Basis set and electron correlation effects on initial convergence for vibrational nonlinear optical properties of conjugated organic molecules

The level of ab initio theory which is necessary to compute reliable values for the static and dynamic (hyper)polarizabilities of three medium size π-conjugated organic nonlinear optical (NLO) molecules is investigated. With the employment of field-induced coordinates in combination with a finite field procedure, the calculations were made possible. It is stated that to obtain reasonable values for the various individual contributions to the (hyper)polarizability, it is necessary to include electron correlation. Based on the results, the convergence of the usual perturbation treatment for vibrational anharmonicity was examined

Impact of antenna correlation on the capacity of multiantenna channels

This paper applies random matrix theory to obtain analytical characterizations of the capacity of correlated multiantenna channels. The analysis is not restricted to the popular separable correlation model, but rather it embraces a more general representation that subsumesmost of the channel models that have been treated in the literature. For arbitrary signal-to-noise ratios (SNR), the characterization is conducted in the regime of large numbers of antennas. For the low- and high-SNR regions, in turn, we uncover compact capacity expansions that are valid for arbitrary numbers of antennas and that shed insight on how antenna correlation impacts the tradeoffs between power, bandwidth and rate.

The algebraic equality of two asymptotic tests for the hypothesis that a normal distribution has a specified correlation matrix

It is proved the algebraic equality between Jennrich's (1970) asymptotic$X^2$ test for equality of correlation matrices, and a Wald test statisticderived from Neudecker and Wesselman's (1990) expression of theasymptoticvariance matrix of the sample correlation matrix.

Illusory correlation in the remuneration of chief executive officers: It pays to play golf, and well

Illusory correlation refers to the use of information in decisions that is uncorrelated with the relevantcriterion. We document illusory correlation in CEO compensation decisions by demonstrating thatinformation, that is uncorrelated with corporate performance, is related to CEO compensation. We usepublicly available data from the USA for the years 1998, 2000, 2002, and 2004 to examine the relationsbetween golf handicaps of CEOs and corporate performance, on the one hand, and CEO compensationand golf handicaps, on the other hand. Although we find no relation between handicap and corporateperformance, we do find a relation between handicap and CEO compensation. In short, golfers earnmore than non-golfers and pay increases with golfing ability. We relate these findings to the difficultiesof judging compensation for CEOs. To overcome this and possibly other illusory correlations inthese kinds of decisions, we recommend the use of explicit, mechanical decision rules.

Generalized canonical correlation analysis of matrices with different row and column orders

A Method is offered that makes it possible to apply generalized canonicalcorrelations analysis (CANCOR) to two or more matrices of different row and column order. The new method optimizes the generalized canonical correlationanalysis objective by considering only the observed values. This is achieved byemploying selection matrices. We present and discuss fit measures to assessthe quality of the solutions. In a simulation study we assess the performance of our new method and compare it to an existing procedure called GENCOM,proposed by Green and Carroll. We find that our new method outperforms the GENCOM algorithm both with respect to model fit and recovery of the truestructure. Moreover, as our new method does not require any type of iteration itis easier to implement and requires less computation. We illustrate the methodby means of an example concerning the relative positions of the political parties inthe Netherlands based on provincial data.

Exact tests for correlation and for the slope in simple linear regressions without making assumptions

We present an exact test for whether two random variables that have known bounds on their support are negatively correlated. The alternative hypothesis is that they are not negatively correlated. No assumptions are made on the underlying distributions. We show by example that the Spearman rank correlation test as the competing exact test of correlation in nonparametric settings rests on an additional assumption on the data generating process without which it is not valid as a test for correlation.We then show how to test for the significance of the slope in a linear regression analysis that invovles a single independent variable and where outcomes of the dependent variable belong to a known bounded set.

Exploiting fitness distance correlation of set covering problems

The set covering problem is an NP-hard combinatorial optimization problemthat arises in applications ranging from crew scheduling in airlines todriver scheduling in public mass transport. In this paper we analyze searchspace characteristics of a widely used set of benchmark instances throughan analysis of the fitness-distance correlation. This analysis shows thatthere exist several classes of set covering instances that have a largelydifferent behavior. For instances with high fitness distance correlation,we propose new ways of generating core problems and analyze the performanceof algorithms exploiting these core problems.

Systematic study of the static electrical properties of the CO molecule: influence of the basis set size and correlation energy

The influence of the basis set size and the correlation energy in the static electrical properties of the CO molecule is assessed. In particular, we have studied both the nuclear relaxation and the vibrational contributions to the static molecular electrical properties, the vibrational Stark effect (VSE) and the vibrational intensity effect (VIE). From a mathematical point of view, when a static and uniform electric field is applied to a molecule, the energy of this system can be expressed in terms of a double power series with respect to the bond length and to the field strength. From the power series expansion of the potential energy, field-dependent expressions for the equilibrium geometry, for the potential energy and for the force constant are obtained. The nuclear relaxation and vibrational contributions to the molecular electrical properties are analyzed in terms of the derivatives of the electronic molecular properties. In general, the results presented show that accurate inclusion of the correlation energy and large basis sets are needed to calculate the molecular electrical properties and their derivatives with respect to either nuclear displacements or/and field strength. With respect to experimental data, the calculated power series coefficients are overestimated by the SCF, CISD, and QCISD methods. On the contrary, perturbation methods (MP2 and MP4) tend to underestimate them. In average and using the 6-311 + G(3df) basis set and for the CO molecule, the nuclear relaxation and the vibrational contributions to the molecular electrical properties amount to 11.7%, 3.3%, and 69.7% of the purely electronic μ, α, and β values, respectively

Use of NIR spectroscopy and multivariate process spectra calibration methodology for pharmaceutical solid samples analysis

Accomplish high quality of final products in pharmaceutical industry is a challenge that requires the control and supervision of all the manufacturing steps. This request created the necessity of developing fast and accurate analytical methods. Near infrared spectroscopy together with chemometrics, fulfill this growing demand. The high speed providing relevant information and the versatility of its application to different types of samples lead these combined techniques as one of the most appropriated. This study is focused on the development of a calibration model able to determine amounts of API from industrial granulates using NIR, chemometrics and process spectra methodology.