Field Effects in Condensed Media on Polarized Absorption

The existence of anisotropic local field perturbation on electronic absorption is proved by non-zero linear dichroism of isotropic chromophores (Mo(CO)₆) in anisotropic environment. Two sources of such effects are possible: a) perturbation of the electronic energy levels in the chromophore by the static electric solvent field (= Stark effect) or, in case of anisotropic polarizable or dipolar molecules, similar effects involving molecular orientation, and b) dielectric effects on the effective radiation field. The latter effect was considered by various models: The Lorentz field model predicts an effect with wrong sign, it also yields too large a magitude if the anisotropy of the field is considered. If no local field correction is made and the anisotropy only operates in the radiation intensity a result more in agreement with experiment is obtained. By using the Onsager-Böttcher model one may take into account specific properties of the absorbing molecule, like anisotropy in α/r³ where α is its polarizability and r its Onsager radius.     

Evaluation of Carbon Rod Atomizer for Routine Analysis of Vanadium in Crude Oil by Atomic Absorption Spectroscopy

Abstract

The Carbon Rod Atomizer (CRA) was evaluated for routine trace analysis of vanadium in crude oil by atomic absorption spectroscopy with a carbon (graphite) tube as a micro-furnace. Two crude oil samples were analyzed, both by standard addition and standard working curve methods, and the results confirmed by analysis with flame atomic absorption spectroscopy using a fuel-rich nitrous oxide-acetylene flame. Because of the relative involatility of vanadium at the temperature of the CRA, quantitative recoveries of vanadium in crude oil occur only when the vanadium content of the sample injected into the CRA does not exceed the limit of about 1 × 10^?8 g. A sensitivity (weight/1% absorption) of 7.0 × 10^?11 g and detection limit (signal-to-root-mean-square-noise equal to two) of 6.9 × 10^?12 are reported.     

Non-empirical calculation of spin-orbit coupling constants for some linear triatomic molecules

Higher-order sum rules of the form , are derived for the rotatory strengths of randomly oriented and oriented molecules. In randomly oriented molecules R ⁽ⁿ⁾ = 0 for one-electron systems when n<5, whereas R ⁽⁰⁾=R ⁽²⁾=R ⁽⁴⁾=0 for many-electron systems. In oriented molecules R ⁽ⁿ⁾=0 for one-electron systems when n<3, whereas R ⁽⁰⁾=R ⁽²⁾=0 for many-electron systems. The remaining non-vanishing R ⁽ⁿ⁾ can all be evaluated as diagonal matrix elements of the ground-state wave-function. The resulting expressions are applied to the one-electron model of Condon, Altar and Eyring, and to the coupled oscillator model of Born, Oseen and Kuhn. It is found that the rotatory strengths of the latter model do not fulfil some of the general sum rules. The reason for this discrepancy is discussed. Finally the implications of the present results for the controversy of one-electron versus coupled oscillator models are discussed, and it is proposed that the non-vanishing moments be used as ‘chirality indices’ for specific ground-state wave-functions.     

Painlevé IV with both Parameters Zero: A Numerical Study

The six Painlevé equations were introduced over a century ago, motivated by rather theoretical considerations. Over the last several decades, these equations and their solutions, known as the Painlevé transcendents, have been found to play an increasingly central role in numerous areas of mathematical physics. Due to extensive dense pole fields in the complex plane, their numerical evaluation remained challenging until the recent introduction of a fast “pole field solver” [ 1 ]. The fourth Painlevé equation has two free parameters in its coefficients, as well as two free initial conditions. The present study applies this new computational tool to the special case when both of its parameters are zero. We confirm existing analytic and asymptotic knowledge about the equation, and also explore solution regimes which have not been described in the previous literature.     

Essential elements in connected k-polymatroids

It is a well-known result of Tutte that, for every element x of a connected matroid M, at least one of the deletion and contraction of x from M is connected. This paper shows that, in a connected k-polymatroid, only two such elements are guaranteed. We show that this bound is sharp and characterize those 2-polymatroids that achieve this minimum. To this end, we define and make use of a generalized parallel connection for k-polymatroids that allows connecting across elements of different ranks. This study of essential elements gives results crucial to finding the unavoidable minors of connected 2-polymatroids, which will appear elsewhere.     

A fuzzy set-based approach to origin–destination matrix estimation in urban traffic networks with imprecise data

An important issue in the management of urban traffic networks is the estimation of origin–destination (O–D) matrices whose entries represent the travel demands of network users. We discuss the challenges of O–D matrix estimation with incomplete, imprecise data. We propose a fuzzy set-based approach that utilises successive linear approximation. The fuzzy sets used have triangular membership functions that are easy to interpret and enable straightforward calibration of the parameters that weight the discrepancy between observed data and those predicted by the proposed approach. The method is potentially useful when prior O–D matrix entry estimates are unavailable or scarce, requiring trip generation information on origin departures and/or destination arrivals, leading to multiple modelling alternatives. The method may also be useful when there is no O–D matrix that can be user-optimally assigned to the network to reproduce observed link counts exactly. The method has been tested on some numerical examples from the literature and the results compare favourably with the results of earlier methods. It has also been successfully used to estimate O–D matrices for a practical urban traffic network in Brazil.     

An Algorithm for Nonlinear,Nonparametric Model Choice and Prediction

We introduce an algorithm which, in the context of nonlinear regression on vector-valued explanatory variables, aims to choose those combinations of vector components that provide best prediction. The algorithm is constructed specifically so that it devotes attention to components that might be of relatively little predictive value by themselves, and so might be ignored by more conventional methodology for model choice, but which, in combination with other difficult-to-find components, can be particularly beneficial for prediction. The design of the algorithm is also motivated by a desire to choose vector components that become redundant once appropriate combinations of other, more relevant components are selected. Our theoretical arguments show these goals are met in the sense that, with probability converging to 1 as sample size increases, the algorithm correctly determines a small, fixed number of variables on which the regression mean, g say, depends, even if dimension diverges to infinity much faster than n. Moreover, the estimated regression mean based on those variables approximates g with an error that, to first order, equals the error which would arise if we were told in advance the correct variables. In this sense, the estimator achieves oracle performance. Our numerical work indicates that the algorithm is suitable for very high dimensional problems, where it keeps computational labor in check by using a novel sequential argument, and also for more conventional prediction problems, where dimension is relatively low.