Monotonicity properties of zeros of generalized Airy functions

Summary We show, among other things, that the positive zeros of a solution ofy +x y=0,y(0)=0 decrease to 1 as increases, 0.

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Sommario Si dimostra, tra l'altro, che gli zeri positivi d'una soiuzione diy +x y=0,y(0)=0 decrescono al limite 1, quando cresce, 0.

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To the memory of Milo Háik

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This research was supported by grants from the Natural Sciences and Engineering Research Council (Canada) and Consiglio Nazionale delle Ricerche (Italy). Some of the work was done while the second-named author was visiting the Department of Mathematics, University of Torino.     

Configurational Lability at Tetrahedral Phosphorus: syn/anti-Isomerization of a P-Stereogenic Phosphiranium Cation by Intramolecular Epimerization at Phosphorus

Tetrahedral main-group compounds are normally configurationally stable, but P-epimerization of the chiral phosphiranium cations syn- or anti-[Mes*P(Me)CH₂CHPh][OTf] (Mes*=2,4,6-(t-Bu)₃C₆H₂) occurred under mild conditions at 60 °C in CD₂Cl₂, resulting in isomerization to give a syn-enriched equilibrium mixture. Ion exchange with excess [NBu₄][Δ-TRISPHAT] (Δ-TRISPHAT=Δ-P(o-C₆Cl₄O₂)₃) followed by chromatography on silica removed [NBu₄][OTf] and gave mixtures of syn- and anti-[Mes*P(Me)CH₂CHPh][Δ-TRISPHAT]?x[NBu₄][Δ-TRISPHAT]. NMR spectroscopy showed that isomerization proceeded with epimerization at P and retention at C. DFT calculations are consistent with a mechanism involving P-C cleavage to yield a hyperconjugation-stabilized carbocation, pyramidal inversion promoted by σ-interaction of the P lone pair with the neighboring β-carbocation, and ring closure with inversion of configuration at P.     

C-terminal processing of yeast Spt7 occurs in the absence of functional SAGA complex

Background  

Spt7 is an integral component of the multi-subunit SAGA complex that is required for the expression of ~10% of yeast genes. Two forms of Spt7 have been identified, the second of which is truncated at its C-terminus and found in the SAGA-like (SLIK) complex.