A Study on the Correlation of Bivariate And Trivariate Normal Models

Suppose two or more variables are jointly normally distributed. If there is a common relationship between these variables it would be very important to quantify this relationship by a parameter called the correlation coefficient which measures its strength, and the use of it can develop an equation for predicting, and ultimately draw testable conclusion about the parent population. This research focused on the correlation coefficient ρ for the bivariate and trivariate normal distribution when equal variances and equal covariances are considered. Particularly, we derived the maximum Likelihood Estimators (MLE) of the distribution parameters assuming all of them are unknown, and we studied the properties and asymptotic distribution of . Showing this asymptotic normality, we were able to construct confidence intervals of the correlation coefficient ρ and test hypothesis about ρ. With a series of simulations, the performance of our new estimators were studied and were compared with those estimators that already exist in the literature. The results indicated that the MLE has a better or similar performance than the others.

Empirical correlation of shear wave velocity (Vs) with spt of soils in Madrid

Empirical correlations are usually used as a predictive tool in geotechnical engineering. However, equations calculated for soils very different to the ones to be characterized are frequently used, and so they are not representative of their mechanical properties. This fact, added to the increasing interest of civil engineering in knowing the shear wave velocity (Vs) of the ground, has led to the calculation of different empirical equations to predict the Vs value of the soils of Madrid. In this study this has been achieved by calculating the empirical correlations between the Vs value obtained through the ReMi (Refraction Microtremor) technique and the Standard Penetration Test (500 NSPT values). The empirical correlations proposed are applicable to the whole metropolitan area of Madrid, and have an excellent predictive capability owing to the incorporation of the measurement depth to the equations, which has an important influence in the resistance properties of soils.

La configuración del modelo postconvertibilidad : Políticas y clases. Algunas claves para su caracterización, 2002-2007

El presente artículo se propone realizar un ejercicio de caracterización del modelo de acumulación postconvertibilidad en la Argentina, 2002-2007, analizando sus relaciones con las políticas económicas aplicadas y los cambios en la correlación de fuerzas entre fracciones de clase. En este sentido analizaremos sintéticamente distintas fracciones de clase, tanto dominantes como subalternas, identificando las principales políticas y condiciones estructurales del modelo que las afectan para ver cómo se distribuyen las 'cargas' y 'beneficios' del nuevo modelo. De este modo percibiremos el cambio en la correlación de fuerzas entre fracciones de clase al mismo tiempo que estudiaremos las acciones estatales tendientes a constituir condiciones de compensación y estabilización del modelo a través de un sistema de transferencias de ingresos, que encuentra en el Estado aun actor fundamental

La configuración del modelo postconvertibilidad : Políticas y clases. Algunas claves para su caracterización, 2002-2007

El presente artículo se propone realizar un ejercicio de caracterización del modelo de acumulación postconvertibilidad en la Argentina, 2002-2007, analizando sus relaciones con las políticas económicas aplicadas y los cambios en la correlación de fuerzas entre fracciones de clase. En este sentido analizaremos sintéticamente distintas fracciones de clase, tanto dominantes como subalternas, identificando las principales políticas y condiciones estructurales del modelo que las afectan para ver cómo se distribuyen las 'cargas' y 'beneficios' del nuevo modelo. De este modo percibiremos el cambio en la correlación de fuerzas entre fracciones de clase al mismo tiempo que estudiaremos las acciones estatales tendientes a constituir condiciones de compensación y estabilización del modelo a través de un sistema de transferencias de ingresos, que encuentra en el Estado aun actor fundamental

La configuración del modelo postconvertibilidad : Políticas y clases. Algunas claves para su caracterización, 2002-2007

El presente artículo se propone realizar un ejercicio de caracterización del modelo de acumulación postconvertibilidad en la Argentina, 2002-2007, analizando sus relaciones con las políticas económicas aplicadas y los cambios en la correlación de fuerzas entre fracciones de clase. En este sentido analizaremos sintéticamente distintas fracciones de clase, tanto dominantes como subalternas, identificando las principales políticas y condiciones estructurales del modelo que las afectan para ver cómo se distribuyen las 'cargas' y 'beneficios' del nuevo modelo. De este modo percibiremos el cambio en la correlación de fuerzas entre fracciones de clase al mismo tiempo que estudiaremos las acciones estatales tendientes a constituir condiciones de compensación y estabilización del modelo a través de un sistema de transferencias de ingresos, que encuentra en el Estado aun actor fundamental

Selective double quantum resolved correlation experiment for the complete separation of entire proton NMR spectra of enantiomers

The present study reports a two dimensional NMR experiment which separates single quantum spectra of enantiomers from that of a racemic mixture. This is a blend of selective double quantum refocusing, for resolving couplings and chemical shift interactions along two dimensions followed by correlation of the selectively excited protons to the entire coupled spin network. The concept is solely based on the presence of distinct intra methyl dipolar couplings of different enantiomers when dissolved in chiral orienting media. The analysis of single enantiomer spectrum obtained from respective F-2 cross sections yield all the spectral information. (C) 2011 Elsevier Inc. All rights reserved.

