with a b 1. The shift dynamical system induced by a,b is measure theoretically isomorphic to an exchange of three domains on a compact tile Ta,b with fractal boundary. We prove that Ta,b is homeomorphic to the closed disk iff 2b a 3. This solves a conjecture of Shigeki Akiyama posed in 1997. To this effect, we construct a Hölder continuous parametrization Ca,b W S1 ! Ta,b of the boundary of Ta,...

Parameterization has lots of applications in computer graphics such as texture mapping, remeshing and morphing. Texture mapping a 2D image onto a 3D mesh would previously cost lots of efforts and time for an experienced modeler to tweak the u,v texture coordinates of the mesh. By parameterizing the mesh onto a rectangular 2D domain, this becomes an easy task of mapping a 2D image onto an rectan...

In this paper, we study the implications for hedging Bermudan swaptions of the choice of the instantaneous volatility for the driving Markov process of the one-dimensional swap Markov-functional model. We find that there is a strong evidence in favour of what we term “parametrization by time” as opposed to “parametrization by expiry”. We further propose a new parametrization by time for the dri...

A general parametrization for all three-dimensional crystal lattices is presented in this paper which guarantees that the three primitive vectors constructed by the parametrization are the three shortest possible, linearly independent lattice vectors existing in the whole lattice. The parameter space of this so-called minimum distance parametrization (MDP) can easily be confined to contain only...

purpose despite numerous studies which have been done regarding soccer injuries worldwide, there is lack of available data considering the epidemiology of injuries in the iranian soccer premier league, although it is the most popular sport in the country. the main goal of this research was to determine the incidence of physical injuries in the studied population, considering other characteristi...

We introduce the simple parametrization for the space of codons (triples of nucleotides) by 8 × 8 table. This table (which we call the dyadic plane) possesses the natural 2–adic ultrametric. We show that after this parametrization the genetic code will be a locally constant map of the simple form. The local constancy of this map will describe degeneracy of the genetic code. The map of the genet...

Parametrization of algebraic curves and surfaces is a fundamental topic in CAGD (intersections; offsets and conchoids; etc.) There are many results on rational parametrization, in particular in the curve case, but the class of such objects is relatively small. If we allow root extraction, the class of parametrizable objetcs is greatly enlarged (for example, elliptic curves can be parametrized w...

In this paper we deal with problems of controller parametrization in the context of behavioral systems. Given a full plant behavior, a subbehavior of the manifest plant behavior is called regularly implementable if it can be achieved as the controlled behavior resulting from the interconnection of the full plant behavior with a suitable controller behavior, in such a way that the controller doe...

In this paper, we consider the identification problem arising in the ageperiod-cohort models, as well as in the extended chain ladder model. We propose a canonical parametrization based on the accelerations of the trends in the three factors. This parametrization is exactly identified. It eases interpretation, estimation and forecasting. The canonical parametrization is shown to apply for a cla...