Kazan Federal University Science Tatarstan / Каза́нский федера́льный университе́т Science Tatarstan (E-Journal)
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Algo500 – a New Approach to the Joint Analysis of Algorithms and Computers
No full textThe described project is aimed at a complete solution to the problem of jointanalysis of the properties of algorithms and features of the architecture of computing systems. This problem arose in the mid-70s of the last century, and over time, its importance in the practice of using computer systems is constantly growing. The main reason is a significant complication of the architecture of computers, which determines a strong dependence of the efficiency of their work on the properties of algorithms and programs. Exactly this dependence leads in practice to a huge gap between real and peak performance indicators, which is typical for all classes of computers from mobile devices to supercomputers of the highest performance range. It is this dependence that leads to a decrease in the quality of work of supercomputer centers and a drop in the efficiency of computer systems below a fraction of a percent. And at the same time, the fundamental nature of the problem itself determines two important facts. First, it is characteristic of all computer systems and centers of the world without exception. Second, practically all scientific groups of the world in all science areas, conducting research using high-performance computing systems, face this problem
On the Decomposition of Equations of Micropolar Elasticity and Thin Body Theory
No full textThe motion equations of the micropolar theory of elasticity in displacements and rotations represented by the matrix differential tensor-operator for any inhomogeneousanisotropic materials. As a particular case the micropolar isotropic homogeneous materialswith a center of symmetry is considered. In this case, the matrix differential tensor-operator of cofactors to the matrix differential tensor-operator of the motion equations is constructed. This constructed operator makes possible to decompose the equations. The equations are obtained separately with respect to the displacement and rotation vectors. Decomposed equations also obtained for a reduced medium. In this case, the equation with respect to the displacement vector is the same as the equation of the classical theory, and the equation with respect to the rotation vector has a similar form. In addition, in the absence of volume loads, the equations of the reduced medium do not depend on the properties of the material. This suggests that these equations can be used to identify the material constants of this medium. The cases under which the static boundary conditions are easily split are revealed. From the decomposed equations of the micropolar theories of elasticity, the corresponding decomposed equations of the static (quasistatic) problem of the theories of single-layer and multi-layer prismatic bodies of constant thickness in displacements and rotations are obtained. From the last systems of equations the equations in the moments of unknown vector functions with respect to any systems of orthogonal polynomials are derived. As a particular case, we obtain a system of equations of the eighth approximation in moments with respect to the system of Legendre polynomials, which decomposes into two systems. One of them is the system with respect to the even order moments of the unknown vector function, and the other system is the system with respect to odd order moments of the same functions. Based on the obtained operator of cofactors to the operator of any of these systems we get a high order (the order of the system depends on the order of approximation) elliptic type equation for each moment of the unknown vector function, which characteristic roots are easily found. Using Vekua’s method for solving such equations [66], we can obtain their analytical solution. Note also that the analytic method with the use of the orthogonal polynomial systems (Legendre and Chebyshev) in constructing the one-layer [2, 3, 7, 10, 15, 17, 18, 20–22, 63, 68, 69] and multilayer [4–6, 13, 60, 61] thin body theory was also applied by other authors. In this direction the authors had published the papers [24–31, 33–37, 41–45, 51–53], and others with the application of Legendre and Chebyshev polynomial systems. These expansions can be successfully used in constructing any thin body theory. Despite this, classical theories are far from perfect, and micropolar theories and theories of another rheology are very far from perfect
Capabilities of Layered Ultrasound Tomography
No full textThis article discusses the capabilities of layered "2.5D" schemes in ultrasound tomography, in which the emitters and detectors are located in the same plane. The primary application of this method is medical imaging technology for early-stage breast cancer diagnosis. The inverse problem of tomographic image reconstruction is posed as a coefficient inverse problem for the wave equation, where the wave propagation velocity is an unknown function of two coordinates. In this formulation, the problem has much less computational complexity than in a 3D formulation, in which the wave velocity is reconstructed as a function of three coordinates. Nevertheless, the inverse problem in the layered "2.5D" formulation is non-linear and requires the use of supercomputers. A practically feasible parallel implementation of the image reconstruction algorithms on a GPU cluster is proposed.This study shows that the layered model is applicable if the imaged objects are close to cylindrical. Refraction of ultrasound waves in the vertical direction cannot be taken into account by the layered model. The more significant is the refraction, the more the reconstructed image differs from reality. The experiments were carried out using the test bench developed at the Scientific Research Computing Centre of Lomonosov Moscow State University
