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.

In this paper the modified trapezoidal rule is presented for solving Volterra linear Integral Equations (V.I.E) of the second kind and we noticed that this procedure is effective in solving the equations. Two examples are given with their comparison tables to answer the validity of the procedure.

With wireless sensor network (WSN) wide applications in popularity, securing its data becomes a requirement. This can be accomplished by encrypting sensor node data. In this paper a new an efficient symmetric cryptographic algorithm is presented. This algorithm is called wireless sensor network wavelet curve ciphering system (WSN-WCCS).  The algorithm idea based on discrete wavelet transformation to generate keys for each node in WSN.  It implements on hierarchical clustering WSN using LEACH protocol. Python programming language version 2.7 was used to create the simulator of WSN framework and implement a WSN-WCCS algorithm. The simulation result of the proposed WSN-WCCS with other symmetric algorithms has show

This paper deals with the modeling of a preventive maintenance strategy applied to a single-unit system subject to random failures.

According to this policy, the system is subjected to imperfect periodic preventive maintenance restoring it to ‘as good as new’ with probability

p and leaving it at state ‘as bad as old’ with probability q. Imperfect repairs are performed following failures occurring between consecutive

preventive maintenance actions, i.e the times between failures follow a decreasing quasi-renewal process with parameter a. Considering the

average durations of the preventive and corrective maintenance actions a

Microbial lipases today occupy a place of prominence among biocatalysts owing to their ability to catalyze awide variety of reactions in aqueous and non- aqueous media, A.baumannii were isolated from different clinical specimens from hospitalized patients from Baghdad hospitals and were detected by biochemical tests and API20E system. The percentage of isolation was (16.6%), A. baumannii is an increasingly multidrug – resistant (MDR), it showed high level of resistant to Ceftriaxon, Colistin, Piperacillin, Co-trimoxazol, Tertracycline, Carbenicillin, Amoxicillin, Penicillin G, Gentamicin and Ceftazidim , wherease the isolates were highly sensitive to Imipenem, Ciprofloxacin, Meropenem, Amikacin, and Cefotaxime.

ملخص الدراسة
سعت الدراسة تعرف اثراستعمال الأنموذج المعملي في تصحيح المفاهيم الرياضية شائعة الخطأ لدى طلاب الصف الأول المتوسط بالإجابة عن السؤال "ما اثر استعمال الأنموذج المعملي في تصحيح المفاهيم الرياضية شائعة الخطأ لدى طلاب الصف الأول المتوسط" ولتحقيق هدف الدراسة وضعت الفرضية الصفرية "لايوجد فرق ذو دلالة إحصائية عند مستوى الدلالة (0.05) بين متوسطي درجات طلاب المجموعة التجريبية الذين يدرسون المادة المقرر

Abstract

      In this study, we compare between the autoregressive approximations (Yule-Walker equations, Least Squares , Least Squares ( forward- backword ) and Burg’s (Geometric and Harmonic ) methods, to determine the optimal approximation to the time series generated from the first - order moving Average non-invertible process, and fractionally - integrated noise process, with several values for d (d=0.15,0.25,0.35,0.45) for different sample sizes (small,median,large)for two processes . We depend on figure of merit function which proposed by author Shibata in 1980, to determine the theoretical optimal order according to min