This paper by reviewing the main examples of small to medium-scale Retractable Roof structures covering building courtyards is to present an innovative rigid Retractable Roof system employing spatial frames for a courtyard of an existing building in Tabriz Islamic Art University. The courtyard is currently used for temporary exhibitions and gatherings whenever permitted by environmental conditions. The proposed Retractable Roof will extend the application of the building throughout whole year period and also adds to its beauty and functionality. One of the main advantages of this design that makes it as a good alternative for this building is the way that the Roof is retracted in different segments separately in a regulated deployment process and its potential in being used in different stages of the deployment process. The proposed Roof consists of four Retractable zones all covered with transparent rigid material and a fixed central part being inspired by the patterns of Iranian historic architecture. The Retractable parts are placed at four corners and composed of rigid panels sliding across each other. An actuating force is applied to the first panel of each module and consequently makes the other panels move throughout the associated fixed track.

For the time being, the use of movable structures has drawn the attention of many architects and engineers due to their ability to achieve flexibility. By providing favorable and different conditions for a certain space and creating dynamics and flexibility in buildings, transformable Roofs have been successful in many global projects. In this research, the movement mechanisms of transformable Roofs have been investigated and analyzed. The movement structure of these Roofs is classified into four groups: rigid, membrane, scissor, and umbrella mechanisms. While explaining the processes and the mode of movement in each mechanism, a prominent project has been analyzed as an example of each group. Then, the characteristics of 60 examples of Retractable Roofs built around the world during the last six decades are briefly stated. The results of this study show that most transformable Roofs are used in stadiums and sports centers. The rigid mechanism and membrane are the most useful mechanisms for transformable Roofs. Most transformable Roofs are made of steel trusses and cable structures. These Roofs are used to cover openings up to more than 300 meters. Most openings are covered with a rigid movement mechanism and the smallest openings are covered with a scissor movement mechanism. The ratio of the length of the opening to the thickness of the Roof changes from about 30 to 240, and the highest value is for the membrane mechanism. To cover Retractable Roofs in four groups, light materials including Teflon, ETFE, and PVC are mainly used.

A module M is called epi-Retractable if every submodule of M is a homomorphic image of M. Dually, a module M is called co-epi-Retractable if it contains a copy of each of its factor modules. In special case, a ring R is called co-pli (respectively, copri) if RR (respectively, RR) is co-epi-Retractable. It is proved that if R is a left principal right duo ring, then every left ideal of R is an epi-Retractable R-module. A co-pli strongly prime ring R is a simple ring. A left self-injective co-pli ring R is left Noetherian if and only if R is a left perfect ring. It is shown that a cogenerator ring R is a pli ring if and only if it is a co-pri ring. Moreover, if R is a left perfect ring such that every projective R-module is co-epi-Retractable, then R is a quasi-Frobenius ring.

We call a module MR essentially Retractable if HomR (M,N)¹0 for all essential submodules N of M. For a right FBN ring R, it is shown that: (i) A nonzero module R M is Retractable (in the sense that HomR (M,N) ¹0 for all nonzero N£MR) if and only if certain factor modules of M are essentially Retractable nonsingular modules over R modulo their annihilators. (ii) A non-zero module MR is essentially Retractable if and only if there exists a prime ideal PÎAss (MR) such that HomR (M,N)¹0. Over semiprime right nonsingular rings, a nonsingular essentially Retractable module is precisely a module with nonzero dual. Moreover, over certain rings R, including right FBN rings, it is shown that a nonsingular module M with enough uniforms is essentially Retractable if and only if there exist uniform Retractable R-modules {U i}iÎI and R-homomorphisms M¾®+iÎI U i¾®M with ab;¹0.

Let R be an arbitrary ring and N be a right R-module.  A right R-module M is called N-Retractable if HomR(M,N')≠0, for any nonzero submodule N' of N. This is a generalization of the concept of Retractable modules. The aim of this paper is to study of N-Retractable modules, where N is an arbitrary right R-module. One of the most important results of this paper is the characterization of rings that have a module such that each module is Retractable with respect to it. Also we show that the class of N-Retractable modules is closed under direct sums and direct products.

