In this paper, we investigate the boundedness and uniformly asymptotically stability of solutions to a certain third order non-autonomous differential equations with bounded delay. By constructing Lyapunov functional, sufficient conditions for considered are obtained. We used an example demonstrate feasibility our results. The results essentially improve, include, complement in literature.

In this paper we study some questions in connection with uniform rectifiability and the L boundedness of Calderón-Zygmund operators. We show that uniform rectifiability can be characterized in terms of some new adimensional coefficients which are related to the Jones’ β numbers. We also use these new coefficients to prove that n-dimensional CalderónZygmund operators with odd kernel of type C2 a...

In this paper, finite-time boundedness and stabilization problems for a class of switched linear systems with time-varying exogenous disturbances are studied. Firstly, the concepts of finite-time stability and finite-time boundedness are extended to switched linear systems. Then, based on matrix inequalities, some sufficient conditions under which the switched linear systems are finite-time bou...

It is known that the norm of the solution to a weighted linear least-squares problem is uniformly bounded for the set of diagonally dominant symmetric positive definite weight matrices. This result is extended to weight matrices that are nonnegative linear combinations of symmetric positive semidefinite matrices. Further, results are given concerning the strong connection between the boundednes...

In this paper we prove general logical metatheorems which state that for large classes of theorems and proofs in (nonlinear) functional analysis it is possible to extract from the proofs effective bounds which depend only on very sparse local bounds on certain parameters. This means that the bounds are uniform for all parameters meeting these weak local boundedness conditions. The results vastl...

a new definition of boundedness of linear order-homomorphisms (loh)in $l$-topological vector spaces is proposed. the new definition iscompared with the previous one given by fang [the continuity offuzzy linear order-homomorphism, j. fuzzy math. 5 (4) (1997)829$-$838]. in addition, the relationship between boundedness andcontinuity of lohs is discussed. finally, a new uniform boundednessprincipl...

This paper is a natural continuation of Krylov (2020), where strong Markov processes are constructed in time inhomogeneous setting with Borel measurable uniformly bounded and nondegenerate diffusion drift Ld+1(Rd+1). Here we study some properties these such as higher summability Green’s functions, maximum principle for related transport equations irregular coefficients, boundedness resolvent op...

We consider a spin 1 2 electron in a translation-invariant model of non-relativistic Quantum Electrodynamics (QED). Let H(~ p, σ) denote the fiber Hamiltonian corresponding to the conserved momentum ~ p ∈ R, regularized by a fixed ultraviolet cutoff in its interaction term, and an infrared regularization parametrized by 0 < σ ≪ 1 which we ultimately remove by taking σ ց 0. For |~ p| < 1 3 , all...

In this paper we introduce the notion of string stability of a countably infinite interconnection of a class of nonlinear systems. Intuitively, string stability implies uniform boundedness of all the states of the interconnected system for all time if the initial states of the interconnected system are uniformly bounded. It is well known that the input-output gain of all the subsystems less tha...

We establish quantitative bounds for rates of convergence and asymptotic variances for iterated conditional sequential Monte Carlo (i-cSMC) Markov chains and associated particle Gibbs samplers [1]. Our main findings are that the essential boundedness of potential functions associated with the i-cSMC algorithm provide necessary and sufficient conditions for the uniform ergodicity of the i-cSMC M...