Die Flächen vierter Ordnung hinsichtlich ihrer Knotenpunkte und ihrer Gestaltung,

Bibliographical foot-notes.

Surfaces de Riemann compactes et formule de trace d'Eichler

Dans ce mémoire, nous étudierons quelques propriétés algébriques, géométriques et topologiques des surfaces de Riemann compactes. Deux grand sujets seront traités. Tout d'abord, en utilisant le fait que toute surface de Riemann compacte de genre g plus grand ou égal à 2 possède un nombre fini de points de Weierstrass, nous allons pouvoir conclure que ces surfaces possèdent un nombre fini d'automorphismes. Ensuite, nous allons étudier de plus près la formule de trace d'Eichler. Ce théorème nous permet de trouver le caractère d'un automorphisme agissant sur l'espace des q-différentielles holomorphes. Nous commencerons notre étude en utilisant la quartique de Klein. Nous effectuerons un exemple de calcul utilisant le théorème d'Eichler, ce qui nous permettra de nous familiariser avec l'énoncé du théorème. Finalement, nous allons démontrer la formule de trace d'Eichler, en prenant soin de traiter le cas où l'automorphisme agit sans point fixe séparément du cas où l'automorphisme possède des points fixes.

Sur une classe remarquable de courbes et de surfaces algébriques et sur la théorie imaginaire,

Available on demand as hard copy or computer file from Cornell University Library.

Kummer's quartic surface,

Prefatory note by H.F. Baker.

Some surface profiles of a strip after plane-strain indentation by rigid bodies with serrated surfaces

This paper is concerned with the surface profiles of a strip after rigid bodies with serrated (saw-teeth) surfaces indent the strip and are subsequently removed. Plane-strain conditions are assumed. This has application in roughness transfer of final metal forming process. The effects of the semi-angle of the teeth, the depth of indentation and the friction on the contact surface on the profile are considered.

Understanding the physical processes of pollutant build-up and wash-off on roof surfaces

Pollutants originating with roof runoff can have a significant impact to urban stormwater quality. This signifies the importance of understanding pollutant processes on roof surfaces. Additionally, knowledge of pollutant processes on roof surfaces is important as roofs are used as the primary catchment surface for domestic rainwater harvesting. In recent years, rainwater harvesting has become one of the primary sustainable water management techniques to counteract the growing demand for potable water. Similar to all impervious services, pollutants associated with roof runoff undergo two primary processes: build-up and wash-off. The knowledge relating to these processes is limited. This paper presents outcomes of an in-depth research study into pollutant build-up and wash-off for roof surfaces. The knowledge will be important in order to develop appropriate strategies to safeguard rainwater users from possible health risks.

