Thesis (Ph.D.)--McMaster University, 2005. / Advisor: Ian Hambleton. Includes bibliographical references (leaves 74-75). Also available via World Wide Web.

Thesis (M.S.)--University of Akron, Dept. of Mathematics, 2007. / "May, 2007." Title from electronic thesis title page (viewed 4/28/2009) Advisor, Ali Hajjafar; Faculty readers, Linda Marie Saliga, Lala Krishna; Department Chair, Joseph W. Wilder; Dean of the College, Ronald F. Levant; Dean of the Graduate School, George R. Newkome. Includes bibliographical references.

Thesis (M.S. in Electrical Engineering)--Naval Postgraduate School, September 2002. / Thesis advisor(s): Tri Ha, Roberto Cristi. Includes bibliographical references (p. 69). Also available online.

Thesis (M. A.)--Marshall University, 2009. / Title from document title page. Includes abstract. Document formatted into pages: contains 43 p. Includes bibliographical references (p.42-43)

Thesis (Ph. D.)--University of Chicago, Dept. of Physics, March 2003. / Includes bibliographical references. Also available on the Internet.

The topological entropy of a continuous map quantifies the amount of chaos observed in the map. In this dissertation we present computational methods which enable us to compute topological entropy for given time series data generated from a continuous map with a transitive attractor. A triangulation is constructed in order to approximate the attractor and to construct a multivalued map that approximates the dynamics of the linear interpolant on the triangulation. The methods utilize simplicial homology and in particular the Lefschetz Fixed Point Theorem to establish the existence of periodic orbits for the linear interpolant. A semiconjugacy is formed with a subshift of nite type for which the entropy can be calculated and provides a lower bound for the entropy of the linear interpolant. The dissertation concludes with a discussion of possible applications of this analysis to experimental time series. / by Mark Wess. / Thesis (Ph.D.)--Florida Atlantic University, 2008. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2008. Mode of access: World Wide Web.

Thesis (Ph.D.)--Baylor University, 2009. / Includes bibliographical references (p. 77-79).

The relationship between the convergence of a sequence of self mappings of a metric space and their fixed points, known as the stability (or continuity) of fixed points has been of continuing interest and widely studied in fixed point theory. In this thesis we study the stability of common fixed points in a Hausdorff uniform space whose uniformity is generated by a family of pseudometrics, by using some general notations of convergence. These results are then extended to 2-metric spaces due to S. Gähler. In addition, a well-known theorem of T. Suzuki that generalized the Banach Contraction Principle is also extended to 2-metric spaces and applied to obtain a coincidence theorem for a pair of mappings on an arbitrary set with values in a 2-metric space. Further, we prove the existence of coincidence and fixed points of Ćirić type weakly generalized contractions in metric spaces. Subsequently, the above result is utilized to discuss applications to the convergence of modified Mann and Ishikawa iterations in a convex metric space. Finally, we obtain coincidence, fixed and stationary point results for multi-valued and hybrid pairs of mappings on a metric space.

