A note on finite determinacy for corank 2 map germs from surfaces to 3-space

We study properties of finitely determined corank 2 quasihomogeneous map germs f: (C(2), 0) -> (C(3), 0). Examples and counter examples of such map germs are presented.

A FREE BOUNDARY ISOPERIMETRIC PROBLEM IN HYPERBOLIC 3-SPACE BETWEEN PARALLEL HOROSPHERES

We investigate the isoperimetric problem of finding the regions of prescribed volume with minimal boundary area between two parallel horospheres in hyperbolic 3-space (the part of the boundary contained in the horospheres is not included). We reduce the problem to the study of rotationally invariant regions and obtain the possible isoperimetric solutions by studying the behavior of the profile curves of the rotational surfaces with constant mean curvature in hyperbolic 3-space. We also classify all the connected compact rotational surfaces M of constant mean curvature that are contained in the region between two horospheres, have boundary partial derivative M either empty or lying on the horospheres, and meet the horospheres perpendicularly along their boundary.

Space, authenticity and utopia in the hip-hop teen dance film

The dance film flourished in the 2000s in the form of the hip-hop teen dance film. Such films as Save the Last Dance (Thomas Carter, 2001), Honey (Billy Woodruff, 2002) and Step Up (Anne Fletcher, 2006) drew on hip-hop’s dominance of the mainstream music industry and combined the teen film’s pre-existing social problem and musical narratives. Yet various tension were created by their interweaving of representations of post-industrial city youth with the utopian sensibilities of the classical Hollywood musical. Their narratives celebrated hip-hop performance, and depicted dance’s ability to bridge cultural boundaries and bring together couples and communities. These films used hip-hop to define space and identity yet often constructed divisions within their soundscapes, limiting hip-hop’s expressive potential. This article explores the cycle’s celebration of, yet struggle with, hip-hop through examining select films’ interactions between soundscape, narrative and form. It will engage with these films’ attempts to marry the representational, narrative and aesthetic meanings of hip-hop culture with the form and ideologies of the musical genre, particularly the tensions and continuities that arise from their engagement with the genre’s utopian qualities identified by Richard Dyer (1985). Yet whilst these films illustrate the tensions and challenges of combining hip-hop culture and the musical genre, they also demonstrate an effective integration of hip-hop soundscape and the dancing body in their depiction of dance, highlighting both form’s aesthetics of layering, rupture and flow (Rose, 1994: 22).

Total absolute horospherical curvature of submanifolds in hyperbolic space

We study the horospherical geometry of submanifolds in hyperbolic space. The main result is a formula for the total absolute horospherical curvature of M, which implies, for the horospherical geometry, the analogues of classical inequalities of the Euclidean Geometry. We prove the horospherical Chern-Lashof inequality for surfaces in 3-space and the horospherical Fenchel and Fary-Milnor`s theorems.

Horo-tight spheres in hyperbolic space

We study horo-tight immersions of manifolds into hyperbolic spaces. The main result gives several characterizations of horo-tightness of spheres, answering a question proposed by Cecil and Ryan. For instance, we prove that a sphere is horo-tight if and only if it is tight in the hyperbolic sense. For codimension bigger than one, it follows that horo-tight spheres in hyperbolic space are metric spheres. We also prove that horo-tight hyperspheres are characterized by the property that both of its total absolute horospherical curvatures attend their minimum value. We also introduce the notion of weak horo-tightness: an immersion is weak horo-tight if only one of its total absolute curvature attends its minimum. We prove a characterization theorem for weak horo-tight hyperspheres.

Double point curves for corank 2 map germs from C-2 to C-3

We characterize finite determinacy of map germs f : (C-2, 0) -> (C-3, 0) in terms of the Milnor number mu(D(f)) of the double point curve D(f) in (C-2, 0) and we provide an explicit description of the double point scheme in terms of elementary symmetric functions. Also we prove that the Whitney equisingularity of 1-parameter families of map germs f(t) : (C-2, 0) -> (C-3, 0) is equivalent to the constancy of both mu(D(f(t))) and mu(f(t)(C-2)boolean AND H) with respect to t, where H subset of C-3 is a generic plane. (C) 2011 Elsevier B.V. All rights reserved.

