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A Class of Starlike Functions Defined by the Dziok-Srivastava Operator
Silverman, Herb,Murugusundaramoorhty, Gangadharan,Vijaya, Kaliappan Department of Mathematics 2009 Kyungpook mathematical journal Vol.49 No.1
A comprehensive class of starlike univalent functions defined by Dziok-Srivastava operator is introduced. Necessary and sufficient coefficient bounds are given for functions in this class to be starlike. Further distortion bounds, extreme points and results on partial sums are investigated.
EMPIRICAL BAYES THRESHOLDING: ADAPTING TO SPARSITY WHEN IT ADVANTAGEOUS TO DO SO
Silverman Bernard W. The Korean Statistical Society 2007 Journal of the Korean Statistical Society Vol.36 No.1
Suppose one is trying to estimate a high dimensional vector of parameters from a series of one observation per parameter. Often, it is possible to take advantage of sparsity in the parameters by thresholding the data in an appropriate way. A marginal maximum likelihood approach, within a suitable Bayesian structure, has excellent properties. For very sparse signals, the procedure chooses a large threshold and takes advantage of the sparsity, while for signals where there are many non-zero values, the method does not perform excessive smoothing. The scope of the method is reviewed and demonstrated, and various theoretical, practical and computational issues are discussed, in particularly exploring the wide potential and applicability of the general approach, and the way it can be used within more complex thresholding problems such as curve estimation using wavelets.
Michael J. Silverman 한국음악치료학회 2015 한국음악치료학회지 Vol.17 No.2
The purpose of this study was to determine the effects of educational music therapy on knowledge of triggers and coping skills, motivation, and treatment eagerness in patients on a detoxification unit. Participants were cluster randomized to one of three treatment conditions: educational music therapy, education without music, or recreational music therapy. Participants (N=58) completed brief pre- and posttests to assess knowledge of triggers and coping skills, motivation, and treatment eagerness. Educational music therapy participants were involved in a highly structured group songwriting intervention wherein first verse lyrics concerned triggers for using substances and second verse lyrics concerned positive coping skills. Between-group results were not significant for knowledge of triggers for using substances, coping skills, or treatment eagerness. Regardless of treatment condition, there were significant increases from pre- to posttest on perceptions of motivation to reach and maintain sobriety and treatment eagerness. Concerning motivation for reaching and maintaining sobriety, there was a statistically significant posttest between-group difference: Participants in the educational music therapy condition had significantly higher motivation than participants in education without music or recreational music therapy conditions. Highly structured songwriting interventions concerning triggers for using substances and coping skills may be an engaging and effective way to educate and motivate patients in detoxification and other short-term substance abuse rehabilitation settings. Limitations, implications for clinical practice, and suggestions for future research are provided.