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.

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.

This study focuses on the investigation of intelligent form-finding and vibration analysis of a triangular polyhedral tensegrity that is enclosed within a sphere and subjected to external loads. The nonlinear dynamic equations of the system are derived using the Lagrangian approach and the finite element method. The proposed form-finding approach, which is based on a basic genetic algorithm, can determine regular or irregular tensegrity shapes without dimensional constraints. Stable tensegrity structures are generated from random configurations and based on defined constraints (nodes located on the sphere, parallelism, and area of upper and lower surfaces), and shape finding is performed using the fitness function of the genetic algorithm and multi-objective optimization goals. The genetic algorithm's efficacy in determining the shape of structures with unpredictable configurations is evaluated in two distinct scenarios: one involving a known connection matrix and the other involving fixed or random member positions (struts and cables). The shapes obtained from the algorithm suggested in this study are validated using the force density approach, and their vibration characteristics are examined. The findings of the comparative study demonstrate the efficacy of the proposed methodology in determining the vibrational behavior of tensegrity structures through the utilization of intelligent shape seeking techniques.

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.

Probability density functions of the involved random variables are essential for the reliability-based design of offshore structures. The objective of present research was the derivation of probability density function (PDF) for the local joint flexibility (LJF) factor, fLJF, in two-planar tubular DK-joints commonly found in jacket-type offshore structures. A total of 162 finite element (FE) analyses were carried out on 81 FE models of DK-joints subjected to two types of axial loading. Generated FE models were validated using available experimental data, FE results, and design formulas. Based on the results of parametric FE study, a sample database was prepared for the fLJF values and density histograms were generated for respective samples based on the Freedman-Diaconis rule. Nine theoretical PDFs were fitted to the developed histograms and the maximum likelihood (ML) method was applied to evaluate the parameters of fitted PDFs. In each case, the Kolmogorov-Smirnov and chi-squared tests were used to evaluate the goodness of fit. Finally, the Inverse Gaussian model was proposed as the governing probability distribution function for the fLJF. After substituting the values of estimated parameters, two fully defined PDFs were presented for the fLJF in tubular DK-joints subjected to two types of axial loading.

In this paper we present the development from paradoxism to neutrosophy, which gave birth to neutrosophic set and logic and especially to NeutroAlgebraic structures (or NeutroAlgebras) and AntiAlgebraic structures (or AntiAlgebras) that are generalizations and alternatives of the classical algebraic structures.

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.

In this paper we introduce the concept of Dirac structures on (Hermiti an) modules and vector bundles and deduce some of their properties. Among other things we prove that there is a one to one correspondence between the set of all Dirac structures on a (Hermitian) module and the group of all automorphisms of the module. This correspondence enables us to represent Dirac structures on (Hermitian) modules and on vector bundles in a very suitable form and define induced Dirac structures in a natural way.