The Laplace equation and the related p-Laplace equation are closely associated with Sobolev spaces. During the last 15 years people have been exploring the possibility of solving partial differential equations in general metric spaces by generalizing the concept of Sobolev spaces. One such generalization is the Newtonian space where one uses upper gradients to compensate for the lack of a derivative. All papers on this topic are written for an audience of fellow researchers and people with graduate level mathematical skills. In this thesis we give an introduction to the Newtonian spaces accessible also for senior undergraduate students with only basic knowledge of functional analysis. We also give an introduction to the tools needed to deal with the Newtonian spaces. This includes measure theory and curves in general metric spaces. Many of the properties of ordinary Sobolev spaces also apply in the generalized setting of the Newtonian spaces. This thesis includes proofs of the fact that the Newtonian spaces are Banach spaces and that under mild additional assumptions Lipschitz functions are dense there. To make them more accessible, the proofs have been extended with comments and details previously omitted. Examples are given to illustrate new concepts. This thesis also includes my own result on the capacity associated with Newtonian spaces. This is the theorem that if a set has p-capacity zero, then the capacity of that set is zero for all smaller values of p.

In this thesis, we will present examples of Voronoi diagrams that are not tessellations. Moreover, we will find sufficient conditions on subspaces of E2, S2 and the Poincaré disk and the sets of sites that guarantee that the Voronoi diagrams are pre-triangulations. We will also study g-spaces, which are metric spaces with ‘extendable’ geodesics joining any 2 points and give properties for a set of sites in a g-space that again guarantees that the Voronoi diagram is a pre-triangulation.

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Metric spaces, which generalise the properties of commonly-encountered physical and abstract spaces into a mathematical framework, frequently occur in computer science applications. Three major kinds of questions about metric spaces are considered here: the intrinsic dimensionality of a distribution, the maximum number of distance permutations, and the difficulty of reverse similarity search. Intrinsic dimensionality measures the tendency for points to be equidistant, which is diagnostic of high-dimensional spaces. Distance permutations describe the order in which a set of fixed sites appears while moving away from a chosen point; the number of distinct permutations determines the amount of storage space required by some kinds of indexing data structure. Reverse similarity search problems are constraint satisfaction problems derived from distance-based index structures. Their difficulty reveals details of the structure of the space. Theoretical and experimental results are given for these three questions in a wide range of metric spaces, with commentary on the consequences for computer science applications and additional related results where appropriate.

The study of coding theory aims to detect and correct the errors during the transmission of the data. It enhances the quality of data transmission and provides better control over the noisy channels.The perfect codes are collected and analyzed in the premises of the Hamming metric.This classification yields that there exists only a few perfect codes. The perfect codes do not guarantee the perfection by all means but just satisfy certain bound and properties. The detection and correction of errors is always very important for better data transmission.

Metric spaces, which generalise the properties of commonly-encountered physical and abstract spaces into a mathematical framework, frequently occur in computer science applications. Three major kinds of questions about metric spaces are considered here: the intrinsic dimensionality of a distribution, the maximum number of distance permutations, and the difficulty of reverse similarity search. Intrinsic dimensionality measures the tendency for points to be equidistant, which is diagnostic of high-dimensional spaces. Distance permutations describe the order in which a set of fixed sites appears while moving away from a chosen point; the number of distinct permutations determines the amount of storage space required by some kinds of indexing data structure. Reverse similarity search problems are constraint satisfaction problems derived from distance-based index structures. Their difficulty reveals details of the structure of the space. Theoretical and experimental results are given for these three questions in a wide range of metric spaces, with commentary on the consequences for computer science applications and additional related results where appropriate.

With the rapid growing of economic activities and populations, available land resources have become unable to meet the demand. Originally considered as a mere frontier between land and sea, the coastal zone has become an essential zone for human development. As any kind of human exploitation of the coastal zone is likely to induce some changes in the local environment. Gradual and permanent alterations in coastal ecosystems have led to losses in abundance in numerous species, such as the black-faced spoonbill. To mitigate the impact, the government declares the North bank of the Tsengwen River Estuary as a protected area. However, land-use changes outside the protected area, such as the development of fish ponds or changes in the spatial patterns of farmlands and bodies of water, are still affecting birds¡¦ survival. This study is based on landscape ecology, using several analytical tools including Geographic Information System (GIS), Spatial Analysis, Landscape metric and Markov Chains. Changes in landscape structure at Chi-Gu between 2003 and 2008, and long-term birds census have been combined in order to discuss the relations between land-based activities and bird¡¦s abundance. Furthermore, a Markov chain was built to predict the most likely land-use pattern in 2013 and its eventual impacts on birds¡¦ conservation. The results of this study show that the reduction of spatial segregation in Chi-Gu has, on average, mitigated the adverse effects on birds. However, further analysis showed that migrant birds are increasing whereas resident birds are decreasing. We therefore suggest that the land-uses, closely related to resident birds¡¦ conservation, such as forests, should be managed with special care in order to assure an effective protection of both migrant and resident birds.

