Статьи журнала - Вестник Южно-Уральского государственного университета. Серия: Математическое моделирование и программирование
Все статьи: 729
Статья научная
Preparation of the target-protein, particularly the protein protonation method can affect considerably the spatial arrangement of the attached hydrogen atoms and the charge state of individual molecular groups in amino acid residues. This means that the calculated protein-ligand binding energies can vary significantly depending on the method of the protein preparation, and it also can lead to the different docked positions of the ligand in the case of docking (positioning of the ligand in the protein active site). This work investigates the effect of the hydrogen atoms arrangement method in the target-protein on the protein-ligand binding energy. All hydrogen atoms of target-protein are fixed or movable. The comparison of the protein-ligand binding energies obtained for the test set of target-proteins prepared using six different programs is performed and it is shown that the protein-ligand binding energy depends significantly on the method of hydrogen atoms incorporation, and differences can reach 100 kcal/mol. It is also shown that taking into account solvent in the frame of one of the two continuum implicit models smooths out these differences, but they are still about 10-20 kcal/mol. Moreover, we carried out the docking of the crystallized (native) ligands from the protein-ligand complexes using the SOL program and showed that the different methods of the hydrogen atoms addition to the protein can give significantly different results both for the positioning of the native ligand and for its protein-ligand binding energy.
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Intellectual mathematical support software and inner architecture of LMS MAI Class.Net
Статья научная
Distance education prove to be effective in improving the learning and teaching environment. One of the main advantages of distance learning is that web-based courses can be taken anytime and anywhere. The implementation of an e-learning management system (LMS) requires not only good and fast hardware, but also the use of modern software technologies and architectural solutions. This article outlines the main ways of forming the LMS architecture based on a microservice approach, which allows the achievement of high performance and fault tolerance. A distinctive feature of the CLASS.NET system is the presence of a special mathematical software package that allows the optimization of educational processes and tasks (such as students tests generation, students progress analysis, knowledge level assessment, task difficulty analysis, personal learning curve planning). The process of interaction between the LMS system and mathematical software package, as well as the main ways of forming such software as completely independent applications for their further integration into other learning management systems, are thoroughly described. The efficiency of the microservice architecture in terms of scaling, performance and general behavior in case of critical errors in comparison with other systems based on classical architectural approaches is shown. The algorithm of predicting the time a student spends to answer the tasks, which is included in the mathematical software package, is considered.
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Статья научная
The paper is devoted to dosimetric modelling of the human red bone marrow (RBM) internal exposure due to beta-emitting 90Sr incorporated in spongiosa bone. The dose factor calculation (absorbed dose rate due to unit specific activity of 90Sr) is based on the modelling of radiation transport in segments of the skeleton bones with active hematopoiesis. Segmentation considerably simplifies the modelling, but can lead to an underestimation due to electron emission from the neighboring parts of the bone adjacent to the studied segment. The objective of the study is to determine this cross-fire effect on the absorbed dose in RBM. For this purpose, we analyze the results of the numerical experiment on modelling of dose absorption within the bone segments of various shape and size that were parts of the computational phantoms of skeletons of people of different sex and age. We analyze dose factor dependencies on the area of the spongiosa bone surface and the ratio of weights of bone and RBM. It is found that if the area of the spongiosa surface (SS) > 6 cm2, then the effect of neighboring bone parts exposure is negligible. For a smaller SS the extension of the linear dimensions of the spongiosa bone by 2 mean electron path lengths results in dose factor increase proportional to the ratio of the extended spongiosa bone surface area to the original one to the power of 0,28. For human computational phantoms, these values are in the range 1,03-1,21 and are used as adjustment coefficients for the dose factors. Relative standard uncertainty of the adjustment coefficient is 5%.
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Статья научная
This work considers hypersonic aircraft open-loop control problem in a presence of terminal and phase constraints. By the discretization process this problem is transformed into a nonlinear programming problem which is solved numerically by the interval explosion search algorithm. This algorithm belongs to metaheuristic algorithms of interval global optimization. Desired control is constructed in a class of interval piecewise-constant and piecewise-linear functions. Also this work demonstrates the comparison of results obtained by the proposed method and by Galerkin projection technique. This comparison confirms the efficiency of the interval based control algorithm.
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Introducing a power of the operator in direct spectral problems
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The resolvent method, proposed by Sadovnichiy and Dubrovsky in the 1990s, is successfully applied in the direct spectral problem to calculate the asymptotics of eigenvalues of the perturbed operator, find formulas for the regularized trace, and recover perturbation. But the application of this method faces difficulties when the resolvent of the unperturbed operator is non-nuclear. Therefore, a number of physical problems could only be considered on the interval. This article describes a justification of the transition to the power of an operator in order to expand the area of possible applications of the resolvent method. Considering the problem of calculating the regularized trace of the Laplace operator on a parallelepiped of arbitrary dimension, we show that for every fixed dimension it is possible to choose the required power of the operator and to calculate the regularized traces. These studies are relevant due to the need to study important applied problems, particularly in hydrodynamics, electronics, elasticity theory, quantum mechanics, and other fields.
