Elimination theory is at the origin of algebraic geometry in the 19-th century and deals with algorithmic solving of multivariate polynomial equation systems over the complex numbers, or, more generally, over an arbitrary algebraically closed field. In this paper we investigate the intrinsic sequential time complexity of universal elimination procedures for arbitrary continuous data structures ...

A new class of compact Kähler manifolds, called special, is defined: they are the ones having no fibration with base an orbifold of general type, the orbifold structure on the base being defined by the multiple fibres of the fibration (see §1). The special manifolds are in many respect higher-dimensional generalisations of rational and elliptic curves. For example, we show that being rationally...

We produce skew loops—loops that lack any pair of parallel tangent lines—homotopic to any loop in a flat torus, or any other quotient of Rn by a discrete subgroup. The interesting case here is n = 3 . More subtly for any n , we then characterize the homotopy classes that will contain a skew loop having a specified loop τ ⊂ S as tangent indicatrix.

This Thesis describes the basic framework of a relativistic ray-tracing code for analyzing accretion processes around Kerr black holes. We begin in Chapter 1 with a brief historical summary of the major advances in black hole astrophysics over the past few decades and outline some of the important questions still open today. In Chapter 2 we present a detailed description of the ray-tracing code...

Given a hyperbolic 3-manifold containing an embedded geodesic, we estimate the volume of a complete hyperbolic metric after drilling the geodesic from the manifold in terms of the radius of an embedded tube about the geodesic.

This paper addresses the problem of the separation of rotational and internal motion. It introduces the concept of average angular velocity as the moment of inertia weighted average of particle angular velocities. It extends and elucidates the concept of Jellinek and Li (1989) of separation of the energy of overall rotation in an arbitrary (non-linear) N -particle system. It generalizes the so ...

We prove that the lower bounds for Betti numbers of the rack, quandle and degeneracy cohomol-ogy given in [CJKS] are in fact equalities. We compute as well the Betti numbers of the twisted cohomology introduced in [CES]. We also give a group-theoretical interpretation of the second cohomology group for racks.

We prove R = T theorems for certain reducible residual Galois representations. We answer in the positive a question of Gross and Lubin on whether certain Hecke algebras T are discrete valuation rings. In order to prove these results we determine (using the theory of Breuil modules) when two finite flat group schemes G and H of order p over an arbitrarily tamely ramified discrete valuation ring ...

A construction of expander codes is presented with the following three properties: (i) the codes lie close to the Singleton bound, (ii) they can be encoded in time complexity that is linear in their code length, and (iii) they have a linear-time bounded-distance decoder. By using a version of the decoder that corrects also erasures, the codes can replace MDS outer codes in concatenated construc...