Admissible slopes for monotone and convex interpolation

Summary In many applications, interpolation of experimental data exhibiting some geometric property such as nonnegativity, monotonicity or convexity is unacceptable unless the interpolant reflects these characteristics. This paper identifies admissible slopes at data points of variousC ¹ interpolants which ensure a desirable shape. We discuss this question, in turn for the following function classes commonly used for shape preserving interpolations: monotone polynomials,C ¹ monotone piecewise polynomials, convex polynomials, parametric cubic curves and rational functions.     

Eigenvalues of Hermite and Laguerre ensembles: large beta asymptotics

In this paper we examine the zero and first order eigenvalue fluctuations for the β-Hermite and β-Laguerre ensembles, using tridiagonal matrix models, in the limit as β→∞. We prove that the fluctuations are described by multivariate Gaussians of covariance O(1/β), centered at the roots of a corresponding Hermite (Laguerre) polynomial. The covariance matrix itself is expressed as combinations of Hermite or Laguerre polynomials respectively.We show that the approximations are of real value even for small β; we can use them to approximate the true functions even for the traditional β=1,2,4 values.     

Optical characteristics of a transverse volume discharge in a helium-hydrogen chloride mixture

The emission characteristics of a transverse volume discharge in a He: HCl = 10: 1 mixture at a total pressure of 1–8 kPa were investigated. The plasma volume was 18 × 2.2 × 1 cm³, the interelectrode distance was d=2.2 cm, and the charging voltage of the main storage capacitor was 5–10 kV. The emission characteristics of the discharge were studied in the spectral range of 500–1000 nm. This type of discharge can be used in pulsed dry-etching plasmochemical reactors. The density of atomic chlorine radicals in the plasma was optimized in terms of the pressure of the initial working He-HCl mixture by measuring the relative radiation intensity of the Cl 837(5)-nm spectral line. The density of molecular radicals can be monitored indirectly by recording radiation from the excited chlorine-free decomposition products of HCl molecules (the H_α 656-nm line).     

Broadband emission spectrum of a continuous plasma jet in a mixture of noble gases with SF6 molecules

A broad band in the visible emission spectrum of a continuous Ar/Kr/SF₆ plasma jet is detected at a distance l>75 mm from the plasmatron nozzle. Experimental dependences of the maximum emission intensity on the parameters of the plasma source are presented.     

Optical characteristics of laser-produced antimony plasma

The processes occurring in expanding laser-produced antimony plasma are investigated by the emission spectroscopy method. The plasma expansion velocity, the recombination time of SbII, and the electron temperature and density are determined from the dynamics of SbI line emission. Based on the results obtained, the processes occurring during the formation and expansion of laser-produced antimony plasma are qualitatively analyzed.     

Average speaking fundamental frequency in soprano singers with and without symptoms of vocal attrition

Nineteen trained soprano singers aged 18–30 years vocalized tasks designed to assess average speaking fundamental frequency (SFF) during spontaneous speaking and reading. Vocal range and perceptual characteristics while singing with low intensity and high frequency were also assessed, and subjects completed a survey of vocal habits/symptoms. Recorded signals were digitized prior to being analyzed for SFF using the Kay Computerized Speech Lab program. Subjects were assigned to a normal voice or impaired voice group based on ratings of perceptual tasks and survey results. Data analysis showed group differences in mean SFF, no differences in vocal range, higher mean SFF values for reading than speaking, and 58% ability to perceive speaking in low pitch. The role of speaking in too low pitch as causal for vocal symptoms and need for voice classification differentiation in vocal performance studies are discussed.     

On characterizing collections arising from N-gons in the plane

Consider a labeled convex n-gon in the plane and a point x in general position in the interior. We associate with this a collection (x) of 3-element sets, namely those 3-element subsets of the vertices which contain x in their interior. We investigate the problem of characterizing those collections of subsets which can be represented in this matter. We give a complete characterization of this and a related problem.School of Mathematics, University of Minnesota, Minneapolis, MN 55455. This work was supported in part by NSF grant DMS-8700995.Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, England. Work done while Hill Visiting Professor at the University of Minnesota.     

A new ligand system based on a bipyridine-functionalized calix[4]arene backbone leading to mono- and bimetallic complexes

The synthesis of a new ligand system for mono- and bimetallic complexes based on a calixarene is described. Ligand BBPC (3, bis(bipyridine)-calix[4]arene) is obtained in three steps in 40% overall yield by first brominating one of the methyl groups of the 4,4'-dimethyl-2,2'-bipyridine in two steps and subsequently reacting it with p-tert-butylcalix[4]arene under basic conditions. Reaction of BBPC (3) with 2 equiv of [Rh(NBD)(2)]BF(4) or [Rh(NBD)(CH(3)CN)(2)]BF(4) (NBD = norbornadiene) produces the bimetallic compound BBPC[Rh(NBD)BF(4)](2) (4). Treatment of the ligand with PdCl(2)(CH(3)CN)(2) leads to the isolation of the bimetallic complex BBPC[PdCl(2)](2) (5). When the nickel precursor NiBr(2)(DME) (DME = dimethoxyethane) is reacted with BBPC, the bimetallic complex BBPC[NiBr(2)](2) (6) is isolated which, upon crystallization from methanol, gives the mononuclear bis(bipyridine) complex BBPC[NiBr(OMe)] (7). Full characterization includes X-ray structural studies of complexes 4, 5, and 7. The bimetallic compounds 4 and 5 show metal to metal distances of 4.334 A (for 4) and 3.224 A (for 5). For all three complexes, unique molecular packing arrangements were found, based on hydrophobic/hydrophilic interactions.     

Nucleophilic de-coordination and electrophilic regeneration of "hemilabile" pincer-type complexes: formation of anionic dialkyl, diaryl, and dihydride Pt(II) complexes bearing no stabilizing pi-acceptors

Novel anionic dialkyl, diaryl, and dihydride platinum(II) complexes based on the new "long-arm" hemilabile PCN-type ligand C6H4[CH2P(tBu)2](CH2)2N(CH3)2 with the general formula Li+[Pt(PCN)(R)2]- (R=Me (4), Ph (6) and H (9)) were prepared by reaction of [Pt(PCN)(R)] complexes (obtained from the corresponding chlorides) with an equivalent of RLi, as a result of the opening of the chelate ring. Alkylating agents based on other metals produce less stable products. These anionic d8 complexes are thermally stable although they bear no stabilizing pi acceptors. They were characterized by 1H, 31P[1H], 13C, and 7Li NMR spectroscopy; complex 9 was also characterized by single crystal X-ray crystallography, showing that the Li+ ion is coordinated to the nitrogen atom of the open amine arm and to the hydride ligand (trans to the P atom) of a neighboring molecule (H--Li=2.15 A), resulting in a dimeric structure. Complexes 4 and 9 exhibit high nucleophilic reactivity, upon which the pincer complex is regenerated. Reaction of 4 with water, methyl iodide, and iodobenzene resulted in the neutral complex [Pt(PCN)(CH3)] (3) and methane, ethane, or toluene, respectively. Labeling studies indicate that the reaction proceeds by direct electrophilic attack on the metal center, rather than attack on the alkyl ligand. The anionic dihydride complex 9 reacted with water and methyl iodide to yield [Pt(PCN)(H)] (8) and H2 or methane, respectively.