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Invariant Manifolds of the Hoff Model in "Noise"
Статья научная
The work is devoted to the study the stochastic analogue of the Hoff equation, which is a model of the deviation of an I-beam from the equilibrium position. The stability of the model is shown for some values of the parameters of this model. In the study, the model is considered as a stochastic semilinear Sobolev type equation. The obtained results are transferred to the Hoff equation, considered in specially constructed “noise” spaces. It is proved that, in the vicinity of the zero point, there exist finite-dimensional unstable and infinite-dimensional stable invariant manifolds of the Hoff equation with positive values of parameters characterizing the properties of the beam material and the load on the beam
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Invariant manifolds of semilinear Sobolev type equations
Статья научная
The article is devoted to a review of the author's results in studying the stability of semilinear Sobolev type equations with a relatively bounded operator. We consider the initial-boundary value problems for the Hoff equation, for the Oskolkov equation of nonlinear fluid filtration, for the Oskolkov equation of plane-parallel fluid flow, for the Benjamin-Bon-Mahoney equation. Under an appropriate choice of function spaces, these problems can be considered as special cases of the Cauchy problem for a semilinear Sobolev type equation. When studying stability, we use phase space methods based on the theory of degenerate (semi)groups of operators and apply a generalization of the classical Hadamard-Perron theorem. We show the existence of stable and unstable invariant manifolds modeled by stable and unstable invariant spaces of the linear part of the Sobolev type equations in the case when the phase space is simple and the relative spectrum and the imaginary axis do not have common points.
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Inverse problem for Sobolev type mathematical models
Статья научная
The work is devoted to the study of an inverse problem for the linear Sobolev type equation of higher order with an unknown coefficient depending on time. Since the equation might be degenerate the phase space method is used. It consists in construction of projectors splitting initial spaces into a direct sum of subspaces. Actions of operators also split. Therefore, the initial problem is reduced to two problems: regular and singular. The regular one is reduced to the first order nondegenerate problem which is solved via approximations. The needed smoothness of the solution is obtained. Then it is substituted into the singular problem which is solved using the methods of relatively polynomially bounded operator pencils theory. The main result of the work contains sufficient conditions for the existence and uniqueness of the solution to the inverse problem for a complete Sobolev type model of the second order. This technique can be used to investigate inverse problems of the considered type for Boussinesq-Love mathematical model.
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Inverse problem for a linearized quasi-stationary phase field model with degeneracy
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The inverse problem for a linearized quasi-stationary phase field model is considered. The inverse problem is reduced to a linear inverse problem for the first order differential equation in a Banach space with a degenerate operator at the derivative and an overdetermination condition on the degeneracy subspace. The unknown parameter in the problem dependens on the source time function. The theorem of existence and uniqueness of classical solutions is proved by methods of degenerate operator semigroup theory at some additional conditions on the operator. General results are applied to the original inverse problem.
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Статья научная
We consider inverse problems of evolution type for mathematical models of quasistationary electromagnetic waves. It is assumed in the model that the wave length is small as compared with space inhomogeneities. In this case the electric and magnetic potential satisfy elliptic equations of second order in the space variables comprising integral summands of convolution type in time. After differentiation with respect to time the equation is reduced to a composite type equation with an integral summand. The boundary conditions are supplemented with the overdetermination conditions which are a collection of functionals of a solution (integrals of a solution with weight, the values of a solution at separate points, etc.). The unknowns are a solution to the equation and unknown coefficients in the integral operator. Global (in time) existence and uniqueness theorems of this problem and stability estimates are established.
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Inverse problems for some Sobolev-type mathematical models
Статья научная
The present article is devoted to the study of mathematical models based the Sobolev-type equations and systems arising in dynamics of a stratified fluid, elasticity theory, hydrodynamics, electrodynamics, etc. Along with a solution we determine an unknown right-hand side and coefficients in a Sobolev-type equations of the forth order. The overdetermination conditions are the values of a solution in a collection of points of a spatial domain. The problem is reduced to an operator equation whose solvability is established with the help of a priori estimates and the fixed point theorem. The existence and uniqueness theorems of solutions for the linear and nonlinear cases are proven. In the linear case the result is global in time and it is local in the nonlinear case. The main spaces in question are the Sobolev spaces.
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Inverse spectral problems and mathematical models of continuum mechanics
Статья научная
The article contains results in the field of spectral problems for mathematical models with discrete semi-bounded operator. The theory is based on linear formulas for calculating the eigenvalues of a discrete operator. The main idea is to reduce spectral problem to the Fredholm integral equation of the first kind. A computationally efficient numerical method for solving inverse spectral problems is developed. The method is based on the Galerkin method for discrete semi-bounded operators. This method allows to reconstruct the coefficient functions of boundary value problems with a high accuracy. The results obtained in the article are applicable to the study of problems for differential operators of any order. The results of a numerical solution of the inverse spectral problem for a fourth-order perturbed differential operator are presented. We study some mathematical models of continuum mechanics based on spectral problems for a discrete semi-bounded operator.