Molecular dynamics simulations of the full-length prion protein
No full textMany serious medical conditions are caused by the accumulation of amyloid aggregates in tissues and organs. One of the most well-known amyloidogenic proteins is the prion protein (PrP), which may undergo conformational change between the normal cellular isoform PrPC and aggregation-prone isoform PrPSc. Elucidation of this conformational transition is necessary for understanding the onset and propagation of prion diseases. However, the flexibility of PrP hinders its research by the experimental methods of protein structure determination. Here, we implement de novo protein modelling and molecular dynamics simulations to predict the interdomain interactions of the full-length PrPC. Our theoretical findings can serve as the basis for mutational analysis and further studies of the amyloidogenic behavior of the prion protein
Mathematical Model of Enterprise with Revolving Funds Deficit: Analysis of Demand Shocks 2020
No full textRussian enterprises of manufacturing complex are facing financial crisis because of the dramatic drop in demand for products due to the pandemic. Since a significant part of the population is employed in this sector, measures to support production in manufacturing industries are discussed at various levels. Based on the mathematical model of production, taking into account unstable demand, we propose a methodology for analyzing the effectiveness of support measures. Financial performance of the enterprise are calculated using an analytical solution of theBellman equation that determines the valuation of the company, as well as the ergodicity property of the random process of product sales. The application of the methodology is illustrated by the example of KAMAZ Group
Inductive Sequences of Toeplitz Algebras and Limit Automorphisms
No full textThe note is concerned with inductive sequences of Toeplitzalgebras. The Toeplitz algebra is the -subalgebra in thealgebra of all bounded linear operators. This subalgebra isgenerated by the right shift operator on the Hilbert space of allsquare summable complex-valued functions defined on the additivesemigroup of non-negative integers. We study the inductive sequencesof Toeplitz algebras whose bonding -homomorphisms are definedby arbitrary sequences of natural numbers. The inductive limits ofsuch sequences are the reduced semigroup -algebras generated byrepresentations for semigroups of non-negative rational numbers. Weconsider the limit -endomorphisms of these inductive limits.Such an endomorphism is induced by a morphism between two copies ofthe same inductive sequence of Toeplitz algebras. We give thenecessary and sufficient conditions for these endomorphisms to be -automorphisms of -algebras. These criteria are formulated in algebraic, number-theoretical and functional terms
Thermohydrodynamic studies of vertical wells in non-linear ltration
No full textIn this paper the computational algorithm for interpreting the results of hydrodynamicand thermohydrodynamic studies in non-linear ltration is proposed. The algorithmallows to determine the conductivity of the reservoir, the limiting pressure gradient, reservoirpressure and the regularization parameter. Temperature and pressure changes data, measuredon a vertical well, are taken as the initial information
Multiple Interpolation by the Functions of Finite Order in the Half-plane
No full textThe aim of this paper is to study the multiple interpolation problem in the spaces of analytical functions of finite order in the half-plane. The necessary and sufficient conditions for solvability of interpolation problem are obtained. These conditions are obtained in terms of the Nevanlinna product of interpolation nodes. The solution of the interpolation problem is constructed in the form of the Jones interpolation series, which is a generalization of the Lagrange interpolation series
Balayage of Measures with respect to (Sub-)Harmonic Functions
No full textWe investigate some properties of balayage, or, sweeping (out), of measures with respect to subclasses of subharmonic functions. The following issues are considered: relationships between balayage of measures with respect to classes of harmonic or subharmonic functions and balayage of measures with respect to significantly smaller classes of specific classes of functions; integration of measures and balayage of measures; sensitivity of balayage of measures to polar sets, etc
On the Existence of Periodic and Bounded Solutions for Functional Differential Equations of Pointwise Type with a Strongly Nonlinear Right-Hand Side
No full textSolutions of functional differential equation of pointwise type (FDEPT) are in one-to-one correspondence with the traveling-wave type solutions for the canonically induced infinite-dimensional ordinary differential equation and vice versa. In particular, such infinite-dimensional ordinary differential equations are finite difference analogues of equations of mathematical physics. An important class of traveling-wave type solutions is made up of periodic and bounded traveling-wave type solutions. On the other hand, an important class of such systems is systems with strongly nonlinear potentials (polynomial potentials), for which periodic and bounded traveling wave solutions are studied. Such a problem is equivalent to the study of periodic and bounded solutions of the induced FDEPT to which the present work is devote