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 examined. The equilibrium points’ asymptotic stability is analyzed using linear stability. Then, global stability and persistence are investigated using the Lyapunov strategy. The occurrence of bifurcations of the model, such as of trans-critical or Hopf type, is also explored. Numerical simulations are used to verify the theoretical analysis. The Runge–Kutta method of fourth order is used in the simulation of the model. The analytical study and simulation findings show that the immune system is boosted by regular vitamin consumption, inhibiting the growth of tumor cells. Further, the chemotherapy drug contributes to the control of tumor cell progression. Vitamin intake and chemotherapy are treated both individually and in combination, and in all situations, the minimal level required to eliminate the cancer is determined.
Abstract
Research title: The legal ruling of advice.
This research deals with the topic of advice, as the research included the following:
Preamble: I explained in it the meaning of advice in the Qur’an and Sunnah, and that what is meant by it is a good performance of the duty, then explaining its importance, importing it, and the difference between advice and what is similar to it, from enjoining good, denial, reproach and reprimand, backbiting and the will.
The first topic: It dealt with the ruling on advice, whether it is recommended or disliked, or forbidden, because what is meant by it is to give advice to others may be an obligation in kind, or it may be desirable or dislike
... Show MoreIn the process of translating Qur’anic texts, there is an urgent need for interpretations of the Qur’anic text due to the presence of many incomprehensible Qur’anic verses or words because of our distance from the standard Arabic, language in which the Holy Qur’an was revealed, and the introduction of the foreign words into our language, in addition to the fact that many Qur’anic words are no longer used. All this prompted the need for the interpretation of the Qur'anic text, Therefore, it is necessary for the translator to resort to the books of interpretation if he intends to translate the Qur’an
This Book is intended to be textbook studied for undergraduate course in multivariate analysis. This book is designed to be used in semester system. In order to achieve the goals of the book, it is divided into the following chapters. Chapter One introduces matrix algebra. Chapter Two devotes to Linear Equation System Solution with quadratic forms, Characteristic roots & vectors. Chapter Three discusses Partitioned Matrices and how to get Inverse, Jacobi and Hessian matrices. Chapter Four deals with Multivariate Normal Distribution (MVN). Chapter Five concern with Joint, Marginal and Conditional Normal Distribution, independency and correlations. Many solved examples are intended in this book, in addition to a variety of unsolved relied pro
... Show MoreThis Book is intended to be textbook studied for undergraduate course in multivariate analysis. This book is designed to be used in semester system. In order to achieve the goals of the book, it is divided into the following chapters. Chapter One introduces matrix algebra. Chapter Two devotes to Linear Equation System Solution with quadratic forms, Characteristic roots & vectors. Chapter Three discusses Partitioned Matrices and how to get Inverse, Jacobi and Hessian matrices. Chapter Four deals with Multivariate Normal Distribution (MVN). Chapter Five concern with Joint, Marginal and Conditional Normal Distribution, independency and correlations. Many solved examples are intended in this book, in addition to a variety of unsolved relied pro
... Show MoreThe study sheds lights on the simple verbal formulas with its particular time suffixes as found in the Turgut Özakman’s play These Crazy Turks.
The introduction of the study sheds light on the life of the author and playwright, as well as traces the different types of the verbal formulas in Turkish language.
Oh Those Young is one of the most significant products of the Turkish literature of the young and Children where the literary messages of the playwright are addressed in a simple comic sarcastic style. Hence, the play, that has been studied and acted by many students and academics, drives its importance from this particular course of action.
... Show MoreIs a day or series of days celebrated by Jews for religious or worldly important event in Jewish history as an occasion in Hebrew is called Eid יום טוב good day or good or חג תענית celebrate the festival or celebration. Most of the Jewish holidays are of a religious nature, and there is a worldly character with festivals such as the Festival of Lights חג החנוכה the holiday of Purim and the holidays, although a religious appearance, but she celebration in mundane aspects of the history and traditions of the Jewish occasions. Mass over the holidays when Jews are those mentioned in the Bible in my Leviticus and Deuteronomy. And some holidays established by rabbis in the vicinity of the anc
... Show MoreThe use of economic resources enjoyed Iraq by especially oil resources, which constitute the main source of financial revenue, would the economic surplus outside the oil sector increases by mobilizing and rallying the labor power and turn it into an access capitalism, , was the cause of "the inaction of the productive sectors of the economy, made the investment planning process and even investment in human capital was not rationality with the increasing number of unemployed, particularly certificates and specializations high campaign, direction of the government towards market liberalism after 2003 through the, was focused not follow a clear economic policies, and the absence of planning, and the absence
... Show Moreالملخص ان حق الملكية هو الحق الاوسع نطاقا يمنح صاحبه صلاحية ممارسة السلطات كافة ويكون محل هذه السلطات كل ما يملك الشخص سواء كان شقه او طبقة اسوة بالعقارات الاخرى كدار للسكن او ارض ، ومن اهم هذه السلطات واوسعها نطاقا ( هو سلطة التصرف ). تعد هذه السلطة جوهر حق الملكية وأخطر السلطات الممنوحة للمالك كونه بواسطتها يمكنه الاستغناء عن ملكه بأي تصرف ناقل له كالبيع أو الهبة او الوصية مثلا ، ولأهمية هذه السلط
... Show MoreLet R be a commutative ring with unity and an R-submodule N is called semimaximal if and only if
the sufficient conditions of F-submodules to be semimaximal .Also the concepts of (simple , semisimple) F- submodules and quotient F- modules are introduced and given some properties .