An Invariant Theory of Surfaces in the Four-Dimensional Euclidean or Minkowski Space

2010 Mathematics Subject Classification: 53A07, 53A35, 53A10.

Spacelike maximal surfaces in 3D Lorentz-Minkowski space

We investigate spacelike maximal surfaces in 3-dimensional Lorentz-Minkowski space, give an Enneper-Weierstrass representation of such surfaces and classify those with a Lorentzian or Euclidian rotation symmetry.

Bjorling problem for timelike surfaces in the Lorentz-Minkowski space

We solve the Bjorling problem for timelike surfaces in the Lorentz-Minkowski space through a split-complex representation formula obtained for this kind of surface. Our approach uses the split-complex numbers and natural split-holomorphic extensions. As applications, we show that the minimal timelike surfaces of revolution as well as minimal ruled timelike surfaces can be characterized as solutions of certain adequate Bjorling problems in the Lorentz-Minkowski space. (C) 2010 Elsevier Inc. All rights reserved.

3-manifolds in Euclidean space from a contact viewpoint

We study the geometry of 3-manifolds generically embedded in R(n) by means of the analysis of the singularities of the distance-squared and height functions on them. We describe the local structure of the discriminant (associated to the distribution of asymptotic directions), the ridges and the flat ridges.

Spacelike Surfaces in L(4) with Degenerate Gauss Map

In this paper we study and present a complete classification of spacelike surfaces with degenerate Gauss map in the Lorentz-Minkowski space L(4).

Projections of hypersurfaces in 'R POT.4' with boundary to planes

We study orthogonal projections of generic embedded hypersurfaces in 'R POT.4' with boundary to 2-spaces. Therefore, we classify simple map germs from 'R POT.3' to the plane of codimension less than or equal to 4 with the source containing a distinguished plane which is preserved by coordinate changes. We also go into some detail on their geometrical properties in order to recognize the cases of codimension less than or equal to 1.

Visual attention to surfaces in three-dimensional space.

Although attention plays a significant role in vision, its spatial deployment and spread in the third dimension is not well understood. In visual search experiments we show that we cannot easily focus attention across isodepth loci unless they are part of a well-formed surface with locally coplanar elements. Yet we can easily spread our attention selectively across well-formed surfaces that span an extreme range of stereoscopic depths. In cueing experiments, we show that this spread of attention is, in part, obligatory. Attentional selectivity is reduced when targets and distractors are coplanar with or rest on a common receding stereoscopic plane. We conclude that attention cannot be efficiently allocated to arbitrary depths and extents in space but is linked to and spreads automatically across perceived surfaces.

Curtains and carnality : processural seductions in eighteenth century text and space

Libertine erotic novellas included a number of seductive descriptions of unfolding spaces often seen through the eyes of a narrator. Instructional volumes such as Point de lendermain by Vivant Denon (1777) aimed at the sexual education of young women and the titillation of men also followed suit. Similarly architectural theory such as Le Camus de Mézières’, The Genius of Architecture (1780) also promoted the sensuous and seductive aspects of surfaces and spatial arrangements. In the erotic settings of the cabinet, descriptions of curtains generate as much arousal as the outline of a naked body, and for some players it is the space that is desired above their lover.

A Method for Delineation of Bone Surfaces in Photoacoustic Computed Tomography of the Finger

Photoacoustic (PA) imaging of interphalangeal peripheral joints is of interest in the context of using the synovial membrane as a surrogate marker of rheumatoid arthritis. Previous work has shown that ultrasound (US) produced by absorption of light at the epidermis reflects on the bone surfaces within the finger. When the reflected signals are backprojected in the region of interest, artifacts are produced, confounding interpretation of the images. In this work, we present an approach where the PA signals known to originate from the epidermis are treated as virtual US transmitters, and a separate reconstruction is performed as in US reflection imaging. This allows us to identify the bone surfaces. Furthermore, the identification of the joint space is important as this provides a landmark to localize a region-of-interest in seeking the inflamed synovial membrane. The ability to delineate bone surfaces allows us to identify not only the artifacts but also the interphalangeal joint space without recourse to new US hardware or a new measurement. We test the approach on phantoms and on a healthy human finger.

The distribution of cirripeds and gastropods on plain vertical rock surfaces in the upper intertidal and splash zones

This is a student paper done for a University of California Berkeley Zoology class. Since UCB didn't have its own marine lab at the time, it rented space at Hopkins Marine Station where this work was done. Cadet Hand earned his Ph.D. from Berkeley and went on to become Director of the Bodega Marine Laboratory. Donald Putnam Abbott also earned his Ph.D. from Berkeley and later became a Stanford professor at Hopkins Marine Station. (PDF contains 26 pages)

Looking for safe harbor in a crowded sea: Coastal space use conflict and marine renewable energy development

Technological advances in the marine renewable energy industry and increased clarity about the leasing and licensing process are fostering development proposals in both state and federal waters. The ocean is becoming more industrialized and competition among all marine space users is developing (Buck et al. 2004). More spatial competition can lead to conflict between ocean users themselves, and to tensions that spill over to include other stakeholders and the general public (McGrath 2004). Such conflict can wind up in litigation, which is costly and takes agency time and financial resources away from other priorities. As proposals for marine renewable energy developments are evaluated, too often decision-makers lack the tools and information to properly account for the cumulative effects and the tradeoffs associated with alternative human uses of the ocean. This paper highlights the nature of marine space conflicts associated with marine renewable energy literature highlights key issues for the growth of the marine renewable energy sector in the United States. (PDF contains 4 pages)

Gas permeability in polyimides from oxydianiline and isomeric thiaphthalic dianhydride or 1,4-bis(dicarboxyphenoxy) benzene dianhydride

The gas permeability and permselectivity properties were investigated of polyimides, prepared from 3,3',4,4'- and 2,2',3,3'-thiaphthalic dianhydride (p-TDPA and m-TDPA, respectively), or 1,4-bis(3,4-dicarboxyphenoxy)- and 1,4-bis(2,3-dicarboxyphenoxy) benzene dianhydride (p-HQDPA and m-HQDPA, respectively), and 4,4-oxydianiline. The polyimides prepared from meta-dianhydrides, which have lower chain-segment packing density, possess higher permeability and lower permselectivity than those prepared from para-dianhydrides. Copyright (C) 1996 Elsevier Science Ltd.

Negotiating Civic Space in Belfast or The Tricolour: Here Today, Gone Tomorrow’

What role does public civic space in Belfast city centre play in the negotiation of different political identities within the city? Focusing on key public events in this space the paper traces shifts in identity practices and focuses on negotiations over the uses of public space associated with Irish nationalism and British unionism. This, it is argued, gives a more sophisticated understanding of different types of ‘shared space’. The events probed are seen as precursors and possibly drivers of political change. It is concluded that the increased sharing of civic space has probably contributed to improved political relations within the city, though there remains the challenge of
understanding how public space might more effectively be used to influence
relationships between the city’s political identities in the longer term.