2 resultados para Matrix-Variate Statistical Distributions
em DigitalCommons@University of Nebraska - Lincoln
Resumo:
The reaction of living anionic polymers with 2,2,5,5-tetramethyl-1-(3-bromopropyl)-1-aza-2,5- disilacyclopentane (1) was investigated using coupled thin layer chromatography and matrix-assisted laser desorption/ionization time-of-flight mass spectrometry. Structures of byproducts as well as the major product were determined. The anionic initiator having a protected primary amine functional group, 2,2,5,5-tetramethyl- 1-(3-lithiopropyl)-1-aza-2,5-disilacyclopentane (2), was synthesized using all-glass high-vacuum techniques, which allows the long-term stability of this initiator to be maintained. The use of 2 in the preparation of well-defined aliphatic primary amine R-end-functionalized polystyrene and poly(methyl methacrylate) was investigated. Primary amino R-end-functionalized poly(methyl methacrylate) can be obtained near-quantitatively by reacting 2 with 1,1-diphenylethylene in tetrahydrofuran at room temperature prior to polymerizing methyl methacrylate at -78 °C. When 2 is used to initiate styrene at room temperature in benzene, an additive such as N,N,N',N'- tetramethylethylenediamine is necessary to activate the polymerization. However, although the resulting polymers have narrow molecular weight distributions and well-controlled molecular weights, our mass spectra data suggest that the yield of primary amine α-end-functionalized polystyrene from these syntheses is very low. The majority of the products are methyl α-end-functionalized polystyrene.
Resumo:
We develop spatial statistical models for stream networks that can estimate relationships between a response variable and other covariates, make predictions at unsampled locations, and predict an average or total for a stream or a stream segment. There have been very few attempts to develop valid spatial covariance models that incorporate flow, stream distance, or both. The application of typical spatial autocovariance functions based on Euclidean distance, such as the spherical covariance model, are not valid when using stream distance. In this paper we develop a large class of valid models that incorporate flow and stream distance by using spatial moving averages. These methods integrate a moving average function, or kernel, against a white noise process. By running the moving average function upstream from a location, we develop models that use flow, and by construction they are valid models based on stream distance. We show that with proper weighting, many of the usual spatial models based on Euclidean distance have a counterpart for stream networks. Using sulfate concentrations from an example data set, the Maryland Biological Stream Survey (MBSS), we show that models using flow may be more appropriate than models that only use stream distance. For the MBSS data set, we use restricted maximum likelihood to fit a valid covariance matrix that uses flow and stream distance, and then we use this covariance matrix to estimate fixed effects and make kriging and block kriging predictions.