Assignment of the C-13 NMR spectrum by correlation to dipolar coupled proton-pairs and estimation of order parameters of a thiophene based liquid crystal

Materials with widely varying molecular topologies and exhibiting liquid crystalline properties have attracted considerable attention in recent years. C-13 NMR spectroscopy is a convenient method for studying such novel systems. In this approach the assignment of the spectrum is the first step which is a non-trivial problem. Towards this end, we propose here a method that enables the carbon skeleton of the different sub-units of the molecule to be traced unambiguously. The proposed method uses a heteronuclear correlation experiment to detect pairs of nearby carbons with attached protons in the liquid crystalline core through correlation of the carbon chemical shifts to the double-quantum coherences of protons generated through the dipolar coupling between them. Supplemented by experiments that identify non-protonated carbons, the method leads to a complete assignment of the spectrum. We initially apply this method for assigning the C-13 spectrum of the liquid crystal 4-n-pentyl-4'-cyanobiphenyl oriented in the magnetic field. We then utilize the method to assign the aromatic carbon signals of a thiophene based liquid crystal thereby enabling the local order-parameters of the molecule to be estimated and the mutual orientation of the different sub-units to be obtained.

Shape and spatial correlation control of InAs-InAlAs-InP(001) nanostructure superlattices

The control of shape and spatial correlation of InAs-InAlAs-InP(001) nanostructure superlattices has been realized by changing the As overpressure during the molecular-beam epitaxy (MBE) growth of InAs layers. InAs quantum wires (QWRs) are obtained under higher As overpressure (1x10(-5) Torr), while elongated InAs quantum dots (QDs) are formed under lower As overpressure (5x10(-6) or 2.5x10(-6) Torr). Correspondingly, spatial correlation changes from vertical anti-correlation in QWR superlattices to vertical correlation in QD superlattices, which is well explained by the different alloy phase separation in InAlAs spacer layers triggered by the InAs nanostrcutures. It was observed that the alloy phase separation in QD superlattices could extend a long distance along the growth direction, indicating the vertical correlation of QD superlattices can be kept in a wide range of spacer layer thickness.

Three-Particle Coincidence of the Long Range Pseudorapidity Correlation in High Energy Nucleus-Nucleus Collisions

We report the first three-particle coincidence measurement in pseudorapidity (Delta eta) between a high transverse momentum (p(perpendicular to)) trigger particle and two lower p(perpendicular to) associated particles within azimuth |Delta phi| < 0.7 in root s(NN) = 200 GeV d + Au and Au + Au collisions. Charge ordering properties are exploited to separate the jetlike component and the ridge (long range Delta eta correlation). The results indicate that the correlation of ridge particles are uniform not only with respect to the trigger particle but also between themselves event by event in our measured Delta eta. In addition, the production of the ridge appears to be uncorrelated to the presence of the narrow jetlike component.

Study of the rheological behaviour of Sn-Ag-Cu solder pastes and their correlation with printing performance

Solder paste plays an important role in the electronic assembly process by providing electrical, mechanical and thermal bonding between the components and the substrate. The rheological characterisation of pastes is an important step in the design and development of new paste formulations. With the ever increasing trend of miniaturisation of electronic products, the study of the rheological properties of solder pastes is becoming an integral part in the R&D of new paste formulations and in the quality monitoring and control during paste manufacture and electronic assembly process. This research work outlines some of the novel techniques which can be successfully used to investigate the rheology of leadfree solder pastes. The report also presents the results of the correlation of rheological properties with solder paste printing performance. Four different solder paste samples (namely paste P1, P2, P3 and P4) with different flux vehicle systems and particle size distributions were investigated in the study. As expected, all the paste samples showed shear thinning behaviour. Although the samples displayed similar flow behaviour at high shear rates, differences were observed at low shear rates. In the stencil printing trials, round deposits showed better results than rectangular deposits in terms of paste heights and aperture filling. Our results demonstrate a good correlation between higher paste viscosity and good printing performance. The results of the oscillatory and thixotropy tests were also successfully correlated to the printing behaviour of solder paste.

