On General Mixed Quasivariational Inequalities

In this paper, we suggest and analyze several iterative methods for solving general mixed quasivariational inequalities by using the technique of updating the solution and the auxiliary principle. It is shown that the convergence of these methods requires either the pseudomonotonicity or the partially relaxed strong monotonicity of the operator. Proofs of convergence is very simple. Our new methods differ from the existing methods for solving various classes of variational inequalities and related optimization problems. Various special cases are also discussed.     

Parametric Quintic-Spline Approach to the Solution of a System of Fourth-Order Boundary-Value Problems

In this paper, we use parametric quintic splines to derive some consistency relations which are then used to develop a numerical method for computing the solution of a system of fourth-order boundary-value problems associated with obstacle, unilateral, and contact problems. It is known that a class of variational inequalities related to contact problems in elastostatics can be characterized by a sequence of variational inequations, which are solved using some numerical method. Numerical evidence is presented to show the applicability and superiority of the new method over other collocation, finite difference, and spline methods.     

Some algorithms for hemiequilibrium problems

In this paper, we suggest and analyze a class of iterative methods for solving hemiequilibrium problems using the auxiliary principle technique. We prove that the convergence of these new methods either requires partially relaxed strongly monotonicity or pseudomonotonicity, which is a weaker condition than monotonicity. Results obtained in this paper include several new and known results as special cases.     

Modified Householder iterative method free from second derivatives for nonlinear equations

In this paper, we suggest and analyze a new two-step predictor–corrector type iterative method free from second derivatives for solving nonlinear equations of the type f(x)=0. This new method includes the two-step Newton method as a special case. We prove that the new iterative method is of fourth-order. Several examples are given to illustrate the efficiency of this new method and its comparison with other iterative methods. This method can be considered as a significant improvement of the Newton method and its variant forms.     

Iterative Schemes for Nonconvex Variational Inequalities

In this paper, we suggest and analyze some iterative methods for solving nonconvex variational inequalities using the auxiliary principle technique, the convergence of which requires either only pseudomonotonicity or partially relaxed strong monotonicity. Our proofs of convergence are very simple. As special cases, we obtain earlier results for solving general variational inequalities involving convex sets.     

On Commutativity of Rings With Derivations

Let R be a ring and d : R → R a derivation of R. In the present paper we investigate commutativity of R satisfying any one of the properties (i)d([x,y]) = [x,y], (ii)d(x o y) = xoy, (iii)d(x) o d(y) = 0, or (iv)d(x) o d(y) = x o y, for all x, y in some apropriate subset of R.     

Depolymerization Study of Pakistani Lignite Coal Influence of Pre‐treatments on Product Slate

Influence of pretreatments, i.e., demineralization and pre‐soaking in some solvents on the yields of liquefied products obtained from hydro‐depolymerization of Pakistani coal in a pool of hydrogen has been discussed. Results of hydrogenation experiments demonstrated that demineralizing the coal sample prior to liquefaction caused the yields to decrease compared with the virgin coal samples. The contribution of mineral matter of coal has been evaluated by comparing the yields of liquid products of virgin and leached samples. Increase in the yields obtained from the hydrogenation experiments of swollen coal samples was not satisfactorily significant.     

Selected valence electron split-shell molecular orbital calculations on the diatomic interhalogen molecules

Selected valence electron split-shell molecular orbital calculations have been performed on the diatomic interhalogen molecules in order to obtain their binding energies, equilibrium internuclear distances, vibrational force constants, dipole moments and nuclear quadrupole coupling constants. The results are compared with the corresponding closedshell values and with those of some previous semiempirical and nonempirical all valence electron calculations. It is observed that the selected valence electron split-shell molecular orbital method which involves the least amount of computations yields results in better agreement with experiment than other methods.     

Preparation and Properties of Aramid-Silica Hybrids with Inter-Phase Bonding Through (3-glycidoxypropyl)-trimethoxysilane

Nano-composites from aramid-silica system have been prepared via sol-gel process. Poly (phenyleneterephthalamide) copolymer chains were prepared by reacting a mixture of p- and m-phenylenediamines with terephthaloyl chloride in dimethylacetamide used as solvent. The sol-gel process in the polymer matrix was carried out through hydrolysis and condensation of a mixture of tetraethoxysilane and (3-glycidoxypropyl) trimethoxysilane. The latter was used to develop linkage, on one hand with silica network structure using alkoxy groups and on the other hand with aramid chains at its secondary amine groups through glycidal groups of silane. Mutual interaction between the two disparate phases aramid and silica network was thus created. Thin films of the composites containing different proportions of silica ranging from 5.0 to 25.0-wt% were cast by the solvent elution technique. The α-relaxation temperature associated with the glass transition was measured by the dynamic mechanical thermal analysis. The results showed an increase in the glass transition temperature from 328°C for the pure aramid to 352°C for the hybrid materials containing 25-wt% silica, an indicative of the increased interfacial interaction between the two phases. Films having relatively low silica content were flexible and transparent, but those with high silica content were opaque and brittle. These films were tested for their tensile strength, modulus and toughness. The mechanical strength of the composites as compared to the pure aramid increased initially but with further addition of silica the strength decreased. The initial increase can be explained due to increased interfacial interaction between the two phases, however agglomeration of silica particles was responsible for decreasing strength at higher silica contents.