A fourth order method for a singular two-point boundary value problem

Recently, Chawla et al. described a second order finite difference method for the class of singular two-point boundary value problems:

Two-step fourth orderP-stable methods for second order differential equations

A family of symmetric (hybrid) two-step fourth order methods is derived fory'=f(x,y). We then show the existence of a sub-family of these methods which when applied toy'=– ² y, real, areP-stable. We also note that a general (order) symmetric two-step method isP-stable iff it is unconditionally stable.     

An eighth order tridiagonal finite difference method for nonlinear two-point boundary value problems

We present an eighth order finite difference method for the second order nonlinear boundary value problemy=f(x, y), y(a)=A, y(b)=B; the method iseconomical in the sense that each discretization of the differential equation at an interior grid point is based on seven evaluations off. For linear differential equations, the scheme leads to tridiagonal linear systems. We showO(h ⁸)-convergence of the method and demonstrate computationally its eighth order.     

Molecular weight distribution studies. I. Radiation-induced polymerization of liquid α-methylstyrene

The concentration of water in purified and BaO-dried α-methylstyrene was found to be 1.1 × 10^?4M. The radiation-induced bulk polymerization of the α-methylstyrene thus prepared was studied in the temperature range of ?20°C to 35°C. The polymerization rate varied as the 0.55 power of the dose rate. The theoretical molecular weights and molecular weight distribution were calculated from a proposed kinetic scheme and these values were then compared with those found experimentally. The agreement between these two was reasonably close, and therefore it was concluded that, from the molecular weight distribution point of view, the proposed kinetic scheme for the cationic polymerization of α-methylstyrene is an acceptable one. The rate constant for chain transfer to monomer k_f changed with temperature and was found to be responsible for the decrease in the molecular weight of the polymer with increase in temperature. k_f and k_p at 20°C were found to be 0.95 × 10⁴ l./mole-sec and 0.99 × 10⁶ l./mole-sec, respectively.     

New diorganotin(IV) derivatives of 7-hydroxycoumarin (umbelliferone) and their adducts with 1,10-phenanthroline

New diorganotin(IV) derivatives of the general formula R2Sn(Umb)2 (where R = n-Bu, n-Oct and Ph; Umb = umbelliferone anion) have been synthesized either by the reaction of R2SnO with umbelliferone under azeotropic removal of water or by the reaction of R2SnCl2 with sodium salt of umbelliferone. Further, the adducts of the general formula R2Sn(Umb)2.phen (where R = n-Bu and n-Oct; phen = 1,10-phenanthroline) have also been synthesized by the interaction of R2Sn(Umb)2 with 1,10-phenanthroline. The bonding and coordination behavior in these derivatives are discussed on the basis of IR and 119Sn M?ssbauer spectroscopic studies in solid state. Their coordination behavior in solution is discussed by the multinuclear (1H, 13C and 119Sn) NMR spectral studies. The M?ssbauer and IR studies indicate that umbelliferone acts as a monoanionic bidentate ligand in R2Sn(Umb)2 coordinating through O(7) and O(1). A distorted octahedral geometry around tin has been proposed for R2Sn(Umb)2 as well as for R2Sn(Umb)2.phen in solid state. The newly synthesized derivatives have been tested for their anti-inflammatory and cardiovascular activities. The average LD50 value >1000 mg kg(-1) of these compounds indicates their safety margin.     

Thermodynamic studies of some binary mixtures containing a self-associated component. II. Excess volumes of some mixtures of tetrahydrofuran with alcohols

Excess volumes of mixing, V^E, for binary mixtures of tetrahydrofuran (THF) with methanol, ethanol, n-butanol, tert-butanol, 2-bromoethanol and ethylene glycol have been determined from the experimental density measurements at 298.15 K over the entire composition range. The V^E data follow the order: ethylene glycol < 2-bromoethanol < methanol < ethanol < n-butanol < tert-butanol. The results have been explained in terms of self-association and the hydrogen bond-donating abilities of alcohols.     

Depression in the cloud point of Tween in the presence of glycol additives and triblock polymers

Cloud point (C_P) measurements of Tween 20 and Tween 80 were carried out in the presence of various glycol oligomers and triblock polymers (TBP). The cloud points of both Tween 20 and 80 decrease in the presence of both types of additives. Among the glycol oligomeric additives, ethylene glycol monobutyl ether was found to reduce the C_P maximum. An increase in the repeating units of polymeric glycol additives leads to a decrease in C_P. Reduction in the C_P in the presence of TBP depends upon the increase in hydrophobic/hydrophilic ratio among the polypropylene to polyethylene units.