Convolution quadrature and discretized operational calculus. I

Numerical methods are derived for problems in integral equations (Volterra, Wiener-Hopf equations) and numerical integration (singular integrands, multiple time-scale convolution). The basic tool of this theory is the numerical approximation of convolution integrals

Interpolatory properties of best rationalL 1-approximations

In this paper the distribution of the zeros of the error function for bestL ₁-approximation by rational functions fromR _n,m is considered. It is shown that the maximal distance between such zeros isO(1/(n–m)), ifn > m.Communicated by Edward B. Saff.     

A proof of Freud's conjecture for exponential weights

LetW (x) be a function nonnegative inR, positive on a set of positive measure, and such that all power moments ofW ²(x) are finite. Let {p _n (W ²;x)} ₀ denote the sequence of orthonormal polynomials with respect to the weightW ²(x), and let {A _n } ₁ and {B _n } ₁ denote the coefficients in the recurrence relation

Purification and partial characterization of two lectin isoforms fromCratylia mollis mart. (camaratu bean)

Two additional electrophoretically distinct molecular forms, isoforms (iso) 2 and 3, with lectin properties were isolated fromCratylia mollis Mart, seeds (FABACEAE), by extraction with 0.15M NaCl and ammonium sulfate fractionation, followed by chromatography on Sephadex G-75 and Bio-Gel P-200 (iso 2), as well as CM-Cellulose and Sephadex G-75 (iso 3). Both isoforms were human group nonspecific and showed distinct specificity. Polyacrylamide gel electrophoresis resolved iso 2 and 3 in polypeptides of apparent mol wts 60 and 31 kDa, respectively; a distinct isoelectric focusing pattern was obtained for iso 2 and 3, under denaturing and reducing conditions.     

Calculation of the electronic properties of metal dimers

The low-energy excitation spectra of metal dimers are determined by solving exactly a realistic many-body Hamiltonian with inter- and intra-atomic Coulomb interactions. Our results for Cu₂ and Ag₂ are in very good agreement with the excitation energies derived from recent photodetachment experiments. The characteristics of the many-body excited states in these clusters are briefly discussed.     

Comparison of yellow poplar pretreatment between NREL digester and sunds hydrolyzer

Single-stage cocurrent dilute acid pretreatments were carried out on yellow poplar (Liriodendron tulipifera) sawdust using an as-installed and short residence time modified pilot-scale Sunds hydrolyzer and a 4-L bench-scale NREL digester (steam explosion reactor). Pretreatment conditions for the Sunds hydrolyzer, installed in the NREL process development unit (PDU), which operates at 1 t/d (bone-dry t) feed rate, spanned the temperature range of 160 – 210°C, 0.1 – 1.0% (w/w) sulfuric acid, and 4-10-min residence times. The batch pretreatments of yellow poplar sawdust in the bench-scale digester were carried out at 210 and 230°C, 0.26% (w/w) sulfuric acid, and 1-, 3-, and 4-min residence times. The dilute acid prehydrolysis solubilized more than 90% of the hemicellulose, and increased the enzymatic digestibility of the cellulose that remained in the solids. Compositional analysis of the pretreated solids and liquors and mass balance data show that the two pretreatment devices had similar pretreatment performance.     

Optimization of sucrose ethanol fermentation for K,Na, Ca,and cu metal contents

The effect of the trace metals Cu, K, Na, and Ca, separately or in mixture, on fermentation time, ethanol production rate, and cell growth in the fermentation of synthetic media containing sucrose is discussed. The results are related to the range of contents found in raw materials, molasses and raisins, in order to determine their optimum concentrations for alcohol production.     

The effect of ph and gas composition on the bubble fractionation of proteins

Studies were conducted to establish the effect of the variation of environmental factors on the separation occurring in protein systems, resulting from bubble fractionation in a bioreactor. The measure of separation was selected to be the separation ratio. This is defined to be the ratio of either the top or the middle position concentration in the vessel to the bottom concentration of the vessel. Invertase and α-amylase were the two “model” enzymes considered. It was observed that, under certain conditions, i.e., a combination of the nature of the sparging gas and the medium pH, varying degrees of protein separation were achieved. The pH of the system dramatically influenced the separation. It was found that the best separation occurred at a certain pH, assumed to be at or close to thepI of the protein in question. Furthermore, it was observed that systems sparged with CO₂ exhibited greater separation than systems sparged with air. In fact, in the case of invertase, almost threefold separation was observed at the top port when the solution was sparged with CO₂.     

Enzymatic synthesis of neopentylpolyol esters in organic media

Utilization of lipases for synthesis of esters of hydrophilic polyols has been investigated. The choice of a suitable solvent is crucial in this type of reaction. An interesting case is fatty acid esters from neopentylpolyols, such as trimethylolpropane, which are of great interest as high temperature lubricants. Enzymatic synthesis of trimethylolpropane tricaprylate was studied as an alternative to chemical manufacturing. Triester production occurred only if the water produced by esterification was continuously removed from the medium. In these condition, kinetics of appearance and transformation of mono-, di- and triesters were determined in order to define optimal conditions.