Stuttgart, University, Diss., 1999.

Universiẗat, Diss., 2001--Kiel.

Chemnitz, Techn. Univ., Diss., 2006.

Stuttgart, Univ., Diss., 1999.

Among the presently known numerical solvers of integral equations, two main categories of approaches can be traced: mesh-free approaches, mesh-based approaches. We will propose some techniques to process geometric data so that they can be efficiently used in subsequent numerical treatments of integral equations. In order to prepare geometric information so that the above two approaches can be automatically applied, we need the following items: (1) Splitting a given surface into several four-sided patches, (2) Generating a diffeomorphism from the unit square to a foursided patch, (3) Generating a mesh M on a given surface, (4) Patching of a given triangulation. In order to have a splitting, we need to approximate the surfaces first by polygonal regions. We use afterwards quadrangulation techniques by removing quadrilaterals repeatedly. We will generate the diffeomorphisms by means of transfinite interpolations of Coons and Gordon types. The generation of a mesh M from a piecewise Riemannian surface will use some generalized Delaunay techniques in which the mesh size will be determined with the help of the Laplace-Beltrami operator. We will describe our experiences with the IGES format because of two reasons. First, most of our implementations have been done with it. Next, some of the proposed methodologies assume that the curve and surface representations are similar to those of IGES. Patching a mesh consists in approximating or interpolating it by a set of practical surfaces such as B-spline patches. That approach proves useful when we want to utilize a mesh-free integral equation solver but the input geometry is represented as a mesh.

Pest control of cultivated plant species has been usually performed by insecticides, which is undesirable because of economical and environmental concerns, since successive applications affect natural enemies and increase the possibility of development of resistant population toward insecticides. These problems can be minimized with alternative control methods as the use of resistant varieties, use of substances that induce resistance and biological control. Those studies involving the interaction of plant, pest and natural enemies are of fundamental importance. Thus, this study aimed: a) to study the effect of volatile organic compounds in tritrophic interactions between pepper Capsicum spp., the aphid Aphis gossypii and its parasitoid Aphidius colemani; b) to study the role of cis-jasmone in the tritrophic interaction between the pepper, the aphid A. gossypii and the parasitoid A. colemani and its role in activating the defense mechanism of the plant. Pepper varieties were evaluated for resistance to the aphid A. gossypii and their volatiles were collected before and after infestation. Volatiles compounds were tentatively identified by gas chromatography/mass spectrometry. Olfactometry bioassays were performed with volatile regarding the behavior of A. gossypii and A. colemani. The main conclusions obtained in this work were: a) there is genetic variability among genotypes of Capsicumin relation to the release of volatile compounds and in the susceptibility toward A. gossypii; b) genotype Cambuci can be used in breeding programs aiming Capsicum cultivars more resistant to A. gossypii; c) there were significant differences between the effects of volatiles from the two cultivars on behavior of A. gossypii and A. colemani; d) the volatiles emitted by Cambuci cultivar after infestation produced repellent effect on A. gossypii and were attractive to A. colemani; e) the cis-jasmone applied to pepper plants provided emission of volatiles that had repellent action on the A. gossypii and attractive one to A. colemani; f) the genetic variability between genotypes, after infestation indicates that volatile organic compounds present as variables can be used for selection and development of bell pepper cultivars resistant to the aphid A. gossypii. / O controle de pragas das espécies vegetais cultivadas tem sido normalmente realizado por meio de inseticidas, o que é indesejável tanto por motivos econômicos quanto ambientais, já que as aplicações sucessivas afetam os inimigos naturais e aumentam a possibilidade de desenvolvimento de populações da praga resistentes aos inseticidas. Esses problemas podem ser minimizados com métodos alternativos de controle como o emprego de variedades resistentes, o uso de substâncias indutoras e o controle biológico. Para isso, estudos envolvendo a interação planta, praga e inimigo natural são de fundamental importância. Dessa forma, este trabalho teve como objetivos: a) Estudar a ação dos compostos orgânicos voláteis na interação tritrófica entre o pimentão Capsicum spp., o pulgão Aphis gossypiie seu parasitóide Aphidiuscolemani; b) Estudar a ação da cis-jasmona na interação tritrófica entre o pimentão, o pulgão A. gossypii e o parasitóide A. colemani e seu papel na ativação do mecanismo de defesa do vegetal. Variedades de pimentão foram avaliadas em relação à resistência ao pulgão A. gossypii e os seus compostos voláteis foram coletados antes e após a infestação. Os compostos voláteis foram tentativamente identificados por cromatografia gasosa/espectrometria de massas. Bioensaios de olfatometria foram realizados com os compostos voláteis em relação ao comportamento de A. gossypii e A. colemani. As principais conclusões obtidas neste trabalho foram: a) Existe variabilidade genética entre os genótipos de Capsicum em relação à emissão de compostos voláteis e em relação à susceptibilidade ao A. gossypii; b) O genótipo Cambuci poderá ser utilizado em programas de melhoramento genético visando cultivares de Capsicum mais resistentes ao A. gossypii; c) Houve diferenças significativas entre os efeitos dos compostos voláteis das duas cultivares sobre os comportamentos de A. gossypii e de A. colemani; d) Os compostos voláteis emitidos pela cultivar Cambuci após a infestação proporcionaram efeito repelente a A. gossypii e atrativo a A. colemani; f) A cis-jasmona aplicada sobre plantas de pimentão induziu a emissão e/ou produção de compostos voláteis que teve ação de repelência a A. gossypii e ação atraente para A. colemani; i) A variabilidade genética entre os genótipos, após a infestação, indica que os compostos orgânicos voláteis apresentam-se como variáveis que podem ser utilizadas para seleção e desenvolvimento de cultivares de pimentão resistente ao pulgão A. gossypii.

