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 .

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 .

Abstract.The goal of this article is to find the CEO of Iraqi companies that use strategic planning and determine if they are capable of diagnosing the traits of strategic planning systems that improve these companies' capacity to successfully address crisis-related needs. The capacity of the company to successfully react to crisis needs and demands is enhanced by the use of strategic planning, according to a review of data from 64 enterprises utilizing statistical analysis. Furthermore, top and division or unit managers must be involved and committed for strategic planning to be successful. It also has to be planned with an external orientation and get more than just lip service from top and unit or division level managers. In other words,

The current research aims to identify the level of effective leadership practices dimensions (clear vision and specific goals, good planning and effective influence, and monitoring well as evaluation) among the senior leaders in the Office of the Iraqi Interior Ministry., The researchers adopted the descriptive analytical approach to collect data through the questionnaire as a main tool, developed by relying on international standards after making adjustments to its items consisting of (25) items that included the research variable, the questionnaire was distributed to all the research community (comprehensive inventory) by 120 forms from emplo

The Accommodation industry in Iraq suffers from many problems, especially after 2003, when the Accommodation industry was exposed to many crises due to the security and political situation in Iraq, which negatively affected the administrative operations inside the industry and created many problems, the most important of which are deterioration, high costs and poor performance, so some hotel administrations sought To find alternative solutions that help in the advancement of hotels, one of the proposals is to go to technology, as technology is currently one of the most important solutions to solve large complex problems, as the world has turned to automation to solve complex problems such as increasing production, reducing costs, and rai

ABSTRACT

            The aim of the research is to identify the impact of the areas of organizational change in strategic marketing planning in cement factories operating within the city of Al-Khums, and this effect was measured using a questionnaire consisting of 28 phrases, and it was relied on the descriptive approach that suits the nature of the subject of the research, while the research community consists of heads And members of the board of directors, authorized managers, unit managers and heads of departments in the factories under study, which numbered 55 respondents, during the month of September of the year 2021, and a sample of the compreh

In this paper, we consider inequalities in which the function is an element of n-th partially order space. Local and Global uniqueness theorem of solutions of the n-the order Partial differential equation Obtained which are applications of Gronwall's inequalities.

Background: A wound is defined as a break or damage in the skin, resulting from physical or thermal damage or as a result of the presence of an underlying medical or physical condition. Herbal medicine can be called one of the branches of medicine in various forms.Phyllunthus amarus is a small herb well known for its medicinal properties and widely used worldwide. P. amarus is an important plant of Indian Ayurvedic system of medicine. Fibronectin is a major component of the extracellular matrix. It is secreted by various cells, primarily fibroblasts, as a soluble protein dimer and is then assembled into an insoluble matrix in a complex cell-mediated process. Materials and methods: Forty rats will be subjected for a surgical operation

Analysis the economic and financial phenomena and other requires to build the appropriate model, which represents the causal relations between factors. The operation building of the model depends on Imaging conditions and factors surrounding an in mathematical formula and the Researchers target to build that formula appropriately. Classical linear regression models are an important statistical tool, but used in a limited way, where is assumed that the relationship between the variables illustrations and response variables identifiable. To expand the representation of relationships between variables that represent the phenomenon under discussion we used Varying Coefficient Models

Localization is an essential demand in wireless sensor networks (WSNs). It relies on several types of measurements. This paper focuses on positioning in 3-D space using time-of-arrival- (TOA-) based distance measurements between the target node and a number of anchor nodes. Central localization is assumed and either RF, acoustic or UWB signals are used for distance measurements. This problem is treated by using iterative gradient descent (GD), and an iterative GD-based algorithm for localization of moving sensors in a WSN has been proposed. To localize a node in 3-D space, at least four anchors are needed. In this work, however, five anchors are used to get better accuracy. In GD localization of a moving sensor, the algo