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Coupling linearity and twist: an extension of the Poincaré–Birkhoff theorem for Hamiltonian systems
We provide an extension of the Poincaré–Birkhoff Theorem for systems coupling linear components with twisting components. Applications are given both...
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Quaternion offset linear canonical transform in one-dimensional setting
In this paper, we introduce quaternion offset linear canonical transform of integrable and square integrable functions. Moreover, we show that the...
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Stability and instability of standing-wave solutions to one-dimensional quadratic-cubic Klein–Gordon equations
We study the stability of standing-waves solutions to a scalar non-linear Klein–Gordon equation in dimension one with a quadratic-cubic...
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Homotopy Analysis Method For Oscillatory Systems With Cubic and Trigonometric Non-Linearity
Analytical solutions to nonlinear oscillating systems cannot be represented without the help of special functions or they can be studied only using...
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Modeling the Inter-Industry Economy as a Critical Infrastructure: Generating Scenarios for the Development of the Economy of Ukraine under the Conditions of War and the Post-War Recovery
The input-output scheme is considered as applied to the analysis of the cross-industry reproduction of the economy of Ukraine as a critical...
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Clifford-valued linear canonical wave-packet transform and corresponding uncertainty principles
In an effort to express Clifford-valued signals efficiently in time–frequency domain, we introduce the notion of the novel integral transform known...
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Concavity Property of Minimal \(L^{2}\) Integrals with Lebesgue Measurable Gain VII–Negligible Weights
In this article, we present characterizations of the concavity property of minimal...
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Bifurcations in Continuous Piecewise Linear Differential Systems Applications to Low-Dimensional Electronic Oscillators
The book is devoted to the qualitative study of differential equations defined by piecewise linear (PWL) vector fields, mainly continuous, and...
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Multi-Factor Polynomial Diffusion Models and Inter-Temporal Futures Dynamics
In stochastic multi-factor commodity models, it is often the case that futures prices are explained by two latent state variables which represent the...
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Reduced Basis Approach for Convection-Diffusion Equations with Non-linear Boundary Reaction Conditions
This paper aims at an efficient strategy to solve drift-diffusion problems with non-linear boundary conditions as they appear, e.g., in heterogeneous...
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A Conservative a-Posteriori Time-Limiting Procedure in Quinpi Schemes
The superior stability properties of implicit time schemes allow to avoid small time steps required to satisfy restrictive stability conditions for...
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Homogenization for space-time-dependent KPP reaction–diffusion equations and G-equations
We prove stochastic homogenization for reaction–advection–diffusion equations with random space-time-dependent KPP reactions with temporal...
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Synchronization in a Class of Chaotic Systems
In this work, the synchronization problem of a master–slave system of autonomous ordinary differential equations (ODEs) is considered. Here, the...
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Introduction
The fundamental works of Doob, Hunt, Kakutani, Kolmogorov, Lévy, and many others have shown a profound and powerful connection between the classical...
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Presure Boundary Conditions in the Collocated Finite-Volume Method for the Steady Navier–Stokes Equations
AbstractThe pressure boundary conditions for the steady-state solution of the incompressible Navier–Stokes equations with the collocated...
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Control of a Discrete Dynamical System with Noise
For a discrete dynamical control system with noise, we consider the problem of retaining a phase point in a given family of sets at discrete instants...
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Partial Differential Equations
We start with an introduction to basic concepts such as the order and linearity type of a partial differential equation, followed by a discussion...