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In this paper, we study the problem of boundary control and final observation for one degenerate mathematical model of motion speed potentials distribution of filtered liquid free surface with the Showalter-Sidorov initial condition. The mathematical model is based on the degenerate Boussinesq equation with an inhomogeneous Dirichlet condition. This model belongs to the class of semilinear Sobolev-type models in which the nonlinear operator is p-coercive and s-monotone. In the paper, the problem of boundary control and final observation for a semilinear Sobolev-type model is considered and conditions for the existence of a control-state pair of the problem are found. In applied studies of a research problem, it is allowed to find such a potentials distributionof filtered liquid free surface, at which the system transitions from the initial condition to a given final state within a certain period of time T.
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Статья научная
Analysis of complex hydraulic networks, electric circuits, electronic schemes, chemical processes etc. often results in a system of interconnected differential and algebraic equations. If the process under study has after-effect, then the system includes integral equations. This paper addresses simulation of hydraulic networks by means of the theory for singular systems of integral differential equations. We present theoretical tools that help investigate qualitative properties of such systems and search for effective methods of solution. A mathematical model for the straight through boiler circuit has been developed and a numerical method for its solution has been constructed. Experimental results showed that the theory for singular systems of integral differential equations performs well when applied to simulation of the hydraulic networks.
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Статья научная
In the design of iterative learning control (ILC) algorithm for stochastic nonlinear networked systems, the underlying assumption is differentiability of the system dynamics. In many cases, in reality, stochastic nonlinear networked systems have non-differentiable dynamics, but their dynamics functions after discretization by using conventional methods have global Lipschits’ continuous (GLC) condition. In this paper, we apply an ILC algorithm for stochastic nonlinear networked systems that have the GLC condition. We demonstrate that to design the ILC algorithm, differentiability of the system dynamics is not necessary, and the GLC condition is sufficient for designing the ILC algorithm for stochastic nonlinear networked systems with non-differentiable dynamics. We investigate the analysis of convergence and the tracking performance of the proposed update law for stochastic nonlinear networked systems with GLC condition. We show that there exists no limited condition for the stochastic data dropout probabilities in the convergence investigation of the input error. Then, the results are reviewed and confirmed with a numerical example.
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Статья научная
Constant structure closed semantic systems are the systems each element of which receives its definition through the correspondent unchangeable set of other elements (neighbors) of the system. The definitions of the elements change iteratively and simultaneously based on the neighbor portraits from the previous iteration. In this paper, I study the behavior of such model systems, starting from the zero state, where all the system's elements are equal. The development of constant-structure discrete time closed semantic systems may be modelled as a discrete time coloring process on a connected graph. Basically, I consider the iterative redefinition process on the vertices only, assuming that the edges are plain connectors, which do not have their own colors and do not participate in the definition of the incident vertices. However, the iterative coloring process for both vertices and edges may be converted to the vertices-only coloring case by the addition of virtual vertices corresponding to the edges assuming the colors for the vertices and for the edges are taken from the same palette and assigned in accordance with the same laws. I prove that the iterative coloring (redefinition) process in the described model will quickly degenerate into a series of pairwise isomorphic states and discuss some directions of further research.
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L-stability of nonlinear systems represented by state models
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Stability theory plays a key role in systems theory and engineering. The stability of equilibrium points is usually considered within the framework of the stability theory developed by the Russian mathematician and mechanic A.M. Lyapunov (1857-1918), who laid its foundations and gave it its name. Nowadays, the point of view on stability has become very widespread, as stability in relation to disturbance of the input signal. The research is based on the space-state approach for modelling nonlinear dynamic systems and an alternative "input-output'' approach. The input-output model is implemented without explicit knowledge of the internal structure determined by the equation of state. The system is considered as a "black box'', which is accessed only through the input and output terminals ports. The concept of stability in terms of "input-output'' is based on the definition of L-stability of a nonlinear system, the method of Lyapunov functions and its generalization to the case of nonlinear dynamical systems. The interpretation of the problem on accumulation of perturbations is reduced to the problem on finding the norm of an operator, which makes it possible to expand the range of models under study, depending on the space in which the input and output signals act.
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Статья научная
Modelling of various natural and technical processes often results in systems that comprise ordinary differential equations and algebraic equations This paper studies systems of quasi-linear integral-differential equations with a singular matrix multiplying the higher derivative of the desired vector-function. Such systems can be treated as differential algebraic equations perturbed by the Volterra operators. We obtained solvability conditions for such systems and their initial problems and consider possible ways of linearization for them on the basis of the Newton method. Applications that arise in the area of thermal engineering are discussed and as an example we consider a hydraulic circuit presented as a system comprising an interconnected set of discrete components that transport liquid. Numerical experiments that employed the implicit Euler scheme showed that the mathematical model of the straight-through boiler with a turbine and a regeneration system has a solution and this solution tends to the stationary mode preset by regulators.
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Lord Kelvin and Andrey Andreyevich Markov in a queue with single server
Статья научная
We use Lord Kelvin's method of images to show that a certain infinite system of equations with interesting boundary conditions leads to a Markovian dynamics in an L1-type space. This system originates from the queuing theory.
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