عندما تواجهنا مشكلة صنع القرار في ظل ظروف تنافسية تتسم بتناقص مواقف المتنافسين وتعارض المصالح فيما بينهم، فإن عملية اتخاذ القرار تصبح صعبة في مثل هذه الظروف لان نتائج القرار وأثره لا تعتمد على القرار المتخذ فقط، بل تتأثر بنتائج القرارات التي يتخذها المتنافسون. وتصبح المشكلة هي اتخاذ قرار يتعلق بالمصالح المتعارضة وحل مثل هذا التعارض هو محور اهتمام نظرية الألعاب حيث تساعد نظرية الألعاب في فهم إستراتيجيات المتنافسين وتحليل احتمالاتها المختلفة واتخاذ القرار المناسب لمقابلة المواقف المختلفة للخصم. ونحن سوف نقتصر على مايسمى (ألعاب المجموع الصفري لشخصين) حيث قدم هذا البحث طرق حل الألعاب ذات المجموع الصفري لشخصين وذلك بتحديد أفضل إستراتيجية لكل متنافس وتناولت الدراسة كذلك حل ألعاب المجموع الصفري باستخدام البرمجة الخطية وقمنا بإعداد برنامج لها بلغة الفوتران للاستفادة منه لحل الألعاب ذات الحجم الكبير التي تتطلب كثير من الجهد والحسابات والوقت. كما تتم التركيز على الشكل الموسع للألعاب وقمنا بمعالجة مجموعة من الألعاب بواسطة شجرة اللعب. كما تم توضيح الصلة بين الشكل الإستراتيجي والشكل الموسع للعبة. Abstract When we encounter the problem of decision making under competent circumstances shaped with the contradiction of players positions and the contradictions of interrelated interests, the decision making process becomes difficult under such circumstances, because the decision outcome and its affect is not dependent of the said decision, instead, they are affected by the results of the decisions taken by the players. Then the problem is in taking a decision relevant to those contradicted interests and how to solve such contradictions is the basic interest of the games theory. The games theory helps in understanding the strategies of the players and analyzing the strategies various possibilities and thus arriving at the proper decision to deal with the different positions of the other player. We shall restrict our work on to what so called (two-person zero- sum games). As this research has suggested a solution method for the games of the zero sum for two persons, via determination of the best strategy possible for each player. The study as well dealt with the solution of the zero-sum games using the linear programming. We prepared a program for that end- FORTRAN language in order to benefit from it in solving the games of the bigger size which require much efforts and calculations and time too. Great concentration was also being given to the extensive configuration of the games, where we treated a set of games by means of the play tree. We also attempted to clarify the relation between the strategic form and the extensive form of game.
عواطف أحمد العزابي (2008)

تم دراسة المرنانات غير المستقرة في المنظومة الليزريه بشكل عام والتركيز على أحد المشاكل التي يواجهها هذا النوع من المرنانات وهي تأتيرات الحيود. فرغم ان هذه الظاهرة تعتبرالوسيله التي يخرج عن طريقها الشعاع من المنظومه الليزريه الا انها تسبب في فقدا كبيرا في قدرة الشعاع الليزري الخارج . احدي الطرق المقترحه للتقليل من تاتيرات الحيود السلبيه في هذه الحاله هو احدات تدرج في المرآه , فقد تم في هذا البحث مقارنة نتائج متقاربه وعليه تم استنباط معادلة خاصه بالحيود عبر مرآة بتدرجين وحساب القيمة الذاتية للشعاع الليزري الخارج وتحدي مدي التحسن في التقليل من الخسارة الناتجه من خلال التغير في قيمة عدد فرنيل وذلك بمقارنة العلاقات البيانية لمرآة عادية ومرآة بتدريج واحد وبتدرجين للمرنان نفسه , و تم أيضا دراسة تاثير القيمة الذاتية بعرض الدرجة في المرآة وعرض المنحنيات الخاصة بها . Abstract Unstable resonators in laser systems have been studied in general and the focus was on one of the problem facing this type of resonators namely the effect of diffraction .although diffraction Is the mean to get the laser rays out of the system, it causes major loss of power in the output If it is treated adequately. One of the suggested method to reduce the negative effect of diffraction is to make a gradual step on the output mirror. a comparison has been made between the results for a single step mirror with result from previous study . the two results agreed with each other to an acceptable range . an equation for a two-step mirror was derived and the Eigen Values of the outgoing laser beam were calculated . the amount of improvement in the output power was calculated by changing the value of Fresnel number and comparing the situation for an ordinary mirror , single step mirror and two-step mirror. The results show good improvement for the two-step mirror. also the dependence of the step with on the eigen value was studied. We can conclude from the current work that by introducing certain step width specific width could improve the output power from unstable resonators by minimizing the negative diffraction effect. The amount of improvement seems to increase with increasing number of steps. For future work we suggest that more exact methods to calculate the eigen values, such as proni method, should be tried and the effect of the output mirror tilt must be taken into account.
سهير محمود احمد ابو حجر (2001)

Abstract In this thesis, we study different numerical methods used to solve ordinary differential equations of the first and second orders and where related important definitions are given . We will concentrate first on Differential Equations of the first order and the truncation errors which are derived for various methods and those compared with the expected errors , whenever possible . Two applications were given in science of biology and physics which were studied in details . Finally we draw our attention to ordinary differential equations of the second order where we study initial-value problems and boundary-value problems with the application of the wellknown numerical procedures :the shooting method and the finite difference method . The important conclusion we came up with is that the truncation error is always greater than the expected error for all methods used, and this which was expected .
عفاف احمد الجطلاوي (2014)