Among the presently known numerical solvers of integral equations, two main categories of approaches can be traced: mesh-free approaches, mesh-based approaches. We will propose some techniques to process geometric data so that they can be efficiently used in subsequent numerical treatments of integral equations. In order to prepare geometric information so that the above two approaches can be automatically applied, we need the following items: (1) Splitting a given surface into several four-sided patches, (2) Generating a diffeomorphism from the unit square to a foursided patch, (3) Generating a mesh M on a given surface, (4) Patching of a given triangulation. In order to have a splitting, we need to approximate the surfaces first by polygonal regions. We use afterwards quadrangulation techniques by removing quadrilaterals repeatedly. We will generate the diffeomorphisms by means of transfinite interpolations of Coons and Gordon types. The generation of a mesh M from a piecewise Riemannian surface will use some generalized Delaunay techniques in which the mesh size will be determined with the help of the Laplace-Beltrami operator. We will describe our experiences with the IGES format because of two reasons. First, most of our implementations have been done with it. Next, some of the proposed methodologies assume that the curve and surface representations are similar to those of IGES. Patching a mesh consists in approximating or interpolating it by a set of practical surfaces such as B-spline patches. That approach proves useful when we want to utilize a mesh-free integral equation solver but the input geometry is represented as a mesh.

In this dissertation we study basic metrical properties of 2-dimensional normed linear spaces, so-called (Minkowski or) normed planes. In the first chapter we introduce a notion of angular measure, and we investigate under what conditions certain angular measures in a Minkowski plane exist. We show that only the Euclidean angular measure has the property that in an isosceles triangle the base angles are of equal size. However, angular measures with the property that the angle between orthogonal vectors has a value of pi/2, i.e, a quarter of the full circle, exist in a wider variety of normed planes, depending on the type of orthogonality. Due to this we have a closer look at isosceles and Birkhoff orthogonality. Finally, we present results concerning angular bisectors. In the second chapter we pay attention to convex quadrilaterals. We give definitions of different types of rectangles and rhombi and analyse under what conditions they coincide. Combinations of defining properties of rectangles and rhombi will yield squares, and we will see that any two types of squares are equal if and only if the plane is Euclidean. Additionally, we define a ``new\'\' type of quadrilaterals, the so-called codises. Since codises and rectangles coincide in Radon planes, we will explain why it makes sense to distinguish these two notions. For this purpose we introduce the concept of associated parallelograms. Finally we will deal with metrically defined conics, i.e., with analogues of conic sections in normed planes. We define metric ellipses (hyperbolas) as loci of points that have constant sum (difference) of distances to two given points, the so-called foci. Also we define metric parabolas as loci of points whose distance to a given point equals the distance to a fixed line. We present connections between the shape of the unit ball B and the shape of conics. More precisely, we will see that straight segments and corner points of B cause, under certain conditions, that conics have straight segments and corner points, too. Afterwards we consider intersecting ellipses and hyperbolas with identical foci. We prove that in special Minkowski planes, namely in the subfamily of polygonal planes, confocal ellipses and hyperbolas intersect in a way called Birkhoff orthogonal, whenever the respective ellipse is large enough.

In this dissertation we study basic metrical properties of 2-dimensional normed linear spaces, so-called (Minkowski or) normed planes. In the first chapter we introduce a notion of angular measure, and we investigate under what conditions certain angular measures in a Minkowski plane exist. We show that only the Euclidean angular measure has the property that in an isosceles triangle the base angles are of equal size. However, angular measures with the property that the angle between orthogonal vectors has a value of pi/2, i.e, a quarter of the full circle, exist in a wider variety of normed planes, depending on the type of orthogonality. Due to this we have a closer look at isosceles and Birkhoff orthogonality. Finally, we present results concerning angular bisectors. In the second chapter we pay attention to convex quadrilaterals. We give definitions of different types of rectangles and rhombi and analyse under what conditions they coincide. Combinations of defining properties of rectangles and rhombi will yield squares, and we will see that any two types of squares are equal if and only if the plane is Euclidean. Additionally, we define a ``new\'\' type of quadrilaterals, the so-called codises. Since codises and rectangles coincide in Radon planes, we will explain why it makes sense to distinguish these two notions. For this purpose we introduce the concept of associated parallelograms. Finally we will deal with metrically defined conics, i.e., with analogues of conic sections in normed planes. We define metric ellipses (hyperbolas) as loci of points that have constant sum (difference) of distances to two given points, the so-called foci. Also we define metric parabolas as loci of points whose distance to a given point equals the distance to a fixed line. We present connections between the shape of the unit ball B and the shape of conics. More precisely, we will see that straight segments and corner points of B cause, under certain conditions, that conics have straight segments and corner points, too. Afterwards we consider intersecting ellipses and hyperbolas with identical foci. We prove that in special Minkowski planes, namely in the subfamily of polygonal planes, confocal ellipses and hyperbolas intersect in a way called Birkhoff orthogonal, whenever the respective ellipse is large enough.:1 Introduction 2 On angular measures 3 Types of convex quadrilaterals 4 On conic sections