On inductively free reflection arrangements

Suppose that W is a finite, unitary reflection group acting on the complex vector space V. Let A = A(W) be the associated hyperplane arrangement of W. Terao has shown that each such reflection arrangement A is free. There is the stronger notion of an inductively free arrangement. In 1992, Orlik and Terao conjectured that each reflection arrangement is inductively free. It has been known for quite some time that the braid arrangement as well as the Coxeter arrangements of type B and type D are inductively free. Barakat and Cuntz completed this list only recently by showing that every Coxeter arrangement is inductively free. Nevertheless, Orlik and Terao's conjecture is false in general. In a recent paper, we already gave two counterexamples to this conjecture among the exceptional complex reflection groups. In this paper we classify all inductively free reflection arrangements. In addition, we show that the notions of inductive freeness and that of hereditary inductive freeness coincide for reflection arrangements. As a consequence of our classification, we get an easy, purely combinatorial characterization of inductively free reflection arrangements A in terms of exponents of the restrictions to any hyperplane of A.Comment: 16 pages; references updated; final version; to appear in J. Reine Angew. Mat

Addition-Deletion Theorems for Factorizations of Orlik-Solomon Algebras and nice Arrangements

We study the notion of a nice partition or factorization of a hyperplane arrangement due to Terao from the early 1990s. The principal aim of this note is an analogue of Terao's celebrated addition-deletion theorem for free arrangements for the class of nice arrangements. This is a natural setting for the stronger property of an inductive factorization of a hyperplane arrangement by Jambu and Paris. In addition, we show that supersolvable arrangements are inductively factored and that inductively factored arrangements are inductively free. Combined with our addition-deletion theorem this leads to the concept of an induction table for inductive factorizations. Finally, we prove that the notions of factored and inductively factored arrangements are compatible with the product construction for arrangements.Comment: 24 pages; v2 26 pages: added new example over complex numbers of an inductively free and factored arrangement which is not inductively factored, added comment on proper containment of hereditary factored classes; v3 final version, small changes as suggested by referees; to appear in European. J. Com

Airborne Oceanographic Lidar (AOL) flight mission participation

From February 1986 to the present, the AOL participated in six interagency flight missions. (1) Shelf Edge Exchange Processes (SEEP II) (Department of Energy). The SEEP experiments are designed to assess the assimilative capacity of the Continental Shelf to absorb the energy by-products introduced into the near-shore ocean environment from coastal communities and marine activities such as energy production plants and offshore oil operations. (2) BIOWATT II (Office of Naval Research). The major objective of this study was to provide a better understanding of the relationships between ocean physics, biology, bioluminescence, and optics in oligotrophic portions of the Atlantic Ocean. (3) Fall Experiment (FLEX) (Department of Energy). The FLEX studies were designed to determine the fate of low salinity water in the coastal boundary zone that is advected south towards the Florida coast during autumn. (4) Greenland Sea and Icelandic Marine Biological Experiments (NASA). The investigations were designed to evaluate the distribution of surface layer chlorophyll in the Greeland Sea and in the coastal waters in the vicinity of Iceland. (5) Submerged Oceanic Scattering Layer Experiment (Naval Ocean Systems Center). This flight experiment demonstrated for the first time the feasibility of detecting and metrically measuring the depth to submerged layers of particulate matter in the shelf break region and in the inner coastal zone. (6) Microbial Exchanges and Coupling in Coastal Atlantic Systems (National Science Foundation). This investigation was designed to study the transportation and fate of particulates in coastal waters and in particular the Chesapeake Bay/coastal Atlantic Ocean. Shortly after the conduct of the flight experiments, airborne laser-induced chlorophyll a and phycoerythrin fluorescence data, as well as sea surface temperature and airborne expendable bathythermograph water column temperature profiles are supplied to cooperating institutions

Application of the NASA airborne oceanographic lidar to the mapping of chlorophyll and other organic pigments

Laser fluorosensing techniques used for the airborne measurement of chlorophyll a and other naturally occurring waterborne pigments are reviewed. Previous experiments demonstrating the utility of the airborne oceanographic lidar (AOL) for assessment of various marine parameters are briefly discussed. The configuration of the AOL during the NOAA/NASA Superflux experiments is described. The participation of the AOL in these experiments is presented and the preliminary results are discussed. The importance of multispectral receiving capability in a laser fluorosensing system for providing reproducible measurements over wide areas having spatial variations in water column transmittance properties is addressed. This capability minimizes the number of truthing points required and is usable even in shallow estuarine areas where resuspension of bottom sediment is common. Finally, problems encountered on the Superflux missions and the resulting limitations on the AOL data sets are addressed and feasible solutions to these problems are provided