Smoothed cross-validation

Summary For bandwidth selection of a kernel density estimator, a generalization of the widely studied least squares cross-validation method is considered. The essential idea is to do a particular type of presmoothing of the data. This is seen to be essentially the same as using the smoothed bootstrap estimate of the mean integrated squared error. Analysis reveals that a rather large amount of presmoothing yields excellent asymptotic performance. The rate of convergence to the optimum is known to be best possible under a wide range of smoothness conditions. The method is more appealing than other selectors with this property, because its motivation is not heavily dependent on precise asymptotic analysis, and because its form is simple and intuitive. Theory is also given for choice of the amount of presmoothing, and this is used to derive a data-based method for this choice.Research of the second author was done while on leave from the University of North Carolina. That of both the second and third was partially supported by National Science Foundation Grants DMS-8701201 and DMS-8902973     

Infrared Spectra of the Square Planar Rhodium(I) Complexes cis-[Rh(CO)2(pyridine) (X)] (X = Cl,Br): Isotopic Labelling Studies and Normal Coordinate Analysis

Abstract

The infrared spectra (4000 - 50 cm^?1) of the square planar rhodium(I) complexes cis-[Rh(CO)₂ (pyridine) (X)] (X = Cl, Br) and their isotopomers with pyridine-d ₅ and ¹³CO have been determined. Assignments are based on earlier studies on pyridine and its complexes and on the shifts in infrared bands which are caused by the isotopic substitutions employed. Normal coordinate analysis following the procedure of Becher and Mattes has been used to confirm the empirical assignments. The two v(RhC) bands are observed near 490 and 450 cm^?1. v(RhN) is found near 210 cm^?1 and v(RhX) occurs at 310 (X = Cl) and 235 (X = Br) cm^?1. At frequencies below 200 cm^?1, the bands are assigned to bending modes in the following sequence: δ (RhN) > δ (CRhC) > δ (RhCl) > γ (RhCl) > γ (RhN).     

Computing inertia sets using atoms

We consider the problem of computing inertia sets for graphs. By using tools for combining the inertia sets of smaller graphs we can reduce this problem to understanding the inertia sets for three-connected graphs that are not joins. We term such graphs atoms and give the inertia sets for all atoms on at most seven vertices. This can be used to compute the inertia sets for all graphs on at most seven vertices.     

Relaxation mechanisms of the Zeeman sublevels of the phosphorescent triplet state of pyrazine at 1·6K

The observed change in the phosphorescence decay of the spin-aligned triplet state of pyrazine at 1·6K upon application of a magnetic field is examined both experimentally and theoretically. Experimentally, the decay curve is resolved into the three decay components of the three triplet sublevels in the field range of 0–6000 G. Both the decay constants and the fraction of total initial intensity of each decay component are determined for each field strength. Theoretically, the observed change in the decay characteristics is assumed to be solely due to the Zeeman mixing of the zero-field levels in the absence of spin-lattice relaxation processes. This has the effect of distributing the radiative strength of the strongly radiative zero-field level among the other two weakly radiative zero field levels. A simple approximate calculation gives excellent and encouraging agreement with experimental quantities in the range of validity of the approximations made (below 1000 G). A rigorous calculation was then performed using the exact solution of the secular equation resulting from the Hamiltonian including the spin-spin and Zeeman interactions. Due to the difficulty in finding a host of known crystal structure in which pyrazine can dissolve substitutionally and uniquely, the comparison between theory and experiment is made using a polycrystalline sample. A special averaging procedure is used in calculating a theoretical decay curve for each magnetic field strength used. The theoretical decay curve is then decomposed into three components employing the same computer programme used for decomposing the experimental decay curve. The agreement between the observed and the more rigorous calculated decay quantities is excellent up to 2000 G, but observed disagreement appears above 3000 G and increases with field strength. The calculated lifetimes above 3000 G are found to be longer than the observed ones. The difference is due to other relaxation mechanisms at these high fields, for example, in spin-lattice relaxation processes between the Zeeman sublevels of the lowest triplet state.     

