We study a heavy piston that separates finitely many ideal gas particles moving inside a one-dimensional gas chamber. Using averaging techniques, we prove precise rates of convergence of the actual motions of the piston to its averaged behavior. The convergence is uniform over all initial conditions in a compact set. The results extend earlier work by Sinai and Neishtadt, who determined that th...

We study a heavy piston that separates finitely many ideal gas particles moving inside the unit interval. Using averaging techniques, we prove precise rates of convergence of the actual motions of the piston to its averaged behavior. The convergence is uniform over all initial conditions in a compact set. The results extend earlier work by Sinai and Neishtadt, who determined that the averaged b...

An old question of T. Jech and K. Prikry asks if an existence of a precipitous ideal implies necessary existence of a normal precipitous ideal. The aim of the paper is to prove some results in the positive direction. Thus, it is shown that under some mild assumptions, an existence of a precipitous ideal over א1 implies an existence of a normal precipitous ideal over א1 once a Cohen subset is ad...

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 $r$,...

The Zap Q-learning algorithm introduced in this paper is an improvement of Watkins’ original algorithm and recent competitors in several respects. It is a matrix-gain algorithm designed so that its asymptotic variance is optimal. Moreover, an ODE analysis suggests that the transient behavior is a close match to a deterministic Newton-Raphson implementation. This is made possible by a two time-s...

In this paper, we generalize the concept of unbounded norm (un) convergence: let X be a normed lattice and Y a vector lattice such that X is an order dense ideal in Y ; we say that a net (yα) un-converges to y in Y with respect to X if ∥∥|yα−y|∧x∥∥→ 0 for every x ∈ X+. We extend several known results about unconvergence and un-topology to this new setting. We consider the special case when Y is...

This paper presents two adaptive control laws that have improved parameter convergence properties. These adaptive control laws are derived through the framework of Model Reference Adaptive Control and are applicable to plants with structured or unstructured modeling uncertainty. The presented adaptive control laws use both recorded and current data concurrently to improve parameter convergence ...

let $l$ be a completely regular frame and $mathcal{r}l$ be the ‎ring of continuous real-valued functions on $l$‎. ‎we show that the‎ ‎lattice $zid(mathcal{r}l)$ of $z$-ideals of $mathcal{r}l$ is a‎ ‎normal coherent yosida frame‎, ‎which extends the corresponding $c(x)$‎ ‎result of mart'{i}nez and zenk‎. ‎this we do by exhibiting‎ ‎$zid(mathcal{r}l)$ as a quotient of $rad(mathcal{r}l)$‎, ‎the‎ ‎...

The main purpose of this article is to introduce and study some new spaces I-convergence triple sequences in intuitionistic fuzzy normed space defined by compact operator i.e 3SI (μ,ν)(T ) 3SI0(μ,ν)(T examine fundamental properties, topology verify inclusion relations lying under these spaces.

In this paper, we generalize the concept of I statistical convergence, which is a recently introduced summability method, with an in…nite matrix of complex numbers and a modulus function. Lacunary sequences will also be included in our de…nitions. The name of our new method will be AI -lacunary statistical convergence with respect to a sequence of modulus functions. We also de…ne strongly AI -l...