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 .

The research aims to build a training program to develop the willpower in the kindergarten children. In order to achieve the objective of the research, the two researchers have developed a Training Program according to the following steps:

- Determining the general objective of the Training Program.

- Determining the behavioral objectives of the Training Program.

- Determining the content of the Training Program.

- Implementing the content of the Training Program sessions.

- Evaluating the Training Program.

The training program consisted of (15) sessions, each session included a set of parts (title, general objective, methods, time and place to implement the sessions, behavioral goals, tool

Societies developed throughout history with the development of life technology, that ideas presented by the contemporary art have been crystallized. The development included all the artistic fields such as the dramatic arts which depend on many effects and elements that led to the completion of the structure of the theater show. Scenography is considered one of the most important elements that the theatre show depends on such as the decoration, lighting, sound effects, costumes and accessories. The research addressed the following question: what are the characteristics and traits of scenography in the theatre show?
The research importance has become clear because it sheds lights on the characteristics of scenography in the Iraqi thea

While the impact of the fourth Industrial Revolution on the economy keeps accelerating, the signs of the fifth industrial revolution, whose key is innovation and creativity started to evolve. However, the challenge of achieving sustainable development and its goals remains faced by the global organizations; In this situation, Islamic banks are exposed to many challenges among which is the challenge of keeping themselves abreast of the latest developments in the modern technology which in turn is a tool for continuity and competition. On the flip side, to avoid the negative impact that these changes can have such as an increased gap between financial innovations and the requirements of sustainable development. Islamic banks in the

The purpose of this paper is to identifying the relationship between some visual functions and the level of achievement of air rifle shooting among young Iraqi female, and identifying the relationship between some functional variables of the respiratory and nervous systems at the level of achievement of air rifle shooting among young Iraqi female. The researchers used the descriptive approach in the correlative relationships style for its suitability and the research problem. The researchers determined the research community by the intentional method represented by (10) young female shooters who represent the national team with air rifle shooting effectiveness, and who represent (100%) of the research community. One of the most important re

The search aims to find out the most important requirements for the success of marshes investment and maximize the expected returns of investment was marked by a problem find aquestion for availability requirements necessary for the success of marshes investment has a research community owners decision in the province Maysan the most important conclusions to the search is that the investment great importance in support of the economy and raising the cultural and social level, there is no investment successful but only with configure the investment environment appropriate economic, social, cultural, political, and security ways. the most important recommendations are working on the provision of the investment environment appropria

Psychosocial Alienation is a modern concept that arises from the capitalist and materialistic conceptions of individuals. The evergrowing competitive nature of domestic societies crystallised the concept in its modern form. The intensity of the rapid changes in the urbanised societies prevents the individuals from exploring their inner selves. Thus, a new generation is created with an alienation crisis which is reflected inward towards the self and outwards toward society. Alan Ayckbourn (1939), A British playwright, presents Alienated characters inspired by his life on and off stage. He explores their Alienation and their path toward recovery and self-realization. A Brief History of Women (2017) Ayckbourn explores the depth of the individu

The aim of this study was to propose and evaluate an eco-epidemiological model with Allee effect and nonlinear harvesting in predators. It was assumed that there is an SI-type of disease in prey, and only portion of the prey would be attacked by the predator due to the fleeing of the remainder of the prey to a safe area. It was also assumed that the predator consumed the prey according to modified Holling type-II functional response. All possible equilibrium points were determined, and the local and global stabilities were investigated. The possibility of occurrence of local bifurcation was also studied. Numerical simulation was used to further evaluate the global dynamics and the effects of varying parameters on the asymptotic behavior of

This paper presents an analytical study for the magnetohydrodynamic (MHD) flow of a generalized Burgers’ fluid in an annular pipe. Closed from solutions for velocity is obtained by using finite Hankel transform and discrete Laplace transform of the sequential fractional derivatives. Finally, the figures are plotted to show the effects of different parameters on the velocity profile.