Extensions of Szegö's theory of orthogonal polynomials,III

Let {ø _n (dμ)} be a system of orthonormal polynomials on the unit circle with respect to a measuredμ. Szegö's theory is concerned with the asymptotic behavior ofø _n (dμ) when logμ′∈L ¹. In what follows we will discuss the asymptotic behavior of the ratioø _n (dμ ₂)/ø _n (dμ ₁) on the unit circle whendμ ₁ anddμ ₂ are close in a sense (e.g.,dμ ₂=gdμ ₁, where g≥0 is such thatQ(e ^it )g(t) andQ(e ^it )/g(t) are bounded for a suitable polynomialQ) and μ ₁ ^′ >0 almost everywhere or (a somewhat weaker requirement) lim _n→∞Φ _n (dμ ₁,0)=0 for the monic polynomial Φ _n . The asymptotic behavior of the same fraction outside the unit circle was discussed in an earlier paper.     

A phase cell approach to Yang-Mills theory

In this paper the basic local stability result is obtained, in a form valid in both small field and large field regions. To achieve this, some modifications are made in both the action and the renormalization group transformation. Though there is some sacrifice of elegance in these modifications, the establishment of this local stability estimate yields the most basic ingredient of the phase cell cluster expansion, good estimates for all the actions.Incidental to the estimates of this paper we establish some results on lattice geometry, interesting in their own right. A bound on the minimum area of a loop of lengthl, ind dimensions, is obtained asl ²/8(1–1/d). This, a best possible bound, was obtained for us by A. Blass. We also construct a radial maximal tree for the lattice ind dimensions. We hope to stimulate someone to find a better construction of radial trees.This work was supported in part by the National Science Foundation under Grant No. PHY 85-02074     

Collision-induced and infrared multiphoton dissociation studies on M(acetone)2 + (M=Al,Fe, Co,Cu, ScO) in the gas phase

In this paper we report an extension of our earlier study on the structure of Alfacetone)₂ ⁺ Collision-induced dissociation (CID) on MfacetoneXacetone-d₆)⁺ for M = Al, Fe, Co, and Cu yields primarily, if not exclusively, nearly equal amounts of acetone and acetone-d₆. Likewise, infrared multiphoton dissociation (IRMPD) at 10.6 μm yields, exclusively, nearly equal losses of the labeled and unlabeled acetones. These results suggest that the two acetone ligands bind in an equivalent fashion. Sc⁺ was also studied, which proved to be the most interesting. Sc⁺ reacts with acetone to form primarily ScO⁺, which undergoes higher order reactions leading to several products including ScO(acetone)₂ ⁺. IRMPD on this ion produces ScO(acetone-d₆)(CD₂CO)⁺, while its perdeuterated analog also produces ScO(acetone-d₆)⁺ in addition to ScO(acetone-d₆(CD₂CO)⁺. The IRMPD results are supplemented by studying the primary and higher order reactions of Sc⁺ with acetone, as well as the CID of ScO(acetone)₂ ⁺. Finally, a qualitative assessment of the infrared photodissociation cross sections is given. It is found that the relative photodissociation cross sections follow the orders Co(acetone-d₆)₂ ⁺ > Co(acetone)(acetone-d₆) > Co(acetone)₂ ⁺ and Co(acetone-d₆)⁺ > Co(acetone)⁺.     

Ternary rare-earth alumo-silicides—single-crystal growth from Al flux, structural and physical properties

A number of rare-earth alumo-silicides (R-Al-Si) have been synthesized from the corresponding elements by high-temperature reactions, carried out in excess of aluminum to serve as a flux. Under these experimental conditions, large single crystals of all R-Al-Si ternary phases were readily produced. The crystal structures these ternaries adopt were studied by means of powder and single-crystal X-ray diffraction and were classified as follows: (1) the early rare-earths (R=La, Ce, Pr, Nd, Sm, Gd) yield RAl_xSi_2−x, x∼1, non-stoichiometric ternary derivatives of the body-centered α-ThSi₂-type; (2) the late rare-earths (R=Tb, Dy, Ho, Er, Tm) form stoichiometric R₂Al₃Si₂ compounds that crystallize in the C-centered monoclinic Y₂Al₃Si₂-type; (3) the divalent Eu and Yb produce EuAl₂Si₂ and YbAl₂Si₂ with the trigonal CaAl₂Si₂-type, whereas the last lanthanide element, Lu, forms LuAlSi with C-centered orthorhombic YAlGe-type. These structural trends are reviewed, and the evolution of the basic physical properties such as magnetism, heat capacity and electrical resistivity when moving across the series is described in detail.     

