A proof of Howard’s conjecture in homogeneous parallel shear flows

A rigorous mathematical proof of Howard's conjecture which states that the growth rate of an arbitrary unstable wave must approach zero, as the wave length decreases to zero, in the linear instability of nonviscous homogeneous parallel shear flows, is presented here for the first time under the restriction of the boundedness of the second derivative of the basic velocity field with respect to the vertical coordinate in the concerned flow domain.     

Binding of sodium dodecyl sulfate and hexaethylene glycol mono-n-dodecyl ether to the block copolymer L64: electromotive force, microcalorimetry, surface tension, and small angle neutron scattering investigations of mixed micelles and polymer/micellar surfactant complexes

The interactions of sodium dodecyl sulfate (SDS) with the triblock copolymer L64 (EO13-PO30-EO13) and hexaethylene glycol mono-n-dodecyl ether (C12EO6) were studied using electromotive force, isothermal titration microcalorimetry, differential scanning microcalorimetry, and surface tension measurements. In certain regions of binding, mixed micelles are formed, and here we could evaluate an interaction parameter using regular solution theory. The mixed micelles of L64 with both SDS and C12EO6 exhibit synergy. When L64 is present in its nonassociated state, it forms polymer/micellar SDS complexes at SDS concentrations above the critical aggregation concentration (cac). The cac is well below the critical micellar concentration (cmc) of pure SDS, and a model suggesting how bound micelles are formed at the cac in the presence of a polymer is described. The interaction of nonassociated L64 with C12EO6 is a very rare example of strong binding between a nonionic surfactant and a nonionic polymer, and C12EO6/L64 mixed micelles are formed. We also carried out small angle neutron scattering measurement to determine the structure of the monomeric polymer/micellar SDS complex, as well as the mixed L64/C12EO6 aggregates. In these experiments, contrast matching was achieved by using the h and d forms of SDS, as well as C12EO6. During the early stages of the formation of polymer-bound SDS micelles, SDS aggregates with aggregation numbers of approximately 20 were found and such complexes contain 4-6 bound L64 monomers. The L64/C12EO6 data confirmed the existence of mixed micelles, and structural information involving the composition of the mixed micelle and the aggregation numbers were evaluated.     

A semi-classical approach to two-frequency solitons in a three-level cascade atomic system

A semi-classical theory of two intense optical fields interacting with a third-order non-linear medium composed of a three-level cascade atomic system is presented. It is predicted that non-linear atom-field interactions allow the formation of two-frequency bright, dark and grey spatial solitons. We demonstrate through numerical simulations and analytic stability analysis that the bright and grey solitons are stable.     

Cell Disruption Optimization and Covalent Immobilization of β-D-Galactosidase from <Emphasis Type="Italic">Kluyveromyces marxianus</Emphasis> YW-1 for Lactose Hydrolysis in Milk

β-D-galactosidase (EC 3.2.1.23) from Kluyveromyces marxianus YW-1, an isolate from whey, has been studied in terms of cell disruption to liberate the useful enzyme. The enzyme produced in a bioreactor on a wheat bran medium has been successfully immobilized with a view to developing a commercially usable technology for lactose hydrolysis in the food industry. Three chemical and three physical methods of cell disruption were tested and a method of grinding with river sand was found to give highest enzyme activity (720 U). The enzyme was covalently immobilized on gelatin. Immobilized enzyme had optimum pH and temperature of 7.0 and 40 °C, respectively and was found to give 49% hydrolysis of lactose in milk after 4 h of incubation. The immobilized enzyme was used for eight hydrolysis batches without appreciable loss in activity. The retention of high catalytic activity compared with the losses experienced with several previously reported immobilized versions of the enzyme is significant. The method of immobilization is simple, effective, and can be used for the immobilization of other enzymes.     

Modified families of multi-point iterative methods for solving nonlinear equations

We further present some semi-discrete modifications to the cubically convergent iterative methods derived by Kanwar and Tomar (Modified families of Newton, Halley and Chebyshev methods, Appl. Math. Comput. http://dx.doi.org/10.1016/j.amc.2007.02.119) and derived a number of interesting new classes of third-order multi-point iterative methods free from second derivatives. Furthermore, several functions have been tested and all the methods considered are found to be effective and compared to the well-known existing third and fourth-order multi-point iterative methods.