In this work, the set of all functions that are Fourier Transformable with regard to their structure both algebraic and topological is taken into account. Certain topological properties of the set of Fourier Transformable functions with the help of a metric are described. Also determines the proofs of the statements that the set of all Fourier Transformable functions is a commutative semi-group with respect to the convolution operation as well as Abelian group with respect to the operation of addition. Metric for two functions belonging to the set of all Fourier Transformable functions is defined and the proof that the Fourier Transformable functions space is complete with our metric is given. The separability theorem and that the Fourier Transformable functions space is disconnected are also discussed.

Flexibility is a concept associated with variable needs of human beings. Today Transformable structures are used to meet human changeable demands with different purposes and functions such as facades, roofs, sunshades, etc. A Flexible structure must be able to change physically and adapt to predetermined conditions. To provide flexibility and adaptability, Transformable systems are required to possess appropriate covering and a proper mechanism. Given their high elasticity, membranes can be considered as the first and easiest solution, but not necessarily the best one, for such deployable structures as they may interfere with the function of the structure; so that the use of membranes in deployable structures often leads to functional, operational and visual problems which indicate the necessity of application and investigations into rigid covers for such structures. Aimed at finding a new solution to improve flexibility of Transformable structures with rigid covers, this paper attempts to evaluate and assess a variety of coverings suitable for the structure proposed in this research. Being widely used, suiting various functions and having capability of design in different forms, scissor-like structures are chosen among other types of Transformable systems and a design is proposed for rigid cover of scissor-hinged Transformable domes. The solution for adding rigid covering involves adding additional kinetic elements to the scissor-like structure. Reciprocal elements, are connected to the structure in two directions, on which rigid covers are installed. One of the advantages of this proposal is that the elements are designed in such a way that rigid covers can be installed through various forms and configurations of modules.

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.

Background: To increase the effectiveness of orthodontic treatment in children with various degrees of dental enamel caries resistance using a personified orthodontic treatment. Materials and Methods: The present study included 108 adults (6-16 years old) with the first class of occlusion who referred for the Department of Pediatric Dentistry with orthodontics in Voronezh pediatrics’ dental clinic № 2" Russian Federation. According to the study design, it can be characterized as open, prospective, and clinical. The electrometric diagnostics of dental enamel and electromyography of the masseter and temporalis were recorded. Results: Functional therapy with the proposed personified orthodontic treatment normalized the mean number of biopotential masseters and temporalis muscles and improved caries resistance of hard dental tissues. However, the examination on the group of children with a low degree caries resistance of dental enamel resulted in the decrease in the mean number of electrometric diagnostics from 4. 0 (3. 6; 6. 0) μ A-1. 6 (1. 5; 3. 37) μ A (differences are statistically significant, p˂ 0. 05) after 18 months of replacement therapy. In turn, the mean number of bioelectric activity of masseter and temporalis muscles changed from 324. 25 (303. 75; 345. 75) μ V-332. 5 (318. 75; 347. 25) μ V, p˂ 0. 05. Conclusion: Employing the personified orthodontic treatment depending on the degree of caries resistance of the tooth enamel, determination of the functional state of the masseter and temporalis, and electrometric diagnosis of dental hard tissues enhanced the effectiveness of orthodontic treatment.

Transformable elements of all different types have become increasingly utilized in architecture in order to respond to varying building conditions. Adaptive strategies and geometries found in nature have inspired a need for buildings to respond to the changing environments in their immediate context. In today’s realm of environmental awareness, Transformable architecture has the ability to respond to environmental conditions, and in turn increase the efficiency, occupant comfort and energy consumption of building systems. This paper discusses different movements, mechanisms and applications of Transformable architecture, specifically foldable systems using pantographic elements. Case studies have been examined and evaluated in order to develop a final façade system with the ability to control the penetration of sunlight to a building under variable conditions. Sunlight can enable the passive heating of space, but may be detrimental and increase cooling loads and occupant discomfort through the summer months. In order to reduce the consumption of energy throughout the year, an occupant or computer controlled Transformable façade system, like the one proposed, can be utilized. The proposed design seeks to emulate the adaptive nature of plants and animals when it comes to being light sensitive or light responsive. This shading system, when applied to buildings, will attempt to provide a solution which can help buildings become more Transformable, and ultimately, more efficient. Despite of many Transformable proposals, this four-panel shading system is to transform itself responsively and is able to function not only in fully open configuration but also in various stages of deployment. The proposed design not only provides occupants with natural lighting conditions or protection from solar glare, it optimizes solar heat gain through the heating season or mitigates it throughout the cooling season, satisfying both the energy efficiency and occupant comfort.