Applying a QSPR correlation to the prediction of surface tensions of ionic liquids

Ionic liquids (ILs) have attracted large amount of interest due to their unique properties. Although large effort has been focused on the investigation of their potential application, characterization of ILs properties and structure–property relationships of ILs are poorly understood. Computer aided molecular design (CAMD) of ionic liquids (ILs) can only be carried if predictive computational methods for the ILs properties are available. The limited availability of experimental data and their quality have been preventing the development of such tools. Based on experimental surface tension data collected from the literature and measured at our laboratory, it is here shown how a quantitative structure–property relationship (QSPR) correlation for parachors can be used along with an estimation method for the densities to predict the surface tensions of ILs. It is shown that a good agreement with literature data is obtained. For circa 40 ionic liquids studied a mean percent deviation (MPD) of 5.75% with a maximum deviation inferior to 16% was observed. A correlation of the surface tensions with the molecular volumes of the ILs was developed for estimation of the surface tensions at room temperature. It is shown that it can describe the experimental data available within a 4.5% deviation. The correlations here developed can thus be used to evaluate the surface tension of ILs for use in process design or in the CAMD of new ionic liquids.

Development of a QSPR correlation for the parachor of 1,3-dialkyl imidazolium based ionic liquids

Ionic liquids have received significant interest from both academia and industry for a wide range of applications which often requires knowledge of their thermophysical properties. Quantitative structure-property relationship correlations and group contribution methods for thermophysical properties of ionic liquids are a basic necessity for the development of computer aided molecular design approaches for these liquids and subsequently offer the potential for designing an ionic liquid having a desirable set of thermophysical properties. However, the limited availability of experimental thermophysical data and their quality have prevented the development of such tools. Based on previously reported experimental surface tension data, a correlation of the parachors with the molar volume of the ionic liquids has been developed. The predicted parachor values have been shown to be in good agreement with the experimental data. A maximum deviation of

A Correlation between the Dynamic Viscosity and Crystallisation of Felodipine from its Amorphous Polymer Solid Dispersion

Purpose Previously, it has been reported that molecular mobility determines the rate of molecular approach to crystal surfaces, while entropy relates to the probability of that approaching molecule having the desirable configuration for further growth of the existing crystal; and the free energy dictates the probability of that molecule not returning to the liquid phase1. If we plot the crystal growth rate and viscosity of a supercooled liquid in a log-log format, the relationship between the two is linear, indicating the influence viscosity has upon crystal growth rate. However, such approximation has been derived from pure drug compounds and it is apparent that further understanding of crystallization from drug-polymer solid dispersion is required in order to stabilise drugs embedded within amorphous polymeric solid dispersions. Methods Mixtures of felodipine and polymer (HPMCAS-HF, PVPK15 and Soluplus®) at specified compositions were prepared using a Restch MM200 ball mill. To examine crystal growth within amorphous solid dispersions, samples were prepared by melting 5-10 mg of ball milled mixture at 150°C for 3-5 minutes on a glass slip pre-cleaned with methanol and acetone. All prepared samples were confirmed to be crystal free by visual observation using a polarised light microscope (Olympus BX50). Prepared samples were stored at 0% RH (P2O5), inside desiccators, maintained in ovens at 80°C. For the dynamic viscosity measurement, approximately 100-200mg ball milled mixture was heated on the base plate of a rotational rheometer at 150°C for 5 minutes and the top plate was lowered to a defined gap to form a good contact with the material. The sandwiched amorphous material was heated to 80°C and the viscosity was measured. Results The equation was used to probe the correlation of viscosity to crystal growth rate. In comparison to the value of xi in log-log equation reported from pure drug compound, a value of 1.63 was obtained for FD-polymer solid dispersions irrespective of the polymer involved. &#8733 Conclusion The high xi value suggests stronger viscosity dependence may exist for amorphous FD once incorporated with amorphous polymer.

Effect of electron correlation on positronium formation in positron-helium scattering

A three-parameter correlated wave function for the helium ground state is used to study the scattering reaction e(+) + He --> He+ + Ps, where Ps stands for positronium atom. An exact analytical expression is constructed for the first Born scattering amplitude for Ps formation from helium. Based on this numerical results are presented for both differential and total cross-sections. It is demonstrated that the inner electronic correlation of the target atom plays a crucial role in explaining the discrepency between theory and experiment.

Correlation between the spectroscopic and structural properties with the occupation of Eu3+ sites in powdered Eu3+-doped LiTaO3 prepared by the Pechini method

In this work we studied the structural and optical properties of lithium tantalate (LiTaO3) powders doped with Eu3+ ions. We have examined the different sites occupied by the rare earth ion through the correlation of the DRX data analyzed with the Rietveld method and some spectroscopic parameters derived from the Eu3+ luminescence. Adirect relation was established between the lattice parameters and the occupation fraction of Eu3+ in each LiTaO3 site. The occupation fraction was set as the relative population of Eu3+ ions for each site obtained by means of the intensity, baricenter, and the spontaneous emission coefficients of the D-5(0)-> F-7(0) transitions. We concluded that the unit cell parameter a presents the same behavior of the Eu3+ occupation fraction in Ta5+ sites as a function of the Eu3+ content in LiTaO3. The same was observed for the variation in Eu3+ occupation fraction in the Li+ site and the unit cell parameter c with the Eu3+ content. (C) 2009 American Institute of Physics. [doi: 10.1063/1.3204967]