the rings considered in this article are commutative with identity $1neq 0$. by a proper ideal of a ring $r$,  we mean an ideal $i$ of $r$ such that $ineq r$.  we say that a proper ideal $i$ of a ring $r$ is a  maximal non-prime ideal if $i$ is not a prime ideal of $r$ but any proper ideal $a$ of $r$ with $ isubseteq a$ and $ineq a$ is a prime ideal. that is, among all the proper ideals of $r$,...

We present a design scheme to generate tight and semi-tight frames in the space of discrete-time periodic signals, which are originated from four-channel perfect reconstruction periodic filter banks. The filter banks are derived from interpolating and quasi-interpolating polynomial splines. Each filter bank comprises one linear phase low-pass filter (in most cases interpolating) and one high-pa...

Nonlinear semi-analytic filtering methods to sequentially estimate spacecraft states and their associated uncertainties are presented. We first discuss the state transition tensors that characterize the localized nonlinear behavior of the trajectory statistics and illustrate the importance of higher-order effects on orbit uncertainty propagation. We then present a semi-analytic filtering method...