Norms of basic elementary operators on algebras of regular operators

We show that if E is an atomic Banach lattice with an ordercontinuous norm, A, B ∈ L^r(E) and M_A,_B is the operator on L^r(E) defined by M_A,_B(T) = AT B then ||M_A,_B||r = ||A||_r||B||_r but that there is no real α > 0 such that ||MA,B || ≥ α ||A||r||B ||r.

On the generalized Kato spectrum

2010 Mathematics Subject Classification: 47A10.

Operators with Polynomial Coefficients and Generalized Gelfand-Shilov Classes

2010 Mathematics Subject Classification: Primary 35S05, 35J60; Secondary 35A20, 35B08, 35B40.

FINALE of the U.N. International Year of Forests : culmination with a concert

Our Counselling and ISS team organised, in early December, 2011 a celebration of two years of art workshops and activities provided for our University post-graduate research students. The workshops had a number of benefits. They were to raise awareness of biodiversity and forests as well as providing a forum for engaging with others and an opportunity to belong to a semi-regular group. The 2010 theme had been the United Nations International Year of Biodiversity and the 2011 theme had been the United Nations International Year of Forests.

FINALE of the U.N. International Year of Forests : culmination with a concert

Our Counselling and ISS team organised, in early December, 2011 a celebration of two years of art workshops and activities provided for our University post-graduate research students. The workshops had a number of benefits. They were to raise awareness of biodiversity and forests as well as providing a forum for engaging with others and an opportunity to belong to a semi-regular group. The 2010 theme had been the United Nations International Year of Biodiversity and the 2011 theme had been the United Nations International Year of Forests.

Some regularity theorems for CR mappings

The purpose of this article is to study Lipschitz CR mappings from an h-extendible (or semi-regular) hypersurface in . Under various assumptions on the target hypersurface, it is shown that such mappings must be smooth. A rigidity result for proper holomorphic mappings from strongly pseudoconvex domains is also proved.

A gene cluster that regulates both heterocyst differentiation and pattern formation in Anabaena sp strain PCC 7120

Wild-type Anabaena sp. strain PCC 7120, a filamentous nitrogen-fixing cyanobacterium, produces single heterocysts at semi-regular intervals. asr0100 (patU5) and alr0101 (patU3) are homologous to the 5' and 3' portions of patU of Nostoc punctiforme. alr0099 (hetZ) overlaps the 5' end of patU5. hetZ, patU5 and patU3 were all upregulated, or expressed specifically, in proheterocysts and heterocysts. Mutants of hetZ showed delayed or no heterocyst differentiation. In contrast, a patU3 mutation produced a multiple contiguous heterocyst (Mch) phenotype and restored the formation of otherwise lost intercalary heterocysts in a patA background. Decreasing the expression of patU3 greatly increased the frequency of heterocysts in a mini-patS strain. Two promoter regions and two principal, corresponding transcripts were detected in the hetZ-patU5-patU3 region. Transcription of hetZ was upregulated in a hetZ mutant and downregulated in a patU3 mutant. When mutants hetZ::C.K2 and hetZ::Tn5-1087b were nitrogen-deprived, P-hetC-gfp was very weakly expressed, and in hetZ::Tn5-1087b, P-hetR-gfp was relatively strongly expressed in cells that had neither a regular pattern nor altered morphology. We conclude that the hetZ-patU5-patU3 cluster plays an important role in co-ordination of heterocyst differentiation and pattern formation. The presence of homologous clusters in filamentous genera without heterocysts is suggestive of a more general role.

Stochastic Mesh-Based Multiview Reconstruction

A method for reconstruction of 3D polygonal models from multiple views is presented. The method uses sampling techniques to construct a texture-mapped semi-regular polygonal mesh of the object in question. Given a set of views and segmentation of the object in each view, constructive solid geometry is used to build a visual hull from silhouette prisms. The resulting polygonal mesh is simplified and subdivided to produce a semi-regular mesh. Regions of model fit inaccuracy are found by projecting the reference images onto the mesh from different views. The resulting error images for each view are used to compute a probability density function, and several points are sampled from it. Along the epipolar lines corresponding to these sampled points, photometric consistency is evaluated. The mesh surface is then pulled towards the regions of higher photometric consistency using free-form deformations. This sampling-based approach produces a photometrically consistent solution in much less time than possible with previous multi-view algorithms given arbitrary camera placement.

Two dimensional unital Riesz algebras, their representations and norms

We describe all two dimensional unital Riesz algebras and study representations of them in Riesz algebras of regular operators. Although our results are not complete, we do demonstrate that very varied behaviour can occur even though all these algebras can be given a Banach lattice algebra norm.

Template-based quadrilateral meshing

Generating quadrilateral meshes is a highly non-trivial task, as design decisions are frequently driven by specific application demands. Automatic techniques can optimize objective quality metrics, such as mesh regularity, orthogonality, alignment and adaptivity; however, they cannot make subjective design decisions. There are a few quad meshing approaches that offer some mechanisms to include the user in the mesh generation process; however, these techniques either require a large amount of user interaction or do not provide necessary or easy to use inputs. Here, we propose a template-based approach for generating quad-only meshes from triangle surfaces. Our approach offers a flexible mechanism to allow external input, through the definition of alignment features that are respected during the mesh generation process. While allowing user inputs to support subjective design decisions, our approach also takes into account objective quality metrics to produce semi-regular, quad-only meshes that align well to desired surface features. Published by Elsevier Ltd.