Related papers: A discrete Hardy's Uncertainty Principle and discr…
This paper derives two stabilizability theorems for a basic class of discrete-time nonlinear systems with multiple unknown parameters. First, we claim that a discrete-time multi-parameter system is stabilizable if its nonlinear growth rate…
Multiple hypotheses/models have been put forward regarding the cooling history of the Earth. The search for life beyond Earth has brought these models into a new light as they connect to one of the two energy sources life can tap. The…
The thermodynamic uncertainty relation offers a universal energetic constraint on the relative magnitude of current fluctuations in nonequilibrium steady states. However, it has only been derived for long observation times. Here, we prove a…
This paper presents the unsteady Darcy's equations coupled with two nonlinear reaction-diffusion equations, namely this system describes the mass concentration and heat transfer in porous media. The existence and uniqueness of the solution…
Recent advancements in machine learning have emphasized the need for transparency in model predictions, particularly as interpretability diminishes when using increasingly complex architectures. In this paper, we propose leveraging…
We study boundary uniqueness properties of Hardy space functions in several complex variables. Along the way, we develop properties of the Lumer Hardy space.
A new exponentially fitted version of the Discrete Variational Derivative method for the efficient solution of oscillatory complex Hamiltonian Partial Differential Equations is proposed. When applied to the nonlinear Schroedinger equation,…
We propose a variational formulation for the nonequilibrium thermodynamics of discrete open systems, i.e., discrete systems which can exchange mass and heat with the exterior. Our approach is based on a general variational formulation for…
We introduce a discrete delayed exponential depending on sequence of matrices. This discrete matrix gives a representation of a solution to the Cauchy problem for a discrete linear system with pure delay with sequence of matrices. We…
Numerical models of weather and climate critically depend on long-term stability of integrators for systems of hyperbolic conservation laws. While such stability is often obtained from (physical or numerical) dissipation terms, physical…
Dempster-Shafer theory is widely applied to uncertainty modelling and knowledge reasoning due to its ability of expressing uncertain information. However, some conditions, such as exclusiveness hypothesis and completeness constraint, limit…
We discuss a discrete approach to the multiscale reductive perturbative method and apply it to a biatomic chain with a nonlinear interaction between the atoms. This system is important to describe the time evolution of localized solitonic…
We prove the existence of a family of slow decay positive solutions of a supercritical elliptic equation with Hardy potential in the entire space and study stability and oscillation properties of these solutions. We also establish the…
We give new proofs of Hardy space estimates for fractional and singular integral operators on weighted and variable exponent Hardy spaces. Our proofs consist of several interlocking ideas: finite atomic decompositions in terms of $L^\infty$…
In this paper we investigate the Cauchy problem for Schr\"odinger ultrahyperbolic equations with singular (less than continuous) coefficients. We prove $H^\infty$ well-posedness in the very weak sense under suitable assumptions of the…
A recently proposed discrete version of the Schrodinger spectral problem is considered. The whole hierarchy of differential-difference nonlinear evolution equations associated to this spectral problem is derived. It is shown that a discrete…
In a previous work [arXiv:2211.02945] we made an attempt to set up a discrete octonionic Stokes' formula. Due to an algebraic property that we have not considered in that attempt, the formula however turned out to involve an associator term…
The uncertainty relation, as one of the fundamental principles of quantum physics, captures the incompatibility of noncommuting observables in the preparation of quantum states. In this work, we derive two strong and universal uncertainty…
We prove a dispersive estimate for periodic discrete Schr\"odinger operators on the line with optimal rate of decay. Additionally, by standard methods, we deduce dispersive estimates for the discrete nonlinear Schr\"odinger equation with…
Shannon entropy for discrete distributions is a fundamental and widely used concept, but its continuous analogue, known as differential entropy, lacks essential properties such as positivity and compatibility with the discrete case. In this…