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Advanced research frontiers are extended from biophysics relations on the Earth upto the discovering any type of alive matter within the whole space. Microorganisms’ motion within the molecular biology processes integrates variety of microorgnisms functions. In continuation of our Brownian motion phenomena research, we consistently build molecular-microorganisms structures hierarchy. We recognize everywhere biomimetic similarities between the particles in alive and nonalive matter. The research data are based on real experiments, without external energy impulses. So, we develop the analysis, inspired by fractal nature Brownian motion, as recognized joint parameter between particles in alive and nonalive biophysical systems. This is also in line with advance trends in hybrid submicroelectronic integrations. The important innovation in this paper is that we introduced approximation of trajectory and error calculations, using discrete mean square approximation, what cumulatively provide much more precise biophysical systems parameters. By this paper, we continue to generate new knowledge in direction to get complex relations between the particles clusters in biophysical systems condensed matter.

Biophysical and condensed matter systems connection is of great importance nowadays due to the need for a new approach in microelectronic biodevices, biocomputers or biochips advanced development. Considering that the living and nonliving systems’ submicroparticles are identical, we can establish the biunivocally correspondent relation between these two particle systems, as a biomimetic correlation based on Brownian motion fractal nature similarities, as the integrative property. In our research, we used the experimental results of bacterial motion under the influence of energetic impulses, like music, and also some biomolecule motion data. Our goal is to define the relation between biophysical and physical particle systems, by introducing mathematical analytical forms and applying Brownian motion fractal nature characterization and fractal interpolation. This work is an advanced research in the field of new solutions for high-level microelectronic integrations, which include submicrobiosystems like part of even organic microelectronic considerations, together with some physical systems of particles in solid-state solutions as a nonorganic part. Our research is based on Brownian motion minimal joint properties within the integrated biophysical systems in the wholeness of nature.

It is of great interest to determine the relation between biophysical and condensed matter systems, because this biomimetical approach provides new frontiers for further microelectronic circuits integrations. Molecular and submolecular particles are identical in living and nonliving organisms, which implies the possibility of considering these particles motion as the biunivocal phenomenon. Brownian motion and its fractal nature, as a general phenomenon existing within both systems, is an integrative property based on which we can establish the relation between these two systems. We used some experimental data, based on the bacterial motion experiments, regarding influence of different energy impulses on bacterial trajectories. The goal of this research is to introduce the asymptotic approaching of biophysical and condensed matter systems, based on Brownian motion fractal nature similarities, presented in mathematical analytical forms.

In Type-1 Fuzzy Sets (T1FS), membership functions have not associated with uncertainty. Type-2 Fuzzy Sets (T2FS) provides an opportunity to incorporate the uncertainty of membership functions into the theory of fuzzy sets at the expense of the number of additional computational operations. Therefore, Interval Type-2 Fuzzy Sets (IT2FS) is introduced where the number of computational operations is reduced to T2FS while preserving the good properties that T2FS possesses. This paper presents a comparative study of the Fuzzy Analytic Hierarchy Process (FAHP) with T1FS and IT2FS. The proposed methods rank the criteria to find the dominant indicators for creating optimal access in the implementation of Information and Communication Technology (ICT) in the concept development of the smart city. In this paper, we measure the similarity of the ranks in decision problems, applying Spearman’s rank correlation coefficient and the new Salabun’s coefficient suitable for comparing rankings in the field of decision making.

The goal of our research is to establish the direction of coronavirus chaotic motion to control corona dynamic by fractal nature analysis. These microorganisms attaching the different cells and organs in the human body getting very dangerous because we don’t have corona antivirus prevention and protection but also the unpredictable these viruses motion directions what resulting in very important distractions. Our idea is to develop the method and procedure to control the virus motion direction with the intention to prognose on which cells and organs could attach. We combined very rear coronavirus motion sub-microstructures images from worldwide experimental microstructure analysis. The problem of the recording this motion is from one point of view magnification, but the other side in resolution, because the virus size is minimum 10 times less than bacterizes. But all these images have been good data to resolve by time interval method and fractals, the points on the motion trajectory. We successfully defined the diagrams on the way to establish control over Brownian chaotic motion as a bridge between chaotic disorder to control disorder. This opens a very new perspective to future research to get complete control of coronavirus cases.