Horizontal development of the cities has resulted in much destruction environmentally and economically. Two of the major consequences of such destruction is imbalanced development and inappropriate application of lands in the cities that are referred brownfield in this article. Brownfield in the urban planning jargon, a brownfield site (or simply a brownfield), is a type of land formerly used for industrial purposes or some commercial applications. The brownfield concept was first introduced by the British government and was used in accordance with the sustainable development policies which is mostly focused on the environmentally polluted lands. In the last two decades, redevelopment policies of brownfield as a crucial practical solution for preventing disperse growth of cities and also supporting the concentrated growth of cities have been attracted more attention. The main features of the brownfields are: -1 Pollution: each land in which an environmental complication has the occurrence probability. -2 Empty and leaved without using and in general lands and properties that their activities have been closed or not been used anymore. Of course, some of the terms that must be separated from the brownfield areas are: greenfields and grayfields.Greenfields are those lands that previously has not been developed and often are rural or suburban. These green sites are located in the edge of small or large cities and have better accessibility and more palatability with additional space for future development.The term gray field, was defined in 1998 by new urbanism congress. Unlike the famous terms of greenfields (the rural undeveloped) and brownfields (polluted urban sites), the gray lands are called to the large undeveloped sites that have good reasons for redevelopment. The term of grayfield can be used to describe any kind of redevelopment that significantly is not polluted. But regarding the importance of environmental protection and sustainable development and realization their policies, it is essential to eliminate or reduce the environmental pollutions purposefully to achieve the redevelopment of brownfields.For the sake of importance and novelty of the subject, redevelopment of Brownfield with the objective of efficient applications of lands in cities and reducing the environmental pollution and also improving the social-economical context of these fields is the subject of this article. Brownfield of Kan stream in Tehran was selected as the case study. The field was selected as it is one of the few major barren Brownfield in Tehran. They are not only in the leaved brownfields but also regarding the river-valley nature, the fields has specific ecological and tourism features. Unfortunately, due to lack of planning and management, these brownfields have been converted to the locations of rubbish depot and uncontrolled polluted waters and therefore infected with the environmental pollution. The methodology of this article is descriptive analytical using library studies. After studying the theoretical framework, defining features of brownfield, literature review, objectives and the importance and of these fields, the redevelopment process of Kan stream Brownfield are presented. Finally, the conclusion and analysis of the actions are conducted in redevelopment of brownfield with social, economical and tourism approach.After comprehensive studies, in order to determine the kind of landuses in Kan brownfields, establishing a national and even an international performance scale park is designated as the planning vision. In this context, the objectives of the redevelopment planning process Kan brownfield included: creating a touristic space to enhance the region›s tourism identity, planning with emphasis on providing recreational services for all social classes, such as children, elderly people and women and people with disabilities (all divisions with regard to sex, age and physical aspects), strengthening of the relationship between people and nature and to replacing normal social activities and improvement environmental conditions; Developing ecotourism in urban environment regarding and it s benefits beyond natural landscapes, enhancing green space for per capita in Tehran city and attainment to the standard limits for environment qualities by using marginal lands and rivers sanctums. steel plates. In addition these bars are pre- tensioned by means of cable passing through them in order to behave properly to the applied forces.The way that the bars are moved through the retraction process and the function of the building effects on the selection of the covering materials. In this structure, as the distance between the bars is changed during the deployment process it is required to use a flexible but strong material that can resist repeated retraction. Therefore, a flexible membrane that is strong enough during movement and has a proper foldability such as ETFE is one of the best alternatives for covering the Roof. ETFE is also able to penetrate enough light inside of the building when the Roof is in fully closed position and this in turn reduce the energy required for running the building.The membrane is also attached to the bars though the slots that have already been created during fabrication and is fasted by means of pinned curve plate. This is also worth to mention that in this structure, the placement of the moveable components underneath the covering material support the whole structure even in severe weather conditions. Therefore, this increase the life cycle of the system and decrease the maintenance cost.In summary, this paper proposes a new solution for a Retractable curved Roof system that can not only be transformed from an open to closed configuration but is also able to support itself structurally even during movement and transformation. In other word, the structural and transformable components are integrated and are able to make the whole structure stable during transformation.

Generalizing concepts “right Bezout ” and “principal right ideal ” of a ring R to modules, an R-module M is called n-epiRetractable (resp. epi-Retractable) if every n-generated submodule (resp. submodule) of MR is a homomorphic image of M. It is shown that if MR is finitely generated quasi-projective 1-epi-Retractable, then EndR(M) is a right Bezout (resp. principal right ideal) ring if and only if MR is n-epi-Retractable for all n³1 (resp. epiRetractable). For a ring R and an infinite ordinal b³|R|, the R-module M = FÅN is epi-Retractable where F is a free R-module with a basis set of cardinality b and N is a g-generated R-module with g£b. A ring R is quasi Frobenius if every injective R-module is epi-Retractable. Injective modules in s[NR] are epi-Retractable for every NÎs [MR] if and only if every non-zero factor ring of S is a quasi Frobenius ring where S is an endomorphism ring of a progenerator in s[MR].

Several characterizations of a ring R is given for which any non-zero finitely generated module M is Retractable in the sense that HomR(M,N) is non-zero whenever N is a non-zero submodule of M. Such rings are called finite Retractable. It is shown that any ring being Morita equivalent to a commutative ring is finite Retractable. Also, if the commutative ring is semi-Artinian then any non-zero module is Retractable. The class of finite Retractable rings is shown to be closed under Morita equivalence and finite direct products. Moreover, for a finite Retractable ring R which is a right order in a ring Q, it is shown that Q is also finite Retractable.

First Roof weighting interval in mechanized longwall mining is related directly to the applied loads on support system and thus, has important role on stability, safety, and continuity of operation. This paper presents an innovative approach based on cavability of immediate Roof to estimate first Roof weighting interval. Nine inherent parameters of Roof strata and its surrounding environment which affect caving process were taken into account to develop a classification system, incorporating fuzzy hybrid multi criteria decision-making technique. Roof Strata Cavability index (RSCi) was defined as summation of ratings for all parameters. Subsequently, the relationship between RSCi and extracted volume until the first caving moment (i. e. the extraction height× panel width × first Roof weighting interval) was determined using linear and non-linear regression models. Models were proposed and validated using the actual field data collected from different longwall panels around the world. Results indicated that the quadratic polynomial model gave a better performance in the estimation of first Roof weighting interval, compared to the other models. It was concluded that the proposed approach is an accurate and flexible tool to estimate first Roof weighting interval in longwall mining.