Jugni, Dhola and Mahiya: Comparing

Among the amazing variety of forms of poetic expression by the folk of the Punjab region, this essay has selected three genres: mahiya, dhola and jugni. The study is meant to compare these three genres of Punjabi folklore, in their evolution, structure, expression and themes. The study finds that the three genres are very old in time origin and tracing their exact origins in history is impossible, only few hints are available. Their structures are variable, as mahiya has a fixed structure, dhola has rather loose structure giving more freedom to the singer-poet, and jugni has a specific meter in certain lines, but it has freedom to repeat some lines for perfect expression of the melody. The structures in fact follow the tunes, distinct for each genre. Three genres have many themes common, but jugni has spirituality as dominant theme, dhola has expression of love as dominant them and mahiya has now become quite inclusive, but it originated as expression of love and it still retains that character in its core. The folk heart of Punjab has endeared these three genres so much that these are appreciated far and wide in original tunes, but new experiments of tunes and themes are also underway. Being a true mirror of simple unsophisticated villagers these folk songs would lose popularity if these villagers become sophisticated hence the need for their preservation is highlighted in this study.

Analytical Solutions to Some Nonlinear Boundary Value Problems Arising in Applied Mathematics

In this thesis, we use the Optimal Homotopy Asymptotic Method (OHAM), Differential Tranform Method (DTM), Multistage Optimal Homotopy Asymptotic Method (MOHAM), Adomian decomposition method (ADM) and Homotopy analysis method (HAM) for the solution of nonlinear initial and boundary value problems for ordinary and partial differential equations. The obtained results are compared with the results obtained from these methods and numerical results. These method do not required the linearization and discritization techniques like numerical methods andestablished better accuracy at low order approximation and its accuracy increases with increase in approximation orders; it uses a flexible auxiliary function that control the convergence of the solution and convergence region can easily be adjusted. Moreover, the procedure of these method are simple, well defined, and can easily be used the recursive relations explicitly. Except from the application of these methods, we have formulated some fluid problems and its solutions have been done. The physical interpretations of the parameters are discussed in detail. The conclusion of each model is given at the end of each chapter. The convergence regions for each problem have been mentioned graphically and the convergence is discussed. Also we have developed a new scheme for namely MOHAM which gives better accuracy not even for small domain problems but works very well for large domain boundary value problems. The implementation of this scheme is almost simple as the optimal homotopy asymptotic method.To shows its effectiveness we have used it to different bench mark problems from literature and compare the results with those obtained by other method. Fordeterminationofoptimalvaluesofconstantswe usemethodofleastsquareand collocation method for OHAM and MOHAM. For HAM h curves determine the convergence region and rate of convergence. We use Mathematica 9 for symbolic computation. Most of theworkpresentedinchapters2, 3,4,and5ofthisthesishasbeen publishedin different well reputed international journals and the remaining are submitted for possible publications. The details of published/accepted/submitted are included in the list of publications.