Truncation error bounds for modified continued fractions with applications to special functions

Much recent work has been done to investigate convergence of modified continued fractions (MCF's), following the proof by Thron and Waadeland [35] in 1980 that a limit-periodic MCFK(a _n , 1;x ₁), with andnth approximant

Synthesis and molecular structure of [Al(CH3)2]2[C10H22N4] [Al(CH3)3]2: Condensation product of trimethylaluminum and a multidentate open-chain amine

The crystalline condensation product [Al(CH₃)₂]₂[C₁₀H₂₂N₄][Al(CH₃)₃]₂ is prepared from reaction of the multidentate open-chain amine 1,4-bis(3-aminopropyl)piperazine with trimethylaluminum in methylene chloride. The compound crystallized in the monoclinic space groupC2/c with unit cell parametersa=25.166(12),b=7.268(4),c=17.316(4) Å,=115.3(4)°, andD _c =1.06 g cm^–3 forZ=4. Least-squares refinement based on 1054 observed reflections with intensitiesI 3(I) in the range 2<2<45° led to a finalR factor of 0.053 (R _w =0.064). The title compound resides on a crystallographic center of symmetry with independent Al-N distances of 1.889(5), 2.058(5), and 2.030(5) Å.     

Defect of the five-thirds law using the Wiener-Hermite expansion

Application of the refined Wiener-Hermite expansion with moderate to high Reynolds numbers Re to homogeneous, isotropic turbulence is presented. The results show a defect to Kolmogorov's five-thirds law, increase in the absolute value of the exponent comparable with many theoretical predictions. Midrange spectra up to fluctuation Reynolds numbers of 10⁸ show little, if any, dependence of the defect on Re, as long as the initial spectra do not deviate too far from their equilibrium states. The renormalization scheme has also been proven to have no effect on the final shape of the spectrum.     

Mechanism of the acid-catalyzed hydrolysis of N-acylsulfamates

The kinetics of hydrolysis of a series of N-acylsulfamate esters p-XC₆H₄OSO₂NHCOR as models for more complex, biologically important compounds has been examined. Structure-reactivity, solvent-reactivity, thermodynamic data, etc. support a bimolecular mechanism involving water in the transition state (TS).     

The synthesis of 1,4-diazacycl[3,2,2]azine

The diazaanalog of “cycl[3,2,2]azine”, “1,4-diazacycl[3,2,2]azine” (1,4,7b-triazacyclopent-[cd]indene) and its 2-methyl derivative were prepared. These compounds are subject to facile acid-catalyzed hydrolysis affording substituted imidazo[1,2-a]pyridines.     

Functionalization of saturated hydrocarbons. High temperature bromination of octahydropentalene. Part 19

The synthesis and thermal bromination of octahydropentalene was studied. The reaction afforded 1a,3a,4b,6b-tetrabromo-1,2,3,4,5,6-hexahydropentalene (14) with remarkable regio- and stereospecificity. The structure of the product was determined by ¹H and ¹³C NMR data and single X-ray structural analysis. The treatment of octahydropentalene with tenfold bromine gave the octabromopentalene derivative. The formation mechanism of the products is discussed.     

Natural abundance 13C - 13C coupling constants observed via double quantum coherence. Structural elucidation by the one- and the two-dimensional NMR experiements of velloziolone,a new seco-diterpene.

With the help of Natural Abundance ¹³C - ¹³C Coupling Constants, observed via double quantum coherence, the structural determination of VELLOZIOLONE (1), a new diterpene, has been carried out.     

Gas-phase ion/molecule reactions between dimethoxyphosphonium ions and aromatic hydrocarbons

Ion/molecule reactions between O=P(OCH(3))(2)(+) phosphonium ions and six aromatic hydrocarbons (benzene, toluene, 1,2,4-trimethylbenzene, naphthalene, acenaphthylene and fluorene) were performed in a quadrupole ion trap mass spectrometer. The O=P(OCH(3))(2)(+) phosphonium ions, formed by electron impact from neutral trimethyl phosphite, were found to react with aromatic hydrocarbons (ArHs) to give (i) an adduct [ArH, O=P(OCH(3))(2)](+) and (ii) for ArHs which have an ionization energy below or equal to 8.14 eV, a radical cation ArH(+ *) by charge transfer reaction. Collision-induced dissociation experiments, which produce fragment ions other than the O=P(OCH(3))(2)(+) ions, indicate that the adduct ions are covalent species. Isotope-labeled ArHs were used to elucidate fragmentation mechanisms. The charge transfer reactions were investigated using density functional theory at the B3LYP/6-311 + G(3df,2p)//B3LYP/6-31G(d,p) level of theory. The potential energy surface obtained from B3LYP/6-31G(d,p) calculations for the reaction between O=P(OCH(3))(2)(+) and benzene is described.     

Direct quantitative analysis of peptides using matrix assisted laser desorption ionization

The protocol and various matrices were examined for quantification of biomolecules in both the low ca. 1200 amu and mid mass 6000-12000 amu ranges using an internal standard. Comparative studies of different matrices of MALDI quantitative analysis showed that the best accuracy and standard curve linearity were obtained for two matrices: (a) 2,5-dihydroxybenzoic acid (DHB) combined with a comatrix of fucose and 5-methoxysalicylic acid (MSA) and (b) ferulic acid/fucose. In the low mass range, the quantitative limit was in the 30 fmol range and in the mid mass range the quantitative limit was in the 250 fmol range. Linear response was observed over 2-3 decades of analyte concentration. The relative error of the standard curve slope was 1.3-1.8% with correlation coefficients of 0.996-0.998.The main problem for quantitative measurement was suppression of the signal of the less concentrated component (analyte or internal standard) by the more concentrated component. The effect was identified with saturation of the matrix by the analyte. The threshold of matrix saturation was found to be in the range of 1/(3000-5000) analyte/matrix molar ratio. To avoid matrix saturation the (analyte+internal standard) to matrix molar ratio should be below this threshold. Thus the internal standard concentration should be as low as possible.DHB/MSA/fucose and ferulic acid/fucose matrices demonstrated good accuracy and linearity for standard curves even when the internal standard had chemical properties different from the analyte. However, use of an internal standard with different chemical properties requires highly stable instrumental parameters as well as constant (analyte+internal standard)/matrix molar ratio for all samples.