The existence and uniqueness of a periodic solution of the system of differential equations d dt x(t) = A(t)x(t − ) are proved. In particular the Krasnoselskii’s fixed point theorem and the contraction mapping principle are used in the analysis. In addition, the notion of fundamental matrix solution coupled with Floquet theory is also employed.  

We derive strong mixing conditions for many existing discrete-valued time series models that include exogenous covariates in the dynamic. Our main contribution is to study how a condition on covariate process transfers response. Using coupling method, we first some Markov chains random environments, which gives result autoregressive categorical processes with strictly regressors. then extended ...

This work addresses a pattern-moving-based partial form dynamic linearization model free adaptive control (P-PFDL-MFAC) scheme and illustrates the bounded convergence of its tracking error for class unknown nonaffine nonlinear discrete-time systems. The concept pattern moving is to take system output condition as operation variable, purpose ensure that outputs belong certain or some desired cla...

Let (M, θ) be a strictly pseudoconvex pseudo-Hermitian compact hypersurface in C in the sense of Webster [34] with a pseudo-Hermitian real oneform θ on M . Let Rθ be the Webster pseudo scalar curvature for M with respect to θ. By the solution of the CR Yamabe problem given by Jerison and Lee [18], Gamara and Yacoub [10] and Gamara [9] (for n = 1), there is a pseudo-Hermitian real one-form θ so ...

let $x$ be a reflexive banach space, $t:xto x$ be a nonexpansive mapping with $c=fix(t)neqemptyset$ and $f:xto x$ be $delta$-strongly accretive and $lambda$- strictly pseudocotractive with $delta+lambda>1$. in this paper, we present modified hybrid steepest-descent methods, involving sequential errors and functional errors with functions admitting a center, which generate convergent sequences t...