Conditional independence models for seemingly unrelated regressions with incomplete data

We consider normal ≡ Gaussian seemingly unrelated regressions (SUR) with incomplete data (ID). Imposing a natural minimal set of conditional independence constraints, we find a restricted SUR/ID model whose likelihood function and parameter space factor into the product of the likelihood functions and the parameter spaces of standard complete data multivariate analysis of variance models. Hence, the restricted model has a unimodal likelihood and permits explicit likelihood inference. In the development of our methodology, we review and extend existing results for complete data SUR models and the multivariate ID problem.     

Dependence of the H2-H2 Interaction on the Monomer Bond Lengths: Steps Toward an Accurate ab initio Estimate

We compute the vibrational coupling between two H₂ molecules from ab initio quantum chemical calculations of the H₂-H₂ potential carried out at the full configuration interaction level of theory using the atom-centered aug-cc-pVTZ basis set for hydrogen. We compare the full configuration interaction results with those obtained using two variants of coupled cluster theory and find that a fully iterative treatment of connected triples may be required to estimate the H₂-H₂ vibrational coupling accurately using coupled cluster theory.     

Influence of Azimuthal Structure of Surface Waves on Efficiency of their Excitation by Tubular Electron Beams

The excitation of eigen surface waves by tubular electron beams in cylindrical discharge devices is studied. The influence of the wave‐field azimuthal structure on the excitation efficiency and nonlinear stage of the plasmabeam instability is investigated both numerically and analytically. Analytical expressions for the saturation amplitude and excitation efficiency of the wave under study are derived. They are found to agree well with results obtained by numerical modelling of the plasma‐beam interaction presented in this paper. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Method of lines with boundary elements for 1‐D transient diffusion‐reaction problems

Time‐dependent differential equations can be solved using the concept of method of lines (MOL) together with the boundary element (BE) representation for the spatial linear part of the equation. The BE method alleviates the need for spatial discretization and casts the problem in an integral format. Hence errors associated with the numerical approximation of the spatial derivatives are totally eliminated. An element level local cubic approximation is used for the variable at each time step to facilitate the time marching and the nonlinear terms are represented in a semi‐implicit manner by a local linearization at each time step. The accuracy of the method has been illustrated on a number of test problems of engineering significance. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2006     

Roles of SiH4 and SiF4 in growth and structural changes of poly-Si films

The structural properties of polycrystalline silicon films, prepared by plasma enhanced chemical vapor deposition system, with different flow rates of SiH₄/SiF₄ mixtures at 300 °C were investigated. This study indicates that the low hydrogen coverage on the growing surface, under optimum fluorine radicals, will be leaded to an improvement of crystallized area as compared with case of high hydrogen coverage surface. Moreover, the studies of the role of SiH₄ and SiF₄ radicals show that the SiH₄ radicals are important in the nucleation and growth of grains. However, SiF₄ radicals are effective in the structural change of grain boundaries regions and by this way, in the present system, establish the growth of grains under the dominant 〈1 1 0〉 direction. The stress investigation indicates that addition of high flow rate of SiF₄ in amorphous film, results in the nearly stress free films. Finally, we found that the changes in g-value reflect the changes in the intrinsic compressive and tensile stress in the both polycrystalline and amorphous silicon films.     

Sequential Importance Sampling Algorithms for Dynamic Stochastic Programming

This paper gives a comprehensive treatment of EVPI-based sequential importance sampling algorithms for dynamic (multistage) stochastic programming problems. Both theory and computational algorithms are discussed. Under general assumptions it is shown that both an expected value of perfect information (EVPI) process and the corresponding marginal EVPI process (the supremum norm of the conditional expectation of its generalized derivative) are nonanticipative nonnegative supermartingales. These processes are used as importance criteria in the class of sampling algorithms treated in the paper. When their values are negligible at a node of the current sample problem scenario tree, scenarios descending from the node are replaced by a single scenario at the next iteration. On the other hand, high values lead to increasing the number of scenarios descending from the node. Both the small sample and asymptotic properties of the sample problem estimates arising from the algorithms are established, and the former are evaluated numerically in the context of a financial planning problem. Finally, current and future research is described. Bibliography: 49 titles. __________ Published in Zapiski Nauchnykh Seminarov POMI, Vol. 312, 2004, pp. 94–129.     

Periodic Integrable Systems with Delta-Potentials

In this paper we study root system generalizations of the quantum Bose-gas on the circle with pair-wise delta-function interactions. The underlying symmetry structures are shown to be governed by the associated graded algebra of Cherednik's (suitably filtered) degenerate double affine Hecke algebra, acting by Dunkl-type differential-reflection operators. We use Gutkin's generalization of the equivalence between the impenetrable Bose-gas and the free Fermi-gas to derive the Bethe ansatz equations and the Bethe ansatz eigenfunctions.     

Chaos and hyperchaos in a gyrotron

We study oscillation in a gyrotron with allowance for reflections from an output horn. Regions with different system behaviors, such as stationary oscillation, self-modulation, and complex-dynamics regimes are found in the parameter plane. The scenarios of appearance of chaotic oscillations are considered. It is shown that they can emerge via either a sequence of period-doubling bifurcations or destruction of quasiperiodic motion. For chaotic attractors, Lyapunov exponents are calculated and their dimensions are estimated on the basis of the Kaplan-Yorke formula. The dimension values turn out to be anomalously large, which is stipulated by the presence of a large number of high-Q eigenmodes in the gyrotron cavity due to operation near the cutoff frequency of an electrodynamic system. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 10, pp. 887–899, October 2006.