Application of a generalized residual model to frequency domain modal parameter estimation

Residuals have long been used in frequency domain parameter estimation methods to model the influence of out-of-band modes but, typically, as a fixed set of no more than two or three terms. Recently, a systematic approach to the use of residual polynomials has led to the development of a generalized residual model. The use of a generalized residual model with rational fraction polynomial frequency domain parameter estimation methods allows the contribution of out-of-band modes to be included without increasing the model order and creating additional computational poles. Of particular interest is the use of the generalized residual for single-degree-of-freedom (s.d.o.f.) techniques, which generally do not consider the residual effects and suffer accordingly. With the use of generalized residuals, it becomes possible to properly account for nearby modes and also extract accurate residues with an s.d.o.f. algorithm. The development of the generalized residual polynomial model is outlined and a new s.d.o.f. frequency domain algorithm with generalized residuals is developed.     

The decay of theτ lepton to six pions

We present the branching ratio predictions of an isospin statistical model forτ decays to four, five and six pions. Limits on the branching ratios of the three possible six pionτ decay modes using the Conserved Vector Current (CVC) Hypothesis and thee ⁺ e ^?→6π cross section data are also presented. We find that the isospin model prediction is in good agreement with the well-measured four pion decay modes and consistent with the five pion decay modes. However, we find that some of the recent six pionτ measurements do not agree with the isospin model and the CVC prediction.     

Enzymatic synthesis of 7-deoxy-N-acetylneuraminic acid and 7-O-methyl-N-acetylneuraminic acid

7-Deoxy-N-acetylneuraminic Acid and 7-O-methyl-N-acetylneuraminic acid were synthesized through the sialic acid aldolase-catalyzed aldol addition reactions of 4-deoxy-N-acetyl-D-mannosamine and 4-O-methyl-N-acetyl-D-mannosamine, respectively, with pyruvate. The obtained sialic acids will be used as probes for the investigation of the unusual mechanism of a novel sialidase from leech.     

The foam analogy: from phases to elasticity

By mapping the interactions of colloidal particles onto the problem of minimizing areas, the physics of foams can be used to understand the phase diagrams of both charged and fuzzy colloids. We extend this analogy to study the elastic properties of such colloidal crystals and consider the face-centered cubic, body-centered cubic and A15 lattices. We discuss two types of soft interparticle potentials corresponding to charged and fuzzy colloids, respectively, and we analyze the dependence of the elastic constants on density as well as on the parameters of the potential. We show that the bulk moduli of the three lattices are generally quite similar, and that the shear moduli of the two non-close-packed lattices are considerably smaller than in the face-centered cubic lattice. We find that in charged colloids, the elastic constants are the largest at a finite screening length, and we discuss a shear instability of the A15 lattice.     

Anomalous grazing incidence small-angle x-ray scattering studies of platinum nanoparticles formed by cluster deposition

The size evolution of platinum nanoparticles formed on a SiO2/Si(111) substrate as a function of the level of surface coverage with deposited clusters has been investigated. The anisotropic shapes of sub-nanometer-size nanoparticles are changed to isotropic on the amorphous substrate as their sizes increased. Using anomalous grazing incidence small-angle x-ray scattering (AGISAXS), the scattering from nanoparticles on the surface of a substrate is well separated from that of surface roughness and fluorescence. We show that AGISAXS is a very effective method to subtract the background and can provide unbiased information about particle sizes of less than 1 nm.     

Gas chromatographic optimization studies on the side chain and ring regioisomers of methylenedioxymethamphetamine

Gas chromatographic (GC) optimization studies are conducted for the 10 methylenedioxyphenethylamine regioisomeric substances related to the drug of abuse 3,4-methylenedioxymethamphetamine (MDMA, Ecstasy). These 10 compounds, having the same molecular weight and equivalent major mass spectral fragments, are not completely resolved using typical GC-mass spectrometry screening methods for illicit drugs. MDMA coelutes with at least one nondrug regioisomer under standard drug screening conditions. Separation of the 10 regioisomers is studied using stationary phases of varying polarities. Resolution optimization shows that very slow program rates give the best separation for the nonpolar stationary phases, requiring analysis times of as much as 85 min. Narrow-bore columns containing the same nonpolar stationary phases improve the analysis time to approximately 29 min. The polar stationary phase DB-35MS allows high-temperature programming rates, yielding complete resolution of all 10 compounds in less than 7 min. Temperature program optimization studies on the DB-35MS phase allow the separation time to be reduced to approximately 4.5 min.     

Exotic differentiable structures and general relativity

We review recent developments in differential topology with special concern for their possible significance to physical theories, especially general relativity. In particular we are concerned here with the discovery of the existence of non-standard (fake or exotic) differentiable structures on topologically simple manifolds such asS ⁷, ⁴ andS ³ X ¹. Because of the technical difficulties involved in the smooth case, we begin with an easily understood toy example looking at the role which the choice of complex structures plays in the formulation of two-dimensional vacuum electrostatics. We then briefly review the mathematical formalisms involved with differentiable structures on topological manifolds, diffeomorphisms and their significance for physics. We summarize the important work of Milnor, Freedman, Donaldson, and others in developing exotic differentiable structures on well known topological manifolds. Finally, we discuss some of the geometric implications of these results and propose some conjectures on possible physical implications of these new manifolds which have never before been considered as physical models.