The significance of the work is to introduce the new class of open sets, which is said Ǥ- -open set with some of properties. Then clarify how to calculate the boundary area for these sets using the upper and lower approximation and obtain the best accuracy.

This paper contains an equivalent statements of a pre-  space, where  are considered subsets of with the product topology. An equivalence relation between the preclosed set  and a pre-  space, and a relation between a pre-  space and the preclosed set  with some conditions on a function  are found. In addition, we have proved that the graph  of  is preclosed in if  is a pre-  space, where the equivalence relation  on  is open.

     On the other hand, we introduce the definition of a pre-stable ( pre-stable) set by depending on the concept of a pre-neighborhood, where we get that every stable set is pre-stable. Moreover, we obtain that

Some Results on Fuzzy Zariski

Topology  on Spec(J.L)

   Singled current study on the subject of shorthand in structure designs logos (Iraqi sports clubs model), as the current study Tdmt four chapters, was in the first chapter defines the research problem and its significance, as well as the aim of the research in the know shorthand formal in structure designs logos (Iraqi sports clubs model ), and identifies Find time limits: - slogans Iraqi sports clubs for the years (1956 - 1970), because it represented the years to include designs slogans official Iraqi sports clubs that have been elected in this period for the purpose of examining the reality of the design in the current search. And it represented the spatial limits: - the Republic of Iraq - Iraqi slogans designs sports

An experimental and theoretical analysis was conducted for simulation of open circuit cross flow heat
exchanger dynamics during flow reduction transient in their secondary loops. Finite difference
mathematical model was prepared to cover the heat transfer mechanism between the hot water in the
primary circuit and the cold water in the secondary circuit during transient course. This model takes under
consideration the effect of water heat up in the secondary circuit due to step reduction of its flow on the
physical and thermal properties linked to the parameters that are used for calculation of heat transfer
coefficients on both sides of their tubes. Computer program was prepared for calculation purposes which
cover a

The research aims to identify the bedroom furniture designs for children who are in ages range between (4-6) years and the rate of employing them in developing their aesthetic sense. To achieve this objective, the researchers developed the two research tools represented by a analysis-description form of bedroom furniture designs included a number of domains that were represented in the shapes, colors, and sizes of the furniture, as well as the availability of the safety factor, ease of use, cleaning and movement. As for the aesthetic sense scale included (30) paragraphs and alternatives (always, sometimes, never), they were distributed among a representative sample of (170) mothers of children were chosen randomly from (17) kindergartens

Find taught dimension aesthetic in the formation of post-modernism, which is one of the themes of aesthetics in the stream of postmodernism, is problematic because of the lack of provisions and fixed values reinforce the concept of beauty, and put done technical plastic in the circle of evaluation and judgment aesthetic, this research as an attempt to reveal the aesthetic concepts that can be drawn from artistic experiments in the formation of post-modernism, through the development of those concepts viable mainstream.
Search contains four chapters: the first chapter includes a general approach to the research, has been showcasing the research problem and the importance of research and goal of Search: detection dimension aesthetic in

Background: The role of prophylactic antibiotics remains controversial. It is clear that actively facial fractures are considered as clean contaminated and should be treated with therapeutic antibiotics; however, there is widespread variability in the use, type, timing, and duration of prophylactic antibiotic administrated in practice today. There is an adverse effect of increased antibiotic resistance, as well as costs, it is important to review the current evidence for the role of prophylactic antibiotics in compound facial fractures. The purpose of this study is to evaluate the role and significance of preoperative, perioperative and postoperative antibiotic prophylaxis for patients when there is already an infective focus, such as co

Consider a simple graph   on vertices and edges together with a total  labeling . Then ρ is called total edge irregular labeling if there exists a one-to-one correspondence, say  defined by  for all  where  Also, the value  is said to be the edge weight of . The total edge irregularity strength of the graph G is indicated by  and is the least  for which G admits   edge irregular h-labeling.  In this article,   for some common graph families are examined. In addition, an open problem is solved affirmatively.