The exploration of complex systems is a fundamental pursuit in various scientific disciplines, includingphysics, biology, finance and engineering. The inherent complexity and dynamics within these systemspose significant challenges for traditional analytical methods. In recent years, the emergence of Topological Data Analysis (TDA) has provided a promising framework for uncovering hidden structures andpatterns in dynamic data sets. This thesis investigates the application of Topological Data Analysis to analyze system dynamics,aiming to enhance our understanding of their behavior. Through a detailed review of existing literature,we examine the theoretical foundations of TDA and its relevance to discrete and continuous processes.We discuss conceptual underpinnings of persistent homology, a key technique in TDA, and its potentialfor capturing essential features of system dynamics. By applying TDA to two distinct models, thestochastic ODE and the discrete logistic equation, we demonstrate its effectiveness in revealing underlyingstructures that traditional methods might overlook, thereby offering new insights into the analysis ofstochastic and discrete dynamical systems.

<p>The purpose of this study was to investigate the epistemological obstacles that mathematics students at undergraduate level encounter in coming to understand the limit concept. The role played by language and symbolism in understanding the limit concept was also investigated. A group of mathematics students at undergraduate level at the National University of Lesotho (NUL) was used as the sample for the study. Empirical data were collected by using interviews and questionnaires. These data were analysed using both the APOS framework and a semiotic perspective.</p> <p><br /> Within the APOS framework, the pieces of knowledge that have to be constructed in coming to understand the limit concept are actions, processes and objects. Actions are interiorised into processes and processes are encapsulated into objects. The conceptual structure is called a schema. In investigating the idea of limit within the context of a function some main epistemological obstacles that were encountered when actions were interiorised into processes are over-generalising and taking the limit value as the function value. For example, in finding the limit value L for f(x) as x tends to 0, 46 subjects out of 251 subjects said that they would calculate f(0) as the limit value. This method is appropriate for calculating the limit values for continuous functions. However, in this case, the method is generalised to all the functions. When these subjects encounter situations in which the functional value is equal to the limit value, they take the two to be the same. However, the two are different entities conceptually.</p>

M.Sc. (Applied Mathematics) / Numerous studies on linear and nonlinear Volterra integral equations (VIEs), have been performed. These studies mainly considered the existence and uniqueness of the solution, and numerical solutions of these equations. In this work, a class of nonlinear (nonstandard) Volterra integral equation that has received very little attention in the literature is considered. The existence and uniqueness of the solution for the nonlinear VIE is proved using the contraction mapping theorem in the space C[0; d]. Collocation methods, repeated trapezoidal rule and repeated Simpson's rule are used to solve the nonlinear (nonstandard) VIE. For the collocation solutions we considered two cases: implicit Euler method and implicit midpoint method. Examples are used to compare the performance of these methods and the results show that the repeated Simpson's rule performs better than the other methods. An analysis of the collocation solution and the solution by the repeated trapezoidal rule is performed. Su cient conditions for existence and uniqueness of the numerical solution are given. The collocation methods and repeated trapezoidal rule yield convergence of order one.

by Sin Yu Tsang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 40-42). / Chapter Chapter 1. --- Introduction --- p.1 / Chapter Chapter 2. --- Two-level structural equation model --- p.5 / Chapter Chapter 3. --- Estimation of the model under general constraints --- p.11 / Chapter Chapter 4. --- Estimation of the model under linear constraints --- p.22 / Chapter Chapter 5. --- Simulation results --- p.27 / Chapter 5.1 --- "Artificial examples for ""modified"" EM algorithm" --- p.27 / Chapter 5.2 --- "Artificial examples for ""restricted"" EM algorithm" --- p.34 / Chapter Chapter 6. --- Discussion and conclusion --- p.38 / References --- p.40 / Tables --- p.43

No description available.

<p>This thesis consists of three parts. The first part is a introduction to the theory of domains of holomorphy through holomorphic convexity. The second part gives a introduction to Stein neighborhood bases in <strong>C</strong>ⁿ<strong> </strong>and presents some minor results on the Nebenhülle of a compact set in <strong>C</strong>ⁿ. The third and final part reviews some results on the existence of Stein neighborhood bases.</p> / <p>Denna uppsats består av tre delar. Den första delen introducerar holomorfiområden genom teorin för konvexitet med avseende på holomorfa funktioner. Den andra delen är en introduktion till Steinomgivningsbaser i <strong>Cⁿ</strong> och presenterar några smärre resultat rörande Nebenhüllet till en kompakt mängd i <strong>Cⁿ</strong>. Den tredje och sista delen ger en överblick över en del resultat om existensen av Steinomgivningsbaser.</p>

This paper is divided into two parts. The first part traces (in details providing proofs and examples) the history of the solutions of polynomial equations(of the first, second, third, and fourth degree) by radicals from Babylonian times (2000 B.C.) through 20th century. Also it is shown that there is no solution by radicals for the quintic (fifth degree) and higher degree equations. The second part of this thesis illustrates both numerical and graphical solutions of the quintic and higher degree polynomial equations using modern technology such as graphics calculators (TI-85, and HP-48G) and software packages (Matlab, Mathematica, and Maple). / Graduation date: 1995

