On the depth of blowup algebras of ideals with analytic deviation one

Let I be an ideal in a local Cohen-Macaulay ring (A, m). Assume I to be generically a complete intersection of positive height. We compute the depth of the Rees algebra and the form ring of I when the analytic deviation of I equals one and its reduction number is also at most one. The formu- las we obtain coincide with the already known formulas for almost complete intersection ideals.

Representations of swinging London in 1960s British cinema : Blowup (1966), Smashing Time (1967), and Performance (1970)

This thesis explores the representation of Swinging London in three examples of 1960s British cinema: Blowup (Michelangelo Antonioni, 1966), Smashing Time (Desmond Davis, 1967) and Performance (Donald Cammell and Nicolas Roeg, 1970). It suggests that the films chronologically signify the evolution, commodification and dissolution of the Swinging London era. The thesis explores how the concept of Swinging London is both critiqued and perpetuated in each film through the use of visual tropes: the reconstruction of London as a cinematic space; the Pop photographer; the dolly; representations of music performance and fashion; the appropriation of signs and symbols associated with the visual culture of Swinging London. Using fashion, music performance, consumerism and cultural symbolism as visual narratives, each film also explores the construction of youth identity through the representation of manufactured and mediated images. Ultimately, these films reinforce Swinging London as a visual economy that circulates media images as commodities within a system of exchange. With this in view, the signs and symbols that comprise the visual culture of Swinging London are as central and significant to the cultural era as their material reality. While they attempt to destabilize prevailing representations of the era through the reproduction and exchange of such symbols, Blowup, Smashing Time, and Performance nevertheless contribute to the nostalgia for Swinging London in larger cultural memory.

Lower bounds on blow up solutions of the three-dimensional Navier-Stokes equations in homogeneous Sobolev spaces

Suppose that u(t) is a solution of the three-dimensional Navier-Stokes equations, either on the whole space or with periodic boundary conditions, that has a singularity at time T. In this paper we show that the norm of u(T - t) in the homogeneous Sobolev space (H)over dot(s) must be bounded below by c(s)t(-(2s-1)/4) for 1/2 < s < 5/2 (s not equal 3/2), where c(s) is an absolute constant depending only on s; and by c(s)parallel to u(0)parallel to((5-2s)/5)(L2)t(-2s/5) for s > 5/2. (The result for 1/2 < s < 3/2 follows from well-known lower bounds on blowup in Lp spaces.) We show in particular that the local existence time in (H)over dot(s)(R-3) depends only on the (H)over dot(s)-norm for 1/2 < s < 5/2, s not equal 3/2. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4762841]

On Sandwiched Singularities

Sandwich-Singularitäten sind die Singularitäten auf derNormalisierung von Aufblasungen eines regulärenFlächenkeimes. In der Arbeit wird ein enger Zusammenhangzwischen Topologie und Deformationstheorie vonSandwich-Singularitäten einerseits und ebenenKurvensingularitäten andererseits dargestellt. NeueErgebnisse betreffen u.a. Deformationen vonnulldimensionalen komplexen Räumen in der Ebene, die durchvollständige Ideale beschrieben werden, z.B. wann'simultanes Aufblasen' der Fasern einer solchen Deformationmöglich ist. Zudem werden Glättungskomponenten und dieKollar-Vermutung für Sandwich-Singularitäten untersucht undim Zusammenhang damit numerische Kriterien für die Frage, obdie symbolische Algebra einer Raumkurve endlich erzeugt ist.

Branching Particle Representation of a Class of Semilinear Equations

2000 Mathematics Subject Classification: 60J80, 60J85

Sub- and Super-solutions of a Nonlinear PDE, and Application to a Semilinear SPDE

2010 Mathematics Subject Classification: 35R60, 60H15, 74H35.