Let R be a 2-torision free prime ring and ?, ?? Aut(R). Furthermore, G: R×R?R is a symmetric generalized (?, ?)-Biderivation associated with a nonzero (?, ?)-Biderivation D. In this paper some certain identities are presented satisfying by the traces of G and D on an ideal of R which forces R to be commutative

  Necessary and sufficient conditions for the operator equation I AXAX n  * , to have a real positive definite solution X are given. Based on these conditions, some properties of the operator A as well as relation between the solutions X andAare given.

Abstract
Dame Ngaio Edith Marsh (1899-1982), a writer of detective fiction, was born
at Christchurch, New Zealand. Her hero, Chief Detective Inspector Roderick Alleyn,
appears in her first novel, A Man Lay Dead (1934), and in subsequent novels
including Death and the Dancing Footman (1942). She wrote twenty detective novels.
The Dancing Footman, Thomas, listening to a playful song from the smokingroom's
radio where William lay dead after being killed by his brother, Nicholas,
provides the most suspected guest at Highfold with badly needed alibi. The murderer,
Nicholas, plans an almost perfect crime, but the dance of this footman spoils his
scheme. When Alleyn and his group of policemen stage a show in which the

This experiment was conducted to study the effect of injecting hatching eggs into a flock of broiler aged mothers with different concentrations of the alcoholic extract of Moringa oleifera powder on productive performance of broilers during the period of rearing of 35 days. The study included two experiments for a period at 2/10/2021 to 28/11/2021, where eggs were injected into the Mustafa Poultry Hatchery/ Wasit Governorate- Aziziyah District. A 400 hatching eggs of 308 Ross  mothers of modern broilers used at age  of 48  week, eggs of average weight  66 ± 1 g/egg were collected in same day then stored for two days. A quarter of treatments were randomly distributed with 100 eggs for each treatment.

In the field of data security, the critical challenge of preserving sensitive information during its transmission through public channels takes centre stage. Steganography, a method employed to conceal data within various carrier objects such as text, can be proposed to address these security challenges. Text, owing to its extensive usage and constrained bandwidth, stands out as an optimal medium for this purpose. Despite the richness of the Arabic language in its linguistic features, only a small number of studies have explored Arabic text steganography. Arabic text, characterized by its distinctive script and linguistic features, has gained notable attention as a promising domain for steganographic ventures. Arabic text steganography harn

 The current specialized research tagged (intellectual and artistic concepts of the cultural context and their impact on contemporary ceramic sculpture) paves the way for the emergence of the context in ceramics active in life, so that this relationship will indicate the development and presence of ceramics or not and the volume of its circulation in the joints of the culture of the Arab recipient. As a result, the researcher collected scientific materials to serve the subject of the research in four chapters: Chapter One (General Methodological Framework) To clarify the problem of the research, the importance of the research to achieve benefit in higher education and education for scholars and teachers, while the research aims to revea

The aim of the research is to clarify the importance of documentary credits in foreign trade and especially their impact on the balance by limiting imports we highlighted the reality of documentary credits in Iraq and the accompanying changes and developments highlighted the indicators of foreign trade and finding solutions for harmonizing the fund Documentary and trade balance in order to achieve long term economic development.

The local banks are urged to restore the documentary credit system despite the backwardness and primitive methods used. The documentary credits have increased especially in the last years of the study period.

The advantages of the documentary credits have

يعد بيان التدفق النقدي من البيانات المهمة الصادرة من الوحدات الحكومية غير الهادفة للربح، بعد تبنيها معايير IPSASs ، مما يوفر معلومات اوسع تلبي حاجات المستخدمين لأتخاذ القرارات المناسبة . أذ يتضمن بيان التدفق النقدي بموجب المعيار رقم ( 2 ) التدفقات النقدية حسب الأنشطة التشغيلية و الاستثمارية والتمويلية ، وهذا لا ينسجم مع مخرجات النظام المحاسبي الحكومي العراقي . وان هدف البحث هو  التعرف