Thermal and mechanical properties of radiation crosslinked poly(tetrafluoroethylene-co-perfluoromethyl vinyl ether)

The effect of irradiation temperature on the polymer properties was investigated for the fluoroelastomer poly(tetrafluoroethylene-co-perfluoromethylvinyl ether) (TFE/PMVE). TFE/PMVE samples were γ-irradiated to 150 kGy at temperatures ranging from 77 K to 373 K. Analysis of the sol/gel behaviour, tensile properties, and glass transition temperatures indicated that crosslinking commenced in the temperature range 195 to 263 K, for a dose of 150 kGy. The latter temperature was 13 K below the glass transition temperature. Crosslinking remained relatively constant to higher temperatures. Chain scission reactions were found to occur well below the glass transition temperature and increased at higher temperatures. The optimum temperature for the radiation crosslinking of TFE/PMVE, for the temperatures investigated, was 263 K.     

1,3-Dipolar cycloaddition approach to isoxazole, isoxazoline and isoxazolidine analogues of C-nucleosides related to pseudouridine

Isoxazole, isoxazoline and isoxazolidine analogues of C-nucleosides related to pseudouridine have been synthesized by 1,3-dipolar cycloaddition reactions of nitrile oxides and nitrones derived from mono and disubstituted uracil-5-carbaldehydes and 2,4-dimethoxypyrimidine-5-carbaldehyde. The dimethoxy derivatives have been easily deprotected to the corresponding uracils bearing the heterocyclic ring instead of a sugar moiety. The regio and stereoselectivity of the reactions are discussed.     

Eigenfunction expansions for infinite dimensional Ornstein-Uhlenbeck processes

Summary We give a general construction of infinite dimensional Ornstein-Uhlenbeck processes. We present expansions of these processes based on the expansion of the covariance operators in generalized eigenfunctions, and we answer positively some question left open by J.B. Walsh on properties of the hitting times of these processes.Partially supported by NSF-Grant MCS 8202045     

Kinematic-wave analysis of particle settling in tube centrifuges

The kinematic-wave theory of particle settling in tube centrifuges is subject to controversy. G. Anestis and W. Schneider [1] made the common assumption that the flow in a rotating tube of large length/diameter ratio can be treated in one-dimensional approximation. Their results have been found in agreement with measurements [2], [3]. However, M. Ungarish [4] performed an analysis of the two-dimensional settling process in the limit of vanishing particle concentration and obtained results that are not in accord with the one-dimensional flow approximation, irrespective of the length/diameter ratio. It is the aim of the present investigation to gain a better understanding of the process. According to this analysis, quasi-one-dimensional kinematic waves are embedded in a two-dimensional bulk flow that is governed by the boundary conditions at the walls of the tube. The results are compared with those of the one-dimensional flow approximation. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Wavelet-Based Estimation for Univariate Stable Laws

Stable distributions are characterized by four parameters which can be estimated via a number of methods, and although approximate maximum likelihood estimation techniques have been proposed, they are computationally intensive and difficult to implement. This article describes a fast, wavelet-based, regression-type method for estimating the parameters of a stable distribution. Fourier domain representations, combined with a wavelet multiresolution approach, are shown to be effective and highly efficient tools for inference in stable law families. Our procedures are illustrated and compared with other estimation methods using simulated data, and an application to a real data example is explored. One novel aspect of this work is that here wavelets are being used to solve a parametric problem, rather than a nonparametric one, which is the more typical context in wavelet applications.     

Variable Selection in Varying-Coefficient Models Using P-Splines

In this article, we consider nonparametric smoothing and variable selection in varying-coefficient models. Varying-coefficient models are commonly used for analyzing the time-dependent effects of covariates on responses measured repeatedly (such as longitudinal data). We present the P-spline estimator in this context and show its estimation consistency for a diverging number of knots (or B-spline basis functions). The combination of P-splines with nonnegative garrote (which is a variable selection method) leads to good estimation and variable selection. Moreover, we consider APSO (additive P-spline selection operator), which combines a P-spline penalty with a regularization penalty, and show its estimation and variable selection consistency. The methods are illustrated with a simulation study and real-data examples. The proofs of the theoretical results as well as one of the real-data examples are provided in the online supplementary materials.     

A penalty method for nonparametric estimation of the intensity function of a counting process

Nonparametric estimators are proposed for the logarithm of the intensity function of some univariate counting processes. An Aalen multiplicative intensity model is specified for our counting process and the estimators are derived by a penalized maximum likelihood method similar to the method introduced by Silverman for probability density estimation. Asymptotic properties of the estimators, such as uniform consistency and normality, are investigated and some illustrative examples from survival theory are analyzed.This work was conducted while the author was visiting the Department of Mathematics, University of California at Irvine.