This dissertation investigates the factors that affect testability and testing cost of object- oriented software systems. Developing a software program which eases the testing process by increasing testability is crucial. Also, to assess whether or not the testing effort and cost consumed or planned is adequate or not is another critical matter this dissertation aims to answer by composing a new way to evaluate the links between software design parameters and testing effort via source-based metrics. An automated metric plug-in is used as the primary tool for obtaining the metric measurements. Our study is based on the investigation of many open-source projects written in Java to achieve our goals. By the help of the statistical evaluation of project data, we both propose a new model to assess testing effort and testability, and find significant relations and associations between software design and testing effort and testability of object-oriented software systems via source-based metrics.

Thesis (Ph. D.)--University of Oregon, 2000. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 123-128). Also available for download via the World Wide Web; free to University of Oregon users.

Wireless technology has become the most interesting field in the area of communications and networking. Video transmission plays a major role in this area. Data transmission via wireless communications is a major task, especially to send the data without loss of packets. The digital video decoder produces dropped or repeated frames from the encoded video due to packet loss. Brief frame drops of one frame duration are referred as dips. This research work investigates how to identify these frame dips and drops and also to measure the quality of the video which contain frame dips and frame drops. A dynamic threshold estimator is implemented to identify these frame dips. The qualitative analysis of a video is performed using a No Reference metric. In this metric the quality assessment can be achieved by identification of frame dips and drops and calculating Modified Fraction of Dropped Frames. Dips and abrupt temporal variation occurring at the end of frame freezing event of a video fluidity impairment caused by frame dropping will be taken into account using this metric. The parameters which are generated from Structural Similarity Index Metric (SSIM) analysis are efficient enough to compare the video quality and estimate the metric performance objectively. Our proposed metric has predicted the SSIM with a Pearson correlation coefficient of 0.99 in test1, 0.92 in test2 and 0.99 in test3. Therefore in terms of prediction accuracy the proposed metric has a good correlation with the deployed metric and obtained robustness to our approach. / Trådlös teknik har blivit den mest intressanta fältet inom kommunikation och nätverk. Videoöverföring spelar en viktig roll på detta område. Dataöverföring via trådlös kommunikation är en stor uppgift, särskilt för att skicka data utan förlust av paket. Den digitala videoavkodare producerar tappade eller upprepade bildrutor från den kodade videon grund paketförluster. Kort ram droppar en ram varaktighet kallat dips. Denna forskning undersöker hur man identifierar dessa ram dips och droppar och även att mäta kvaliteten på video som innehåller ram dips och droppar ram. En dynamisk tröskel estimatorn genomförs för att identifiera dessa ram dips. Den kvalitativa analysen av ett videoklipp utförs med hjälp av en No Reference metrisk. I denna statistik kvalitetsbedömningen kan uppnås genom identifiering av ram nedgångar och droppar och beräkning modifierad Andel bildrutor. Dips och abrupt temporal variation inträffar i slutet av ramen frysning händelse av en video flytbarhet orsakats av ram släppa kommer att beaktas med denna metrik. De parametrar som genereras från strukturell likhet Index Metric (SSIM) analys är effektiva nog att jämföra videokvalitet och uppskatta det metriska prestanda objektivt. Vår föreslagna värdet har förutspådde SSIM med Pearson korrelationskoefficient av 0,99 i test1, 0,92 i test2 och 0,99 i test3. Därför gäller förutsägelse noggrannhet föreslagna måttet har en god korrelation med utplacerade metriska och fick robusthet till vår strategi. / Vydik Mopidevi, D.No: 5-162, Sri Vijetha Public School, Tallapudi, West Godavari District, Pin Code: 534341 Phone Number: Home: 00813282979 Work: 0046734784445 Email: vydik.mopidevi@gmail.com