This paper generalizes and improves the results of Margenstren, by proving that the number of -practical numbers  which is defined by   has a lower bound in terms of . This bound is more sharper than Mangenstern bound when  Further general results are given for the existence of -practical numbers, by proving that the interval contains a -practical for all

the reality of small and medium enterprises analysis reflects weaknesses plaguing these enterprises and strengths that are characterized by, and thus the formulation of appropriate solutions to the obstacles faced by these enterprises to enhance its contribution to the achievement of economic and social development. Iraqi small and medium enterprises suffer from several obstacles stand in front of development and  support their competitiveness, the finance one of the main obstacles which impede growth and development of these enterprises, noting the banking system in Iraq reluctance to lend to small and medium-sized enterprises, as a result of the high cost of lending these enterprises compared to large projects, as well as

The current research deals with practical studies that explain to the Iraqi consumer multiple instances about the phenomenon of water hammer which occur in the water pipeline operating with pressure. It concern a practical study of the characteristics of this phenomenon and economically harmful to the consumer the same time. Multiple pipe fittings are used aimed to reduce this phenomenon and its work as alternatives to the manufactured arresters that used to avoid water hammer in the sanitary installations, while the consumer did not have any knowledge as to the non-traded for many reasons, including the water pressure decreases in the networks and the use of consumer pumps to draw water directly from the network. Study found a number of

The current research deals with practical studies that explain to the Iraqi consumer multiple instances about the phenomenon of water hammer which occur in the water pipeline operating with pressure. It concern a practical study of the characteristics of this phenomenon and economically harmful to the consumer the same time. Multiple pipe fittings are used aimed to reduce this phenomenon and its work as alternatives to the manufactured arresters that used to avoid water hammer in the sanitary installations, while the consumer did not have any knowledge as to the non-traded for many reasons, including the water pressure decreases in the networks and the use of consumer pumps to draw water directly from the network. Study found a numbe

Simplifying formulas that are used for calculations and design are the aim of researchers. For present work, the approach to distinguish the flow under sluice gate was conducted in a laboratory. The extensive experimental program was done to collect fifty-four data points for both free and submerged flow conditions. The data included different discharges, gate openings, flow depths at upstream as well as the flow depths represent a tail water and at a contracted section for downstream. The collected data are analyzed according to a problematic that may encounter in the field, to present a more straightforward (but with acceptable accurate) practical features equations and charts. Based on the proposed formulas, five meth

The geopolities considering as build from the basies builds of the polities
geography, participating in appointing the military geography, and submit to it
geo-polities purveyed, playing important role to appointing the builds relations
between the high strategy and the military strategy, while the foreign polities of
the state, which considering as a tool for the state outside it environment and
borders playing the role of the performance and the functional works to the
peaceful or hostile reaction according to the geopolities purveyed which
participating in amassing the recourse for the economical, political, social,
military and technology strategies and activating it to achieving the state interests
and obj

The study aimed to identify the awareness degree of teacher students in the department of Arabic language and their supervisors at Al-aqsa University for their future roles in the age of knowledge. To achieve this objective, descriptive- analytical approach was used. The instruments of this study were two questionnaires: first one consist of (20) item for teacher students, and the second consist of (27) item for educational supervisors which covered three roles: professional, technological, and humanitarian. The sample was (120) student selected randomly, and (39) supervisors of Arabic language. The result revealed that the mean of degree awareness of teacher students and their supervisors of future role are (3.857), (3.472) respectively

The research tagged (functional enhancement and its reflection on industrial product systems) focused on the possibility of enhancing industrial products in terms of form and functionality in a way that they are able to meet the needs of the user through the impact of technology and modern technologies on the functional enhancement of industrial products and their effectiveness in achieving formal and functional design variables, and producing products Industrial products are highly efficient and durable in order to improve them in order to meet the needs of the user, the transfer of technology between life forms and industrial products is desirable because the functional enhancement processes that occurred in general on industrial produ

The current research dealt with the study of space compatibility and its role in enhancing the functional aspect of the design of the interior spaces of isolation hospitals by finding a system or format that is compatible with the nature of the changes occurring in the structure and function of the space system, as well as contributing to enhancing compatibility between the functional aspect and the interior space. Therefore, the designer must The interior is the study of the functional and spatial aspects as they are the basic aspects for achieving suitability, and through the interaction between the person and the place, the utilitarian performance characteristics are generated that the interior designer is interested in and tries to d

Due to the developments taking place in the field of communications, informatics systems and knowledge management in the current century, and the obligations and burdens imposed on the business organization to keep pace with these developments, the traditional methods of administrative decision-making are no longer feasible, as recent trends have emerged in management that focus on the need to rely on quantitative methods such as operations research.. The latter is one of the results of World War II, which appeared for the first time in Britain to manage war operations. The first method used in this field is the linear programming method. The use of operations research has developed greatly in the past years, and the methods of analysis in