In this paper we present the theoretical foundation of forward error analysis of numerical algorithms under;• Approximations in "built-in" functions.• Rounding errors in arithmetic floating-point operations.• Perturbations of data.The error analysis is based on linearization method. The fundamental tools of the forward error analysis are system of linear absolute and relative a prior and a posteriori error equations and associated condition numbers constituting optimal of possible cumulative round – off errors. The condition numbers enable simple general, quantitative bounds definitions of numerical stability. The theoretical results have been applied a Gaussian elimination, and have proved to be very effective means of both a prior

      الحمدُ للهِ رب العالمين ، والصلاة والسلام على نبيه الأمين محمد r وعلى آله الطيبين الطاهرين ، وأصحابه الغر الميامين:

             تعد الصورة السمعية مفهوما بيانيا نجده في البلاغة العربية واضحاً مؤثرا، مؤديا دورا جوهريا في إيصال الفكرة التي يروم الأديب إيصالها إلى المتلقي   ولا تبدو السمعية واضحة إلاّ إذا نظر إليها في حالة أدبيه تهز كيان الشاعر &nbsp

The city of Baghdad underwent various changes and developments, which significantly influenced its urban character. And other urban fabric. The most prominent changes in the architecture of that period characterized by the emergence and spread of modern architecture, it represents the period between the 1940s and the late seventies of the twentieth century, which had its many reasons and various factors that paved and supported, and even encouraged the spread of modern architecture of the world, The advanced world in the adoption of a global architecture spread in the city of Baghdad by a number of international architects and Iraqis, who came from those countries and saturation ideas

The enemies of religion are still following the approach of undermining the Islamic faith in various ways through the diversity of methods of smear campaigns by raising suspicions to obliterate the Islamic identity and threaten security and stability of social life under the Islamic religion in Islamic societies, as we find that they have employed the doctrine of atheistic thought in order to distance people from the path of truth, distort the features of religion, destabilize psychological security and family stability, and thus destroy societal security by questioning the tolerant faith at times, and by raising suspicions at other times.

Hence, this research came to review the legal duty that requires Islamic scholars to protec

This study aims at recognizing Pesticides and how the process of pesticides biodegradation by microbiology took place, and the effect of environmental condition on this process. And how the research uncovered the efficiency of microbiology in the biodegradation process of pesticides, as the perfect temperature for the biodegradation process is 40 °C and humidity effect on pesticides efficiency, when high humidity reduces pesticide efficiency and the perfect acidity to increase bacteria efficiency is 7, for the incubation period, it was found during the previous studies that the best incubation period is 5-7 days, in this period the bacteria imprint on pesticides and increase biodegradation of it.

The goal of current research to identify the implications of intellectual and psychological drawings of women in prison in Sulaimaniya province through her paint and collected through cooperation with the creativity of the development organization of women in Sulaimaniya, consisted search of five chapters, the first chapter contains the goals of the research and its problem and its significance in addition to its limits and determine the terminology, while the second chapter included the theoretical framework and the literature on the subject of the search, and in the third quarter where he explained the researchers research methodology and procedures, either in the fourth quarter may offer researchers graphics prisoners and then read th