Thesis (MSc)--University of Stellenbosch, 2005. / ENGLISH ABSTRACT: The majority of tra c on the Internet uses the Transmission Control Protocol (TCP) as a transport layer protocol for the end-to-end control of information transfer. Measurement, simulation and analytical models are the techniques and tools that can be used to understand and investigate the Internet and its performance. Measurements can only be used to explore existing network scenario or otherwise become costly and in exible with the growth and complexity of the Internet. Simulation models do not scale with the growth of network capacities and the number of users. Computationally e cient analytical models are therefore important tools for investigating, designing, dimensioning and planning IP (Internet Protocol) networks. Existing analytical models of TCP performance are either too simple to capture the internal dynamics of TCP or are too complex to be used to analyze realistic network topologies with several bottleneck links. The literature shows that the xed point algorithm (FPA) is a very useful way of solving analytical models of Internet performance. This thesis presents fast and accurate analytical models of TCP performance with the FPA used to solve them. Apart from what is observed in experimental literature, no comprehensive proof of the convergence and uniqueness of the FPA is given. In this thesis we show how the FPA of analytical models of reliable Internet protocols such as TCP converges to a unique xed point. The thesis speci es the conditions necessary in order to use the FPA for solving analytical models of reliable Internet protocols. We also develop a general implementation algorithm of the FPA of analytical models of TCP performance for realistic and arbitrary network topologies involving heterogenous TCP connections crossing many bottleneck links. The models presented in this thesis give Internet performance metrics, assuming that only basic network parameters such as the network topology, the number of TCP connections, link capacity, distance between network nodes and router bu er sizes are known. To obtain the performance metrics, TCP and network sub{models are used. A closed network of :=G=1 queues is used to develop each TCP sub-model where each queue represents a state of a TCP connection. An M=M=1=K queue is used for each network sub{model which represents the output interface of an IP router with a bu er capacity of K 􀀀��������1 packets. The two sub-models are iteratively solved. We also give closed form expressions for important TCP performance values and distributions. We show how the geometric, bounded geometric and truncated geometric distributions can be used to model reliable protocols such as TCP. We give models of the congestion window cwnd size distribution by conditioning on the slow start threshold ssthresh distribution and vice-versa. We also present models of the probabilities of TCP timeout and triple duplicate ACK receptions. Numerical results based on comparisons against ns2 simulations show that our models are more accurate, simpler and computationally more e cient than another well known TCP model. Our models can therefore be used to rapidly analyze network topologies with several bottlenecks and obtain detailed performance metrics. / AFRIKAANSE OPSOMMING: Die meerderheid van die verkeer op die Internet gebruik die Transmission Control Protocol (TCP) as `n vervoer laag protokol vir die einde-tot-einde kontrole van inligting oordrag. Meting, simulasie en analitiese modelle is die tegnieke en gereedskap wat gebruik kan word om die Internet te ondersoek en verstaan. Meting kan slegs gebruik word om bestaande netwerke scenarios te verken. Meting is duur en onbuigsaam met die groei en samegesteldheid van die Internet. Simulasie modelle skaal nie met die groei van netwerk kapasiteit en gebruikers nie. Analitiese modelle wat berekening e ektief is is dus nodige gereedskap vir die ondersoek, ontwerp, afmeting en beplanning van IP (Internet Protocol) netwerke. Bestaande analitiese TCP modelle is of te eenvoudig om die interne dinamiek van die TCP saam te vat of hulle is te ingewikkeld om realistiese netwerk topologie met heelwat bottelnek skakels te analiseer. Literatuur toon dat die xed point algorithm (FPA) baie handig is vir die oplos van analitiese modelle van Internet verrigting. In hierdie tesis word vinnige en akkurate analitiese modelle van TCP verrigting opgelos deur FPA weergegee. Buiten wat deur eksperimentele literatuur aangedui word is daar geen omvattende bewyse van die konvergensie en uniekheid van die FPA nie. In hierdie tesis word aangedui hoe die FPA van analitiese modelle van betroubare Internet protokolle soos die TCP konvergeer na `n unieke vaste punt. Hierdie tesis spesi seer die voorwaardes benodig om die FPA te gebruik vir die oplos van analitiese modelle van realistiese Internet protokolle. `n Algemene uitvoer algoritme van die FPA van analitiese modelle van TCP vir realistiese en arbitr^ere netwerk topogra e insluitende heterogene TCP konneksies oor baie bottelnek skakels is ontwikkel. Die model in hierdie tesis gee Internet verrigting metodes met die aanname dat slegs basiese netwerk parameters soos netwerk topologie, die aantal TCP konneksies, die konneksie kapasiteit, afstand tussen netwerk nodusse en die roete bu er grotes bekend is. Om die verrigting metodes te verkry, word TCP en netwerk sub-modelle gebruik. `n Geslote netwerk van :=G=1 rye is gebruik om elke TCP sub-model, waar elke ry 'n toestand van `n TCP konneksie voorstel, te ontwikkel. `n M=M=1=K ry is gebruik vir elke netwerk sub-model wat die uitset koppelvlak van `n IP roetemaker met `n bu er kapasiteit van K 􀀀������� 1 pakkies voorstel. Die twee submodelle word iteratief opgelos. Geslote vorm uitdrukkings vir belangrike TCP verrigting waardes en verspreidings word gegee. Daar word getoon hoe geometriese, begrensde geometriese en geknotte geometriese verspreidings gebruik kan word om betroubare protokolle soos die TCP te modelleer. Modelle van die kongestie venster cwnd grootte verspreiding word gegee deur die kondisionering van die stadige aanvang drempel ssthresh verspreiding en andersom. Modelle van die voorspelling van TCP tyduit en trippel duplikaat ACK resepsie word weergegee. Numeriese resultate gebaseer op vergelykings met ns2 simulasies wys dat ons modelle meer akkuraat, eenvoudiger en berekeningsgewys meer e ektief is as ander wel bekende TCP modelle. Ons modelle kan dus gebruik word vir vinnig analise van netwerk topologie met verskeie bottelnekke en om gedetailleerde verrigting metodes te bekom.

In almost all works in the literature there are several results showing asymptotic relationships between the solutions of x&prime / &prime / = f (t, x) (0.1) and the solutions 1 and t of x&prime / &prime / = 0. More specifically, the existence of a solution of (0.1) asymptotic to x(t) = at + b, a, b &isin / R has been obtained. In this thesis we investigate in a systematic way the asymptotic behavior as t &rarr / &infin / of solutions of a class of differential equations of the form (p(t)x&prime / )&prime / + q(t)x = f (t, x), t &ge / t_0 (0.2) and (p(t)x&prime / )&prime / + q(t)x = g(t, x, x&prime / ), t &ge / t_0 (0.3) by the help of principal u(t) and nonprincipal v(t) solutions of the corresponding homogeneous equation (p(t)x&prime / )&prime / + q(t)x = 0, t &ge / t_0. (0.4) Here, t_0 &ge / 0 is a real number, p &isin / C([t_0,&infin / ), (0,&infin / )), q &isin / C([t_0,&infin / ),R), f &isin / C([t_0,&infin / ) &times / R,R) and g &isin / C([t0,&infin / ) &times / R &times / R,R). Our argument is based on the idea of writing the solution of x&prime / &prime / = 0 in terms of principal and nonprincipal solutions as x(t) = av(t) + bu(t), where v(t) = t and u(t) = 1. In the proofs, Banach and Schauder&rsquo / s fixed point theorems are used. The compactness of the operator is obtained by employing the compactness criteria of Riesz and Avramescu. The thesis consists of three chapters. Chapter 1 is introductory and provides statement of the problem, literature review, and basic definitions and theorems. In Chapter 2 first we deal with some asymptotic relationships between the solutions of (0.2) and the principal u(t) and nonprincipal v(t) solutions of (0.4). Then we present existence of a monotone positive solution of (0.3) with prescribed asimptotic behavior. In Chapter 3 we introduce the existence of solution of a singular boundary value problem to the Equation (0.2).