Dissertação (mestrado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Matemática, 2015. / Submitted by Raquel Viana (raquelviana@bce.unb.br) on 2015-10-27T18:39:19Z No. of bitstreams: 1 2015_RicardoEdmundoZamoraVargas.pdf: 5385234 bytes, checksum: b50a9906f3a7644b3dcaca8825522885 (MD5) / Approved for entry into archive by Marília Freitas(marilia@bce.unb.br) on 2015-12-20T16:06:46Z (GMT) No. of bitstreams: 1 2015_RicardoEdmundoZamoraVargas.pdf: 5385234 bytes, checksum: b50a9906f3a7644b3dcaca8825522885 (MD5) / Made available in DSpace on 2015-12-20T16:06:46Z (GMT). No. of bitstreams: 1 2015_RicardoEdmundoZamoraVargas.pdf: 5385234 bytes, checksum: b50a9906f3a7644b3dcaca8825522885 (MD5) / Neste trabalho, apresentamos um estudo da geometria de Laguerre no espaço Euclidiano, apresentando a geometria de esferas e planos orientados, bem como das transformações de Laguerre. Através deste estudo, apresentamos as superfícies e a métrica de Laguerre, cujo elemento de volume é conhecido como funcional de Laguerre. Em seguida, estudamos superfícies mínimas generalizadas de Laguerre, isto é, superfícies que são pontos críticos deste funcional e que admitem pontos isolados com curvatura zero. Analogamente à representação de Weierstrass para superfícies mínimas apresentamos uma representação do tipo Weierstrass que permite descrever globalmente as superfícies mínimas de Laguerre generalizadas usando três dados: uma função meromorfa, uma forma holomorfa e uma função real harmônica. Tal representação é chamada de representação conforme e coincide com a representação de Weierstrass quando a função real harmônica é nula. / In this work, we present a study of Laguerre geometry in Euclidean space, presenting the geometry of oriented spheres and planes, as well as the Laguerre transformations. Through this study, we present the Laguerre surfaces and the Laguerre metric , whose volume element is known as the Laguerre functional. Then, study generalized Laguerre minimal surfaces, i.e. surfaces which are critical points of this functional and which allow isolated points with curvature zero. Similarly to the Weierstrass representation for minimal surfaces, we present a kind of Weierstrass representation that allows describe globally generalized Laguerre minimal surfaces using three data: a meromorphic function, a holomorphic form and a real harmonic function. This representation is called conformal representation and coincides with the Weierstrass representation when the harmonic real function is zero.

Στόχος λοιπόν της διπλωματικής εργασίας είναι να δούμε πως μπορούμε να αναγνωρίσουμε ένα μη γραμμικό σύστημα ομοιόμορφα παρατηρήσιμο χρησιμοποιώντας την κανονική μορφή παρατηρησιμότητας και τα πολυώνυμα Laguerre. / The Objective of therefore diplomatic work is to see how we can identify a non linear system, uniformly observable using the observable canonical form and the polynomials Laguerre.

Applications of Laguerre geometry to computer aided geometric design are presented, realized through Minkowski actions. Basic Laguerre geometry is first discussed. Then quaternions, set multiplication, and the use of quaternion sets to define Minkowski actions are described and used to achieve results used in geometric design.

Thesis (Ph. D.)--York University, 2001. Graduate Programme in Mathematics and Statistics. / Typescript. Includes bibliographical references (leaves 170-177). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://wwwlib.umi.com/cr/yorku/fullcit?pNQ66344.

Thesis--University of Wisconsin--Madison. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 80-81).

published_or_final_version / Mathematics / Master / Master of Philosophy

No description available.

Dissolving multicomponent NAPL as a source of contamination in subsurface water is considered. In particular, two processes are analyzed with regard to how they alter inter-species concentration ratios at remote monitoring locations relative to inter-species molar ratios in the NAPL: nonlinear dissolution governed by Raoult’s Law and differential sorption during subsurface transport. An analytic solution for Raoult’s Law-governed dissolution is presented. Separately, it is shown how a variety of 1D analytic transport models for simple boundary conditions may be adapted to use arbitrary time-varying concentrations by use of some properties of Laguerre series. This is combined with the analytic solution so that Raoult’s Law-governed multicomponent NAPL dissolution may be employed as the boundary condition for analytic transport models. A new computer model implementing this technique in an environment of discrete, parallel fractures is presented, and its accuracy verified for specific conditions against an existing code. The new code is applied to a parametric study on the plume separation of PAH and phenolic compounds from the dissolution of creosote. Narrow fracture spacing as well as significant values of matrix organic carbon are seen as particularly conducive to separation of these types of plumes, which in some circumstances may be entirely disjoint. Concentration ratios downgradient are shown largely unrelated to concentration ratios at the source. Finally, a study of PCB speciation is undertaken in fractured rock with known parameters, for which a rigorous, least squares speciation approach is developed. Even at distances of 5 m from the source, given perfect information about the subsurface, it is found not possible to chemically fingerprint a source PCB mixture from a list of three absent a model of the weathering of the NAPL. Both the PCB and creosote studies demonstrate that forensic inference of source compositions from field data is unreliable and the need for coupled dissolution and transport models like the one developed here. / Thesis (Ph.D, Civil Engineering) -- Queen's University, 2012-09-25 21:43:29.04

Zugl.: München, Techn. University, Diss., 2009.

Universiẗat, Diss., 2001--Kiel.