相关论文: Theory And Applications Of One-Sided Coupled Opera…

We study some natural operators acting on configurations of points and lines in the plane and remark that many interesting configurations are fixed points for these operators. We review ancient and recent results on line or point…

In this article we study a class of hyperbolic partial differential equations of order one on the semi-axis. The so-called port-Hamiltonian systems cover for instance the wave equation and the transport equation, but also networks of the…

Koopman operator based models emerged as the leading methodology for machine learning of dynamical systems. But their scope is much larger. In fact they present a new take on modeling of physical systems, and even language. In this article…

We design observer-based controllers to stabilise abstract linear boundary control systems on Hilbert spaces. Our main results introduce conditions for exponential, strong, and polynomial stability, and establish external well-posedness of…

We introduce a new fixed point theorem of Krasnoselskii type for discontinuous operators. As an application we use it to study the existence of positive solutions of a second-order differential problem with separated boundary conditions and…

We consider two-point non-self-adjoint boundary eigenvalue problems for linear matrix differential operators. The coefficient matrices in the differential expressions and the matrix boundary conditions are assumed to depend analytically on…

Koopman operator theory offers a rigorous treatment of dynamics and has been emerging as an alternative modeling and learning-based control method across various robotics sub-domains. Due to its ability to represent nonlinear dynamics as a…

We conduct the first detailed analysis in quantum information of recently derived operator relations from the study of quantum one-way local operations and classical communications (LOCC). We show how operator structures such as operator…

Connection matrices are one of the central tools in Conley's approach to the study of dynamical systems, as they provide information on the existence of connecting orbits in Morse decompositions. They may be considered a generalisation of…

We study forward and inverse problems for a semilinear radiative transport model where the absorption coefficient depends on the angular average of the transport solution. Our first result is the well-posedness theory for the transport…

We apply an operator-theoretic viewpoint to a class of non-smooth dynamical systems that are exposed to event-triggered state resets. The considered benchmark problem is that of a pendulum which receives a downward kick under certain fixed…

In this note, we survey some elementary theorems and proofs concerning dynamical matrices theory. Some mathematical concepts and results involved in quantum information theory are reviewed. A little new result on the matrix representation…

Many studies have been conducted on statistical convergence, and it remains an area of active research. Since its introduction, statistical convergence has found applications many fields. Nevertheless, there is a shortage of research…

We develop an elliptic theory based in $L^2$ of boundary value problems for general wedge differential operators of first order under only mild assumptions on the boundary spectrum. In particular, we do not require the indicial roots to be…

We study stability of abstract differential equations coupled by means of a general algebraic condition. Our approach is based on techniques from operator theory and systems theory, and it allows us to study coupled systems by exploiting…

We introduce a constrained optimal transport problem where origins $x$ can only be transported to destinations $y\geq x$. Our statistical motivation is to describe the sharp upper bound for the variance of the treatment effect $Y-X$ given…

Chaos is a fundamental feature of many complex dynamical systems, including weather systems and fluid turbulence. These systems are inherently difficult to predict due to their extreme sensitivity to initial conditions. Many chaotic systems…

In this paper, we study the feasibility of a class of optimization-based boundary control of one-dimensional macroscopic traffic flow models, where stability and invariance are achieved by a single boundary control. We define the sets of…

We provide a new perturbation theorem for substochastic semigroups on abstract AL spaces extending Kato's perturbation theorem to non-densely defined operators. We show how it can be applied to piecewise deterministic Markov processes and…

Inspired by recent developments in the theory of stability results in the context of certain wave type phenomena, we discuss abstract damped hyperbolic type equations given in a block operator matrix form with regards to asymptotic…