Poincare submersions

We prove two kinds of fibering theorems for maps X --> P, where X and P are Poincare spaces. The special case of P = S^1 yields a Poincare duality analogue of the fibering theorem of Browder and Levine.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-2.abs.html Version 5: Statement of Theorem B corrected, see footnote p2

Complementary Lipschitz continuity results for the distribution of intersections or unions of independent random sets in finite discrete spaces

We prove that intersections and unions of independent random sets in finite spaces achieve a form of Lipschitz continuity. More precisely, given the distribution of a random set $\Xi$, the function mapping any random set distribution to the distribution of its intersection (under independence assumption) with $\Xi$ is Lipschitz continuous with unit Lipschitz constant if the space of random set distributions is endowed with a metric defined as the $L_k$ norm distance between inclusion functionals also known as commonalities. Moreover, the function mapping any random set distribution to the distribution of its union (under independence assumption) with $\Xi$ is Lipschitz continuous with unit Lipschitz constant if the space of random set distributions is endowed with a metric defined as the $L_k$ norm distance between hitting functionals also known as plausibilities. Using the epistemic random set interpretation of belief functions, we also discuss the ability of these distances to yield conflict measures. All the proofs in this paper are derived in the framework of Dempster-Shafer belief functions. Let alone the discussion on conflict measures, it is straightforward to transcribe the proofs into the general (non necessarily epistemic) random set terminology

On the homotopy invariance of configuration spaces

For a closed PL manifold M, we consider the configuration space F(M,k) of ordered k-tuples of distinct points in M. We show that a suitable iterated suspension of F(M,k) is a homotopy invariant of M. The number of suspensions we require depends on three parameters: the number of points k, the dimension of M and the connectivity of M. Our proof uses a mixture of Poincare embedding theory and fiberwise algebraic topology.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-35.abs.htm

The importance of batteries in unmanned missions

The planetary program has historically used batteries to supply peak power needs for mission specific applications. Any time that additional power has been required in order to meet peak power demands or those applications where only limited amounts of power were required, batteries have always been used. Up until the mid to late 70's they have performed their task admirably. Recently, however, we have all become aware of the growing problem of developing reliable NiCd batteries for long mission and high cycle life applications. Here, the role rechargeable batteries will play for future planetary and earth observing spacecraft is discussed. In conclusion, NiCds have been and will continue to be the mainstay of the power system engineers tools for peak power production. Recent experience has tarnished its once sterling reputation. However, the industry has stood up to this challenge and implemented wide ranging plans to rectify the situation. These efforts should be applauded and supported as new designs and materials become available. In addition, project managers must become aware of their responsibility to test their batteries and insure quality and mission operating characteristics. Without this teamwork, the role of NiCds in the future will diminish, and other batteries, not as optimum for high performance applications (low mass and volume) will take their place