相关论文: Relatively inertial delays

This tutorial, addressing physics teachers and undergraduate students, aims at clarifying some aspects of time in special relativity. In particular, time dilation is usually presented only as the well-known ratio of lab time over proper…

We discuss the relation between three recent approaches of describing the dynamics and the spatial distribution of particles suspended in turbulent flows: phase-space singularities in the inertial particle dynamics (caustics), real-space…

Relative algebroids provide a framework that unifies Lie algebroids with partial differential equations. In this set of notes, we explain how relative algebroids arise from geometric problems, and give an introduction to their structural…

We discuss Vassiliev invariants for virtual knots, expanding upon the theory of quantum virtual knot invariants developed in arXiv:1509.00578. In particular, following the theory of quantum invariants we work with 'rotational' virtual…

Robust hyperbolicity and stability results for linear partial differential equations with delay will be given and, as an application, the effect of small delays to the asymptotic properties of feedback systems will be analyzed.

We study the stability of general $n$-dimensional nonautonomous linear differential equations with infinite delays. Delay independent criteria, as well as criteria depending on the size of some finite delays are established. In the first…

The fundamental matrix and the delay Lyapunov matrix of linear delay difference equations are introduced. Some properties of the Lyapunov matrix, and the jump discontinuities of its derivative are proven, leading to its construction in the…

In this paper we obtain estimates on the distance of inertial manifolds for dynamical systems generated by evolutionary parabolic type equations. We consider the situation where the systems are defined in different phase spaces and we…

A proper discretization of the logistic differential equation, which is preserving these two distinct equilibrium solutions and their unstability and stability, suggest that we need to examine the time delay of the logistic map. According…

We consider a system of coupled oscillators with finite inertia and time-delayed interaction, and investigate the interplay between inertia and delay both analytically and numerically. The phase velocity of the system is examined; revealed…

The (non-initialized, non-deterministic) asynchronous systems (in the input-output sense) are multi-valued functions from m-dimensional signals to sets of n-dimensional signals, the concept being inspired by the modeling of the asynchronous…

A robust controller is developed for uncertain, second-order nonlinear systems subject to simultaneous unknown, time-varying state delays and known, time-varying input delays in addition to additive, sufficiently smooth disturbances. An…

Complete Hamiltonian formalism is suggested for inertial waves in rotating incompressible fluid. Resonance three-wave interaction processes -- decay instability and confluence of two waves -- are shown to play a key role in the weakly…

We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…

This paper studies a class of random nonlinear systems with time-varying delay, in which the $r$-order moment ($r\geq1$) of the random disturbance is finite. Firstly, some general conditions are proposed to guarantee the existence and…

We study the quadratic regulator problem for linear control systems in Hilbert spaces, where the cost functional is in some sense unbounded. Our motivation comes from delay equations with the feedback part containing discrete delays or, in…

This paper concerns some spectral properties of the scalar dynamical system defined by a linear delay-differential equation with two positive delays. More precisely, the existing links between the delays and the maximal multiplicity of the…

The purpose of this article is to motivate the study of invariant, and especially conformally invariant, differential pairings. Since a general theory is lacking, this work merely presents some interesting examples of these pairings,…

The fundamental model of a periodic structure is a periodic point set up to rigid motion or isometry. Our recent paper in SoCG 2021 defined isometry invariants (density functions), which are complete in general position and continuous under…

This paper establishes the equivalence between systems described by a single first-order hyperbolic partial differential equation and systems described by integral delay equations. System-theoretic results are provided for both classes of…