Search

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.

Using a new fixed point relation, the interval methods for the simultaneous inclusion of complex multiple zeros in circular complex arithmetic are constructed. Using the concept of the R-order of convergence of mutually dependent sequences, we present the convergence analysis for the total-step and the single-step methods with Schroder's and Halley-like corrections under computationally verifiable initial conditions. The suggested algorithms possess a great computational efficiency since the increase of the convergence rate is attained without additional calculations. Two numerical examples are given to demonstrate convergence characteristics of the proposed method.

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.

Using a suitable zero-relation and the inclusion isotonicity property, new interval iterative methods for the simultaneous inclusion of simple complex zeros of a polynomial are derived. These methods produce disks in the complex plane that contain the polynomial zeros in each iteration, providing in this manner an information about upper error bounds of approximations. Starting from the basic method of the fourth order, two accelerated methods with Newton’s and Halley’s corrections, having the order of convergence five and six respectively, are constructed. This increase of the convergence rate is obtained without any additional operations, which means that the methods with corrections are very efficient. The convergence analysis of the basic method and the methods with corrections is performed under computationally verifiable initial conditions, which is of practical importance. Two numerical examples are presented to demonstrate the convergence behavior of the proposed interval methods.

Higher-order methods for the simultaneous inclusion of complex zeros of algebraic polynomials are presented in parallel (total-step) and serial (single-step) versions. If the multiplicities of each zeros are given in advance, the proposed methods can be extended for multiple zeros using appropriate corrections. These methods are constructed on the basis of the zero-relation of Gargantini's type, the inclusion isotonicity property and suitable corrections that appear in two-point methods of the fourth order for solving nonlinear equations. It is proved that the order of convergence of the proposed methods is at least six. The computational efficiency of the new methods is very high since the acceleration of convergence order from 3 (basic methods) to 6 (new methods) is attained using only n polynomial evaluations per iteration. Computational efficiency of the considered methods is studied in detail and two numerical examples are given to demonstrate the convergence behavior of the proposed methods.

The aim of this paper is to present some modifications of Newton's type method for the simultaneous inclusion of all simple complex zeros of a polynomial. Using the concept of the R-order of convergence of mutually dependent sequences, the convergence analysis shows that the convergence rate of the basic method is increased from 3 to 6 using Jarratt's corrections. The proposed method possesses a great computational efficiency since the acceleration of convergence is attained with only few additional calculations. Numerical results are given to demonstrate convergence properties of the considered methods.

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.

Using a fixed point relation based on the logarithmic derivative of the k-th order of an algebraic polynomial and the definition of the k-th root of a disk, a family of interval methods for the simultaneous inclusion of complex zeros in circular complex arithmetic was established by Petkovic [M.S. Petkovic, On a generalization of the root iterations for polynomial complex zeros in circular interval arithmetic, Computing 27 (1981) 37-55]. In this paper we give computationally verifiable initial conditions that guarantee the convergence of this parallel family of inclusion methods. These conditions are significantly relaxed compared to the previously stated initial conditions presented in literature.

Improved iterative method of Euler’s type for the simultaneous inclusion of polynomial zeros is considered. To accelerate the convergence of the basic method of the fourth order we applied Borsch–Supan’s correction. It is proved that the R-order of convergence of the improved Euler-like method is six. The convergence analysis is derived under computationally verifiable initial conditions. The proposed algorithm possesses great computational efficiency since the increase of the convergence rate from 4 to 6 is obtained with negligible number of additional calculations. In order to demonstrate convergence properties of the suggested method, two numerical examples are given.

A modification of the iterative method of B?rsch-Supan type for the simultaneous inclusion of polynomial zeros is considered. The modified method provides the simultaneous inclusion of k (of n ? k) zeros, dealing with k inclusion disks of these zeros and the point (unchangeable) approximations to the remaining n - k zeros. It is proved that the R-order of convergence of the considered method is two if k < n and three if k = n. Three numerical examples are given to illustrate convergence properties of the presented method. .

A high-order one-parameter family of inclusion methods for the simultaneous inclusion of all simple complex zeros of a polynomial is presented. For specific values of the parameter, some known interval methods are obtained. The convergence rate of the basic fourth-order family is increased to 5 and 6 using Newton's and Halley's corrections, respectively. Using the concept of the R-order of convergence of mutually dependent sequences, we present a convergence analysis of the accelerated total-step and single-step methods with corrections. The suggested inclusion methods have great computational efficiency since an increase of the convergence rate is attained with only a few additional calculations. Two numerical examples are included to demonstrate the convergence properties of the proposed methods.

