In this paper we generalize Jacobsons results by proving that any integer  in   is a square-free integer), belong to . All units of  are generated by the fundamental unit  having the forms

Our generalization build on using the conditions

This leads us to classify the real quadratic fields  into the sets  Jacobsons results shows that  and Sliwa confirm that  and  are the only real quadratic fields in .

عملية تغيير حجم الصورة في مجال معالجة الصور باستخدام التحويلات الهندسية بدون تغيير دقة الصورة تعرف ب image scaling  او image resizing. عملية تغيير حجم الصورة لها تطبيقات واسعة في مجال الحاسوب والهاتف النقال والاجهزة الالكترونية الاخرى. يقترح هذا البحث طريقة لتغيير حجم الصورة باستخدام المعادلات الخاصة بمنحني Bezier وكيفية الحصول على افضل نتائج. تم استخدام Bezier curve في اعمال سابقة في مجالات مختلفة ولكن في هذا البحث تم استخد

The main aim of this paper is to study how the different estimators of the two unknown parameters (shape and scale parameter) of a generalized exponential distribution behave for different sample sizes and for different parameter values. In particular, 

. Maximum Likelihood, Percentile and Ordinary Least Square estimators had been implemented for different sample sizes (small, medium, and large) and assumed several contrasts initial values for the two parameters. Two indicators of performance Mean Square Error and Mean Percentile Error were used and the comparisons were carried out between different methods of estimation  by using monte carlo simulation techniq

The purpose of this research is to demonstrate the impact of deposit insurance to reduce banking risks, as banks in various countries of the world face a variety of risks that led to banking and financial crises that led to the failure and bankruptcy of many of its bank, which led to the banks to find quick and appropriate solutions to get rid of these difficulties These solutions include the use of bank deposit protection system for the many risks and sequences of crises that accompanied the Iraqi banking work of thefts, forgery, embezzlement and changing and unstable circumstances. The importance of studying the subject of research through the theoretical framework of banking risks as well as the framework of consideration In order to

Analysis of Covariance consider to be quite important procedure to reduce the effect of some independents factors before going through the experiment.

By this procedure we can compare variances causes from the difference between treatments and error term variance of they are equals or less than consider to be not significant, otherwise if is significant.

We carry on with this comparison until we find the greatest covser for the significant variance flam the treatments.

There are methods can be used like least significant difference method, Duncan method and Turkeys' w-procedure and Student Newman.

Key Word: Analysis of variatio

المستخلـص

تم في هذا البحث دراسة الطرائق اللامعلمية الرتيبة لتقدير دالة الأنحدار اللامعلمي، ومعالجة القيم الشاذة الموجودة في دالة الأنحدار اللامعلمي لجعل الدالة رتيبة (متزايدة أو متناقصة).

لذا سنقوم أولاً بتقدير دالة الأنحدار اللامعلمي بإستخدام ممهد Kernel ومن ثم تطبيق الطرائق الرتيبة لجعل الدالة متزايدة إذ سنتناول ثلاث طرائق للتقدير:-

1- طريقة ste

The comparison of double informative priors which are assumed for the reliability function of Pareto type I distribution. To estimate the reliability function of Pareto type I distribution by using Bayes estimation, will be  used two different kind of information in the Bayes estimation; two different priors have been selected for the parameter of Pareto  type I distribution . Assuming distribution of three double prior’s chi- gamma squared distribution, gamma - erlang distribution, and erlang- exponential distribution as double priors. The results of the derivaties of these estimators under the squared error loss function with two different double priors. Using the simulation technique, to compare the performance for

The studies in ABC system have become so many nowadays especially in industrial companies. But they are almost rare in service companies and that has put more difficulties in front of the researcher.

This study consists of two sides, theoretical and practical. The first side (theoretical) deals with the most important features of ABC system and it focuses on its characteristics, standards and aims. While the practical side deals with the practice of this system in one of these service companies which is Dar-A’Salam Bank. The researcher has made use of being the accounting adviser of the bank and that he can get the necessary data. He has come up with, after making a comparison between the cost of ABC system and traditional cost

تناول البحث موضوع أثر تمكين المرأة على تحقيق أبعاد التنمية المستدامة وتحسين الأداء المؤسسي،  ويُعدُّ من المواضيع المهمة؛ لأنَّه يمثِّل قضية اجتماعية ورؤًى جديدة لتحقيق التنمية الشاملة، وتمثلت مشكلة البحث بقلة الاهتمام بتمكين المرأة في بعض الوحدات الاقتصادية؛ ممَّا يؤثِّر سلباً على تحقيق التوازن الاقتصادي والثقافي والاجتماعي والبيئي، فضلاً عن انخفاض كفاءة الأداء الوظيفي في تلك الوحدات الاقتصادية؛ ل