Measurement of Large Dipolar Couplings of a Liquid Crystal with Terminal Phenyl Rings and Estimation of the Order Parameters

NMR spectroscopy is a powerful means of studying liquid‐crystalline systems at atomic resolutions. Of the many parameters that can provide information on the dynamics and order of the systems, ¹H–¹³C dipolar couplings are an important means of obtaining such information. Depending on the details of the molecular structure and the magnitude of the order parameters, the dipolar couplings can vary over a wide range of values. Thus the method employed to estimate the dipolar couplings should be capable of estimating both large and small dipolar couplings at the same time. For this purpose, we consider here a two‐dimensional NMR experiment that works similar to the insensitive nuclei enhanced by polarization transfer (INEPT) experiment in solution. With the incorporation of a modification proposed earlier for experiments with low radio frequency power, the scheme is observed to enable a wide range of dipolar couplings to be estimated at the same time. We utilized this approach to obtain dipolar couplings in a liquid crystal with phenyl rings attached to either end of the molecule, and estimated its local order parameters.     

Intramolecular Aza‐Diels‐Alder Cyclization of a Dimerized Citral with Anilines Catalyzed by InCl3

A series of aza‐polycyles containing octahydroacridine core were prepared via an intramolecular aza‐Diels‐Alder reaction of a dimerized citral with various aromatic amines. This reaction is efficiently catalyzed by InCl₃ at ambient temperature to afford the corresponding cyclized products in moderate to good yields.     

Studies on oxygen chemical surface exchange and electrical conduction in thin film nanostructured titania at high temperatures and varying oxygen pressure

We report on oxygen surface exchange studies in ～450-nm-thick nanocrystalline titania films with an average grain size of ～13 nm by electrical conductivity relaxation along with the conductivity measurements at varying temperatures and oxygen partial pressures (pO(2)s). By electrochemical impedance spectroscopy technique, the high temperature conductivity was measured in the pO(2) range from ～10(-16) to ～10(-6) Pa at temperatures from 973 to 1223 K and activation energy, ΔE(a), for conduction was estimated as ～3.23 eV at pO(2) ～10(-11) Pa. Under reducing atmosphere (pO(2) < 10(-6) Pa), two distinct n-type conduction regimes were observed and corresponding predominant defects are discussed while, at high pO(2) regime (pO(2) >10(-6) Pa), ionic conduction appears dominant leading to a conductivity plateau. The surface relaxation was observed to have two independent time constants likely originating from microstructural effects. The surface exchange coefficients are measured as ～10(-8)-10(-7) m∕s and ～10(-9)-10(-8) m∕s for each contribution with ΔE(a)s of 2.79 and 1.82 eV, respectively, without much pO(2) dependence across several orders of pO(2) range of ～10(-16)-10(-6) Pa in the temperature range between 973 and 1223 K. The results are of potential relevance to understanding the near-surface chemical phenomena in nanocrystalline titania which is of great interest for energy and environmental studies.     

Finite element study of free surface turbulent flow in rotating channels

Under certain conditions of liquid flow through rotating channels, the Coriolis force can induce a free surface to be formed. This problem is of practical importance in a Coriolis wear tester, which is used for determining the sliding wear coefficient of wear materials in slurry handling equipment. A deforming Galerkin finite element method is presented for predicting two‐dimensional turbulent free surface mean flow in rotating channels. Reynolds‐averaged Navier–Stokes (RANS) equations are cast into weak(algebraic) form using primitive variables (velocity and pressure). Eddy viscosity is determined via a mixing length model. Velocity is interpolated biquadratically, while pressure is interpolated bilinearly. The kinematic condition is used to form the Galerkin residual for the free surface. The free surface is represented by Hermite polynomials of zeroeth order for continuity of position and slope. Combined Newton's iteration is used to simultaneously solve for the free surface and the field variables. Results of velocity and pressure fields, as well as the free surface are shown to converge with mesh‐size refinement. There is excellent respect for mass conservation. Results are presented for various values of Rossby number (Ro) and height‐based Reynolds number (Re_H). Parameter continuation in Ro and Re_H space is used to compute solutions at higher values of flow rate and angular velocity. Copyright © 2002 John Wiley & Sons, Ltd.     

Theorems of the Alternative over Indefinite Inner Product Spaces

In this paper, we study the Farkas alternative over indefinite inner product spaces using the recently proposed indefinite matrix product.     

Principal bundles on the affine line

We prove that any principal bundle on the affine line over a perfect field with a reductive group as structure group comes from the base field by base change.     

Optimal estimation in random coefficient regression models

In linear regression models with random coefficients, the score function usually involves unknown nuisance parameters in the form of weights. Conditioning with respect to the sufficient statistics for the nuisance parameter, when the parameter of interest is held fixed, eliminates the nuisance parameters and is expected to give reasonably good estimating functions. The present paper adopts this approach to the problem of estimation of average slope in random coefficient regression models. Four sampling situations are discussed. Some asymptotic results are also obtained for a model where neither the regressors nor the random regression coefficients replicate. Simulation studies for normal as well as non-normal models show that the performance of the suggested estimating functions is quite satisfactory.