Über verschränkte Produktordnungen

AbstractThis paper, which is dedicated to Emmy Noether on the occasion of the centenary of her birthday, is concerned with the arithmetics of crossed products. In particular, the definition of a crossed product order is tightened and it is shown that such orders are “one-headed,” i.e., that the “idealizer of radical” method of embedding always leads to the same hereditary order

Dirac Quantization of Parametrized Field Theory

Parametrized field theory (PFT) is free field theory on flat spacetime in a diffeomorphism invariant disguise. It describes field evolution on arbitrary foliations of the flat spacetime instead of only the usual flat ones, by treating the `embedding variables' which describe the foliation as dynamical variables to be varied in the action in addition to the scalar field. A formal Dirac quantization turns the constraints of PFT into functional Schrodinger equations which describe evolution of quantum states from an arbitrary Cauchy slice to an infinitesimally nearby one.This formal Schrodinger picture- based quantization is unitarily equivalent to the standard Heisenberg picture based Fock quantization of the free scalar field if scalar field evolution along arbitrary foliations is unitarily implemented on the Fock space. Torre and Varadarajan (TV) showed that for generic foliations emanating from a flat initial slice in spacetimes of dimension greater than 2, evolution is not unitarily implemented, thus implying an obstruction to Dirac quantization. We construct a Dirac quantization of PFT,unitarily equivalent to the standard Fock quantization, using techniques from Loop Quantum Gravity (LQG) which are powerful enough to super-cede the no- go implications of the TV results. The key features of our quantization include an LQG type representation for the embedding variables, embedding dependent Fock spaces for the scalar field, an anomaly free representation of (a generalization of) the finite transformations generated by the constraints and group averaging techniques. The difference between 2 and higher dimensions is that in the latter, only finite gauge transformations are defined in the quantum theory, not the infinitesimal ones.Comment: 33 page

Mitochondrial DNA mutations, apoptosis, and the misfolded protein response.

Studies of transgenic mice with accelerated accumulation of mtDNA mutations specifically in the heart lead us to propose that apoptotic signaling and cell death is central to the pathogenesis of mtDNA mutations in aging. It is the cellular response to that apoptotic signaling and the organ?s compensatory response to a loss of cells that specify the phenotype of an accumulation of mtDNA mutations. In the heart, cardiomyocytes induce a vigorous anti-apoptotic, pro-survival response to counteract mitochondrial apoptotic signaling. The heart up-regulates contractility of remaining myocytes in order to maintain cardiac output. We hypothesize that mutant mitochondrial proteins originate apoptotic signaling by interacting with proteins already in place in the mitochondrial outer membrane that regulate apoptosis, for example the pro-apoptotic protein Bak. Since it is unlikely that all mutant mitochondrial proteins have the necessary structure and localization within the inner membrane to activate Bak appropriately, only a small fraction of an age-associated burden of mtDNA mutations may be pathogenic. In this model, reactive oxygen species generated by mitochondrial respiration drive the formation of mtDNA mutations, but are not the primary mechanism for their pathogenicity

Sharply 2-transitive linear groups

A group G is sharply 2-transitive if it admits a faithful permutation representation that is transitive and free on pairs of distinct points. Conjecturally, for all such groups there exists a near-field N (i.e. a skew field that is distributive only from the left) such that G is isomorphic to the semidirect product of the multiplicative and additive groups of N. This is well known in the finite case. We prove this conjecture when G < GL(n,F) is a linear group. Here we have to assume that both the characteristic of the field F and the permutational characteristic of the group G (see Definition 2.1) are not equal to 2.Comment: 8 pages, revision matches accepted versio

pp-groups with maximal elementary abelian subgroups of rank 22

Let p be an odd prime number and G a finite p-group. We prove that if the rank of G is greater than p, then G has no maximal elementary abelian subgroup of rank 2. It follows that if G has rank greater than p, then the poset of elementary abelian subgroups of G of rank at least 2 is connected and the torsion-free rank of the group of endotrivial kG-modules is one, for any field k of characteristic p. We also verify the class-breadth conjecture for the p-groups G whose poset has more than one component

FORM version 4.0

We present version 4.0 of the symbolic manipulation system FORM. The most important new features are manipulation of rational polynomials and the factorization of expressions. Many other new functions and commands are also added; some of them are very general, while others are designed for building specific high level packages, such as one for Groebner bases. New is also the checkpoint facility, that allows for periodic backups during long calculations. Lastly, FORM 4.0 has become available as open source under the GNU General Public License version 3.Comment: 26 pages. Uses axodra

Genomic structure of murine mitochondrial DNA polymerase-gamma.

We have sequenced a genomic clone of the gene encoding the mouse mitochondrial DNA polymerase. The gene consists of 23 exons, which span approximately 13.2 kb, with exons ranging in size from 53 to 768 bp. All intron-exon boundaries conform to the GT-AG rule. By comparison with the human genomic sequence, we found remarkable conservation of the gene structure; the intron-exon borders are in almost identical locations for the 22 introns. The 5\u27 upstream region contains approximately 300 bp of homology between the mouse and human sequences that presumably contain the promoter element. This region lacks any obvious TATA domain and is relatively GC rich, consistent with the housekeeping function of the mitochondrial DNA polymerase. Finally, within the 5\u27 flanking region, both mouse and human genes have a region of 73 bp with high homology to the tRNA-Arg gene