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 only makes changes to arxiv meta-data, correcting the abstract and adding a do