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 .

Internet of Things (IoT) is one of the newest matters in both industry and academia of the communication engineering world. On the other hand, wireless mesh networks, a network topology that has been debate for decades that haven’t been put into use in great scale, can make a transformation when it arises to the network in the IoT world nowadays. A Mesh IoT network is a local network architecture in which linked devices cooperate and route data using a specified protocol. Typically, IoT devices exchange sensor data by connecting to an IoT gateway. However, there are certain limitations if it involves to large number of sensors and the data that should be received is difficult to analyze. The aim of the work here is to implement a self-

Population density represents an important indicator for determining the growth of the size of urban areas. Population density has a direct impact on the quality of life, and its excessive rise may lead to the deterioration of basic service facilities. The problem of the research is that the increase in the total population densities of the residential neighborhood may reflect negatively on the nature of the services provided to the residents in these shops, and thus the failure to achieve sustainability in the residential locality. The research assumes that the increase in population densities negatively affects the achievement of sustainability in the residential neighborhood.

The research aims to investigate the possibility of joint auditing in improving the market value of Iraqi companies listed on the Iraq Stock Exchange. The sample was represented by 10 Iraqi companies listed in the Iraq market for the period from 2014-2017 (2 years before implementation and 2 years after implementation) and the research was based on the idea that joint auditing enhances investor confidence and raises their level of security as a result of providing quality and reliable reports, and thus This indicates good news in the market that reflects on the performance of stocks and the market value of companies that adopt joint auditing. The results of the analysis indicate an improvement in the market value, but this improv

Islamic banks are distinguished by providing banking activities that are unique in providing them from the rest of the other types of banks, and these activities are a group of banking services provided by the bank to its customers, whether these banking activities are tangible or intangible. At the same time, it is a source of bank profits, as Islamic banks impose a percentage of Islamic Murabaha on those banking activities , However, these banks have developed new services that they provide with the funds of the Central Bank initiative launched at the beginning of (2016) due to the economic conditions that befell the country due to the (financial security) crisis that the country faced in 2014. To put forward initiatives, and a

 The deficit budget, one of the results of increased public spending for their revenues due to the economic pressures imposed by the interest of the economies of those countries from the need to increase government spending in order to revitalize the national economy and accelerate economic growth rates and provide employment to the growing levels of unemployment in those countries opportunities and what is required to address the current debt crisis (borrowing), which has become a big burden on the governments and the need to move towards the application of austerity spending and tax increases, which inevitably forced those countries will be reflected reduced spending on basic aspects of life and their peoples, particularly earners

Praise be to God, Lord of the worlds, and peace and blessings be upon our master Muhammad and his family and companions as follows:
   For God Almighty has swapped for every age a group of religious scholars who give news to the narrators, so that they can lie against the Sunnah of the Mustafa, who is among those who memorized Ibn Al-Mulqin, as he followed the ruler in his book Al-Badr Al-Munir in the Hadith of Al-Sharh Al-Kabeer, and our research included two topics, which we explained in the first topic: The sequels in which the teacher's son Al-Malqin disagreed, and we discussed in the second topic: the followings in which Ibn Al-Malqin agreed to rule.
   This research included important results, th

Groundwater quality deterioration due to anthropogenic natural activities and its immense utilization in various sectors is considered a great concern. The aim of this study is to determine the groundwater quality parameters at various sources in and around Dhaka city and compare them with Bangladesh drinking water standards. In this study, six groundwater quality parameters (pH, DO, COD, TS, TDS, and arsenic) and ten groundwater samples are analyzed to determine the water quality. The collected samples have maximum and minimum pH values of 6.9 and 6.4, respectively. Maximum and minimum DO values are 0.3 and 0.1 mg/L, respectively. The arsenic concentration is 0 mg/L for all collected groundwater samples. The maximum and minimum COD

Obstruct:                                                                                                                           &nbsp