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.     

Fibers and 3D mesh scaffolds from biodegradable starch-based blends: production and characterization

The aim of this work is the production of fibers from biodegradable polymers to obtain 3D scaffolds for tissue engineering of hard tissues. The scaffolds required for this highly demanding application need to have, as well as the biological and mechanical characteristics, a high degree of porosity with suitable dimensions for cell seeding and proliferation. Furthermore, the open cell porosity should have adequate interconnectivity for a continuous flow of nutrients and outflow of cell metabolic residues as well as to allow cell growth into confluent layers. Blends of corn starch, a natural biodegradable polymer, with other synthetic polymers (poly(ethylene vinyl alcohol), poly(epsilon-caprolactone), poly(lactic acid)) were selected for this work because of their good balance of properties, namely biocompatibility, processability and mechanical properties. Melt spinning was used to produce fibers from all the blends and 3D meshes from one of the starch-poly(lactic acid) blends. The experimental characterization included the evaluation of the tensile mechanical properties and thermal properties of the fibers and the compression stiffness, porosity and degradation behavior of the 3D meshes. Light microscopy picture of 3D meshes.     

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.     

The search for a new model structure of β-Factor XIIa

We present the search for a new model of -factor XIIa, a blood coagulation enzyme, with an unknown experimental 3D-structure. We decided to build not one but three different models using different homologous proteins as well as different techniques and different modellers. Additional studies, including extensive molecular dynamics simulations on the solvated state, allowed us to draw several conclusions concerning homology modelling, in general, and -factor XIIa, in particular.