The Hirzebruch-Mumford covolume of some hermitian lattices

Let $L=diag(1,1,\ldots,1,-1)$ and $M=diag(1,1,\ldots,1,-2)$ be the lattices of signature $(n,1)$. We consider the groups $\Gamma=SU(L,\mathcal{O}_K)$ and $\Gamma'=SU(M,\mathcal{O}_K)$ for an imaginary quadratic field $K=\mathbb{Q}(\sqrt{-d})$ of discriminant $D$ and it's ring of integers $\mathcal{O}_K$, $d$ odd and square free. We compute the Hirzebruch-Mumford volume of the factor spaces $\mathbb{B}^n/\Gamma$ and $\mathbb{B}^n/\Gamma'$. The result for the factor space $\mathbb{B}^n/\Gamma$ is due to Zeltinger, but as we're using it to prove the result for $\mathbb{B}^n/\Gamma'$ and it is hard to find his article, we prove the first result here as well

Nonfreeness of some algebras of hermitian modular forms

We study the algebras of hermitian automorphic forms for the lattice $L_n=diag(1,1,\ldots,1,-1)$ and for the field $K=\mathbb{Q}(\sqrt{-d})$ such that $p=2$ is unramified and the ring of integers $\mathcal{O}_K$ is a p.i.d. We prove that for $d>7$ these algebras can't be free. When $d=7$ and $d=3$ we give an estimate for the dimension of the symmetric spaces for which these algebras might be free. We also compare our results with the known results for $d=3$

Isolation and Structural Determination of the First 8-epi-type Tetrodotoxin Analogs from the Newt, Cynops ensicauda popei, and Comparison of Tetrodotoxin Analogs Profiles of This Newt and the Puffer Fish, Fugu poecilonotus

Identification of new tetrodotoxin (TTX) analogs from TTX-possessing animals might provide insight into its biosynthesis and metabolism. In this study, four new analogs, 8-epi-5,6,11-trideoxyTTX, 4,9-anhydro-8-epi-5,6,11-trideoxyTTX, 1-hydroxy-8-epi-5,6,11-trideoxyTTX, and 1-hydroxy-4,4a-anhydro-8-epi-5,6,11-trideoxyTTX, were isolated from the newt, Cynops ensicauda popei, and their structures were determined using spectroscopic methods. These are the first 8-epi-type analogs of TTX that have been found in a natural source. Furthermore, we examined the composition of the TTX analogs in this newt and in the ovary of the puffer fish, Fugu poecilonotus, using LC/MS. The results indicate that TTX and 11-deoxyTTX were present in both sources. However, 6-epiTTX and 8-epi-type analogs were detected only in the newt, while 5,6,11-trideoxyTTX was a specific and major analog in the puffer fish. Such considerable differences among analog compositions might reflect differences in the biosynthesis or metabolism of TTX between these animals

Central Pb+Pb Collisions at 158 A GeV/c Studied by Pion-Pion Interferometry

Two-particle correlations have been measured for identified negative pions from central 158 AGeV Pb+Pb collisions and fitted radii of about 7 fm in all dimensions have been obtained. A multi-dimensional study of the radii as a function of kT is presented, including a full correction for the resolution effects of the apparatus. The cross term Rout-long of the standard fit in the Longitudinally CoMoving System (LCMS) and the vl parameter of the generalised Yano-Koonin fit are compatible with 0, suggesting that the source undergoes a boost invariant expansion. The shapes of the correlation functions in Qinv and Qspace have been analyzed in detail. They are not Gaussian but better represented by exponentials. As a consequence, fitting Gaussians to these correlation functions may produce different radii depending on the acceptance of the experimental setup used for the measurement.Comment: 13 pages including 10 figure

Search for Disoriented Chiral Condensates in 158 AGeV Pb+Pb Collisions

The restoration of chiral symmetry and its subsequent breaking through a phase transition has been predicted to create regions of Disoriented Chiral Condensates (DCC). This phenomenon has been predicted to cause anomalous fluctuations in the relative production of charged and neutral pions in high-energy hadronic and nuclear collisions. The WA98 experiment has been used to measure charged and photon multiplicities in the central region of 158 AGeV Pb+Pb collisions at the CERN SPS. In a sample of 212646 events, no clear DCC signal can be distinguished. Using a simple DCC model, we have set a 90% C.L. upper limit on the maximum DCC production allowed by the data.Comment: 20 Pages, LaTeX, uses elsart.cls, 8 eps figures included, submitted to Physics Letters

Directed Flow in 158 A GeV 208Pb^{208}Pb + 208Pb^{208}Pb Collisions

The directed flow of protons and positive pions have been studied in 158 A GeV Pb + Pb collisions. A directed flow analysis of the rapidity dependence of the average transverse momentum projected onto the reaction plane is presented for semi-central collisions with impact parameters of approximately 8 fm, where the flow effect is largest. The magnitude of the directed flow is found to be significantly smaller than observed at AGS energies and than RQMD model predictions.The directed flow of protons and positive pions have been studied in 158 A GeV Pb + Pb collisions. A directed flow analysis of the rapidity dependence of the average transverse momentum projected onto the reaction plane is presented for semi-central collisions with impact parameters of approximately 8 fm, where the flow effect is largest. The magnitude of the directed flow is found to be significantly smaller than observed at AGS energies and than RQMD model predictions