Two new methods of the fourth order for the simultaneous determination of multiple zeros of a polynomial are proposed. The presented methods are based on the fixed point relation of Laguerre's type and realized in ordinary complex arithmetic as well as circular complex interval arithmetic. The derived iterative formulas are suitable for the construction of modified methods with improved convergence rate with negligible additional operations. Very fast convergence of the considered methods is illustrated by two numerical examples.

The numerical stability of the fourth order iterative method of Laguerre's type for the simultaneous inclusion of polynomial zeros is analyzed in the presence of rounding errors. We state conditions under which the convergence order of the considered method is preserved. If these conditions are relaxed the convergence rate reduces to three.

Improved iterative methods of Halley's type for the simultaneous inclusion of all simple complex zeros of a polynomial are 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 to 5 and 6 using Newton's and Halley's corrections, respectively. The proposed inclusion methods possess a high computational efficiency since the increase of the convergence is attained without additional calculations. This advantage, together with very fast convergence, make that the presented methods are ranking among the most powerful inclusion methods for polynomial zeros. In order to demonstrate convergence properties of the proposed methods, two numerical examples are given.

Starting from a suitable fixed point relation, a new family of iterative methods for the simultaneous inclusion of multiple complex zeros in circular complex arithmetic is constructed. The order of convergence of the basic family is four. Using Newton’s and Halley’s corrections, we obtain families with improved convergence. Faster convergence of accelerated methods is attained with only few additional numerical operations, which provides a high computational efficiency of these methods. Convergence analysis of the presented methods and numerical results are given.

In this paper, we present iterative methods of Weierstress’ type for the simultaneous inclusion of all simple zeros of a polynomial. The main advantage of the proposed methods is the increase of the convergence rate attained by applying suitable correction terms. Using the concept of the R-order of convergence of mutually dependent sequences, we present the convergence analysis for the total-step and the single-step methods. Numerical examples are given.

Two iterative methods for the simultaneous inclusion of complex zeros of a polynomial are presented. Both methods are realized in circular interval arithmetic and do not use polynomial derivatives. The first method of the fourth order is composed as a combination of interval methods with the order of convergence two and three. The second method is constructed using double application of the inclusion method of Weierstrass’ type in serial mode. It is shown that its R-order of convergence is bounded below by the spectral radius of the corresponding matrix. Numerical examples illustrate the convergence rate of the presented methods

In this paper we construct iterative methods of Ostrowski's type for the simultaneous inclusion of all zeros of a polynomial. Using the concept of the R-order of convergence of mutually dependent sequences, we present the convergence analysis of the total-step and the single-step methods with Newton and Halley's corrections. The case of multiple zeros is also considered. The suggested algorithms possess a great computational efficiency since the increase of the convergence rate is attained without additional calculations. Numerical examples and an analysis of computational efficiency are given.

One of the most important problems in solving nonlinear equations is the construction of such initial conditions which provide both the guaranteed and fast convergence of the considered numerical method. Smale's approach from 1981, known as "point estimation theory", treats convergence conditions and the domain of convergence in solving an equation f(z) = 0 using only the information of f at the initial point z(0). A procedure of this type is applied in this paper to the fourth order iterative method for the simultaneous approximation of simple zeros of polynomials, proposed by Sakurai, Torii and Sugiura in 1991. We have stated initial conditions which ensure the guaranteed convergence of this method. These conditions are of significant practical importance since they are computationally verifiable; they depend only on the coefficients of a given polynomial, its degree n and initial approximations to polynomial zeros. .

A combined method for the simultaneous inclusion of complex zeros of a polynomial, composed of two circular arithmetic methods, is presented. This method does not use polynomial derivatives and has the order of convergence equals four. Computationally variable initial conditions that guarantee the convergence are also stated. Two numerical example are included to demonstrate the convergence speed of the presented method.

Starting from a suitable fixed point relation, a new one-parameter family of iterative methods for the simultaneous inclusion of complex zeros in circular complex arithmetic is constructed. It is proved that the order of convergence of this family is four. The convergence analysis is performed under computationally verifiable initial conditions. An approach for the construction of accelerated methods with negligible number of additional operations is discussed. To demonstrate convergence properties of the proposed family of methods, two numerical examples results are given.