Bayesian Prediction Analysis for Growth Curve Model Using Noninformative Priors

We apply a Bayesian approach to the problem of prediction in an unbalanced growth curve model using noninformative priors. Due to the complexity of the model, no analytic forms of the predictive densities are available. We propose both approximations and a prediction-oriented Metropolis-Hastings sampling algorithm for two types of prediction, namely the prediction of future observations for a new subject and the prediction of future values for a partially observed subject. They are illustrated and compared through real data and simulation studies. Two of the approximations compare favorably with the approximation in Fearn (1975, Biometrika, 62, 89–100) and are very comparable to the more accurate Rao-Blackwellization from Metropolis-Hastings sampling algorithm.     

NMR AND DFT STUDY OF Co-C BOND ACTIVATION MECHANISM IN VITAMIN B_(12) COMPOUNDS

This report focuses on a theoretical study of the cobalt-cabon bond activation mechanism in Vitamin B12, its co enzyme complexes, and model compounds such as cobalamins (Cbl), cobaloximes and cobalt porphyrins. In particular, emphasis is placed on the nucleotide loop and its role in the base on and base off mechanism.     

CP violation and extra dimensions

It is shown that new sources of CP violation can be generated in models with more than one extra dimension. In the supersymmetric models on the space-time , where the radius moduli have auxiliary vacuum expectation values and the supersymmetry breaking is mediated by the Kaluza–Klein states of the gauge supermultiplets, we analyze the gaugino masses and trilinear couplings for two scenarios and obtain the result that there exist relative CP violating phases among the gaugino masses and trilinear couplings. Received: 10 October 2001 / Published online: 20 December 2001     

Carbon diffusion between the volume and surface of (100) molybdenum

The diffusion of carbon atoms between the volume and the surface of (100) molybdenum is directly studied at temperatures between 1400 and 2000 K (i.e., at process temperatures) for the first time. The balance of carbon atoms in the system is determined. The difference in the activation energies of carbon dissolution and precipitation, ΔE=E s 1-E1s, is found for the case when the diffusion fluxes of dissolved and precipitated carbon atoms are in equilibrium. This difference defines the enrichment of the surface by carbon relative to the bulk. The experimentally found activation energy of carbon dissolution is Es1=3.9 eV. The activation energy of carbon precipitation is estimated at E 1 s=1.9 eV. The latter value is close to the energy of bulk diffusion of carbon in molybdenum.     

Metrics of Homogeneous Spaces Admitting (3.1)-Type Complete Sets

A classification has been obtained for spaces which admit complete sets of motion integrals of the (3.1)-type and are spatially homogeneous. The metrics and Killing vectors have been found in explicit form for all types of these spaces. A classification by Bianchi is given for the spaces obtained.     

Tunneling and EPR linewidths due to dislocations in Mn acetate

We compute the width and shape of the EPR and tunneling resonances due to dislocations in Mn₁₂ acetate crystals. Uncorrelated dislocations produce the Gaussian shape of resonances while dislocations bound in pairs produce the Lorentzian shape. We stress that the uniaxial spin Hamiltonian together with crystal defects can explain the totality of experimental data on Mn₁₂. Received 2 August 2001 / Received in final form 15 March 2002 Published online 17 September 2002     

Reception of a Signal with Unknown Duration

The maximum likely and optimal (Bayesian) algorithms for detecting an arbitrary-shaped signal observed against the background of Gaussian white noise and for measuring the duration are synthesized. Exact expressions for the characteristics of the maximum likely algorithms are found. The characteristics of the Bayesian algorithms are obtained using computer simulations.     

Resonances and Gamow States in Non-Local Potentials

For a large class of non-local, non separable potentials with non-compact support, the solution of the radial integrodifferential equation may be reduced to the solution of a homogeneous linear integral equation of Fredholm type with a quadratically integrable kernel. In this way we derive expansions of the wave functions and the Green's function of the Schrödinger equation with a non-local potential in terms of bound states, resonant states and a continuum of scattering functions with complex wave number. The rules of normalization, orthogonality and completeness satisfied by the eigenstates of the Schrödinger equation belonging to complex eigenvalues with Im E_n < 0, (Gamow or resonant states) are also derived. Finally, by means of a realistic example, it is shown how to use these expansions to exhibit the resonant behaviour of the differential cross section. Explicit expressions for the transition amplitudes and the partial widths in terms of expectation values of operators computed with Gamow functions are given.     

Supersymmetry of FRW Barotropic Cosmologies

Barotropic FRW cosmologies are presented from the standpoint of nonrelativistic supersymmetry. First, we reduce the barotropic FRW system of differential equations to simple harmonic oscillator differential equations. Employing the factorization procedure, the solutions of the latter equations are divided into the two classes of bosonic (nonsingular) and fermionic (singular) cosmological solutions. We next introduce a coupling parameter denoted by K between the two classes of solutions and obtain barotropic cosmologies with dissipative features acting on the scale factors and spatial curvature of the universe. The K-extended FRW equations in comoving time are presented in explicit form in the low coupling regime. The standard barotropic FRW cosmologies correspond to the dissipationless limit K = 0.     

An efficient electrophilic N-amination utilizing in situ generated chloramine under phase transfer conditions

An efficient, one-pot, phase transfer N-amination technology was developed. The protocol utilizes chloramine, an inexpensive and safe electrophilic aminating agent potentially viable for commercial manufacturing.