Phase Space Bounds for Quantum Mechanics on a Compact Lie Group

Let K be a compact, connected Lie group and its complexification. I consider the Hilbert space of holomorphic functions introduced in [H1], where the parameter t is to be interpreted as Planck's constant. In light of [L-S], the complex group may be identified canonically with the cotangent bundle of K. Using this identification I associate to each a “phase space probability density”. The main result of this paper is Theorem 1, which provides an upper bound on this density which holds uniformly over all F and all points in phase space. Specifically, the phase space probability density is at most , where and a _t is a constant which tends to one exponentially fast as t tends to zero. At least for small t, this bound cannot be significantly improved. With t regarded as Planck's constant, the quantity is precisely what is expected on physical grounds. Theorem 1 should be interpreted as a form of the Heisenberg uncertainty principle for K, that is, a limit on the concentration of states in phase space. The theorem supports the interpretation of the Hilbert space as the phase space representation of quantum mechanics for a particle with configuration space K. The phase space bound is deduced from very sharp pointwise bounds on functions in (Theorem 2). The proofs rely on precise calculations involving the heat kernel on K and the heat kernel on . Received: 9 July 1996/Accepted: 9 September 1996     

Reactive ligand influence on initiation in phenylene catalyst‐transfer polymerization

Synthesizing conjugated polymers via catalyst‐transfer polymerization (CTP) has led to unprecedented control over polymer sequence and molecular weight. Yet many challenges remain, including broadening the monomer scope and narrowing the molecular weight dispersities. Broad polymer dispersities can arise from nonliving pathways as well as slow initiation. Previously, slow initiation was observed in Ni‐mediated CTP of phenylene monomers. Although precatalysts with faster initiation rates have been reported, the rates still do not exceed propagation. Herein a second‐ and third‐generation of reactive ligands are described, along with a simple method for measuring initiation rates. A precatalyst with an initiation rate that exceeds propagation is now reported, however, the resulting polymer samples still exhibit broad dispersities, suggesting that slow initiation is not the most significant contributing factor in Ni‐mediated phenylene polymerizations. In addition, initiation rates measured under authentic polymerization conditions revealed that both exogenous triphenylphosphine and an ortho‐trifluoroethoxy substituent on the reactive ligand have a strong influence. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 1530–1535     

Synthesis,characterization and energetic properties of novel 1-methyl-1,2,4-triazolium N-aryl/N-pyridinyl ylids

Synthesis, characterization and energetic properties of novel, nitrogen-rich 1-methyl-1,2,4-triazolium N-aryl/N-pyridinyl ylids 3a–m are reported.     

Rounding the expanded uncertainty

Accreditation and Quality Assurance - When reporting expanded uncertainty, rounding the number of significant figures can affect the associated level of confidence. A simple numerical method is...     

Language specificity in the perception of voiceless sibilant fricatives in Japanese and English: implications for cross-language differences in speech-sound development

Both English and Japanese have two voiceless sibilant fricatives, an anterior fricative /s/ contrasting with a more posterior fricative /∫/. When children acquire sibilant fricatives, English children typically substitute [s] for /∫/, whereas Japanese children typically substitute [∫] for /s/. This study examined English- and Japanese-speaking adults' perception of children's productions of voiceless sibilant fricatives to investigate whether the apparent asymmetry in the acquisition of voiceless sibilant fricatives reported previously in the two languages was due in part to how adults perceive children's speech. The results of this study show that adult speakers of English and Japanese weighed acoustic parameters differently when identifying fricatives produced by children and that these differences explain, in part, the apparent cross-language asymmetry in fricative acquisition. This study shows that generalizations about universal and language-specific patterns in speech-sound development cannot be determined without considering all sources of variation including speech perception.