Including human, technological, organizational, and natural resources, contemporary cities represent an urban reflection of civilization development. The globalization and competitiveness have shaped cities commercially, politically, socially, and in terms of their design and growth. Looking for the new urban patterns that could meet the global challenges, culture was recently recognized, as an indispensable part of the sustainability, and the significant pillar for grounding the Smart City initiatives. The management of cultural heritage is a significant factor for recognization, definition, and affirmation of cultural identity. Given that technology primarily enhances the urban infrastructure, the management of built heritage is significant within the Smart City development paradigm. For this paper, in the decision-making process, indicators related to the management of the cultural built heritage are divided into six groups: governing, economic, social, environmental, technological, and architectural factors. The paper aims to identify priority indicators, as necessary in the further development of heritage management, using the Fuzzy Analytic Hierarchy Process (FAHP) and Interval Analytic Hierarchy Process (IAHP) methods. The isolation of dominant indicators should enable a more precise definition of future activities and measures. The application of these methods should address the extent to which differences in fuzzy and interval grading approaches may affect the final ranking.

Contemporary society and modern living in urban areas strive for more sustainable environments, respecting the past, history and their remains. Intangible and tangible cultural heritage has become an important urban resource for city promotion as well as a trigger for economic and social city development. Built heritage, as part of cultural heritage, consists of various buildings from different epochs. Sustainable principles developed within the concept of smart, environmentally-friendly, and responsive cities requires energy optimization while minimizing energy amounts needed for systems of heating and cooling in buildings. Energy rehabilitation seems to become a strategically necessary and legally obligatory task in Serbia too. It means the implementation of various measures in term of the use of renewable energy resources and improvement of the thermal envelope of the already existing facilities. However, this type of interventions often reflects on the visual appearance of the building, changing its form, façade articulation and materialization. Respecting legally prescribed allowance, according to the degree of regime protection of cultural built heritage, the paper goal is to develop a model for the protection of the buildings in term of improvement of their energetic performances. The research aim is to identify the most optimal measures to be applied to increase energy efficiency depending on building's degree of protection, in Serbia, using multi-criteria decision-making methodology.

In civil engineering and architecture, sustainability requires energy optimization minimizing the energy amounts needed for heating and cooling. Revitalization of built heritage, except the renewal of the original identity, and preservation through adaptive reuse, must meet the requirements set within the framework of energy postulates. Given that the physical interventions for improvement of energy efficiency can affect the visual appearance of the building, energy retrofitting of built heritage under the protection regime represents a challenge in the management of cultural heritage. The paper aims to identify the most optimal measures to be applied to increase energy efficiency, depending on the protection level, using the fuzzy Analytic Hierarchy Process (AHP) method. Results show that for the highest protection level, the maximum degree of optimism indicates complete preservation of building identity, favoring indicators related to the technical systems, while for the medium protection level, all degrees of optimism favor internal insulation of thermal barriers and collector walls. Despite the allowed interventions for the lowest protection level, the optimistic view suggests alternative solutions not to greatly undermined identity. At the maximum degree of optimism, the application of indicators for technical systems dominates, which only in the last resort makes changes to the building.

For the past four decades, the methodology of fuzzy analytic hierarchy process based on fuzzy trapezoidal or triangular numbers with the linear type of membership functions has witnessed an expanding development with applicability to a wide variety of areas, such as industry, environment, education, government, economics, engineering, health, and smart city leadership. On the other hand, the interval gray analytic hierarchy process is a more practical method when a significant number of professionals have large variations in preferences and interests in complex decisions. The paper examines the management of architectural heritage in smart cities, using methods of multi-criteria decision making. Two appropriate methods generally recommended by the scientific literature have been applied: fuzzy and interval grey analytic hierarchy process. By using both techniques, there is an opportunity to analyze the consensual results from the aspect of two different stakeholder groups: architectural heritage experts and smart city development experts. Trapezoidal fuzzy analytical hierarchical process shows better stability than a triangular one. Both approaches assign priority to the strategy, but the interval approach gives a more significant rank to architectural heritage factors. The similarity of the proposed methods has been tested, and the similarity factor in the ranking indicates a high degree of similarity in comparing the reference rankings.

