Reference priors for exponential families with simple quadratic variance function

Reference analysis is one of the most successful general methods to derive noninformative prior distributions. In practice, however, reference priors are often difficult to obtain. Recently developed theory for conditionally reducible natural exponential families identifies an attractive reparameterization which allows one, among other things, to construct an enriched conjugate prior. In this paper, under the assumption that the variance function is simple quadratic, the order-invariant group reference prior for the above parameter is found. Furthermore, group reference priors for the mean- and natural parameter of the families are obtained. A brief discussion of the frequentist coverage properties is also presented. The theory is illustrated for the multinomial and negative-multinomial family. Posterior computations are especially straightforward due to the fact that the resulting reference distributions belong to the corresponding enriched conjugate family. A substantive application of the theory relates to the construction of reference priors for the Bayesian analysis of two-way contingency tables with respect to two alternative parameterizations.     

Diffusion in three-dimensional random systems at their percolation thresholds

Extensive Monte Carlo simulations of theant-in-the-labyrinth problem on randomL* L* L simple cubic lattices are performed, forL up to 960 on a CRAY-YMP supercomputer. The exponentk for the rms displacementr witht inrt ^k is found to bek=0.190±0.003. As a second approach, large percolation clusters with chemical shells up to 300 are generated on a simple cubic lattice at criticality. The diffusion equation is then solved by using the exact enumeration technique. The corresponding critical exponentd ^w is found to be 1/d ^w =0.250±0.003.On leave from I. Institut für Theoretische für Physik, Universität Hamburg, D-2000 Hamburg, Federal Republic of Germany.     

Monotone Chemical Reaction Networks

We analyze certain chemical reaction networks and show that every solution converges to some steady state. The reaction kinetics are assumed to be monotone but otherwise arbitrary. When diffusion effects are taken into account, the conclusions remain unchanged. The main tools used in our analysis come from the theory of monotone dynamical systems. We review some of the features of this theory and provide a self-contained proof of a particular attractivity result which is used in proving our main result.     

Crystal and molecular structure of nitrosyl(1,10-phenanthroline)-bis(triphenylphosphine)iridium(I) Dihexafluorophosphate, [Ir(NO)(phen)(PPh3)2][PF6]2

Summary The structure of [Ir(NO)(phen)(PPh₃)₂][PF₆]₂ has been determined from x-ray diffractometer data. The compound crystallizes in space groupPnam with four molecules in a unit cell witha = 19.924(12),b = 14.793(9) andc = 16.348(9) A. Full-matrix least-squares refinement has led to a final R value of 0.061 for the 4796 observed reflections. The structure consists of well-separated ions, and the geometry around the metal is trigonal bipyramidal with nitrosyl and bidentate 1,10-phenanthroline (in spite of the very narrow bite angle of 75.8°) ligands occupying the equatorial positions and the triphenylphosphine ligands the axial positions. The cation has an imposed crystallographicm symmetry. Important bond lengths are as follows: Ir-P, 2.391(3): Ir-N (nitrosyl) 1.700(12): Ir-N (1,10-phenanthroline) 2.103(12) and 2.142(11): N-O, 1.201(18)A. The nitrosyl ligand is linear [Ir-N-O = 179.9(9)°] so that this complex can be formulated as an NO⁺ complex of iridium(I).     

The search for a new model structure of β-Factor XIIa

We present the search for a new model of -factor XIIa, a blood coagulation enzyme, with an unknown experimental 3D-structure. We decided to build not one but three different models using different homologous proteins as well as different techniques and different modellers. Additional studies, including extensive molecular dynamics simulations on the solvated state, allowed us to draw several conclusions concerning homology modelling, in general, and -factor XIIa, in particular.     

Spectrophotometric titration of mercury(II) with ethylenedithiodiacetic acid

Summary Mercuric ions may be determined by titration with ethylenedithiodiacetic acid at a wavelength of 260 nm at any pH less than 1. The method is simple, rapid, and selective, and is applicable in solutions of high electrolyte concentration. Mercury(II) can be determined down to 1.5×10^–5 M with a relative standard deviation less than 2%.

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Zusammenfassung Quecksilber (II) läßt sich mit Äthylendithiodiessigsäure bei 260 nm und pH1 titrieren. Das Verfahren ist einfach, rasch und selektiv. Es läßt sich auch für Lösungen mit hoher Elektrolytkonzentration anwenden. Hg(II)-Konzentrationen über 1,5×10^–5 M sind mit einer relativen Standardabweichung unter 2% bestimmbar.

     

On the 2 and the 3-connectedness of ample divisors on a surface

Let X be a nonsingular complex projective surface and let D be an ample divisor on X such that the associated invertible sheaf is spanned by its global sections. We prove that D is 2-connected apart from a few cases we explicitly describe. We also provide a corresponding result for the 3-connectedness when D²10 and for the 4-connectedness when D²17 and D is very ample.     

Ond-folds whose canonical bundle is not numerically effective,according to Mori and Kawamata

Sunto In questo lavoro si studiano le varietà non singolari di dimensione d il cui divisore canonico non è numericamente effettivo e si estendono alcuni dei risultati ottenuti da Mori nel caso d=3. CiÒ viene ottenuto mediante un uso sistematico della teoria di Mori dei raggi estremali e di un forte teorema di Kawamata-Shokurov. Quest'ultimo risultato fornisce una varietà normale Y e un morfismo : X Y che contrae un raggio estremale R e che dá la struttura di X. Se R è numericamente effettivo, dimY