Praise be to God, and prayers and peace be upon our master Muhammad, the Messenger of God, and upon his family, companions, and those who are guided by his guidance.

Then:

       Our Islamic jurisprudence and its basic principles are fixed, namely: the Noble Qur’an, then the Prophet’s Sunnah, then consensus, then analogy. However, it is characteristic of what makes it developed to meet the requirements of renewed life, including: sent interests, custom, approval, blocking pretexts, changing times. That is why it went through different stages, growth, brilliance, stagnation and endowment; Therefore, many scholars of Islamic jurisprudence divided its stages into four sections: the stage of inf

In this work, we consider a modification of the Lotka-Volterra food chain model of three species, each of them is growing logistically. We found that the model has eight equilibrium points, four of them always exist, while the rest exist under certain conditions. In terms of stability, we found that the system has five unstable equilibrium points, while the rest points are locally asymptotically stable under certain satisfying conditions. Finally, we provide an example to support the theoretical results.

     In this paper, our aim is to solve analytically a nonlinear social epidemic model as an initial value problem (IVP) of ordinary differential equations. The mathematical social epidemic model under study is applied to alcohol consumption model in Spain. The economic cost of alcohol consumption in Spain is affected by the amount of alcohol consumed. This paper refers to the study of alcohol consumption using some analytical methods. Adomian decomposition and variation iteration methods for solving alcohol consumption model have used. Finally, a compression between the analytic solutions of the two used methods and the previous actual values from 1997 to 2007 years is obtained using the absolute and

This paper deals with constructing a model of fuzzy linear programming with application on fuels product of Dura- refinery , which consist of seven products that have direct effect ondaily consumption . After Building the model which consist of objective function represents the selling prices ofthe products and fuzzy productions constraints and fuzzy demand constraints addition to production requirements constraints , we used program of ( WIN QSB )  to find the optimal solution

- The sandy soil with high gypsum content (usually referred to as gypseous soil) covers vast area in south, east, middle and west regions of Iraq, such soil possess a type of cohesive forces when attached with optimum amount of water, then compacted and allowed to cure, but losses its strength when flooded with water again. Much work on earth reinforcement was published which concentrate on the gain in bearing capacity in the reinforced layer using different types of cohesive or cohesion less soil and various types of reinforcement such as plastic, metal, grids, and synthetic textile. Little attention was paid to there enforce gypseous soil. The objective of this work is to study the interaction between such soil and reinforcement strips

In this paper two modifications on Kuznetsov model namely on growth rate law and fractional cell kill term are given. Laplace Adomian decomposition method is used to get the solution (volume of the tumor) as a function of time .Stability analysis is applied. For lung cancer the tumor will continue in growing in spite of the treatment.

Object tracking is one of the most important topics in the fields of image processing and computer vision. Object tracking is the process of finding interesting moving objects and following them from frame to frame. In this research, Active models–based object tracking algorithm is introduced. Active models are curves placed in an image domain and can evolve to segment the object of interest. Adaptive Diffusion Flow Active Model (ADFAM) is one the most famous types of Active Models. It overcomes the drawbacks of all previous versions of the Active Models specially the leakage problem, noise sensitivity, and long narrow hols or concavities. The ADFAM is well known for its very good capabilities in the segmentation process. In this