A study of five cervicocephalic relocation tests in three different subject groups

Objective: To compare head relocation accuracy in traumatic ( whiplash), insidious onset neck pain patients and asymptomatic subjects when targeting a natural head posture (NHP) and complex predetermined positions. Design: A case-control study. Setting: University-based musculoskeletal research clinic. Participants: Sixty-three volunteers divided into three groups of similar gender and age: Group 1 (n=21) an asymptomatic group; group 2 (n=20) insidious onset neck pain; group 3 (n=22) a history of whiplash injury. Intervention: Five randomly ordered tests designed to detect relocation accuracy of the head. Outcome measures: A 3-Space Fastrak system measured the mean absolute relocation error of three trials of each relocation test. Results: A significant difference was found between groups in one of the tests targeting the NHP (p=0.001). Post-hoc pairwise comparisons revealed a significant difference (pless than or equal to0.05) between the asymptomatic group and each symptomatic group. The difference between the symptomatic groups just failed to reach significance (p=0.07). None of the other four tests revealed significant differences. Conclusion: The test of targeting the NHP indicates that relocation inaccuracy exists in patients with neck pain with a trend to suggest that the deficit may be greater in whiplash patients. Tests employing unfamiliar postures or more complex movement were not successful in differentiating subject groups.

Dielectric properties of soft chemical method derived CaCu3Ti4O12 thin films onto Pt/TiO2/Si(100) substrates

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A dictionary of modular threefolds

The thesis deals with the modularity conjecture for three-dimensional Calabi-Yau varieties. This is a generalization of the work of A. Wiles and others on modularity of elliptic curves. Modularity connects the number of points on varieties with coefficients of certain modular forms. In chapter 1 we collect the basics on arithmetic on Calabi-Yau manifolds, including general modularity results and strategies for modularity proofs. In chapters 2, 3, 4 and 5 we investigate examples of modular Calabi-Yau threefolds, including all examples occurring in the literature and many new ones. Double octics, i.e. Double coverings of projective 3-space branched along an octic surface, are studied in detail. In chapter 6 we deal with examples connected with the same modular forms. According to the Tate conjecture there should be correspondences between them. Many correspondences are constructed explicitly. We finish by formulating conjectures on the occurring newforms, especially their levels. In the appendices we compile tables of coefficients of weight 2 and weight 4 newforms and many examples of double octics.

High-Pressure Behavior and Phase Stability of Al5BO9, a Mullite-Type Ceramic Material

Phase stability, elastic behavior, and pressure-induced structural evolution of synthetic boron-mullite Al5BO9 (a = 5.6780(7), b = 15.035(6), and c =7.698(3) Å, space group Cmc21, Z = 4) were investigated up to 25.6(1) GPa by in situ single-crystal synchrotron X-ray diffraction with a diamond anvil cell (DAC) under hydrostatic conditions. No evidence of phase transition was observed up to 21.7(1) GPa. At 25.6(1) GPa, the refined unit-cell parameters deviated significantly from the compressional trend, and the diffraction peaks appeared broader than at lower pressure. At 26.7(1) GPa, the diffraction pattern was not indexable, suggesting amorphization of the material or a phase transition to a high-pressure polymorph. Fitting the P–V data up to 21.7(1) GPa with a second-order Birch–Murnaghan Equation-of-State, we obtained a bulk modulus KT0 = 164(1) GPa. The axial compressibilities, here described as linearized bulk moduli, are as follows: KT0(a) = 244(9), KT0(b) = 120(4), and KT0(c) = 166(11) GPa (KT0(a):KT0(b):KT0(c) = 2.03:1:1.38). The structure refinements allowed a description of the main deformation mechanisms in response to the applied pressure. The stiffer crystallographic direction appears to be controlled by the infinite chains of edge-sharing octahedra running along [100], making the structure less compressible along the a-axis than along the b- and c-axis.

Design of underground installations in rock.

At head of title: Engineering and design.

