For a nonincreasing function $\psi$, let $\textrm{Exact}(\psi)$ be the set of complex numbers that are approximable by rational to order $\psi$ but no better order. In this paper, we obtain Hausdorff dimension and packing when $\psi(x)=o(x^{-2})$. We also prove lower bound is greater than $2-\tau/(1-2\tau)$ $\tau=\limsup_{x\to\infty}\psi(x)x^2$ small enough.

The purpose of this study is to present an approximate numerical method for solving high order linear Fredholm-Volterra integro-differential equations in terms of rational Chebyshev functions under the mixed conditions. The method is based on the approximation by the truncated rational Chebyshev series. Finally, the effectiveness of the method is illustrated in several numerical examples. The p...

In this dissertation, I study decision-making mechanisms in young children and non-human primates across multiple domains—including visual attention and overt choice—in order to discover the efficacy and limitations of rational cognitive theories. Rational cognitive theories posit that intelligent organisms should choose actions that maximize utility (e. Effective utility maximization requires ...

Vibration and dissipation in vibro-acoustic systems can be assessed using frequency response analysis. Evaluating a sweep on full-order model very costly, so order reduction methods are employed to compute cheap-to-evaluate surrogates. This work compares structure-preserving based rational interpolation balanced truncation with specific focus their applicability systems. Such models typically e...

We study a transformation on terms consisting of applying an inverse deterministic rational mapping followed by an unfolding. Iterating these transformations from the regular terms gives a hierarchy of families of terms having a decidable monadic theory. In particular, the family at level 2 contains the morphic innnite words investigated by Carton and Thomas. We show that this hierarchy coincid...