28,154 research outputs found
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
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
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
Green's J-order and the rank of tropical matrices
We study Green's J-order and J-equivalence for the semigroup of all n-by-n
matrices over the tropical semiring. We give an exact characterisation of the
J-order, in terms of morphisms between tropical convex sets. We establish
connections between the J-order, isometries of tropical convex sets, and
various notions of rank for tropical matrices. We also study the relationship
between the relations J and D; Izhakian and Margolis have observed that for the semigroup of all 3-by-3 matrices over the tropical semiring with
, but in contrast, we show that for all full matrix semigroups
over the finitary tropical semiring.Comment: 21 pages, exposition improve
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.
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