Underwater optical wireless communications : depth dependent variations in attenuation

Depth variations in the attenuation coefficient for light in the ocean were calculated using a one-parameter model based on the chlorophyll-a concentration Cc and experimentally-determined Gaussian chlorophyll-depth profiles. The depth profiles were related to surface chlorophyll levels for the range 0–4  mg/m2, representing clear, open ocean. The depth where Cc became negligible was calculated to be shallower for places of high surface chlorophyll; 111.5 m for surface chlorophyll 0.8<Cc<2.2  mg/m3 compared with 415.5 m for surface Cc<0.04  mg/m3. Below this depth is the absolute minimum attenuation for underwater ocean communication links, calculated to be 0.0092  m−1 at a wavelength of 430 nm. By combining this with satellite surface-chlorophyll data, it is possible to quantify the attenuation between any two locations in the ocean, with applications for low-noise or secure underwater communications and vertical links from the ocean surface

Linear determinantal equations for all projective schemes

We prove that every projective embedding of a connected scheme determined by the complete linear series of a sufficiently ample line bundle is defined by the 2-minors of a 1-generic matrix of linear forms. Extending the work of Eisenbud-Koh-Stillman for integral curves, we also provide effective descriptions for such determinantally presented ample line bundles on products of projective spaces, Gorenstein toric varieties, and smooth n-folds.Comment: 17 pages; several improvements in the exposition following the referee's suggestion

On Second-Quantized Open Superstring Theory

The SO(32) theory, in the limit where it is an open superstring theory, is completely specified in the light-cone gauge as a second-quantized string theory in terms of a ``matrix string'' model. The theory is defined by the neighbourhood of a 1+1 dimensional fixed point theory, characterized by an Abelian gauge theory with type IB Green-Schwarz form. Non-orientability and SO(32) gauge symmetry arise naturally, and the theory effectively constructs an orientifold projection of the (weakly coupled) matrix type IIB theory (also discussed herein). The fixed point theory is a conformal field theory with boundary, defining the free string theory. Interactions involving the interior of open and closed strings are governed by a twist operator in the bulk, while string end-points are created and destroyed by a boundary twist operator.Comment: 20 pages,in harvmac.tex `b' mode; epsf.tex for 12 figure

Topological Background Fields as Quantum Degrees of Freedom of Compactified Strings

It is shown that background fields of a topological character usually introduced as such in compactified string theories correspond to quantum degrees of freedom which parametrise the freedom in choosing a representation of the zero mode quantum algebra in the presence of non-trivial topology. One consequence would appear to be that the values of such quantum degrees of freedom, in other words of the associated topological background fields, cannot be determined by the nonperturbative string dynamics.Comment: 1+10 pages, no figure

Exact rings and semirings

We introduce and study an abstract class of semirings, which we call exact semirings, defined by a Hahn-Banach-type separation property on modules. Our motivation comes from the tropical semiring, and in particular a desire to understand the often surprising extent to which it behaves like a field. The definition of exactness abstracts an elementary property of fields and the tropical semiring, which we believe is fundamental to explaining this similarity. The class of exact semirings turns out to include many other important examples of both rings (proper quotients of principal ideal domains, matrix rings and finite group rings over these and over fields), and semirings (the Boolean semiring, generalisations of the tropical semiring, matrix semirings and group semirings over these).Comment: 17 pages; fixed typos, clarified a few points, changed notation in Example 6.

Promoting mathematical communication and community via Blackboard

Major changes in mathematics pedagogy include writing as pedagogy and the role of community in learning. The classroom community is naturally extended by the use of online discussion boards. In this paper several models for student use of online discussion boards that have been successfully used to promote mathematical discourse are presented. Structured and unstructured examples that are easily adaptable and transportable to a variety of mathematics classroom settings are offered. These assignments facilitate student engagement and interaction outside of the classroom. Assessment, utility, and transferability are offered. Although the authors use the discussion boards provided by Blackboard, this particular software package is not necessary

Theory of small aspect ratio waves in deep water

In the limit of small values of the aspect ratio parameter (or wave steepness) which measures the amplitude of a surface wave in units of its wave-length, a model equation is derived from the Euler system in infinite depth (deep water) without potential flow assumption. The resulting equation is shown to sustain periodic waves which on the one side tend to the proper linear limit at small amplitudes, on the other side possess a threshold amplitude where wave crest peaking is achieved. An explicit expression of the crest angle at wave breaking is found in terms of the wave velocity. By numerical simulations, stable soliton-like solutions (experiencing elastic interactions) propagate in a given velocities range on the edge of which they tend to the peakon solution.Comment: LaTex file, 16 pages, 4 figure

Researching Bradford: A review of social research on Bradford District

A synthesis of findings from social research on the District of Bradford. This report synthesises the findings from a wide range of social research undertaken on the District of Bradford, primarily between 1995 and 2005. The researchers reviewed almost 200 pieces of work. The key results are summarised under thematic headings: - The social, economic and institutional context - Community cohesion - Housing, neighbourhoods and regeneration - Business and enterprise - Health, disability and social care - Children and young people - Education, skills and the labour market - Crime and community safety It also identifies a future research agenda. The main purpose of the review was to provide the Joseph Rowntree Foundation and local organisations in Bradford with a firm basis upon which to build future work in the District