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.

The definition of orthogonal generalized higher k-derivation is examined in this paper and we introduced some of its related results.

The study was conducted from November 2021 to May 2022 at the three study sites within the Baghdad governorate. The study aims to identify the impact of human activities on the Tigris River, so an area free of human activities was chosen and represented the first site. A total of 48 types were diagnosed, 6204 ind/m3 spread over three sites. The following environmental indicators were evaluated: Constancy Index (S), Relative abundance index (Ra), Richness Index (between 17.995 and 23.251), Shannon Weiner Index (0.48-1.25 bit/ind.), Uniformity Index (0.124 -0.323). The study showed that the highest percentage recorded was for the phylum Annileda 34%; and the stability index shows that taxes (Stylaria sp., Aoelosoma sp., Branchinra sowerby, Ch

In this paper a Г-ring M is presented. We will study the concept of orthogonal generalized symmetric higher bi-derivations on Г-ring. We prove that if M is a 2-torsion free semiprime    Г-ring ,  and  are orthogonal generalized symmetric higher bi-derivations  associated with symmetric higher bi-derivations   respectively for all n ϵN.

In this research, a new technique is suggested to reduce the long time required by the encoding process by using modified moment features on domain blocks. The modified moment features were used in accelerating the matching step of the Iterated Function System (IFS). The main disadvantage facing the fractal image compression (FIC) method is the over-long encoding time needed for checking all domain blocks and choosing the least error to get the best matched domain for each block of ranges. In this paper, we develop a method that can reduce the encoding time of FIC by reducing the size of the domain pool based on the moment features of domain blocks, followed by a comparison with threshold (the selected  threshold based on experience

تشكل  التغيرات الحاصلة في اسعار النفط تحديا" حقيقيا" لاستمرار عملية النمو في العراق, وامام الحكومة فرصة كبيرة لإيجاد حلول ناجعة لمشكلة تزايد عجز الموازنة العامة من خلال اللجوء الى اصدار ادوات الدين العام الداخلي والخارجي, وهذا يتطلب بناء استراتيجية لإقامة وتطوير سوق السندات الحكومية في العراق, لتتمكن الحكومة من خلاله توفير مصادر تمويل اضافية, تسهم في تمويل الانفاق الاستثماري الحكومي ودعم النمو ودعم

Piled raft is commonly used as foundation for high rise buildings. The design concept of piled raft foundation is to minimize the number of piles, and to utilize the entire bearing capacity. High axial stresses are therefore, concentrated at the region of connection between the piles and raft. Recently, an alternative technique is proposed to disconnect the piles from the raft in a so called unconnected piled raft (UCPR) foundation, in which a compacted soil layer (cushion) beneath the raft, is usually introduced.  The piles of the new system are considered as reinforcement members for the subsoil rather than as structural members. In the current study, the behavior of unconnected piled rafts systems has been studie