The Conformation of Sterically Congested Seven-Membered Rings Containing Tetracoordinate Germanium(IV): A First X-Ray Crystallographic Structure Determination

The X-ray crystallographic analysis of 6,6-dimethyl-2,4,8,10-tetra-tert-octyl-dibenzo[d,f][1,3,2]dioxagermepin, 1 is reported. In the solid-state conformation of 1, the dihedral angle about the C─C sp²-sp ² σ bond connecting the two aryl rings is 50.1°. The observed C₂ symmetry in the solid-state conformation of 1 is consistent with the previously suggested solution conformation.     

A Parallel 3D Unsteady Flow Analysis in an Asymmetrically Constricted Vessel

In this study, parallel computation of unsteady incompressible flow in an asymmetrically constricted 3D vessel has been presented. A time accurate cell centered finite volume method (FVM) in conjunction with pseudo-compressibility technique and Roe's flux difference splitting of nonlinear terms has been employed for solving the Navier-Stokes (NS) equations on the multiple instruction multiple data (MIMD) machine VPP700. The influence of Reynolds' number ( Re ) and the Strouhal number ( St ) on flow dynamic factors like wall pressure (WP), wall shear stress (WSS), central axis velocity (CAV), etc., have been analyzed. Three-dimensional (3D) features in the formation and detachment of separation zones, which are sensitive to both Re and St have been noticed on the diverging wall of the constriction.     

Ab initio path-integral molecular dynamics

A path-integral molecular dynamics technique for strongly interacting atoms using ab initio potentials derived from density functional theory is implemented. This allows the efficient inclusion of nuclear quantum dispersion in ab initio simulations at finite temperatures. We present an application to the quantum cluster H ₅ ⁺ .     

Validity of the transfer-matrix method for a two-dimensional electron waveguide

We solve the singularity problem of the transfer matrix method for a two-dimensional electron wave guide consisting of a sequence of cells. The method is reformulated in terms of intrinsic Bloch waves of a device cell. The resulting method is proved to be both stable and accurate. The transfer matrix is formulated without divergence problems in the open-mode approximation. The formula relating the N-cell transmission probability with that of one cell in the single-mode approximation takes exactly the same form as in the one-dimensional case.     

1/d corrections for interacting spinless fermions: One-particle properties

One-particle properties of the spinless fermion model with repulsion at half filling are calculated within an approach correct to first order in the inverse of the lattice dimensiond. Continuity of the limitd requires a scaling of the nearest-neighbour hopping proportional to and of the nearest-neighbour interaction proportional to 1/d. Due to this scaling the Hartree approximation becomes exact in infinite dimensions. We show that 1/d corrections comprise the Fock diagram and the local correlation diagram in the self-consistent Dyson equation. This approach is applied to simple-cubic systems in dimensiond=1, 2 and 3. Ground state properties and the charge-density wave phase diagram are calculated. AtT=0 the inclusion of 1/d terms gives only small corrections to the leading Hartree contribution ind=2, 3. ForT>0, however, the 1/d corrections are important. They lead to a non-negligible reduction of the critical temperature. Ind=1 the 1/d corrections are very large, but they do not succeed in removing the spurious phase transition atT>0. The 1/d approach provides a good and tractable approximation ind=3 and probably ind=2, which allows also further systematic improvement.     

Spatial dependence of meson correlation functions at high temperature

The spatial dependence of meson correlation functions at high temperature is studied in perturbative QCD, keeping only the lowest order term. We obtain analytic results for the static correlation function in this approximation. Problems connected with the regularization of the divergent expressions are discussed in detail. The meson screening mass is determined from the form of the correlation function at large distances. We obtain , which agrees with the results of Eletskii and Ioffe, for massless quarks (M=0). Finally, the correlation function in the temporal direction is briefly discussed. For massless quarks, we find the corresponding screening massm _scr=2T.Research supported in part by the Polish State Committee for Scientific Research under Grant No. 2.0204.91.01     

A Monte Carlo method for an objective Bayesian procedure

This paper describes a method for an objective selection of the optimal prior distribution, or for adjusting its hyper-parameter, among the competing priors for a variety of Bayesian models. In order to implement this method, the integration of very high dimensional functions is required to get the normalizing constants of the posterior and even of the prior distribution. The logarithm of the high dimensional integral is reduced to the one-dimensional integration of a cerain function with respect to the scalar parameter over the range of the unit interval. Having decided the prior, the Bayes estimate or the posterior mean is used mainly here in addition to the posterior mode. All of these are based on the simulation of Gibbs distributions such as Metropolis' Monte Carlo algorithm. The improvement of the integration's accuracy is substantial in comparison with the conventional crude Monte Carlo integration. In the present method, we have essentially no practical restrictions in modeling the prior and the likelihood. Illustrative artificial data of the lattice system are given to show the practicability of the present procedure.     

On the Exceptional Zeros of Rankin–Selberg L-Functions

The main objects of study in this article are two classes of Rankin–Selberg L-functions, namely L(s,f×g) and L(s, sym²(g)× sym²(g)), where f,g are newforms, holomorphic or of Maass type, on the upper half plane, and sym²(g) denotes the symmetric square lift of g to GL(3). We prove that in general, i.e., when these L-functions are not divisible by L-functions of quadratic characters (such divisibility happening rarely), they do not admit any LandauSiegel zeros. Such zeros, which are real and close to s=1, are highly mysterious and are not expected to occur. There are corollaries of our result, one of them being a strong lower bound for special value at s=1, which is of interest both geometrically and analytically. One also gets this way a good bound onthe norm of sym²(g).     

Prime Rings with Involution Equipped with Some New Product

Let R be a ring with involution *. We consider R as a ring equipped with a new product r s = rs + sr^*. The relationship between (ordinary) ideals of R and right ideals of R with respect to the product is studied.AMS Subject Classification (2000): 16W10, 16D25