Estimating the number of components of a multicomponent nonstationary signal using the short-term time-frequency Rényi entropy

This article proposes a method for estimating the local number of signals components using the short term Rényi entropy of signals in the time-frequency plane. (Additional details can be found in the comprehensive book on Time-Frequency Signal Analysis and Processing (see http://www.elsevier.com/locate/isbn/0080443354). In addition, the most recent upgrade of the original software package that calculates Time-Frequency Distributions and Instantaneous Frequency estimators can be downloaded from the web site: www.time-frequency.net. This was the first software developed in the field, and it was first released publicly in 1987 at the 1st ISSPA conference held in Brisbane, Australia, and then continuously updated).The time-frequency Rényi entropy provides a measure of complexity of a nonstationary multicomponent signal in the time-frequency plane. When the complexity of a signal corresponds to the number of its components, then this information is measured as the Rényi entropy of the time-frequency distribution (TFD) of the signal. This article presents a solution to the problem of detecting the number of components that are present in short-time interval of the signal TFD, using the short-term Rényi entropy. The method is automatic and it does not require a prior information about the signal. The algorithm is applied on both synthetic and real data, using a quadratic separable kernel TFD. The results confirm that the short-term Rényi entropy can be an effective tool for estimating the local number of components present in the signal. The key aspect of selecting a suitable TFD is also discussed

Synthesis and modeling of new phosphorus-containing acrylates

New methacrylate monomers containing phosphonic acid or both phosphonic and carboxylic acids were synthesized through the reaction of t-butyl alpha-bromomethyl acrylate with triethyl phosphite followed by the selective hydrolysis of the phosphonate or t-butyl ester groups with trimethylsilyl bromide and trifluoroacetic acid. The copolymerization of these monomers with 2-hydroxyethylmethacrylate was investigated with photodifferential scanning calorimetry at 40 degrees C with 2,2 '-dimethoxy-2-phenyl acetophenone as a photoinitiator. Quantum mechanical tools were also used to understand the mechanistic behavior of the polymerization reactions of these synthesized monomers. The propagation and chain-transfer reactions were considered and rationalized. A strong effect of the monomer structure on the rate of polymerization was observed. The polymerization reactivities of the monomers increased with decreasing steric hindrance and/or increasing hydrogen-bonding capacity because of the hydrolysis of the phosphonate and the t-butyl ester groups. (c) 2005 Wiley Periodicals, Inc

Origin of Diastereoselectivity in the Synthesis of Chiral Bicyclic Lactams: π-Facial Selective Attack of Singlet Oxygen Induced by Hindered Internal Rotation

Previously reported experimental results indicate that photooxygenation of homochiral N-(hydroxyalkyl)-2-methylpyrroles with singlet oxygen yields transrather than cis-bicyclic lactams as the major product. In this study, the origin of selectivity in this reaction has been investigated with computational methods. Relative stabilities of homochiral N-(hydroxyalkyl)-2-methylpyrrole conformers and their effect on pi-facial selectivity of O-1(2) were extensively studied. Stepwise and concerted reaction mechanisms, starting from the endoperoxide intermediates, were proposed and modeled in vacuum using the UB3LYP method with the 6-31+G** basis set. Solvent calculations were carried out in CH2Cl2, by means of the integral equation formalism-polarizable continuum model (IEF-PCM) at the UB3LYP/6-31+G** level of theory. Free energies of activation leading to both diastereomers were analyzed in an effort to explain the stereoselectivity and product distribution. Steric interactions among the pyrrole substituents were shown to lead to a rotational barrier higher than 10 kcal/mol. Hence, hindered internal rotation is suggested to cause one pyrrole conformer to be substantially overpopulated. This in turn has a major effect on pi-facial selectivity of O-1(2), thereby favoring one endoperoxide over the other and leading to the diastereoselective synthesis o trans-pyrrolooxazolones. The importance of hindered internal rotors, for an accurate calculation of the frequency factors of a chemical reaction, has already been mentioned in the literature many times; however, in this work hindered internal rotors also seem to dictate the diastereoselective outcome of the reaction