10,985 research outputs found
Fiber optic wavelength division multiplexing: Principles and applications in telecommunications and spectroscopy
Design and fabrication tradeoffs of wavelength division multiplexers are discussed and performance parameters are given. The same multiplexer construction based on prism gratings has been used in spectroscopic applications, in the wavelength region from 450 to 1600 nm. For shorter wavelengths down to 200 nm, a similar instrument based on longer fibers (500 to 1000 micrometer) has been constructed and tested with both a fiber array and a photodiode detector array at the output
Bilinear forms on Grothendieck groups of triangulated categories
We extend the theory of bilinear forms on the Green ring of a finite group
developed by Benson and Parker to the context of the Grothendieck group of a
triangulated category with Auslander-Reiten triangles, taking only relations
given by direct sum decompositions. We examine the non-degeneracy of the
bilinear form given by dimensions of homomorphisms, and show that the form may
be modified to give a Hermitian form for which the standard basis given by
indecomposable objects has a dual basis given by Auslander-Reiten triangles. An
application is given to the homotopy category of perfect complexes over a
symmetric algebra, with a consequence analogous to a result of Erdmann and
Kerner.Comment: arXiv admin note: substantial text overlap with arXiv:1301.470
Universal deformation rings of modules for algebras of dihedral type of polynomial growth
Let k be an algebraically closed field, and let \Lambda\ be an algebra of
dihedral type of polynomial growth as classified by Erdmann and Skowro\'{n}ski.
We describe all finitely generated \Lambda-modules V whose stable endomorphism
rings are isomorphic to k and determine their universal deformation rings
R(\Lambda,V). We prove that only three isomorphism types occur for
R(\Lambda,V): k, k[[t]]/(t^2) and k[[t]].Comment: 11 pages, 2 figure
A Development Environment for Visual Physics Analysis
The Visual Physics Analysis (VISPA) project integrates different aspects of
physics analyses into a graphical development environment. It addresses the
typical development cycle of (re-)designing, executing and verifying an
analysis. The project provides an extendable plug-in mechanism and includes
plug-ins for designing the analysis flow, for running the analysis on batch
systems, and for browsing the data content. The corresponding plug-ins are
based on an object-oriented toolkit for modular data analysis. We introduce the
main concepts of the project, describe the technical realization and
demonstrate the functionality in example applications
Ghosts in modular representation theory
A ghost over a finite p-group G is a map between modular representations of G
which is invisible in Tate cohomology. Motivated by the failure of the
generating hypothesis---the statement that ghosts between finite-dimensional
G-representations factor through a projective---we define the ghost number of
kG to be the smallest integer l such that the composition of any l ghosts
between finite-dimensional G-representations factors through a projective. In
this paper we study ghosts and the ghost numbers of p-groups. We begin by
showing that a weaker version of the generating hypothesis, where the target of
the ghost is fixed to be the trivial representation k, holds for all p-groups.
We then compute the ghost numbers of all cyclic p-groups and all abelian
2-groups with C_2 as a summand. We obtain bounds on the ghost numbers for
abelian p-groups and for all 2-groups which have a cyclic subgroup of index 2.
Using these bounds we determine the finite abelian groups which have ghost
number at most 2. Our methods involve techniques from group theory,
representation theory, triangulated category theory, and constructions
motivated from homotopy theory.Comment: 15 pages, final version, to appear in Advances in Mathematics. v4
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