New efficient iterative method of Halley's type for the simultaneous inclusion of all simple complex zeros of a polynomial is proposed. The presented convergence analysis, which uses the concept of the R -order of convergence of mutually dependent sequences, shows that the convergence rate of the basic fourth order method is increased from 4 to 9 using a two-point correction. The proposed inclusion method possesses high computational efficiency since the increase of convergence is attained with only one additional function evaluation per sought zero. Further acceleration of the proposed method is carried out using the Gauss-Seidel procedure. Some computational aspects and three numerical examples are given in order to demonstrate high computational efficiency and the convergence properties of the proposed methods.

Monitoring forests with satellite, remote sensors, and terrestrial measurements are active due to the forests’ great ecological and economic importance. The subject of our research is the reflectance of deciduous and coniferous forests, based on the results of terrestrial measurements by a spectroradiometer in the visible part of the electromagnetic spectrum (EMS) of 400–700 nm. One of the tasks is to show the reflectance of forest vegetation with continuous smooth curves obtained by constructed cubic splines. Interval mathematics was also used as mathematical support for obtaining the continuous representation of the center reflectance values and comparison with corresponding mean values of reflectance given by the spectroradiometer. The field of research is the Pester plateau, which represents the center of biodiversity in terms of richness and diversity of forest vegetation. Their center reflectance values higher than the corresponding values obtained using the spectroradiometer have been researched. Factor analysis of the reflectance of forests has been performed and two factors have been separated. This paper aims to find a mathematical model of forest reflection analysis that facilitates forest classification and, based on the range of the reflection, assessments the health status of the forest.

Information for the sustainable development in Macedonia is insufficient. It is important to meet human needs and the needs of its environment for the sustainable development but raising awareness is the necessary assumption. The sustainable development has multidisciplinary nature, a concept that includes the economy, ecology, ethics, sociology, law and policy and links the well-being of present and future generations with the capacity and limitations of biosphere in a way to make the life more sustainable. The aim of this paper is to examine all these aspects and impact on raising awareness of the need for the sustainable development. Through various forms of the surveys in public sector, the primary and secondary school, the faculty, in health care and factories, offer people the ability to move in wide initiatives for the sustainable development. Based on the results of the survey, which was conducted in the municipality of Gostivar in the Republic of Macedonia, using statistical analysis, appropriate conclusions and proposals were performed. Key words: awareness, information, sustainable development

Previous initiatives developed for the purpose of designing and the realization of a smart, sustainable city have shown that there is no single approach to make a city &ldquo, smarter&rdquo, and more sustainable. Each city represents a unique system where different stakeholders, local authorities, utility companies, and citizens undertake numerous activities, creating a matrix of interactions and interdependencies. In order to understand the ecological and social contexts of the city, as well as its priority activities, history, and specific features, the establishment of an appropriate methodology to support the establishment of a sustainable and smart city has become extremely important. Our research aims to explore key indicators in the development of the concept of the smart city in Serbia, and to assess the prioritization of activities. An integral approach based on a mathematical method a hybrid fuzzy Multi-criteria decision making (MCDM) model based on Interval type-2 fuzzy sets classifies the whole system through different criteria and sub-criteria while respecting the experts&rsquo, opinions. The aim is to offer modelled solutions for our country integrated with the EU by smart cities.

This paper explores and ranks the key performance indicators of multi-criteria decision-making in the process of selecting renewable energy sources (RES). Different categories of factors (e.g., political, legal, technological, economic and financial, sociocultural, and physical) are crucial for the analysis of such projects. In this paper, we apply the fuzzy analytic hierarchy process (fuzzy AHP) method—a mathematical method—in order to analyze the main criteria for such projects, which include the environment, the organizational management structure, project participants, and participants’ relationship with the performance indicators. In order of ranking, the indicators are the following: time, costs, quality, monitoring the project’s sustainability, user feedback, and users’ health and safety. The aim of this paper is to point out the necessity of creating an adjustable model for renewable energy projects in order to proceed with the sustainable development of the southeast part of Serbia. This model should lead the creation process for such a project, with the aim of increasing its energy efficiency.