Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators

We study tensor norms that destroy unconditionality in the following sense: for every Banach space $E$ with unconditional basis, the $n$-fold tensor product of $E$ (with the corresponding tensor norm) does not have unconditional basis. We establish an easy criterion to check weather a tensor norm destroys unconditionality or not. Using this test we get that all injective and projective tensor norms different from $\varepsilon$ and $\pi$ destroy unconditionality, both in full and symmetric tensor products. We present applications to polynomial ideals: we show that many usual polynomial ideals never enjoy the Gordon-Lewis property. We also consider the unconditionality of the monomial basic sequence. Analogous problems for multilinear and operator ideals are addressed.Comment: 23 page

Long-Range Correlations in Self-Gravitating N-Body Systems

Observed self-gravitating systems reveal often fragmented non-equilibrium structures that feature characteristic long-range correlations. However, models accounting for non-linear structure growth are not always consistent with observations and a better understanding of self-gravitating $N$-body systems appears necessary. Because unstable gravitating systems are sensitive to non-gravitational perturbations we study the effect of different dissipative factors as well as different small and large scale boundary conditions on idealized $N$-body systems. We find, in the interval of negative specific heat, equilibrium properties differing from theoretical predictions made for gravo-thermal systems, substantiating the importance of microscopic physics and the lack of consistent theoretical tools to describe self-gravitating gas. Also, in the interval of negative specific heat, yet outside of equilibrium, unforced systems fragment and establish transient long-range correlations. The strength of these correlations depends on the degree of granularity, suggesting to make the resolution of mass and force coherent. Finally, persistent correlations appear in model systems subject to an energy flow.Comment: 20 pages, 21 figures. Accepted for publication in A&

Inflating with Baryons

We present a field theory solution to the eta problem. By making the inflaton field the phase of a baryon of SU(N_c) supersymmetric Yang-Mills theory we show that all operators that usually spoil the flatness of the inflationary potential are absent. Our solution naturally generalizes to non-supersymmetric theories.Comment: 5 page

Motivic Hopf elements and relations

We use Cayley-Dickson algebras to produce Hopf elements eta, nu and sigma in the motivic stable homotopy groups of spheres, and we prove via geometric arguments that the the products eta*nu and nu*sigma both vanish. Along the way we develop several basic facts about the motivic stable homotopy ring

Returns to Human Capital under the Communist Wage Grid and During the Transition to a Market Economy

Under communism, workers had their wages set according to a centrally-determined wage grid. In this paper we use new micro data on men to estimate returns to human capital under the communist wage grid and during the transition to a market economy. We use data from the Czech Republic because it is a leading transition economy in which the communist grid remained intact until the very end of the communist regime. We demonstrate that for decades the communist wage grid maintained extremely low rate of return on education, but that the return increased dramatically and equally in all ownership categories of firms during the transition. Our estimates also indicate that men's wage-experience profile was concave in both regimes and on average it did not change from the communist to the transition period. However, the de novo private firms display a more concave profile than SOEs and public administration. Contrary to earlier studies, we show that men's inter-industry wage structure changed substantially between 1989 and 1996.http://deepblue.lib.umich.edu/bitstream/2027.42/39656/3/wp272.pd