Vad är viktigt när hyllsystem till butiker ska säljas, tillverkas och användas? Jo de måste vara användarvänliga alltså lätta att montera, bära och modifiera. De bör även vara smidiga att frakta, de ska då vara lätta (viktmässigt) och inte otympliga. Framförallt måste de vara prisvärda alternativt billiga att köpa, för att uppnå detta bör de bestå av så lite material som möjligt samtidigt som de ska vara lätta att producera. Detta var några av de frågeställningar som detta arbete utgått ifrån och de har penetrerats mer eller mindre grundligt. För att svara på detta så undersöktes möjligheten att ändra godstjockleken i stolparna till hyllsystemet från 2,5 mm till 2,0 mm, detta skulle vara delvis lösningar till både vikt- och materialfrågan men framförallt prisfrågan då materialet står för en stor del av kostnaden. Detta framkom genom att de olika stolparna räknades på ur flera olika synvinklar för att reda ut om de skulle hålla för denna typ av förändring. De aspekter som bearbetades var böjning av stolpen, att hålen skjuvas sönder (konservburksöppnar-effekt) av krokarna till hyllkonsol och lösfot. Det resultat som framkom var, på vissa storlekar kan förändringen göras utan eftertanke medan på de mindre stolparna krävs lite mer funderande och kanske några praktiska tester innan beslut fattas. Den aspekt som är mest dimensionerande är att stolpen böjs av. I och med att användarvänligheten alltid kan förbättras arbetades en lathund fram. Denna lathund är tänkt att slutanvändaren ska ha som hjälpmedel för att kunna lasta varor på hyllorna på rätt sätt, alltså inte överlasta och riskerar att det rasar. För att reda ut hur Itab´s system står sig gentemot sina konkurrenter på dessa viktiga punkter utfördes även en konkurrentanalys. Det som testades var främst stabiliteten, monteringsvänligheten och om det fanns några uppenbara skaderisker med stativen. Tyvärr så var det svårt att få fram alla konkurrenter som skulle testas, än viktigare var att Itab´s egna inte var tillgänglig så en jämförelse var inte möjlig, men de konkurrenter som var intresserade av att ha med sina stativ fick gärna det så ett test utfördes. Frågan gällande priset testades inte då denna rapport inte riktar sig till slutanvändaren. / What is the most important aspect when shelves are being sold, manufactured and used? Well they must be user-friendly which means they should be easy to assemble, carry and modify. They should also be easy to ship, weight aspect and not ungainly. Most importantly it must be worth its price or just cheap, to accomplish this one should keep the amount of material to a minimum whilst the manufacturing must be easy. These were some of the questions at issue that this work has started from and they have more or less thoroughly been penetrated. In an effort to acquire some answers the possibility to reduce the thickness of the poles to the shelves from 2,5 mm to 2,0 mm, this would present partial solutions to both weight and material issues but before all the price issue though the material contributes to a large piece of the cost. This suggestion appeared when the poles were investigated and calculated from different angels to determine if they would hold out to this kind of change. The angels that were investigated are bending of the pole, the holes in the pole will be sheared (ripped like can opener-effect) by the hooks on the shelf consol and the detachable foot. The result that emerged are that some sizes of the poles can endure the change without any thought whilst the smaller poles requires some further testing and pondering before implementing. The aspect that was found to be norm setting was the bending of the pole. The fact that the user friendliness always can be improved a helper was designed. The helper is meant for the user is so he/she easily can see how much merchandise (weight) a shelf and pole can withstand. In other words to make sure that the shelf/pole is not overloaded and risk a breakdown. To declare where Itabs system is in regards to its competitor on these important questions a competitor analysis was conducted. The primary test-issues were stability, easy to assemble and if there are any apparent hazardous areas on the stand. Unfortunately there were some difficulties in retrieving the stands from some of the competitors or more importantly the stand from Itab themselves. So a comparison was not possible although they who were interested in testing their stands and had sent them in were to be pleased so a test was conducted. The issue regarding the price was not compared though this report is not meant for the users in the stores.

This thesis consists of three parts. The first part is a introduction to the theory of domains of holomorphy through holomorphic convexity. The second part gives a introduction to Stein neighborhood bases in Cn and presents some minor results on the Nebenhülle of a compact set in Cn. The third and final part reviews some results on the existence of Stein neighborhood bases. / Denna uppsats består av tre delar. Den första delen introducerar holomorfiområden genom teorin för konvexitet med avseende på holomorfa funktioner. Den andra delen är en introduktion till Steinomgivningsbaser i Cn och presenterar några smärre resultat rörande Nebenhüllet till en kompakt mängd i Cn. Den tredje och sista delen ger en överblick över en del resultat om existensen av Steinomgivningsbaser.

This thesis project has been written and accomplished in cooperation with HABO AB. The objective of the project was to develop a standard stated packaging system. The background to this is that HABO is not pleased with the system currently in use. The system which HABO is currently using consists of to many sizes. The largest benefit of a standard stated system is that it becomes much easier to organize the packaging with the aid of a computer program. If one manages to standardize the packaging system if will be much easier to calculate how much space that is required for the products in the store. It also enables HABO to sell pre defined product groups. The basic condition for the system is that it should be compatible with Hestra wall panels and store equipment. The store equipment proved to be very determining during the project. Due to its design the number of possible variations of sizes decreased considerably. Much of the work has been simulated in a computer model which has been constructed in ProEngineer. With aid of the model suitable packaging sizes could be tested on Hestras wall panels. The work resulted in a system with three different width sizes (74, 116 and 158 mm), compared to the present five. The number of lengths was set to four (118, 182, 246 and 374 mm) in comparison with today where the length is decided for each product individually. In order for the system to work properly it is crucial the HABOs suppliers can guarantee a specified length for all of the different packaging sizes. The basic principle is that both SB-pack and Skin-pack should be possible to combine to achieve the most effective system. A couple of improvements were also considered. Standard setting of the width proved to be the hardest challenge. Therefore an alternative could be to use a gliding spear instead of Hestras traditional panel. This allows the spear to be continuously variable. This allows more freedom when it comes to designing the packaging. Regarding different types of packaging SB-pack with long back or colored plastic bag is preferred instead of the traditional SB-pack. The products are displayed in a better fashion and it gives a better impression.