Complete intersection singularities of splice type as universal abelian covers

It has long been known that every quasi-homogeneous normal complex surface singularity with Q-homology sphere link has universal abelian cover a Brieskorn complete intersection singularity. We describe a broad generalization: First, one has a class of complete intersection normal complex surface singularities called "splice type singularities", which generalize Brieskorn complete intersections. Second, these arise as universal abelian covers of a class of normal surface singularities with Q-homology sphere links, called "splice-quotient singularities". According to the Main Theorem, splice-quotients realize a large portion of the possible topologies of singularities with Q-homology sphere links. As quotients of complete intersections, they are necessarily Q-Gorenstein, and many Q-Gorenstein singularities with Q-homology sphere links are of this type. We conjecture that rational singularities and minimally elliptic singularities with Q-homology sphere links are splice-quotients. A recent preprint of T Okuma presents confirmation of this conjecture.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper17.abs.htm

Temperature and heat flux measurements: Challenges for high temperature aerospace application

The measurement of high temperatures and the influence of heat transfer data is not strictly a problem of either the high temperatures involved or the level of the heating rates to be measured at those high temperatures. It is a problem of duration during which measurements are made and the nature of the materials in which the measurements are made. Thermal measurement techniques for each application must respect and work with the unique features of that application. Six challenges in the development of measurement technology are discussed: (1) to capture the character and localized peak values within highly nonuniform heating regions; (2) to manage large volumes of thermal instrumentation in order to efficiently derive critical information; (3) to accommodate thermal sensors into practical flight structures; (4) to broaden the capabilities of thermal survey techniques to replace discrete gages in flight and on the ground; (5) to provide supporting instrumentation conduits which connect the measurement points to the thermally controlled data acquisition system; and (6) to develop a class of 'vehicle tending' thermal sensors to assure the integrity of flight vehicles in an efficient manner

Zeno effect and ergodicity in finite-time quantum measurements

We demonstrate that an attempt to measure a non-local in time quantity, such as the time average \la A\ra_T of a dynamical variable $A$, by separating Feynman paths into ever narrower exclusive classes traps the system in eigensubspaces of the corresponding operator \a. Conversely, in a long measurement of \la A\ra_T to a finite accuracy, the system explores its Hilbert space and is driven to a universal steady state in which von Neumann ensemble average of \a coincides with \la A\ra_T. Both effects are conveniently analysed in terms of singularities and critical points of the corresponding amplitude distribution and the Zeno-like behaviour is shown to be a consequence of conservation of probability

The Orevkov invariant of an affine plane curve

We show that although the fundamental group of the complement of an algebraic affine plane curve is not easy to compute, it possesses a more accessible quotient, which we call the Orevkov invariant.Comment: 20 page

Lipschitz geometry of complex surfaces: analytic invariants and equisingularity

We prove that the outer Lipschitz geometry of a germ $(X,0)$ of a normal complex surface singularity determines a large amount of its analytic structure. In particular, it follows that any analytic family of normal surface singularities with constant Lipschitz geometry is Zariski equisingular. We also prove a strong converse for families of normal complex hypersurface singularities in $\mathbb C^3$: Zariski equisingularity implies Lipschitz triviality. So for such a family Lipschitz triviality, constant Lipschitz geometry and Zariski equisingularity are equivalent to each other.Comment: Added a new section 10 to correct a minor gap and simplify some argument

Lipschitz geometry does not determine embedded topological type

We investigate the relationships between the Lipschitz outer geometry and the embedded topological type of a hypersurface germ in $(\mathbb C^n,0)$. It is well known that the Lipschitz outer geometry of a complex plane curve germ determines and is determined by its embedded topological type. We prove that this does not remain true in higher dimensions. Namely, we give two normal hypersurface germs $(X_1,0)$ and $(X_2,0)$ in $(\mathbb C^3,0)$ having the same outer Lipschitz geometry and different embedded topological types. Our pair consist of two superisolated singularities whose tangent cones form an Alexander-Zariski pair having only cusp-singularities. Our result is based on a description of the Lipschitz outer geometry of a superisolated singularity. We also prove that the Lipschitz inner geometry of a superisolated singularity is completely determined by its (non embedded) topological type, or equivalently by the combinatorial type of its tangent cone.Comment: A missing argument was added in the proof of Proposition 2.3 (final 4 paragraphs are new