Convergence estimates of Galerkin-wavelet solutions to a Cauchy problem for a class of periodic pseudodifferential equations

A class of Cauchy problems for interesting complicated periodic pseudodifferential equations is considered. By the Galerkin-wavelet method and with weak solutions one can find sufficient conditions to establish convergence estimates of weak Galerkin-wavelet solutions to a Cauchy problem for this class of equations.

     

Dissolution of ionisable groups and lignocellulosic components during low-temperature kraft pulping of pinus radiata

A wide range of kraft pulps from radiata pine produced by low-temperature kraft pulping in flow-through reactors was assessed for carboxyl and hexenuronic acid (HexA) contents using the conductometric titrations and UV spectrophotometer, respectively. The Kappa number of pulps varied from 20.8 to 84.7 when using a cooking liquor of 1 M effective alkali as Na₂O, 25% sulfidity, and cooking time of 100–250 min. The experimental results showed that the carboxyl groups (including HexA) and HexA groups dissolved and their residual values in the pulp samples correlate linearly with Kappa number and pulp yield. The dissolving rate of all carboxyl groups is much faster than the loss of HexA. The HexA/lignin ratio decreased non-linearly with Kappa number.     

Zymography for Picogram Detection of Lipase and Esterase Activities

Lipases and esterases are important catalysts with wide varieties of industrial applications. Although many methods have been established for detecting their activities, a simple and sensitive approach for picogram detection of lipolytic enzyme quantity is still highly desirable. Here we report a lipase detection assay which is 1000-fold more sensitive than previously reported methods. Our assay enables the detection of as low as 5 pg and 180 pg of lipolytic activity by direct spotting and zymography, respectively. Furthermore, we demonstrated that the detection sensitivity was adjustable by varying the buffering capacity, which allows for screening of both high and low abundance lipolytic enzymes. Coupled with liquid chromatography-mass spectrometry, our method provides a useful tool for sensitive detection and identification of lipolytic enzymes.     

Copper ferrite superparamagnetic nanoparticles as a heterogeneous catalyst for directed phenol/formamide coupling

The copper ferrite-catalyzed, directed coupling of ortho-arylated phenols and dialkylformamides in the presence of a peroxide oxidant is described. Acyclic and cyclic amides were compatible with the reaction conditions. The copper ferrite catalyst is heterogeneous since substantial leaching was not detected and re-use of the catalyst for 9 consecutive reactions proceeded without a significant decrease in yield. To the best of our knowledge, this transformation has not been previously performed under heterogeneous catalysis conditions.     

Pontryagin’s Principle for Optimal Control Problem Governed by 3D Navier–Stokes Equations

This paper deals with the Pontryagin maximum principle for optimal control problems governed by 3D Navier–Stokes equations with pointwise control constraint. The obtained result is proved by using some results on regularity of solutions of the Navier–Stokes equations and techniques of optimal control theory.     

Global energy minimization of alanine dipeptide via barrier function methods

This paper presents an interior point method to determine the minimum energy conformation of alanine dipeptide. The CHARMM energy function is minimized over the internal coordinates of the atoms involved. A barrier function algorithm to determine the minimum energy conformation of peptides is proposed. Lennard-Jones 6-12 potential which is used to model the van der Waals interactions in the CHARMM energy equation is used as the barrier function for this algorithm. The results of applying the algorithm for the alanine dipeptide structure as a function of varying number of dihedral angles are reported, and they are compared with that obtained from genetic algorithm approach. In addition, the results for polyalanine structures are also reported.     

A universal kinetic equation for characterising the fractal nature of delignification of lignocellulosic materials

A kinetic model was developed, based on the power law of growth and Avrami’s nuclei growth concepts, to describe the heterogeneous nature of pulping kinetics, taking into account the effects of chemical concentration and temperature. The general form of the kinetic equation is first order with a time-dependent rate coefficient. The model was statistically tested using published data obtained from delignification of lignocellulosic materials (hemp woody core, giant reed, wheat straw, cottonwood, bamboo and flax fibres). The activation energies of the delignification range from 71 to 136 kJ/mol. The p-values obtained from the regression analysis are significantly small indicating that all the estimates of the model parameters were significant with very high levels of confidence. The correlation coefficients R ² for these models range from 0.76 to 0.98.