Search Results - "Sergeev, I N"

Studying the Oscillation, Rotation, and Wandering Indicators by the First Approximation by Sergeev, I. N.

“…Oscillation, rotation, and wandering indicators similar to Lyapunov exponents and adapted to nonlinear systems of differential equations are studied. A variety…”
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Studying the Perron and Lyapunov Stability Properties by the First Approximation by Sergeev, I. N.

“…We explore opportunities for studying various Perron or Lyapunov stability properties of differential systems by the first approximation. We prove that the…”
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Calcium as a mediator of 1,25-dihydroxyvitamin D3-induced apoptosis by SERGEEV, I. N

“…Cellular calcium has been implicated in induction of apoptosis. We have shown that 1,25(OH)(2)D(3)-induced apoptosis is associated with a sustained increase in…”
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Study of the Complete Oscillation, Rotation, and Wandering Properties of a Differential System by the First Approximation by Sergeev, I. N.

“…The concepts of complete oscillation, rotation, and wandering as well as complete nonoscillation, nonrotation, and nonwandering of a system of differential…”
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Definition and Properties of Measures of Stability and Instability of Zero Solution of a Differential System by Sergeev, I. N.

“…We consider the problem on the possibility of randomly choosing the initial value for a perturbed solution of a given differential system so that it remained…”
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Turnability characteristics of solutions of differential systems by Sergeev, I. N.

“…For each solution of a differential system, we define a set of turnability exponents of various ranks, which are obtained by minimization and time averaging of…”
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Examples of Autonomous Differential Systems with Contrasting Combinations of Lyapunov, Perron, and Upper-Limit Stability Measures by Sergeev, I. N.

“…New characteristics of differential systems are studied, which meaningfully develop the concepts of Lyapunov, Perron, and upper limit stability or instability…”
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Classes of Linear Approximations Providing Different Stability or Instability Types of Differential Systems by Sergeev, I. N.

“…The paper studies relationships (inclusions, coincidences, and noncoincidences) between classes of linear approximations that provide various properties of…”
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The Definition of the Indices of Oscillation, Rotation, and Wandering of Nonlinear Differential Systems by Sergeev, I. N.

“…The definitions of the indices of oscillation, rotation and wandering, similar to the Lyapunov exponents and suitable for nonlinear systems are given…”
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Perron Stability and Its Study at the First Approximation by Sergeev, I. N.

“…Natural concepts of Perron stability, asymptotic stability, and complete instability of the trivial solution to a differential system are introduced. Their…”
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Definition and Some Properties of Perron Stability by Sergeev, I. N.

“…The natural notions of Perron stability, Perron asymptotic stability, and Perron complete instability of the zero solution of a differential system are…”
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Examples of Differential Systems with Contrasting Combinations of Lyapunov, Perron, and Upper-Limit Properties by Bondarev, A. A., Sergeev, I. N.

“…A number of examples of systems of differential equations are given that have, in a sense, opposite properties of stability or instability of various types:…”
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Oscillation, Rotation, and Wandering of Solutions to Linear Differential Systems by Sergeev, I. N.

“…For solutions of a linear system on the semi-axis, we introduce a series of Lyapunov exponents that describe the oscillation, rotation, and wandering…”
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Dependence and Independence of the Perron and Lyapunov Stability Properties on the System Phase Domain by Sergeev, I. N.

“…For a differential system, we study various properties related to Lyapunov and Perron stability. We prove that all of these properties are of specifically…”
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Oscillation, Rotatability, and Wandering Characteristic Indicators for Differential Systems Determining Rotations of Plane by Sergeev, I. N.

“…The oscillation, rotatability, and wandering characteristic indicators of Lyapunov type are studied for two-dimensional linear homogeneous differential systems…”
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Reducibility of Linear Differential Systems to Linear Differential Equations by Sergeev, I. N.

“…Lyapunov reducibility of any bounded and sometimes unbounded linear homogeneous differential system to some bounded linear homogeneous differential equation is…”
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On Simplified Formulas for the Central Exponents of Differential Systems With Non-Uniform Scales by Sergeev, I. N.

“…We study the Vinograd–Millionshchikov central exponents, which represent the exact outer boundaries for the mobility of the extremal values of the Lyapunov and…”
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Criterion for Lyapunov Reducibility of a Linear Autonomous Differential System to a Linear Autonomous Equation by Sergeev, I. N., Umansky, K. V.

“…We establish a unified criterion for the reducibility of a linear homogeneous differential system with constant coefficients to a linear homogeneous…”
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Lyapunov Characteristics of Oscillation, Rotation, and Wandering of Solutions of Differential Systems by Sergeev, I. N.

“…A number of Lyapunov exponents are defined for solutions of linear systems on the half-line. These exponents are responsible for such properties of the…”
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Simultaneous attainability of central exponents of a linear Hamiltonian system under Hamiltonian perturbations by Sergeev, I. N.

“…We show that, for any linear Hamiltonian system, there exists an arbitrarily close (in the uniform metric on the half-line) linear Hamiltonian system whose…”
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