Triangulations and moduli spaces of Riemann surfaces with group actions

Summary We study that subset of the moduli space of stable genusg,g>1, Riemann surfaces which consists of such stable Riemann surfaces on which a given finite groupF acts. We show first that this subset is compact. It turns out that, for general finite groupsF, the above subset is not connected. We show, however, that for ℤ₂ actions this subsetis connected. Finally, we show that even in the moduli space ofsmooth genusg Riemann surfaces, the subset of those Riemann surfaces on which ℤ₂ actsis connected. In view of deliberations of Klein ([8]), this was somewhat surprising. These results are based on new coordinates for moduli spaces. These coordinates are obtained by certainregular triangulations of Riemann surfaces. These triangulations play an important role also elsewhere, for instance in approximating eigenfunctions of the Laplace operator numerically. This work has been supported by the European Communities Science Plan Project No SCI^*-CT91 (TSTS) “Computational Methods in the Theory of Riemann Surfaces and Algebraic Curves,” by Academy of Finland and by the Swiss National Science Foundation Grant 20-34099.92. We thank M. C. Petrus for providing excellent motivation for this work. This article was processed by the author using the LATEX style filecljourl from Springer-Verlag.     

Zur Kenntnis der Chemie der Metallcarbonyle und der Cyanokomplexe in flüssigem Ammoniak. XXXII. Über die Reaktionen von η5-C5H5Mo(CO)3CH3 und η5-C5H5Fe(CO)2CH3 mit flüssigem Ammoniak

The Chemistry of Metal Carbonyls and Cyano Complexes in Liquid Ammonia. XXXII. On the Reaction of η⁵-C₅H₅Mo(CO)₃CH₃ and η⁵-C₅H₅Fe(CO)₂CH₃ with Liquid Ammonia η⁵-C₅H₅Mo(CO)₃CH₃ reacts with liquid NH₃ to give η⁵-C₅H₅Mo(CO)₂(NH₃)H and acetamide: In contrast, η⁵-C₅H₅Fe(CO)₂CH₃ undergoes a carbonyl insertion to give the acetyl complex η⁵-C₅H₅Fe(CO)(NH₃)COCH₃: The NH₃ ligand in η⁵-C₅H₅Fe(CO)(NH₃)COCH₃ can be substituted by pyridine.     

The remote effect of vicinal large groups on the anomeric equilibrium: 2-methoxy-cis- and -trans-5,6-dimethyltetrahydropyrans

The anomeric equilibrium of 2-methoxy-trans-5,6-dimethyltetrahydropyran was found to have an enhanced fraction of axial methoxyl compared to 2-methoxy-4- or 6-methyltetrahydropyran. The 2-methoxy-cis-5,6-dimethyltetrahydropyran did not. The enhanced anomeric effect is attributed to a steric repulsion between the trans vicinal Me groups. A similar effect is postulated for methyl glucoside and glucose pentaacetate.     

A Theoretical Study of Complex Formation between Formaldehyde and Lithium

Ab initio SCF and CI calculations on the cationic and neutral complexes of formaldehyde and lithium are reported. For the cationic complex CH₂O/Li⁺, the stabilization energy of 41.7 kcal/mol obtained from the SCF calculation increases to 51.6 kcal/mol if a configuration interaction is introduced. For the neutral complex CH₂O^?/Li⁺, the C_2v-conformer of the ²A₁-state with the equilibrium bond distances of d(C? O) = 1.23 Å and d (O? Li) = 1.90 Å is calculated to be more stable than the ₂B₁-state with d (C? O) = 1.34 Å, and d (O? Li) = 1.65 Å. Charge transfer and polarization effects upon complex formation are discussed.     

An attempt on the calculation of relativistic potential energy curves: Noble gas difluorides

Total energy SCF calculations were performed for noble gas difluorides in a relativistic procedure and compared with analogous non-relativistic calculations. The discrete variational method with numerical basis functions was used. Rather smooth potential energy curves could be obtained. The theoretical Kr-F and Xe-F bond distances were calculated to be 3.5 a.u. and 3.6 a.u. which should be compared with the experimental values of 3.54 a.u. and 3.7 a.u. Although the dissociation energies are off by a factor of about five it was found that ArF₂ may be a stable molecule. Theoretical ionization energies for the outer levels reproduce the experimental values for KrF₂ and XeF₂ to within 2 eV.     

The Random Average Process and Random Walk in a Space-Time Random Environment in One Dimension

We study space-time fluctuations around a characteristic line for a one-dimensional interacting system known as the random average process. The state of this system is a real-valued function on the integers. New values of the function are created by averaging previous values with random weights. The fluctuations analyzed occur on the scale n ^1/4, where n is the ratio of macroscopic and microscopic scales in the system. The limits of the fluctuations are described by a family of Gaussian processes. In cases of known product-form invariant distributions, this limit is a two-parameter process whose time marginals are fractional Brownian motions with Hurst parameter 1/4. Along the way we study the limits of quenched mean processes for a random walk in a space-time random environment. These limits also happen at scale n ^1/4 and are described by certain Gaussian processes that we identify. In particular, when we look at a backward quenched mean process, the limit process is the solution of a stochastic heat equation.     

Theoretical stability,thin film synthesis and transport properties of the Mon +1GaCn MAX phase

The phase stability of Mo_{n +1}GaC_n has been investigated using ab‐initio calculations. The results indicate stability for the Mo₂GaC phase only, with a formation enthalpy of –0.4 meV per atom. Subsequent thin film synthesis of Mo₂GaC was performed through magnetron sputtering from elemental targets onto Al₂O₃ [0001], 6H‐SiC [0001] and MgO [111] substrates within the temperature range of 500 °C and 750 °C. High structural quality films were obtained for synthesis on MgO [111] substrates at 590 ºC. Evaluation of transport properties showed a superconducting behavior with a critical temperature of approximately 7 K, reducing upon the application of an external magnetic field. The results point towards the first superconducting MAX phase in thin film form. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Tissue-specific and neural activity-regulated expression of human BDNF gene in BAC transgenic mice

Background  

Brain-derived neurotrophic factor (BDNF) is a small secreted protein that has important roles in the developing and adult nervous system. Altered expression or changes in the regulation of the BDNF gene have been implicated in a variety of human nervous system disorders. Although regulation of the rodent BDNF gene has been extensively investigated, in vivo studies regarding the human BDNF gene are largely limited to postmortem analysis. Bacterial artificial chromosome (BAC) transgenic mice harboring the human BDNF gene and its regulatory flanking sequences constitute a useful tool for studying human BDNF gene regulation and for identification of therapeutic compounds modulating BDNF expression.