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

This article examines and proposes a dietary chain model with a prey shelter and alternative food sources. It is anticipated that mid-predators' availability is positively correlated with the number of refuges. The solution's existence and exclusivity are examined. It is established that the solution is bounded. It is explored whether all potential equilibrium points exist and are locally stable. The Lyapunov approach is used to investigate the equilibrium points' worldwide stability. Utilizing a Sotomayor theorem application, local bifurcation is studied. Numerical simulation is used to better comprehend the dynamics of the model and define the control set of parameters.

In this study, we set up and analyze a cancer growth model that integrates a chemotherapy drug with the impact of vitamins in boosting and strengthening the immune system. The aim of this study is to determine the minimal amount of treatment required to eliminate cancer, which will help to reduce harm to patients. It is assumed that vitamins come from organic foods and beverages. The chemotherapy drug is added to delay and eliminate tumor cell growth and division. To that end, we suggest the tumor-immune model, composed of the interaction of tumor and immune cells, which is composed of two ordinary differential equations. The model’s fundamental mathematical properties, such as positivity, boundedness, and equilibrium existence, are exami

Gypseous soil, which covers vast area in west, middle, east and south west regions of Iraq exhibit acceptable strength properties when dry, but it is weak and collapsible when it comes in touch with moisture from rain or other sources. When such weak soil is adopted for earth reinforced embankment construction, it may exhibit hazardous situation. Gypseous soil was investigated for the optimum liquid asphalt requirements of both cutback and emulsion using the one-dimensional unconfined compression strength test. The optimum fluid content was 13% (7% of cutback with 6% water content), and 17% (9% of emulsion with 8% water content). A laboratory model box of 50x50x25 cm was used as a representative of embankment; soil or asphalt stabilize

In a common language based on interpretation and diagnosis in the symbols and signs, the subject of Sufism and artistic semiotics is manifested in the construction and intensity of the reading of the text and the dismantling of its intellectual systems.
The emergence of Sufism in its religious features and the spiritual revelations related to the divine love of life in absolute reality, And images and language in a stream of intellectual and artistic unique and harmonious communicates with the subject of the themes of the Arab literature and its implications, but it is separated by a special entity signals and symbols related to the mysticism and worship.
    The unleashing of the imagination and the diagnosis,

The dynamical behavior of a two-dimensional continuous time dynamical system describing by a prey predator model is investigated. By means of constructing suitable Lyapunov functional, sufficient condition is derived for the global asymptotic stability of the positive equilibrium of the system. The Hopf bifurcation analysis is carried out. The numerical simulations are used to study the effect of periodic forcing in two different parameters. The results of simulations show that the model under the effects of periodic forcing in two different parameters, with or without phase difference, could exhibit chaotic dynamics for realistic and biologically feasible parametric values.

This study aims to design unified  electronic information system to manage students attendance in Lebanese French university/Erbil, as a system that simplifies the process of entering and counting the students absence, and generate absence reports to expel students who passed  the acceptable limit of being absent, and by that we can replace the traditional way of  using papers to count absence,  with  a complete electronically system for managing students attendance, in a way that makes the results accurate and unchangeable by the students.

            In order to achieve the study's objectives, we designed an information syst

This study is concerned with the concept of offering a point of view as a narrative construction element, especially the element and point of view of the novel to the letter Alcinmatugrave both business taken from masterpieces and literary works in the foundation or set of cinema. On the whole, the narrator participate in mock narrative process and support the narrator visual image, especially stories that need to exist scenes prove added to the image that uses signs of reality to take those marks a new dimension not only across the image, but also the intervention of the narrator in the re-formation of this realism marks surrounding Palms perceived and visible and put markers regularly between what the narrative of privacy and image, fo

The parliamentary election is one of the features of democratic systems that give individuals the right to participate in government and political election-making. Typically, the process of parliamentary elections received wide attention from media, as well as attention from large segments of the public because they understand the vast importance to assume political positions and associated fates of people and their destinies. Its importance comes from the fact that it allows citizens the right to participate in managing the public affairs by granting their confidence and voices to the elected president or his representatives in the parliamentary.
Media task is to emerge democratic societies, in particular, in the mission of urging p