this paper, we will prove the following theorem, Let R be a ring with 1 having
a reverse derivation d ≠ 0 such that, for each x R, either d(x) = 0 or d(x) is
invertible in R, then R must be one of the following: (i) a division ring D, (ii) D 2 ,
the ring of 2×2 matrices over D, (iii) D[x]/(x ) 2
where char D = 2, d (D) = 0 and
d(x) = 1 + ax for some a in the center Z of D. Furthermore, if 2R ≠ 0 then R = D 2 is
possible if and only if D does not contain all quadratic extensions of Z, the center of
D.

     Playfair cipher is a substitution scheme. The classical playfair scheme has a limited matrix size  containing only uppercase letters, so it is prone to hackers and cryptanalysis. To increase the resistance of playfair cipher, a new encipherment and decipherment method is proposed in this work, which depends on the permutation and its inverse, respectively. In addition, a modified  key matrix is utilized, which includes capital and small Alphabets, numbers, and 38 special characters collected from ASCII codes. In the proposed method, both substitution and transposition schemes are used, where the first stratum of the cipher is a substitution by using  key matrix and the second stratum is a transposi

The purpose of this paper is applying the robustness in Linear programming(LP) to get rid of uncertainty problem in constraint parameters, and find the robust optimal solution, to maximize the profits of the general productive company of vegetable oils for the year 2019, through the modify on a mathematical model of linear programming when some parameters of the model have uncertain values, and being processed it using robust counterpart of linear programming to get robust results from the random changes that happen in uncertain values ​​of the problem, assuming these values belong to the uncertainty set and selecting the values that cause the worst results and to depend buil

Background: The Harmonic scalpel (HS) has been proven to be an effective, efficient, and safe instrument for dissection and hemostasis in both open and laparoscopic surgical procedures. The primary use of the HS in laparoscopic cholecystectomy (LC) has been for the division of the cystic artery and liver bed dissection. Advancements in the Harmonic scalpel blade tip now provide for the reliable ultrasonic division and closure of the cystic duct.
Objectives: This study was planned to compare the clips and cautery (CC) method of laparoscopic cholecystectomy (LC) versus LC using HS as regard to the safety and efficacy for symptomatic gallstone disease.
Patients and methods: This is a prospective study conducted in Baghdad Teaching Hos

Background: The Harmonic scalpel (HS) has been proven to be an effective, efficient, and safe instrument for dissection and hemostasis in both open and laparoscopic surgical procedures. The primary use of the HS in laparoscopic cholecystectomy (LC) has been for the division of the cystic artery and liver bed dissection. Advancements in the Harmonic scalpel blade tip now provide for the reliable ultrasonic division and closure of the cystic duct.
Objectives: This study was planned to compare the clips and cautery (CC) method of laparoscopic cholecystectomy (LC) versus LC using HS as regard to the safety and efficacy for symptomatic gallstone disease.
Patients and methods: This is a prospective study conducted in Baghdad Teaching Hos

     In this paper, the bi-criteria machine scheduling problems (BMSP) are solved, where the discussed problem is represented by the sum of completion and the sum of late work times  simultaneously. In order to solve the suggested BMSP, some metaheurisitc methods are suggested which produce good results. The suggested local search methods are simulated annulling and bees algorithm. The results of the new metaheurisitc methods are compared with the complete enumeration method, which is considered an exact method, then compared results of the heuristics with each other to obtain the most efficient method.

The communication networks (mobile phone networks, social media platforms) produce digital traces from their usages. This type of information help to understand and analyze the human mobility in very accurate way. By these analyzes over cities, it can give powerful data on daily citizen activities, urban planners have in that way, relevant indications for decision making on design and development. As well as, the Call detail Records (CDRs) provides valuable spatiotemporal data at the level of citywide or even nationwide. The CDRs could be analyzed to extract the life patterns and individuals mobility in an observed urban area and during ephemeral events. Whereas, their analysis gives conceptual views about human density and mobility pattern