The research gained its importance from the importance of technical reserves in the insurance activity and its impact on the result of the activity of insurance companies and their financial position and thus reflected on the insurance prices as the technical reserves are one of the most important and most valuable budget items usually, as well as that the insurance activity has a role in maintaining economic development where some countries develop laws and instructions for the formation of those reserves binding application to insurance companies and the fact that the financial statements in general are of interest to shareholders, banks, the General Tax Authority and other beneficiaries In the insurance activity as policyholders and t

In this paper we generalize Jacobsons results by proving that any integer  in   is a square-free integer), belong to . All units of  are generated by the fundamental unit  having the forms

Our generalization build on using the conditions

This leads us to classify the real quadratic fields  into the sets  Jacobsons results shows that  and Sliwa confirm that  and  are the only real quadratic fields in .

This paper presents the Extended State Observer (ESO) based repetitive control (RC) for piezoelectric actuator (PEA) based nano-positioning systems. The system stability is proved using Linear Matrix Inequalities (LMIs), which guarantees the asymptotic stability of the system. The ESObased RC used in this paper has the ability to eliminate periodic disturbances, aperiodic disturbances and model uncertainties. Moreover, ESO can be tuned using only two parameters and the model free approach of ESO-based RC, makes it an ideal solution to overcome the challenges of nano-positioning system control. Different types of periodic and aperiodic disturbances are used in simulation to demonstrate the effectiveness of the algorithm. The comparison studi

Reverse osmosis membrane desalination is one of the most significant water treatments that is used to offer freshwater. The aim of this research is to study the effect of controlling the value of the zeta potential on the suspended particles in the water and the proximity of the membrane surfaces in the colloidal solution, to keep the water stable electrically and disperse the colloidal particles. To achieve this aim, the experimental study was conducted in the Sanitary Engineering Laboratory, in the engineering college - University of Baghdad. Two systems were set up, one worked normally and the other worked by using the zeta rod placed before the reverse osmosis membrane. The results showed that the effect of the zeta rod increas

Active Magnetic Bearings (AMBs) are progressively being implemented in a wide variety of applications. Their exclusive appealing features make them suitable for solving traditional rotor-bearing problems using novel design approaches for rotating machinery.  In this paper, a linearized uncertain model of AMBs is utilized to develop a nonlinear sliding mode controller based on Lyapunov function for the electromechanical system. The controller requires measurements of the rotor displacements and their derivatives. Since the control law is discontinuous, the proposed controller can achieve a finite time regulation but with the drawback of the chattering problem. To reduce the effect of this problem, the gain of the uni