Momentum distribution and one-body density matrix in liquid3He.

Summary The momentum distributionn(k) and the one-body density matrix ρ₁(r,r' have been calculated in normal liquid³He atT=0. A variational wave function containing two-, three-body and backflow correlations has been used. The Fermi hypernetted chain technique has been employed and the elementary diagrams have been evaluated by the scaling approximation. The present estimate ofn(k) is in good agreement with the Monte Carlo data obtained with similar wave functions.n(k) and the discontinuityZ ofn(k) at the Fermi surface have been computed at several values of the density. The density dependence of the effective massm ^* has been found to be mainly due to that ofZ.     

On orders of approximation of plane curves by parametric cubic splines

The aim of the present paper is to show that the convergence rate of the parametric cubic spline approximation of a plane curve is of order four instead of order three. For the first and second derivatives, the rates are of order three and two, respectively. Finally some numerical examples are given to illustrate the predicted error behaviour.     

Bioconversion potential of Trichoderma viride HN1 cellulase for a lignocellulosic biomass Saccharum spontaneum

The industrialisation of lignocellulose conversion is impeded by expensive cellulase enzymes required for saccharification in bioethanol production. Current research undertakes cellulase production from pretreated Saccharum spontaneum through Trichoderma viride HN1 under submerged fermentation conditions. Pretreatment of substrate with 2% NaOH resulted in 88% delignification. Maximum cellulase production (2603 ± 16.39 U/mL/min carboxymethyl cellulase and 1393 ± 25.55 U/mL/min FPase) was achieved at 6% substrate at pH 5.0, with 5% inoculum, incubated at 35°C for 120 h of fermentation period. Addition of surfactant, Tween 80 and metal ion Mn⁺², significantly enhanced cellulase yield. This study accounts proficient cellulase yield through process optimisation by exploiting cheaper substrate to escalate their commercial endeavour.     

Investigation of Nutrient Feeding Strategies in a Countercurrent Mixed-Acid Multi-Staged Fermentation: Experimental Data

Nutrients are essential for microbial growth and metabolism in mixed-culture acid fermentations. Understanding the influence of nutrient feeding strategies on fermentation performance is necessary for optimization. For a four-bottle fermentation train, five nutrient contacting patterns (single-point nutrient addition to fermentors F1, F2, F3, and F4 and multi-point parallel addition) were investigated. Compared to the traditional nutrient contacting method (all nutrients fed to F1), the near-optimal feeding strategies improved exit yield, culture yield, process yield, exit acetate-equivalent yield, conversion, and total acid productivity by approximately 31%, 39%, 46%, 31%, 100%, and 19%, respectively. There was no statistical improvement in total acid concentration. The traditional nutrient feeding strategy had the highest selectivity and acetate-equivalent selectivity. Total acid productivity depends on carbon–nitrogen ratio.     

Hetarylpyrazoles. IV. Synthesis and reactions of 1,5′-bipyrazoles

A number of 1, 5′-bipyrazoles were obtained from the condensation of pyrazol-5-ylhydrazine and 1, 3-dicarbonyl compounds. Electrophilic substitution reactions of these 1, 5′-bipyrazoles occur at the four position of the pyrazole ring.     

A shape preserving area true approximation of histogram by rational splines

For a given histogram, we consider an application of a simple rational spline to a shape preserving area true approximation of the histogram. An algorithm for determination of the spline is as easy as one with a quadratic polynomial spline, while the latter does not always preserve the shape of the histogram. Some numerical examples are given at the end of the paper.     

Tricyclic heteroaromatic ring systems II A convenient synthesis of 1H-pyrrolo[3,2-c]quinolines

Various quinol-4-yl hydrazones on heating in high boiling solvents undergo cyclizations to give lH-pyrrolo[3,2-c]quinolines in good yields. Some of these pyrroloquinolines were alkylated to provide their N-alkyl derivatives.     

Arylindoles. III. Mannich reaction of 1-arylindoles

1-Phenyl-, and 1-nitrophenylindoles when subjected to Mannich reaction conditions gave the corresponding 3-dialkylaminomethyl derivatives ( IIc-IIk ) in good yields.     

vic‐Tricarbonyl Compounds of Quinolines: Analogues of Ninhydrin: A Short Review

Derivatives of ninhydrin are extensively used in the field of forensic sciences as important latent fingerprint reagents. Many works have been performed upon their synthesis and reactivity, but there are many spaces to work on the compounds of quinoline‐2,3,4(1H)‐triones—analogues of ninhydrin, in both dimensions: synthesis and reactivity, and according to the best of our knowledge, not a single detailed or short compiled article has been published for these compounds. This review briefly summarizes the chemistry of quinoline‐2,3,4(1H)‐triones.