This paper proposes and studies an ecotoxicant system with Lotka-Volterra functional response for predation including prey protective region. The equilibrium points and the stability of this model have been investigated analytically both locally and globally. Finally, numerical simulations and graphical representations have been utilized to support our analytical findings

       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

Introduction: Although soap industry is known from hundreds of years, the development accompanied with this industry was little. The development implied the mechanical equipment and the additive materials necessary to produce soap with the best specifications of shape, physical and chemical properties. Objectives: This research studies the use of vacuum reactive distillation VRD technique for soap production. Methods: Olein and Palmitin in the ratio of 3 to 1 were mixed in a flask with NaOH solution in stoichiometric amount under different vacuum pressures from -0.35 to -0.5 bar. Total conversion was reached by using the VRD technique. The soap produced by the VRD method was compared with soap prepared by the reaction - only method which

In this research, a mathematical model of tumor treatment by radiotherapy is studied and a new modification for the model is proposed as well as introducing the check for the suggested modification. Also the stability of the modified model is analyzed in the last section.

Gender classification is a critical task in computer vision. This task holds substantial importance in various domains, including surveillance, marketing, and human-computer interaction. In this work, the face gender classification model proposed consists of three main phases: the first phase involves applying the Viola-Jones algorithm to detect facial images, which includes four steps: 1) Haar-like features, 2) Integral Image, 3) Adaboost Learning, and 4) Cascade Classifier. In the second phase, four pre-processing operations are employed, namely cropping, resizing, converting the image from(RGB) Color Space to (LAB) color space, and enhancing the images using (HE, CLAHE). The final phase involves utilizing Transfer lea

Spatial Autoregressive Model (SAR) is one of the modeling frameworks that indicates a spatial dependence in the response variable. SAR model has a weakness, which is represented by the unknown variance of the residuals. Therefore, an alternative model has used titled Spatial Autoregressive Quantile Regression (SARQR) model That which is obtained by combining SAR and Quantile Regression (QR) models, is a regression method with the approach of dividing the data into particular quantiles that are likely to have different estimate values. This alternative model addresses the variance issues in SAR models. Additionally, the SARQR model not only resolves the issue of spatial variance but also serves as a solution for dealing with non-normal data

The intellectual and religious characteristics were an influential presence in the same Andalusian poet, especially among the poets of Beni El-Ahmar because they are part of the heritage of poets, and that is to push them towards the glory of this heritage and to take care of it and benefit from its inclusion, inspiration and similarity.

That this inflection on the poetic heritage is justified by the poets of the sons of the Red were inclined to preserve the inherited values, especially as it was related to their poetry, especially that the Andalusian poet did not find embarrassment in the inspiration of heritage and emerged when he mentioned the homes and the ruins and the camel and the journey, although the community Andalusian

Optimization is essentially the art, science and mathematics of choosing the best among a given set of finite or infinite alternatives. Though currently optimization is an interdisciplinary subject cutting through the boundaries of mathematics, economics, engineering, natural sciences, and many other fields of human Endeavour it had its root in antiquity. In modern day language the problem mathematically is as follows - Among all closed curves of a given length find the one that closes maximum area. This is called the Isoperimetric problem. This problem is now mentioned in a regular fashion in any course in the Calculus of Variations. However, most problems of antiquity came from geometry and since there were no general methods to solve suc