In this paper some topological transformations are designed for simplifying certain problems involved in mechanics of structures. For each case, the main problem is stated and the proposed topological transformation is established. Once the required topological analysis is completed. a back transformation results the solution for the main problem. EXPEDIENT transformations studied here employ (1) models drawn on a plane. (2) models embedded into higher dimensional spaces.(3) interchange models defined which have more simple connectivity properties than the corresponding original structural model.

The synthesis of novel coumarin-based sulfonamides was accomplished in good yields via InCl3-catalyzed three-component condensation of N-(2-formylphenyl)-N-methylbenzene sulfonamides, 4-hydroxycoumarin and cyclic secondary amines in toluene.

A simple approach for component reaction between aldehydes, anilines or ammonium acetate, and dimedone in ethanol as a solvent is studied using Ag-SiO2 nanoparticles. This approach results for the synthesis of various decahydroacridines in appropriate yields (80-94%). The use of Ag-SiO2 nanoparticles as a heterogeneous catalyst lets a clean procedure.

In the present study, a modified time relaxed Monte Carlo (MTRMC) method is developed for numerical solution of the Boltzmann equation in rarefied regimes. Taylor series expansion is employed to obtain a generalized form of the Wild sum expansion and consequently the modified collision functions with fewer inter-molecular interactions are obtained. The proposed algorithm is applied on the lid-driven micro cavity flow with different lid velocities and the results for velocity and shear stress distributions are compared with those from the standard DSMC and TRMC methods. The comparisons show excellent agreement between the results of the MTRMC method with their counterparts from TRMC and DSMC methods. The present study illustrates appreciable improvement in the computational expense of the MTRMC method compared to those from standard TRMC and DSMC methods. The improvement is more pronounced compared to the standard DSMC method. It is observed that up to 56% reduction in CPU time is obtained in the studied cases.

The Fe3O4@SiO2@APTMS@Glu-His@V complex was prepared with modification of iron oxide magnetic nanoparticles with (3-aminopropyl) trimethoxysilane (APTMS) and glutaraldehyde-L-histidine Schiff base followed by complexation with VOSO4. Characterization of the Fe3O4@SiO2@APTMS@Glu-His@V complex was carried out by means of FTIR, XRD, SEM, EDX, TEM, AAS and VSM techniques. It was found that Fe3O4@SiO2@APTMS@Glu-His@V complex successfully catalyze the epoxidation of allyl alcohols with tert-butylhydroperoxide (TBHP) in moderate to high yields. The epoxidation of geraniol with 100 % conversion and 100% selectivity within 15 min is remarkable. Short reaction time, high activity, selectivity, stability, reusability and easily magnetic separation of the catalyst with no leaching during the course of reactions are some advantages of this research.