We study the splitting behaviour of quasilinear p-forms in the spirit of the theory of non-singular quadratic forms over fields of characteristic different from 2 using an analogue of Knebusch’s generic splitting tower. Several new applications to the theory of quasilinear quadratic forms are given. Among them, we can mention an algebraic analogue of Vishik’s theorem on ‘outer excellent connect...

We use a recent theorem of N. A. Karpenko and A. S. Merkurjev to settle several questions in the theory of essential dimension. 2010 Mathematics Subject Classification: 20D15, 20C15, 20G15

This paper concerns an index theory for Z-actions induced by a homeomorphism of a compact space. We give a definition of a genus for uniform spaces and prove that the genus for compact spaces is an index. To this end we show a Z-version of the Borsuk-Ulam theorem and the existence of a continuous equivariant extension for these Z-actions.

We derive a convex optimization problem on a steady-state nonequilibrium network of biochemical reactions, with the property that energy conservation and the second law of thermodynamics both hold at the problem solution. This suggests a new variational principle for biochemical networks that can be implemented in a computationally tractable manner. We derive the Lagrange dual of the optimizati...

We find marginal-Fermi-liquid- (MFL) like behavior in the Hubbard model on a square lattice for a range of hole doping and on-site interaction parameter U. Thereby we use a self-consistent projection operator method. It enables us to compute the momentum and frequency dependence of the single-particle excitations with high resolution. The Fermi surface is found to be holelike in the underdoped ...

Risk factors associated with single-vehicle driver fatalities are explored in a sensitivity analysis of data from composite sources. Information on fatalities was taken from the Federal Accident Reporting System data base for 1976-1981. Characteristics of the driving population were given by the 1973 National Roadside Breath Testing Survey (Wolfe 1974). Using Bayes theorem and logistic regressi...

We show that a generic vector field on an affine space of positive characteristic admits an invariant algebraic hypersurface. This contrast with Jouanolou’s Theorem that shows that in characteristic zero the situation is completely opposite. That is a generic vector field in the complex plane does not admit any invariant algebraic curve.

[directeur de thèse/Erstberichterstatter], Helmut Schwichtenberg (Professor an der Universität München) [examinateur/vierter Prüfer].

Although our proof is standard (essentially the same as presented by Serre [2], whose was the first account that I understood) we eschew complexvariable theory. Instead we use simple estimates from real-variable theory. Only one new difficulty is introduced: proving that L(1, χ) 6= 0 for nontrivial real-valued Dirichlet characters χ. We use an argument of Monsky [1] to prove this fact. Our argu...

This paper presents, first, a formal exploration of the relationships between information (statistically defined), statistical hypothesis testing, the use of hypothesis testing in reverse as an investigative tool, channel capacity in a communication system, uncertainty, the concept of entropy in thermodynamics, and Bayes’ theorem. This exercise brings out the close mathematical interrelationshi...