In mathematics curves are typically defined as the images of continuous real functions (parametrizations) defined on a closed interval. They can also be defined as connected one-dimensional compact subsets of points. For simple curves of finite lengths, parametrizations can be further required to be injective or even length-normalized. All of these four approaches to curves are classically equi...

We wish to thank the Tel Aviv Stock Exchange for providing us the data. We thank Yakov Amihud, Eugene Kandel and Orly Sade for very useful comments and suggestions. Wohl thanks the David Orgler and Family Research Fund for Banking and Finance for partial financial support. 2 Abstract In this first direct test of Hellwig's (1980) Noisy Rational Expectations Equilibrium (NREE), we restate the mod...

The representation or order reduction of a rational transfer function by a linear combination of orthogonal rational functions offers several advantages, among which the possibility to work with prescribed poles and hence the guarantee of system stability. Also for multidimensional linear shift-invariant systems with infinite-extent impulse response, stability can be guaranteed a priori by the ...

We consider the problem of deciding whether a given rational function has a power series expansion with all its coefficients positive. Introducing an elementary transformation that preserves such positivity we are able to provide an elementary proof for the positivity of Szegö’s function 1 (1− x)(1− y)+ (1− y)(1− z)+ (1− z)(1− x) which has been at the historical root of this subject starting wi...

If K is a field, and g, h ∈ K(x) are rational functions of degree greater than one, then f = g ◦ h = g(h) is their (functional) composition, (g, h) is a (functional) decomposition of f , and f is a decomposable rational function. The univariate rational functional decomposition problem can be stated as follows: given f ∈ K(x), determine whether there exists a decomposition (g, h) of f with g an...