المقاصد عند الإمام الشاطبي

Scholars of the Usul -early and recent- have paid utmost importance to the Maqâsid al-Shariah or the Objectives of Shariah and tried to substantiate, associate and link them with its sources, Qur’an and Sunnah, then to derive from them the Legislator’s or the Shari‘s purpose, the revelation’s true purpose and how it benefits the creatures in terms of promoting what is in their interest and shunning away what is harmful. These objectives became the point of interest for the jurists and scholars who toiled to understand the texts and what they connoted and they continue to venture into its depths and extract its treasures. It becomes quite evident from their exegeses of Qur’an and the Prophetic Traditions and elucidations of the juristic principles and issues. Imam al-Shâtibī and Ibn ‘Ashoor are two such scholars in this field who studied the Objectives of Shariah and contributed to this discipline so greatly that they became reference points for those who came after them. The basic principles in the field that were inferred by them are still its pillars. The Objectives of Shariah are divided into four kinds with reference to their benefits: the necessities, needs, improvements and supplements. The necessities are further divided into protection of Deen, protection of self, of intellect, of possessions and of race among others. Prudence demands that all means should be employed to safeguard these necessities. Thus knowing the Objectives of Shariah and their promulgation among the masses is quite important for the society since it leads towards promotion of the beneficial and shunning away the harmful elements in it.

Multidimensional Process Models for Seeded Batch Crystallization

This contribution focuses on the modeling and numerical approxima- tion of population balance models describing batch and polymorphic crystallization processes. Such processes have wide range applica- tions inne chemicals, pharmaceutical, minerals, and food indus- tries. Di erent numerical techniques are employed for solving these models in one and two property coordinates. The space-time CE/SE method and the semi-discrete upwindnite volume schemes are de- rived and implemented to solve the batch crystallization models with nes dissolution. Thene dissolution reduces undesirable small crys- tals and improves the quality of a product. A delay in the recycle pipe is also included in the model. Apart from the above mentioned methods, a new numerical technique is introduced to solve a model describing polymorphic crystallization of L-glutamic acid. The sug- gested technique employs together the method of characteristics and Duhamel''s principle to approximate the considered model e ciently and accurately. This technique has capability to produce accurate results on coarse meshes and no mesh re nement technique is needed for further improvement in the results. Furthermore, an alternative bivariate quadrature method of moments (QMOM) is developed for solving two-dimensional batch crystallization model involving crys- tals growth, nucleation, aggregation, and small nuclei dissolution in an external loop. The quadrature points and weights are obtained by using the orthogonal polynomials of lower order moments. Several case studies are carried out. The numerical computations demonstrate the eficiency, accuracy, and robustness of the proposed schemes. The results agree with the experimental predictions and could be used for process design and optimization.