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No description available.

Barycentric coordinates are functions on a polygon, one for each vertex, whose values are coefficients that provide an expression of a point of the polygon as a convex combination of the vertices. Wachspress barycentric coordinates are barycentric coordinates that are defined by rational functions of minimal degree. We study the rational map on P2 defined by Wachspress barycentric coordinates, the Wachspress map, and we describe polynomials that set-theoretically cut out the closure of the image, the Wachspress variety. The map has base points at the intersection points of non-adjacent edges. The Wachspress map embeds the polygon into projective space of dimension one less than the number of vertices. Adjacent edges are mapped to lines meeting at the image of the vertex common to both edges, and base points are blown-up into lines. The deformed image of the polygon is such that its non-adjacent edges no longer intersect but both meet the exceptional line over the blown-up corresponding base point. We find an ideal that cuts out the Wachspress variety set-theoretically. The ideal is generated by quadratics and cubics with simple expressions along with other polynomials of higher degree. The quadratic generators are scalar products of vectors of linear forms and the cubics are determinants of 3 x 3 matrices of linear forms. Finally, we conjecture that the higher degree generators are not needed, thus the ideal is generated in degrees two and three.

Taxonomic boundaries and systematic relationships in the grass subspecific complex Dichanthelium acuminatum were investigated with both morphological and molecular methods. Circumscription of subspecific taxa comprising the complex has been difficult due to a continuum of morphological character variation among taxa and possibly due to infraspecific and interspecific hybridization. Qualitative and quantitative morphological character data was collected from herbarium specimens and field-collected specimens and analyzed using multivariate statistical techniques. Representative specimens were selected for molecular phylogenetic analysis of DNA sequences from the GBSSI (waxy) nuclear gene. Subspecific boundaries as circumscribed in the most recent taxonomic treatment (10 subspecies) were tested from: 1) a morphological perspective with results of the multivariate statistical analysis to determine if the study specimens formed natural groupings that corresponded to the recent treatment; and, 2) with molecular phylogenetic analysis to estimate the evolutionarily significant lineages present and to determine if such lineages supported the natural groupings revealed from the multivariate morphological analysis. A separate investigation was conducted using a molecular technique to screen for putative hybrid specimens from DNA obtained from field-collected specimens. Multivariate statistical analysis of the morphological data provided support for four of the 10 taxa tested and additional support for two taxa considered as a single unit. Further research is needed to determine the appropriate status of the remaining six taxa of the ten taxa tested. Molecular phylogenetic analysis provided support for recognizing four evolutionarily significant units and provided parallel support for four of the five taxa recognized from the morphological analysis. The hybridization investigation identified two putative hybrid specimens, which were confirmed as hybrids with GBSSI sequence data and also with multivariate statistical analysis of morphological data to provide provisional evidence for the role of hybridization in producing specimens with intermediate morphological phenotypes. A taxonomic treatment and dichotomous key was produced for the 10 subspecific taxa of the Dichanthelium acuminatum complex.

Thèse de doctorat : Sciences : Paris, Faculté des sciences : 1867. / Titre provenant de l'écran-titre.

Thesis (M.S.)--University of Toledo, 2007. / Typescript. "Submitted as partial fulfillments of the requirements for the Master of Science Degree in Mechanical Engineering." "A thesis entitled"--at head of title. Bibliography: leaves 196-205.

A lubrication-flow model for a free film in a corner is presented. The model, written in the hyperbolic coordinate system ξ = x² – y², η = 2xy, applies to films that are thin in the η direction. The lubrication approximation yields two coupled evolution equations for the film thickness and the velocity field which, to lowest order, describes plug flow in the hyperbolic coordinates. A free film in a corner evolving under surface tension and gravity is investigated. The rate of thinning of a free film is compared to that of a film evolving over a solid substrate. Viscous shear and normal stresses are both captured in the model and are computed for the entire flow domain. It is shown that normal stress dominates over shear stress in the far field, while shear stress dominates close to the corner.

nÃo hà / Este trabalho tem como objetivo mostrar algumas aplicaÃÃes de matemÃtica na realidade. Tem, tambÃm o objetivo de responder, pelo menos em parte as seguintes perguntas: Professor para que serve isso? Onde vou usar isso? Porque devo estudar isso? Neste trabalho mostra-se algumas dessas aplicaÃÃes da matemÃtica para que o estudante saiba que a matemÃtica està presente onde menos se imagina. Tais perguntas, que muitas vezes ficam sem resposta, causam falta de estÃmulo e entusiasmo nos estudantes, pois estes nÃo conseguem ver utilidade nos conteÃdos ministrados. A matemÃtica aplicada à uma valiosa ferramenta para quem quer ver a matemÃtica em funcionamento. Inicialmente mostra-se uma aplicaÃÃo à localizaÃÃo de um robà mÃvel atravÃs coordenadas no plano e medidas de arcos, depois mostrar-se-à uma linda aplicaÃÃo das tÃo estudadas transformaÃÃes ( Ãlgebra Linear ) e das matrizes, agora aplicadas no espaÃo, para a movimentaÃÃo e localizaÃÃo da extremidade final de um robà manipulador. Estas aplicaÃÃes da matemÃtica sÃo apenas algumas, pois hà uma infinidade de outras mais. / This work has as objective shows some applications of the mathematics in the reality. He has, also the objective of answering, for the less partly the following questions: Teacher so that it serves that? Where will I use that? Because I should study that? In this work it is shown some of those applications of the mathematics so that the student knows that the mathematics is present where less if imagine. Such questions, that a lot of times are without answer, they cause incentive lack in the students, because these donât get to see usefulness in the supplied contents. The applied mathematics is one valuable tool for who wants to see the mathematics operation. Initially an application is shown to a movable robotâs location through coordinates in the plan and measures of arches, later it will be shown a beautiful application of the so studied transformations (Algebra Lineal) and of the head offices, now applied in the space, for the movement and location of a robot manipulatorâs final extremity. These applications of the mathematics are just some, because there is an infinity of other more.

The discrete Fourier transform in Cartesian coordinates has proved to be invaluable in many disciplines. However, less theory has been developed for functions that are best described in polar coordinates. In this thesis, a new discrete 2D-Fourier transform in polar coordinates is proposed and tested by numerical simulations. Guidelines for choosing sample size are developed. Furthermore, to be as useful as its Cartesian counterpart, improvements are made to reduce the computing time.

Network coordinates (NC) system is an efficient mechanism for prediction of Internet distance with limited number of measurement. This work focus on distributed coordinates system which is evaluated by relative error. According to experimental results from simulated application, was created own algorithm to compute network coordinates. Algorithm was tested by using simulated network as well as RTT values from network PlanetLab. Experiments show that clustered nodes achieve positive results of synthetic coordinates with limited connection between nodes. This work propose implementation of own NC system in network with hierarchical aggregation. Created application was placed on research projects web page of the Department of Telecommunications.