اﻷداء اﻟﻤﺄﻣﻮر ﺑﻪ و ﺗﻄﺒﻴﻘﺎﺗﻪ اﻟﻔﻘﻬﻴﺔ

In the Islamic Law i. E. Quran and Sunnah the above mentioned topic has been discussed clearly and repeatedly to avoid any ambiguity in dealings in our daily life and agreements made between two parties or governments national or international levels. After intensive study I discussed and elaborated the said issue referring to the Qura’nic verses and sayings of the Prophet (SAW). The matter is of great importance; hence the Muslims Jurists have also given their valuable opinions in accordance with the Islamic Law which have been incorporated also to solve the issue. If we act upon these verdicts, we will be able to select the best among ourselves and form an ideal government and will discharge our duties honestly, and eventually our every act will show our responsibility to perform our duties and to give due share to the right person.

Non-Stationary Subdivision Algorithms for Geometric Modeling

Subdivision is a method of generating smooth curves or surfaces. In recent years, subdivision curves and surfaces have come to the forefront of geometric modeling. There is a variety of existing subdivision schemes whose classification can be based on different criteria. In this dissertation non-stationary subdivision schemes are de veloped using the hyperbolic form of Lagrange-like interpolant, trigonometric and hy perbolic forms of uniform B-spline. These schemes are presented mainly to overcome the limitation of generation of conics by subdivision schemes especially parabolas and hyperbolas. Asymptotic equivalence method has been used for convergence analysis of the proposed schemes. Curvature plot technique has been employed to check the accuracy and efficiency of the proposed schemes to construct conic-sections. The ge ometrical behavior of the proposed schemes has been depicted through explanatory examples.