Effect of boundary condition description on convergence of solution in a boundary-value problem

It is well known that the numerical accuracy of a series solution to a boundary-value problem by the direct method depends on the technique of approximate satisfaction of the boundary conditions and on the stage of truncation of the series. On the other hand, it does not appear to be generally recognized that, when the boundary conditions can be described in alternative equivalent forms, the convergence of the solution is significantly affected by the actual form in which they are stated. The importance of the last aspect is studied for three different techniques of computing the deflections of simply supported regular polygonal plates under uniform pressure. It is also shown that it is sometimes possible to modify the technique of analysis to make the accuracy independent of the description of the boundary conditions.

A volumetric method for the determination of sulphoxides

A volumetric method for the quantitative determination of Sulphoxides has been developed, based on their oxidation to sulphones by dichromate in presence of 5 M sulphuric acid at 105–110°C. Excess dichromate is titrated by ferrous ammonium sulphate solution. The method is also applicable to the determination of Sulphoxides in metal sulphoxide complexes.

Chemical modification of sheep plasma glycoprotein

Glycoprotein isolated from sheep plasma was chemically modified, and the effect of chemical modification on biological activities and immunological cross reactions has been studied. The removal of sialic acid resulted in a change in the “overall conformation” of the glycoprotein as evidenced by a decrease in viscosity of the glycoprotein solution and an increased susceptibility of the glycoprotein to proteolytic enzymes. Sialic acid-free glycoprotein no longer inhibited the tryptic activity or prolonged the clotting time of plasma. However, it could react with the antiserum to sheep plasma glycoprotein. The periodate oxidation of sheep plasma glycoprotein resulted in a complete loss of inhibition of trypsin activity, prolongation of plasma clotting time, and the ability to cross-react with the rabbit antiserum. The significance of periodate oxidation in relation to the possible sequence of sugars in the carbohydrate prosthetic group in the glycoprotein is discussed. Iodination and heating in buffers of acid and alkaline pH values of sheep plasma glycoprotein resulted in complete loss of trypsin activity and ability to prolong plasma clotting time. Iodination of the glycoprotein did not affect the immunological cross-reactivity.

A colorimetric method for determination of pyrocatechol and related substances

A colorimetric assay for the quantitative determination of catecholic compounds was developed. The method was based on the observation that a red color was formed when nitrite was added to a solution containing pyrocatechol and sodium tungstate. Aromatic amines interfere with the reaction but this could be overcome by the addition of formaldehyde. When interfering substances are present along with pyrocatechol, it can be readily separated by paper chromatography and estimated after elution from the filter paper.

An acid method for the volumetric estimation of water-soluble dithiocarbamates

Dithiocarbamates have been estimated previously by reaction with a strong acid, the carbon disulfide evolved being converted into a xanthate and the latter estimated iodimetrically. In the present method, a water-soluble dithiocarbamate is reacted with a decinormal mineral acid and the excess acid is determined to compute the amount of dithiocarbamate present. This method is applicable for the determination of a dithiocarbamate in a mixture containing thiuram disulfide.

Ultrasonic studies in chemically active liquid media (1) aqueous solution of N2O4

Using a pulse method the ultrasonic absorption has been studied in the frequency range of 2 to 10 Mc/s in dilute aqueous solutions of nitrogen tetroxide gas at room temperature. The absorption peaks (αλ vs frequency) observed in this study are attributed to the ionic dissociation reaction of the nitrous acid into its constituent ions. The rate constants of the forward and backward reactions are calculated using the theory of Tabuchi. The variation of the logarithm of the rate constant of the bimolecular ionic reaction, namely, log10 kb, with the square root of ionic strength qualitatively follows Brönsted's theory for ionic reactions in solutions.

Potassium phosphate as a reagent for the gravimetric estimation of lithium

Previous attempts for the quantitative estimation of lithium as orthophosphate, employing an alkali metal phosphate, have not been successful. A method, is described for the estimation of lithium as trilithium phosphate from 60% ethyl alcohol solution at 65° to 70° C., employing potassium phosphate reagent, at pH 9.5. The method is applicable in the presence of varying amounts of sodium and/or potassium cations and chloride, sulfate, nitrate, and phosphate anions.

Rapid growth of nanotubes and nanorods of wurtzite ZnO through microwave-irradiation of a metalorganic complex of zinc and a surfactant in solution

Large quantities of single-crystalline ZnO nanorods and nanotubes have been prepared by the microwave, irradiation of a metalorganic complex of zinc, in the presence of a surfactant. The method is simple, fast, and inexpensive (as it uses a domestic microwave oven), and yields pure nanostructures of the hexagonal wurtzite phase of ZnO in min, and requires no conventional templating. The ZnO nanotubes formed have a hollow core with inner diameter varying from 140-160 nm and a wall of thickness, 40-50 nm. The length of nanorods and nanotubes varies in the narrow range of 500-600 nm. These nanostructures have been characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), and selected area electron diffraction (SAED). The ZnO nanorods and nanotubes are found by SAED to be single-crystalline. The growth process of ZnO nanorods and nanotubes has been investigated by varying the surfactant concentration and microwave irradiation time. Based on the various results obtained, a tentative and plausible mechanism for the formation of ZnO nanostructures is proposed.