Prosthetic heme modification during halide ion oxidation. Demonstration of chloride oxidation by horseradish peroxidase

Myeloperoxidase (MPO), eosinophil peroxidase (EPO), and chloroperoxidase can oxidize iodide, bromide, and chloride, but most peroxidases, including the prototypical horseradish peroxidase (HRP), reportedly only oxidize iodide and, in some cases, bromide. We report here that incubation of HRP with Br(-) and H(2)O(2) at acidic pH results in both bromination of monochlorodimedone and modification of the heme group. Mass spectrometry indicates that the heme 2- and 4-vinyl groups are modified by either replacement of a vinyl hydrogen by a bromide or addition of HOBr to give a bromohydrin. These reactions do not occur if protein-free heme and Br(-) are co-incubated with H(2)O(2) or if the HRP reaction is carried out at pH 7. Surprisingly, similar prosthetic heme modifications occur in incubations of HRP with H(2)O(2) and Cl(-). A mechanism is proposed involving oxidation of Br(-) or Cl(-) to give HOBr or HOCl, respectively, followed by addition to a vinyl group. In the reaction with Cl(-), a meso-chloro heme adduct is also formed. This first demonstration of Cl(-) oxidation by HRP, and the finding that prosthetic heme modification occurs when Br(-) or Cl(-) is oxidized in the absence of a cosubstrate, show that only modest tuning is required to achieve the unique chloride oxidation activity of MPO and EPO. The results raise the question of how the prosthetic hemes of MPO and EPO, whose function is to produce oxidized halide species, escape modification.     

The effect of hydrolysis time on amino acid analysis

Determining the amino acid content of a protein involves the hydrolysis of that protein, usually in acid, until the protein-bound amino acids are released and made available for detection. Both the variability in the ease of peptide bond cleavage and differences in the acid stability of certain amino acids can significantly affect determination of a protein's amino acid content. By using multiple hydrolysis intervals, a greater degree of accuracy can be obtained in amino acid analysis. Correction factors derived by linear extrapolation of serial hydrolysis data are currently used. Compartmental modeling of the simultaneous hydrolysis (yield) and degradation (decay) of amino acids by nonlinear multiple regression of serial hydrolysis data has also been validated and applied to determine the amino acid composition of various biological samples, including egg-white lysozyme, human milk protein, and hair. Implicit in the routine application of serial hydrolysis in amino acid analysis, however, is an understanding that correction factors, derived either linearly or through the more accurate nonlinear multiple regression approach, need to be determined for individual proteins rather than be applied uniformly across all protein types.     

On the mechanism of THF catalyzed vinylic lithiation of allylamine derivatives: structural studies using 2-D and diffusion-ordered NMR spectroscopy

N-Lithio-N-(trialkylsilyl)allylamines can be deprotonated in the presence of ethereal solvents exclusively at the cis-vinylic position to yield 3,N-dilithio-N-(trialkylsilyl)allylamines under mild conditions. Low temperature (1)H and (7)Li NMR ((1)H NOESY, TOCSY, (1)H/(7)Li HSQC, and DO-NMR) studies on the solution structure of 3,N-dilithio-N-(tert-butyldimethylsilyl)allylamine identified three major aggregates in THF (monomer, dimer and tetramer), but the aggregate structures failed to explain the solvent dependence and regiochemical outcome of the reaction. Low temperature (1)H NMR (NOESY, TOCSY, DO-NMR) studies on the solution structure of N-lithio-N-(tert-butyldimethylsilyl)allylamine in the presence of nBuLi identified amide/nBuLi mixed aggregates in both the ethereal solvent THF (1:1 dimer) and the hydrocarbon solvent toluene (1:3 tetramer). Addition of 2 equiv of THF to toluene solutions induces the formation of the same THF solvated 1:1 dimer as observed in neat THF. NMR evidence suggests that in THF the mixed aggregate has close contact between the olefin and the beta-CH(2) of nBuLi, while in the absence of THF, the allyl chain appears to be pointed away from the nearest nBuLi residues.