Related papers: On the Lyapunov function for complex-balanced mass…
In this paper we present a technique for constructing Lyapunov functions based on Whitney's size functions. Applications to asymptotically stable equilibrium points, isolated sets, expansive homeomorphisms and continuum-wise expansive…
The basic motivation and primary goal of this paper is a qualitative evaluation of the performance of a new weighted statistic for a nonparametric test for stochastic dominance based on two samples, which was introduced in Ledwina and…
We show that the existence of a Lyapunov-Krasovskii functional (LKF) with pointwise dissipation (i.e. dissipation in terms of the current solution norm) suffices for input-to-state stability, provided that uniform global stability can also…
We devise automated workflows for the calculation of Helmholtz and Gibbs free energies and their temperature and pressure dependence and provide the corresponding computational tools. We employ non-equilibrium thermodynamics for evaluating…
In this work, we propose a method for calculating the free energy of anisotropic quantum spin systems. We use the Hubbard-Stratonovich transformation to express the partition function of a generic bilinear super-exchange Hamiltonian in…
We provide the details for Gromov's proof of Stallings' theorem on groups with infinitely many ends using harmonic functions. The main technical result of the paper is a compactness theorem for a certain family of harmonic functions.
We introduce a new class of quadratic functions based on a hierarchy of linear time-varying (LTV) dynamical systems. These quadratic functions in the higher order space can be also seen as a non-homogeneous polynomial Lyapunov functions for…
We give a representation of the fractional integral for symmetric Markovian semigroups as the projection of martingale transforms and prove the Hardy-Littlewood-Sobolev(HLS) inequality based on this representation. The proof rests on a new…
As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…
We consider a continuous-time linear time-invariant dynamical system that admits an invariant cone. For the case of a self-dual and homogeneous cone we show that if the system is asymptotically stable then it admits a quadratic Lyapunov…
In this article, we introduce Lyapunov-type results to investigate the stability of the trivial solution of a Stieltjes dynamical system. We utilize prolongation results to establish the global existence of the maximal solution. Using…
Dynamical systems generated by scalar reaction-diffusion equations on an interval enjoy special properties that lead to a very simple structure for the semiflow. Among these properties, the monotone behavior of the number of zeros of the…
We consider in this paper some class of perturbation for the semilinear wave equation with subcritical (in the conformal transform sense) power nonlinearity. We first derive a Lyapunov functional in similarity variables and then use it to…
We present an expansion of a many-body correlation function in a sum of pseudomodes -- exponents with complex frequencies that encompass both decay and oscillations. The pseudomode expansion emerges in the framework of the Heisenberg…
We demonstrate the extension of unpredictable motions in coupled autonomous systems with skew product structure in the case that generalized synchronization takes place. Sufficient conditions for the existence of unpredictable motions in…
The paper is a continuation of research in the direction of energy function (a smooth Lyapunov function whose set of critical points coincides with the chain recurrent set of a system) construction for discrete dynamical systems. The…
A basic shallow water system with variable topography is analyzed from the point of view of a Lagrangian derivation of momentum, energy, and pseudomomentum balances. A two-dimensional action and associated momentum equation are derived. The…
A new way to construct a fitting formula for the halo mass function is presented. Our formula is expressed as a solution to the modified Jedamzik matrix equation that automatically satisfies the normalization constraint. The characteristic…
Macroscopic entropy production $\sigma^{(tot)}$ in the general nonlinear isothermal chemical reaction system with mass action kinetics is decomposed into a free energy dissipation and a house-keeping heat:…
In this paper, a new proof of the Positive Mass Theorem is established through a newly discovered monotonicity formula, holding along the level sets of the Green's function of an asymptotically flat $3$-manifold. In the same context and for…