized at temperatures well above the crystal melting point. The first type of amorphous states are obtained from the melts stabilized at comparably low temperatures of 3000 and 4000K. These states are characterized by a perfect structure similar to those of the initial crystal and vitreous silica glass without point defects. Completely different amorphous states are obtained from the high temperature melts of 5000K and 6000K. Structures of these amorphous states are less regular and contain point defects of silicon dioxide such as over-coordinated fivefold silicon, threefold oxygen atoms and a new silica defect 2-Bridging Oxygen Center. The latter is detected in the model of amorphous silica for the first time and it is formed by two neighbouring SiO4-tetrahedra with two common oxygen vertexes. The amorphous silica models can be useful for description of amorphous silicon dioxide films obtained by high energy ion-beam deposition process where a fast local melting-quenching process should exist
Stuctures of ternary semigroup of mappings
No full textWe first consider the ternary semigroup of mappings between two nonempty sets X and Y ,that is T [X, Y ] . Then we charcterize differenet types of elements in T [X, Y ]. In particular,we provide some necessary and sufficient conditions for an element of T [X, Y ] to become aleft regular, a right regular, a completely regular and an idempotent element of the ternarysemigroup T [X, Y ]. Our results enrich the structure of the teranary semigroup of mappings
Recognizing Named Entities in Specic Domain
No full textThe paper presents the results of applying the BERT representation model in thenamed entity recognition task (NER) for the cybersecurity domain in Russian. We compareseveral approaches to domain-specic NER combining BERT fine-tuning on a domain-specictext collection, general labeled data, domain-specic data augmentation, and a domain-specicannotated dataset. We showed that using a BERT model fine-tuned on a domain text collection andpre-trained on the combination of a general dataset and augmented data achieves the best resultsof named entity recognition. We also studied computational performance of the BERT model inso-called mixed precision regime
Reduction of Binary Forms via the Hyperbolic Centroid
No full textIn this paper we introduce a reduction theory based on the hyperbolic center of mass, which is different from the reduction introduced by Julia (1917). We show that the zero map via the Julia quadratic is different than the hyperbolic center of mass. Moreover, we discover some interesting formulas for computing the hyperbolic centroid
Shock Waves in Euler Flows of Gases
No full textNon-stationary Euler flows of gases are studied. The system of differential equations describing such flows can be represented by means of 2-forms on zero-jet space and we get some exact solutions by means of such a representation. Solutions obtained are multivalued and we provide a method of finding caustics, as well as wave front displacement. The method can be applied to any model of thermodynamic state as well as to any thermodynamic process. We illustrate the method on adiabatic ideal gas flows
he EulerLagrange Approximation of the Mean Field Game for thePlanning Problem
No full textThe paper presents afinite-difference analogue of the differential problem formulatedin terms of the theory of“Mean Field Games”for solving the planning problem of convey to agiven state. Here optimization problem is formulated as coupled pair of parabolic partial differentialequations of the Kolmogorov (Fokker–Planck) and Hamilton–Jacobi–Bellman type. The proposedEuler–Lagrangefinite-difference analogue inherits the basic properties of an optimization differen-tial problem at a discrete level. As a result, it can serve as an approximation of the original differentialproblem when the discretization steps tend to zero, or as a self-contained optimization task with afinite set of participants. For the proposed analogue, the algorithm of monotonous minimization ofthe value functional is constructed and illustrated on a model economic task
MODIFIED BRANCHING PROCESS AND SADDLEPOINT APPROXIMATIONS
No full textThis article presents a brief on using a saddlepoint approximations technique to solve some branching process problems; this method of approximation provides a good understanding of branching process behaviors such as probability density, mass function, and cumulative distribution function based on a moment generating function for complicated models such as nuclear chain reaction, survival of family name problems, and extinction probability problem
On the parametric continuation method in
No full textThis paper focuses on the study of the parametric continuationmethod for mappings of the unit ball in n-dimensional real space.Using this method, sufficient and necessary conditions for theglobal injectivity of mappings were obtained. It was establishedthat these conditions actually coincide with the known features inn-dimensional complex space. The concretizations of the methodmade here are the generalizations of some classes of functionsanalytic in the unit circle. In addition, the analogue of theKaplan class was derived for mappings in n-dimensional realspace