Integrated visual perception architecture for robotic clothes perception and manipulation

This thesis proposes a generic visual perception architecture for robotic clothes perception and manipulation. This proposed architecture is fully integrated with a stereo vision system and a dual-arm robot and is able to perform a number of autonomous laundering tasks. Clothes perception and manipulation is a novel research topic in robotics and has experienced rapid development in recent years. Compared to the task of perceiving and manipulating rigid objects, clothes perception and manipulation poses a greater challenge. This can be attributed to two reasons: firstly, deformable clothing requires precise (high-acuity) visual perception and dexterous manipulation; secondly, as clothing approximates a non-rigid 2-manifold in 3-space, that can adopt a quasi-infinite configuration space, the potential variability in the appearance of clothing items makes them difficult to understand, identify uniquely, and interact with by machine. From an applications perspective, and as part of EU CloPeMa project, the integrated visual perception architecture refines a pre-existing clothing manipulation pipeline by completing pre-wash clothes (category) sorting (using single-shot or interactive perception for garment categorisation and manipulation) and post-wash dual-arm flattening. To the best of the author’s knowledge, as investigated in this thesis, the autonomous clothing perception and manipulation solutions presented here were first proposed and reported by the author. All of the reported robot demonstrations in this work follow a perception-manipulation method- ology where visual and tactile feedback (in the form of surface wrinkledness captured by the high accuracy depth sensor i.e. CloPeMa stereo head or the predictive confidence modelled by Gaussian Processing) serve as the halting criteria in the flattening and sorting tasks, respectively. From scientific perspective, the proposed visual perception architecture addresses the above challenges by parsing and grouping 3D clothing configurations hierarchically from low-level curvatures, through mid-level surface shape representations (providing topological descriptions and 3D texture representations), to high-level semantic structures and statistical descriptions. A range of visual features such as Shape Index, Surface Topologies Analysis and Local Binary Patterns have been adapted within this work to parse clothing surfaces and textures and several novel features have been devised, including B-Spline Patches with Locality-Constrained Linear coding, and Topology Spatial Distance to describe and quantify generic landmarks (wrinkles and folds). The essence of this proposed architecture comprises 3D generic surface parsing and interpretation, which is critical to underpinning a number of laundering tasks and has the potential to be extended to other rigid and non-rigid object perception and manipulation tasks. The experimental results presented in this thesis demonstrate that: firstly, the proposed grasp- ing approach achieves on-average 84.7% accuracy; secondly, the proposed flattening approach is able to flatten towels, t-shirts and pants (shorts) within 9 iterations on-average; thirdly, the proposed clothes recognition pipeline can recognise clothes categories from highly wrinkled configurations and advances the state-of-the-art by 36% in terms of classification accuracy, achieving an 83.2% true-positive classification rate when discriminating between five categories of clothes; finally the Gaussian Process based interactive perception approach exhibits a substantial improvement over single-shot perception. Accordingly, this thesis has advanced the state-of-the-art of robot clothes perception and manipulation.

Right coronary artery flow velocity and volume assessment with spiral K-space sampled breathhold velocity-encoded MRI at 3 tesla: accuracy and reproducibility.

PURPOSE: To evaluate accuracy and reproducibility of flow velocity and volume measurements in a phantom and in human coronary arteries using breathhold velocity-encoded (VE) MRI with spiral k-space sampling at 3 Tesla. MATERIALS AND METHODS: Flow velocity assessment was performed using VE MRI with spiral k-space sampling. Accuracy of VE MRI was tested in vitro at five constant flow rates. Reproducibility was investigated in 19 healthy subjects (mean age 25.4 +/- 1.2 years, 11 men) by repeated acquisition in the right coronary artery (RCA). RESULTS: MRI-measured flow rates correlated strongly with volumetric collection (Pearson correlation r = 0.99; P < 0.01). Due to limited sample resolution, VE MRI overestimated the flow rate by 47% on average when nonconstricted region-of-interest segmentation was used. Using constricted region-of-interest segmentation with lumen size equal to ground-truth luminal size, less than 13% error in flow rate was found. In vivo RCA flow velocity assessment was successful in 82% of the applied studies. High interscan, intra- and inter-observer agreement was found for almost all indices describing coronary flow velocity. Reproducibility for repeated acquisitions varied by less than 16% for peak velocity values and by less than 24% for flow volumes. CONCLUSION: 3T breathhold VE MRI with spiral k-space sampling enables accurate and reproducible assessment of RCA flow velocity.