Optimal design of multiproduct batch chemical plant using NSGA-II

The optimal design of a multiproduct batch chemical plant is formulated as a multiobjective optimization problem, and the resulting constrained mixed-integer nonlinear program (MINLP) is solved by the nondominated sorting genetic algorithm approach (NSGA-II). By putting bounds on the objective function values, the constrained MINLP problem can be solved efficiently by NSGA-II to generate a set of feasible nondominated solutions in the range desired by the decision-maker in a single run of the algorithm. The evolution of the entire set of nondominated solutions helps the decision-maker to make a better choice of the appropriate design from among several alternatives. The large set of solutions also provides a rich source of excellent initial guesses for solution of the same problem by alternative approaches to achieve any specific target for the objective functions

A new method for the determination of covalent radii

In five-membered aromatic heterocyclic ring systems, a relation between the ratio of the distance between the two α to the two β protons and the covalent radii of the heteroatom is given. It is found that a similar relation is valid for the van der Waals radii also.

Surface chemical studies on pyrite in the presence of polysaccharide-based flotation depressants

The interaction of dextrin and guar gum with pyrite has been investigated through adsorption, flotation, and electrokinetic measurements. The adsorption densities of the polysaccharides onto pyrite reveal a region of higher adsorption density in the pH range 7.5-11, with a maximum around pH 10 for both polymers. The isotherms exhibit Langmuirian behavior. The adsorption density of guar gum onto pyrite is higher than that of dextrin. Electrokinetic measurements indicate a decrease in the electrophoretic mobility values in proportion to the concentration of the polymer added. Co-precipitation tests confirm polymer-ferric species interaction in the bulk solution, especially in the pH range 5.5-8.5. The pH range for higher adsorption, significant co-precipitation, and appreciable depression of pyrite encompass each other. XPS and FTIR spectroscopic studies provide evidence in support of chemical interaction between hydroxylated pyrite and the hydroxyl groups of the polymeric depressants. (C) 2000 Academic Press.

Solution structure of O-glycosylated C-terminal leucine zipper domain of human salivary mucin (MUC7)

Solution structures of a 23 residue glycopeptide II (KIS* RFLLYMKNLLNRIIDDMVEQ, where * denotes the glycan Gal-beta-(1-3)-alpha-GalNAc) and its deglycosylated counterpart I derived from the C-terminal leucine zipper domain of low molecular weight human salivary mucin (MUC7) were studied using CD, NMR spectroscopy and molecular modeling. The peptide I was synthesized using the Fmoc chemistry following the conventional procedure and the glycopeptide II was synthesized incorporating the O-glycosylated building block (N alpha-Fmoc-Ser-[Ac-4,-beta-D-Gal-(1,3)-Ac(2)alpha-D-GalN(3)]-OPfp) at the appropriate position in stepwise assembly of peptide chain. Solution structures of these glycosylated and nonglycosylated peptides were studied in water and in the presence of 50% of an organic cosolvent, trifluoroethanol (TFE) using circular dichroism (CD), and in 50% TFE using two-dimensional proton nuclear magnetic resonance (2D H-1 NMR) spectroscopy. CD spectra in aqueous medium indicate that the apopeptide I adapts, mostly, a beta-sheet conformation whereas the glycopeptide II assumes helical structure. This transition in the secondary structure, upon glycosylation, demonstrates that the carbohydrate moiety exerts significant effect on the peptide backbone conformation. However, in 50% TFE both the peptides show pronounced helical structure. Sequential and medium range NOEs, C alpha H chemical shift perturbations, (3)J(NH:C alpha H) couplings and deuterium exchange rates of the amide proton resonances in water containing 50% TFE indicate that the peptide I adapts alpha-helical structure from Ile2-Val21 and the glycopeptide II adapts alpha-helical structure from Ser3-Glu22. The observation of continuous stretch of helix in both the peptides as observed by both NMR and CD spectroscopy strongly suggests that the C-terminal domain of MUC7 with heptad repeats of leucines or methionine residues may be stabilized by dimeric leucine zipper motif. The results reported herein may be invaluable in understanding the aggregation (or dimerization) of MUC7 glycoprotein which would eventually have implications in determining its structure-function relationship.

properties of Na2O in Nasicon solid solution, Na1+xZr2SixP3-xO12

The thermodynamic activity of sodium oxide (Na2O) in the Nasicon solid solution series, Na1+xZr2SixO12, has been measured in the temperature range 700–1100 K using solid state galvanic cells: Pt|CO2 + O2|Na2CO3?Na1+xZr2SixP3-xO12?(Y2O3)ZrO2?In + In2O3|Ta, Pt for 1 = ? = 2.5, and Pt?CO2 + O2?Na2CO3?ß-alumina?Na1+xZr2SixP3-xO12?Ar + O2?Pt for x = 0, 0.5, 2.5, and 3. The former cell, where the Nasicon solid solution is used as an electrolyte along with yttria-stabilized zirconia, is well suited for Nasicon compositions with high ionic conductivity. In the latter cell, ß-alumina is used as an electrolyte and the Nasicon solid solution forms an electrode. The chemical potential of Na2O is found to increase monotonically with x at constant temperature. The partial entropy of Na2O decreases continuously with x. However, the partial enthalpy exhibits a maximum at x = 2. This suggests that the binding energy is minimum at the composition where ionic conductivity and cell volume have maximum values.