This work deals with some aspects of universal topological and metric dynamic behavior of iterated maps of the interval.

Doctor of Philosophy / Department of Mathematics / Pietro Poggi-Corradini / We consider iteration of an analytic self-map f of the unit ball in the N-dimensional complex space C[superscript]N. Many facts were established about such maps and their dynamics in the 1-dimensional case (i.e. for self-maps of the unit disk), and we generalize some of them in higher dimensions. In one dimension, the classical Denjoy-Wolff theorem states the convergence of forward iterates to a unique attracting fixed point, while backward iterates have much more complicated nature. However, under additional conditions (when the hyperbolic distance between two consecutive points stays bounded), backward iteration sequence converges to a point on the boundary of the unit disk, which happens to be a fixed point with multiplier greater than or equal to 1. In this paper, we explore backward-iteration sequences in higher dimension. Our main result shows that in the case when f is hyperbolic or elliptic, such sequences with bounded hyperbolic step converge to a point on the boundary, other than the Denjoy-Wolff (attracting) point. These points are called boundary repelling fixed points (BRFPs) and possess several nice properties. In particular, in the case when such points are isolated from other BRFPs, they are completely characterized as limits of backward iteration sequences. Similarly to classical results, it is also possible to construct a (semi) conjugation to an automorphism of the unit ball. However, unlike in the 1-dimensional case, not all BRFPs are isolated, and we present several counterexamples to show that. We conclude with some results in the parabolic case.

<p>In the 3G standards, wireless communication system can support 2 Mb/s. With this data rate, multimedia communication is realized on handset. However, it is expected that new applications will require even higher data rates in future. In order to fulfil the growing requirement of high data rate, 100 Mb/s is considered as the aim of 4G standards. Such high data rate will result in very large power consumption, which is unacceptable considering the current battery capability. Therefore, reducing the power consumption of turbo decoders becomes a major issue to be solved. This report explores new techniques for implementing low power, small area and high throughput turbo decoders.</p>

Within the context of the verification of infinite-state systems, 'Regular model checking' is the name of a family of techniques in which states are represented by words or trees, sets of states by finite automata on these objects, and transitions by finite automata operating on pairs of state encodings, i.e. finite-state transducers. In this context, the problem of computing the set of reachable states of a system can be reduced to the one of computing the iterative closure of the finite-state transducer representing its transition relation. This thesis provides several techniques to computing the transitive closure of a finite-state transducer. One of the motivations of the thesis is to show the feasibility and usefulness of this approach through a combination of the necessary theoretical developments, implementation, and experimentation. For systems whose states are encoded by words, the iteration technique proceeds by comparing a finite sequence of successive powers of the transducer, detecting an 'increment' that is added to move from one power to the next, and extrapolating the sequence by allowing arbitrary repetitions of this increment. For systems whose states are represented by trees, the iteration technique proceeds by computing the powers of the transducer and progressively collapsing their states according to an equivalence relation until a fixed point is reached. The proposed iteration techniques can just as well be exploited to compute the closure of a given set of states by repeated applications of the transducer, which has proven to be a very effective way of using the technique. Various examples have been handled completely within the automata-theoretic setting. Another applications of the techniques are the verification of linear temporal properties as well as the computation of the convex hull of a finite set of integer vectors.

Localised optimal initial perturbations are studied to gain an understanding of the global stability properties of streamwise corner-flow. A self-similar and a modified base-flow are considered. The latter mimics a characteristic deviation from the self-similar solution, commonly observed in experiment. Poweriterations in terms of subsequent direct and adjoint linearised Navier-Stokes solution sweeps are employed to converge optimal solutions for two optimisation times. The optimal response manifests as a wave packet that initially gains energy through the Orr mechanism and continues growing exponentially thereafter. The study at hand represents the first global stability analysis of streamwise corner-flow and confirms key observations made in theoretical and/or experimental work on the subject. Namely, the presence of an inviscid instability mechanism in the near-corner region and a destabilising effect of the characteristic mean-flow deformation found in experiment. / <p>QC 20130604</p>

In the 3G standards, wireless communication system can support 2 Mb/s. With this data rate, multimedia communication is realized on handset. However, it is expected that new applications will require even higher data rates in future. In order to fulfil the growing requirement of high data rate, 100 Mb/s is considered as the aim of 4G standards. Such high data rate will result in very large power consumption, which is unacceptable considering the current battery capability. Therefore, reducing the power consumption of turbo decoders becomes a major issue to be solved. This report explores new techniques for implementing low power, small area and high throughput turbo decoders.

<p>Rational unified process är en systemutvecklingsmetod som ofta används som ramverk och stöd vid utveckling. RUP kan även användas i sin helhet, vilket detta arbete handlar om. Metoden består av 5 itererande faser och har detaljerade beskrivningar på hur varje fas ska genomföras vid en utvecklingsprocess. RUP är dock väldigt komplext i sin helhet och innehåller många aktörer samt iterationer som tar tid och kostar pengar. Trots allt så är RUP en metod som blir allt mer vanligare att använda vid utveckling idag. I RUP så försäkrar man användarens behov via s.k. användarfall. För att ta reda på alla användares behov förespråkar Krutchen (2003) att man träffar användarna och gemensamt ritar upp användarfallsmodeller som täcker in behoven. På detta sätt så försäkrar man sedan att behoven är täckta innan man går vidare till nästa fas i utvecklingen. Användarfall är något som även används i andra metoder. Detta arbete beskriver dock enbart hur det används i metoden RUP. Detta arbete ska undersöka användarmedverkan i teori och praktik vid skapandet av användarfall i RUP. Frågeställningen besvarades genom litteraturstudier samt genom intervjuer av utvecklare angående ämnet. Resultatet visade bland annat att det inte alls existerar användarmedverkan i det omfång som det skulle behövas för att försäkra att man får ett användbart system. Det visar även en skillnad mellan teori och praktik vid användandet av RUP.</p>

When many people think of fractals, they think of the beautiful images created by Mandelbrot’s set or the intricate dragons of Julia’s set. However, these are just the artistic stars of the fractal community. The theory behind the fractals is not necessarily pretty, but is very important to many areas outside the world of mathematics. This paper takes a closer look at various types of fractals, the fractal dimensionality of surfaces and chaotic dynamical systems. Some of the history and introduction of creating fractals is discussed. The tools used to prevent a modified Koch’s curve from overlapping itself, finding the limit of a curves length and solving for a surfaces dimensional measurement are explored. Lastly, an investigation of the theories of chaos and how they bring order into what initially appears to be random and unpredictable is presented. The practical purposes and uses of fractals throughout are also discussed. / text

Zugl.: Clausthal, Techn. University, Diss., 2006.

Master-Arbeit Univ. St. Gallen, 2005.