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The Antonov Stability Estimate
The purpose of this short chapter is to provide some more details on the Antonov stability estimate, Theorem 1.2...
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Study of Instability for One-Dimensional Dynamic Equilibrium States of Self-Gravitating Vlasov–Poisson Gas
AbstractIn this paper, the linear stability problem for one-dimensional (1D) states of dynamic equilibrium of a boundless collisionless...
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A Birman-Schwinger Principle in Galactic Dynamics
This monograph develops an innovative approach that utilizes the Birman-Schwinger principle from quantum mechanics to investigate stability...
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An Intelligent Choice of Witnesses in the Miller–Rabin Primality Test. Reinforcement Learning Approach
AbstractThe problem of testing natural numbers for primality is an important problem for the Theory of Numbers and Cryptography. The main instrument...
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Introduction
The Birman-Schwinger principle is a widely used and well-established tool in mathematical quantum mechanics. It was introduced through the...
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Quickest Changepoint Detection in General Multistream Stochastic Models: Recent Results, Applications and Future Challenges
Modern information systems generate large volumes of data with anomalies that occur at unknown points in time and have to be detected quickly and...
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Influence of Noisy Environments on Behavior of HPC Applications
AbstractMany contemporary HPC systems expose their jobs to substantial amounts of interference, leading to significant run-to-run variation. For...
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A Systematic Approach to Multiobjective Optimization
A systematic approach to solving multiobjective optimization problems is proposed. It allows combining the models of individual schemes of...
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Non-convex Optimization in Digital Pre-distortion of the Signal
This paper reviews application of modern optimization methods for functionals describing Digital Pre-distortion (DPD) of signals with orthogonal...
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A Birman-Schwinger Type Operator
As has been outlined in the introduction, the eigenvalues \(\lambda <\delta _1^2\)...
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A brief history of quantitative finance
In this introductory paper to the issue, I will travel through the history of how quantitative finance has developed and reached its current status,...
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Particular features of implementation of an unsaturated numerical method for the exterior axisymmetric Neumann problem
Using Babenko’s profound ideas, we construct a fundamentally new unsaturated numerical method for solving the spectral problem for the operator of...
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Orbital stability of spherical galactic models
We consider the three dimensional gravitational Vlasov Poisson system which is a canonical model in astrophysics to describe the dynamics of galactic...
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Numerical simulation of a nonstationary flow in the vicinity of a hypersonic vehicle
The nonstationary flow around the forebody of a hypersonic vehicle is studied by using a numerical simulation based on quasi-gas dynamic equations....
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Regularization method for solving the quasi-stationary Maxwell equations in an inhomogeneous conducting medium
Nedelec vector finite elements are used for the numerical solution of a regularized version of the quasi-stationary Maxwell equations written in...
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Modeling of self-oscillations and a search for new self-oscillatory flows
A possible mechanism of self-oscillations in flows with shock waves and contact discontinuities is studied. Flows are investigated in the...
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An unsaturated numerical method for the exterior axisymmetric Neumann problem for Laplace’s equation
Basing on the fundamental ideas of Babenko, we construct a fundamentally new, unsaturated , numerical method for solving the axially symmetric...
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On Landau dam**
Going beyond the linearized study has been a longstanding problem in the theory of Landau dam**. In this paper we establish exponential Landau...
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Statistical analysis of operational reliability for electric pump units CN 60–180 of VVER-1000 reactors with root estimation methods
We consider the problem of processing statistical data obtained during the operation of pum** units CN 60–180 operating as standard equipment of...
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Methods for obtaining reliable solutions to systems of linear algebraic equations
The general case of incompatible systems of linear algebraic equations with matrices of arbitrary rank is considered. The estimates for total errors...