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Many researchers recognize that factor analysis can be conducted on both correlation matrices and variance-covariance matrices. Although most researchers extract factors from non-distribution free or parametric methods, researchers can also extract factors from distribution free or non-parametric methods. The nature of the data dictates the method selected. The purpose of this paper is to differentiate between the questions asked by Pearson product-moment correlations and Spearman's rho coefficients. Additionally, the paper compares distribution free and non-distribution free methods for extracting factors using correlational and covariance matrices, and describes the advantages of each method. (Contains 9 tables and 4 figures.)

Many researchers recognize that factor analysis can be conducted on both correlation matrices and variance-covariance matrices. Although most researchers extract factors from non-distribution free or parametric methods, researchers can also extract factors from distribution free or non-parametric methods. The nature of the data dictates the method selected. The purpose of this paper is to differentiate between the questions asked by Pearson product-moment correlations and Spearman's rho coefficients. Additionally, the paper compares distribution free and non-distribution free methods for extracting factors using correlational and covariance matrices, and describes the advantages of each method. (Contains 9 tables and 4 figures.)

A computer aided dynamic and design sensitivity analysis technique for planar dynamic systems undergoing intermittent motion is developed and applied. Planar dynamic systems made up of multiple rigid bodies connected by joints and force elements are modeled. A constrained dynamic system approach that accounts for discontinuous velocities associated with impulsive loading and impact between bodies is developed. A new numerical integration technique for mixed differential and algebraic equations that automatically defines and integrates for independent generalized coordinates has been developed. It has demonstrated an order of magnitude improvement in computing efficiency compared to preceding techniques. Intermittent motion dynamic effects due to impulsive loading or impact have been incorporated into the dynamic simulation, using a pieced interval dynamic analysis technique in which momentum balance relations are used to determine discontinuities in velocity at logical event times. This technique has been demonstrated on multibody, multiple contact point applications in mechanisms and automatic weapons. To assist in design optimization of mechanical system dynamics an adjoint variable design sensitivity analysis technique has been developed for calculation of first and second order derivatives of dynamic response with respect to design. Numerical calculations have demonstrated that accurate first and second derivatives can be obtained for moderate scale dynamic systems. (Author)

Application of fitting techniques to obtain physical parameters---such as ages, metallicities, and $\alpha$-element to iron ratios---of stellar populations is an important approach to understand the nature of both galaxies and globular clusters (GCs). In fact, fitting methods based on different underlying models may yield different results, and with varying precision. In this paper, we have selected 22 confirmed M31 GCs for which we do not have access to previously known spectroscopic metallicities. Most are located at approximately one degree (in projection) from the galactic center. We performed spectroscopic observations with the 6.5 m MMT telescope, equipped with its Red Channel Spectrograph. Lick/IDS absorption-line indices, radial velocities, ages, and metallicities were derived based on the $\rm EZ\_Ages$ stellar population parameter calculator. We also applied full spectral fitting with the ULySS code to constrain the parameters of our sample star clusters. In addition, we performed $\chi^2_{\rm min}$ fitting of the clusters' Lick/IDS indices with different models, including the Bruzual & Charlot models (adopting Chabrier or Salpeter stellar initial mass functions and 1994 or 2000 Padova stellar evolutionary tracks), the GALEV, and the Thomas et al. models. For comparison, we collected their $UVBRIJK$ photometry from the Revised Bologna Catalogue (v.5) to obtain and fit the GCs' spectral energy distributions (SEDs). Finally, we performed fits using a combination of Lick/IDS indices and SEDs. The latter results are more reliable and the associated error bars become significantly smaller than those resulting from either our Lick/IDS indices-only or our SED-only fits.

Galaxies are arranged in interconnected walls and filaments forming a cosmic web encompassing huge, nearly empty, regions between the structures. Many statistical methods have been proposed in the past in order to describe the galaxy distribution and discriminate the different cosmological models. We present in this paper results relative to the use of new statistical tools using the 3D isotropic undecimated wavelet transform, the 3D ridgelet transform and the 3D beamlet transform. We show that such multiscale methods produce a new way to measure in a coherent and statistically reliable way the degree of clustering, filamentarity, sheetedness, and voidedness of a dataset

In order to promote public education and public safety, equal justice for all, a better informed citizenry, the rule of law, world trade and world peace, this legal document is hereby made available on a noncommercial basis, as it is the right of all humans to know and speak the laws that govern them. (For more information: 12 Tables of Code ) Name of Standards Organization: Bureau of Indian Standards (BIS) Division Name: Water Resources Section Name: Hydrometry (WRD 1) Designator of Legally Binding Document: IS 6339 Title of Legally Binding Document: Methods of analysis of concentration, particle size distribution and specific gravity of sediment in streams and canals Number of Amendments: Equivalence: ISO 4365 Superceding: Superceded by: LEGALLY BINDING DOCUMENT Step Out From the Old to the New --Jawaharlal Nehru Invent a new India using knowledge. --Satyanarayan Gangaram Pitroda