Among a variety of approaches introduced in the literature to establish duality theory, Fenchel duality was of great importance in convex analysis and optimization. In this paper we establish some conditions to obtain classical strong Fenchel duality for evenly convex optimization problems defined in infinite dimensional spaces. The objective function of the primal problem is a family of (possible) infinite even convex functions. The strong duality conditions we present are based on the consideration of the epigraphs of the c-conjugate of the dual objective functions and the ε-c-subdifferential of the primal objective functions.

The soft sets were known since 1999, and because of their wide applications and their great flexibility to solve the problems, we used these concepts to define new types of soft limit points, that we called soft turning points.Finally, we used these points to define new types of soft separation axioms and we study their properties.

The overlap between science and knowledge is a feature of the 21st century. This integration, which crosses the traditional boundaries between academic disciplines, has occurred because of the emergence of new needs and new professions. This overlap has overshadowed the arts in general and design in particular. The Design achievements have not been far away from the attempts of integration of more than one type or design application to produce new outputs unique in its functional and aesthetic character, including the terms of internal graphic design.

The researcher raises the question of the functional dimension of graphic design in the internal space, in order to answer it through the methodological framework, which includes th

Philosophy of Abstraction and Construction of Space in Contemporary Iraqi Theater Abstract The aesthetic and stylistic features in the theatrical play develop according to the changes of the age and its developments. Stylistic forms different from the prevailing and familiar in the visions of contemporary theatre directors emerged which adopt the removal of traditional awareness in the creation of the visual space of theatrical discourse, through adopting contemporary formats and structures which depend on the abstraction representations in the aesthetic construction of the contemporary theatre show which is one of the prerequisites of the postmodern theater, that produces aesthetic data based on abstract metaphors in the formation of th

Expansive soil spreads in Iraq and some countries of the world. But there are many problems can be occurred to the structures that built on, so we must study the characteristics of these soils due to the  problems that may be caused to these structures which built on these kinds of soil and then study the methods of treatment. The present study focuses on improving  the geotechnical properties of expansive soils by treating it Metakaolin(M). Metakaolin (M) has never been used before as an improvement material  for stabilizing the expansive soil . Metakaolin  is a pozzolanic material. It’s obtained by calcination of kaolinite clay at temperatures from 700°C to 800°C. Kaolin chemical composition is

Human interest in negative space has existential roots, in addition to its cognitive value of things. In the environment, it includes space features from facts and activities, as negative space plays an active role in the field of visual perception, and this value comes from the need to absorb vital relationships in its environment, Man represents the positive part of negative space through his presence in this environment, and therefore this is reflected in the design of its types and the function of each element in the design, for the real effectiveness that the elements gain and their impact comes through the negative space that surrounds them and organizes their relationships with other elements, that the orientation is distributed a

Purpose: The concept of complete street is one of the modern trends concerned with diversifying means of transportation and reducing the disadvantages of mechanical transportation modes. This paper discusses the role of complete streets can play in developing the urban environment in the Alyarmok District of Baghdad.   Method/design/approach: The linear regression method used to analyze the opinions of 100 respondents surveyed in the study area in order to find the relationship between the urban environment and the complete street elements.   Theoretical framework: The Modern trends in urban planning aim to find alternatives to the policies of traditional transportation planning that focus on vehicular mobi

The aims of this thesis are to study the topological space; we introduce a new kind of perfect mappings, namely j-perfect mappings and j-ω-perfect mappings. Furthermore, we devoted to study the relationship between j-perfect mappings and j-ω-perfect mappings. Finally, certain theorems and characterization concerning these concepts are studied. On the other hand, we studied weakly/ strongly forms of ω-perfect mappings, namely -ω-perfect mappings, weakly -ω-perfect mappings and strongly-ω-perfect mappings; also, we investigate their fundamental properties. We devoted to study the relationship between weakly -ω-perfect mappings and strongly -ω-perfect mappings. As well as, some new generalizations of some definitions wh

Faith is a feature of the Mesopotamian population, since the ancient Mesopotamian was a believer and obedient to his God in any case, and this encouraged the emergence of some of the phenomena interpreted by historians as an integral part of the civilization and ancient history of this country, and these phenomena are the phenomena of the deification of kings for themselves, The first phenomenon was a personal endeavor for the uniqueness of power, sometimes to correct some mistakes in societies to balance the state, and civil rule is independent of religious rule, and the second was the result of divination and predictions of omen, in the case of any bad harbinger of the king, such as the occurrence of eclipse To the sun or a lunar eclip