Validation of 3D models of the outer and inner surfaces of an ovine femur

The validation of Computed Tomography (CT) based 3D models takes an integral part in studies involving 3D models of bones. This is of particular importance when such models are used for Finite Element studies. The validation of 3D models typically involves the generation of a reference model representing the bones outer surface. Several different devices have been utilised for digitising a bone’s outer surface such as mechanical 3D digitising arms, mechanical 3D contact scanners, electro-magnetic tracking devices and 3D laser scanners. However, none of these devices is capable of digitising a bone’s internal surfaces, such as the medullary canal of a long bone. Therefore, this study investigated the use of a 3D contact scanner, in conjunction with a microCT scanner, for generating a reference standard for validating the internal and external surfaces of a CT based 3D model of an ovine femur. One fresh ovine limb was scanned using a clinical CT scanner (Phillips, Brilliance 64) with a pixel size of 0.4 mm2 and slice spacing of 0.5 mm. Then the limb was dissected to obtain the soft tissue free bone while care was taken to protect the bone’s surface. A desktop mechanical 3D contact scanner (Roland DG Corporation, MDX 20, Japan) was used to digitise the surface of the denuded bone. The scanner was used with the resolution of 0.3 × 0.3 × 0.025 mm. The digitised surfaces were reconstructed into a 3D model using reverse engineering techniques in Rapidform (Inus Technology, Korea). After digitisation, the distal and proximal parts of the bone were removed such that the shaft could be scanned with a microCT (µCT40, Scanco Medical, Switzerland) scanner. The shaft, with the bone marrow removed, was immersed in water and scanned with a voxel size of 0.03 mm3. The bone contours were extracted from the image data utilising the Canny edge filter in Matlab (The Mathswork).. The extracted bone contours were reconstructed into 3D models using Amira 5.1 (Visage Imaging, Germany). The 3D models of the bone’s outer surface reconstructed from CT and microCT data were compared against the 3D model generated using the contact scanner. The 3D model of the inner canal reconstructed from the microCT data was compared against the 3D models reconstructed from the clinical CT scanner data. The disparity between the surface geometries of two models was calculated in Rapidform and recorded as average distance with standard deviation. The comparison of the 3D model of the whole bone generated from the clinical CT data with the reference model generated a mean error of 0.19±0.16 mm while the shaft was more accurate(0.08±0.06 mm) than the proximal (0.26±0.18 mm) and distal (0.22±0.16 mm) parts. The comparison between the outer 3D model generated from the microCT data and the contact scanner model generated a mean error of 0.10±0.03 mm indicating that the microCT generated models are sufficiently accurate for validation of 3D models generated from other methods. The comparison of the inner models generated from microCT data with that of clinical CT data generated an error of 0.09±0.07 mm Utilising a mechanical contact scanner in conjunction with a microCT scanner enabled to validate the outer surface of a CT based 3D model of an ovine femur as well as the surface of the model’s medullary canal.

Jacobi quartic curves revisited

This paper provides new results about efficient arithmetic on Jacobi quartic form elliptic curves, y 2 = d x 4 + 2 a x 2 + 1. With recent bandwidth-efficient proposals, the arithmetic on Jacobi quartic curves became solidly faster than that of Weierstrass curves. These proposals use up to 7 coordinates to represent a single point. However, fast scalar multiplication algorithms based on windowing techniques, precompute and store several points which require more space than what it takes with 3 coordinates. Also note that some of these proposals require d = 1 for full speed. Unfortunately, elliptic curves having 2-times-a-prime number of points, cannot be written in Jacobi quartic form if d = 1. Even worse the contemporary formulae may fail to output correct coordinates for some inputs. This paper provides improved speeds using fewer coordinates without causing the above mentioned problems. For instance, our proposed point doubling algorithm takes only 2 multiplications, 5 squarings, and no multiplication with curve constants when d is arbitrary and a = ±1/2.

Enhanced human bone marrow stromal cell affinity for modified poly(L-lactide) surfaces by the upregulation of adhesion molecular genes

To enhance and regulate cell affinity for poly (l-lactic acid) (PLLA) based materials, two hydrophilic ligands, poly (ethylene glycol) (PEG) and poly (l-lysine) (PLL), were used to develop triblock copolymers: methoxy-terminated poly (ethylene glycol)-block-poly (l-lactide)-block-poly (l-lysine) (MPEG-b-PLLA-b-PLL) in order to regulate protein absorption and cell adhesion. Bone marrow stromal cells (BMSCs) were cultured on different composition of MPEG-b-PLLA-b-PLL copolymer films to determine the effect of modified polymer surfaces on BMSC attachment. To understand the molecular mechanism governing the initial cell adhesion on difference polymer surfaces, the mRNA expression of 84 human extracellular matrix (ECM) and adhesion molecules was analysed using quantitative reverse transcriptase polymerase chain reaction (qRT-PCR). It was found that down regulation of adhesion molecules was responsible for the impaired BMSC attachment on PLLA surface. MPEG-b-PLLA-b-PLL copolymer films improved significantly the cell adhesion and cytoskeleton expression by upregulation of relevant molecule genes significantly. Six adhesion genes (CDH1, ITGL, NCAM1, SGCE, COL16A1, and LAMA3) were most significantly influenced by the modified PLLA surfaces. In summary, polymer surfaces altered adhesion molecule gene expression of BMSCs, which consequently regulated cell initial attachment on modified PLLA surfaces.