Search results for: Vedic mathematics

Authors: Yasuhito Tanaka

Abstract:

We present a constructive proof of Tychonoff’s fixed point theorem in a locally convex space for uniformly continuous and sequentially locally non-constant functions.

Keywords: sequentially locally non-constant functions, Tychonoff’s fixed point theorem, constructive mathematics.

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Authors: Xun Ge, Songlin Yang

Abstract:

Soft set theory was initiated by Molodtsov in 1999. In the past years, this theory had been applied to many branches of mathematics, information science and computer science. In 2003, Maji et al. introduced some operations of soft sets and gave some operational rules. Recently, some of these operational rules are pointed out to be not true. Furthermore, Ali et al., in their paper, introduced and discussed some new operations of soft sets. In this paper, we further investigate these operational rules given by Maji et al. and Ali et al.. We obtain some sufficient-necessary conditions such that corresponding operational rules hold and give correct forms for some operational rules. These results will be help for us to use rightly operational rules of soft sets in research and application of soft set theory.

Keywords: Soft sets, union, intersection, complement.

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Authors: Jan Sindelar

Abstract:

The paper presents an applied study of a multivariate AR(p) process fitted to daily data from U.S. commodity futures markets with the use of Bayesian statistics. In the first part a detailed description of the methods used is given. In the second part two BVAR models are chosen one with assumption of lognormal, the second with normal distribution of prices conditioned on the parameters. For a comparison two simple benchmark models are chosen that are commonly used in todays Financial Mathematics. The article compares the quality of predictions of all the models, tries to find an adequate rate of forgetting of information and questions the validity of Efficient Market Hypothesis in the semi-strong form.

Keywords: Vector auto-regression, forecasting, financial, Bayesian, efficient markets.

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Authors: Naiqin Feng, Yuhui Qiu, Yingshan Zhang, Fang Wang

Abstract:

A logic model for analyzing complex systems- stability is very useful to many areas of sciences. In the real world, we are enlightened from some natural phenomena such as “biosphere", “food chain", “ecological balance" etc. By research and practice, and taking advantage of the orthogonality and symmetry defined by the theory of multilateral matrices, we put forward a logic analysis model of stability of complex systems with three relations, and prove it by means of mathematics. This logic model is usually successful in analyzing stability of a complex system. The structure of the logic model is not only clear and simple, but also can be easily used to research and solve many stability problems of complex systems. As an application, some examples are given.

Keywords: Complex system, logic model, relation, stability.

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Authors: V. K. Banga, Jasjit Kaur, R. Kumar, Y. Singh

Abstract:

In this research paper we have presented control architecture for robotic arm movement and trajectory planning using Fuzzy Logic (FL) and Genetic Algorithms (GAs). This architecture is used to compensate the uncertainties like; movement, friction and settling time in robotic arm movement. The genetic algorithms and fuzzy logic is used to meet the objective of optimal control movement of robotic arm. This proposed technique represents a general model for redundant structures and may extend to other structures. Results show optimal angular movement of joints as result of evolutionary process. This technique has edge over the other techniques as minimum mathematics complexity used.

Keywords: Kinematics, Genetic algorithms (GAs), Fuzzy logic(FL), Optimal control.

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Authors: G. Poonkuzhali, K.Thiagarajan, K.Sarukesi

Abstract:

With the enormous growth on the web, users get easily lost in the rich hyper structure. Thus developing user friendly and automated tools for providing relevant information without any redundant links to the users to cater to their needs is the primary task for the website owners. Most of the existing web mining algorithms have concentrated on finding frequent patterns while neglecting the less frequent one that are likely to contain the outlying data such as noise, irrelevant and redundant data. This paper proposes new algorithm for mining the web content by detecting the redundant links from the web documents using set theoretical(classical mathematics) such as subset, union, intersection etc,. Then the redundant links is removed from the original web content to get the required information by the user..

Keywords: Web documents, Web content mining, redundantlink, outliers, set theory.

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Authors: A. Schuchter, M. Promegger

Abstract:

The outbreak of the COVID-19 pandemic has shown us that online education is so much more than just a cool feature for teachers – it is an essential part of modern teaching. In online math teaching, it is common to use tools to share screens, compute and calculate mathematical examples, while the students can watch the process. On the other hand, flipped classroom models are on the rise, with their focus on how students can gather knowledge by watching videos and on the teacher’s use of technological tools for information transfer. This paper proposes a co-educational teaching approach for coding and engineering subjects with the help of drone-building to spark interest in technology and create a platform for knowledge transfer. The project combines aspects from mathematics (matrices, vectors, shaders, trigonometry), physics (force, pressure and rotation) and coding (computational thinking, block-based programming, JavaScript and Python) and makes use of collaborative-shared 3D Modeling with clara.io, where students create mathematics knowhow. The instructor follows a problem-based learning approach and encourages their students to find solutions in their own time and in their own way, which will help them develop new skills intuitively and boost logically structured thinking. The collaborative aspect of working in groups will help the students develop communication skills as well as structural and computational thinking. Students are not just listeners as in traditional classroom settings, but play an active part in creating content together by compiling a Handbook of Knowledge (called “open book”) with examples and solutions. Before students start calculating, they have to write down all their ideas and working steps in full sentences so other students can easily follow their train of thought. Therefore, students will learn to formulate goals, solve problems, and create a ready-to use product with the help of “reverse engineering”, cross-referencing and creative thinking. The work on drones gives the students the opportunity to create a real-life application with a practical purpose, while going through all stages of product development.

Keywords: Flipped classroom, co-creational education, coding, making, drones, co-education, ARCS-model, problem-based learning.

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Authors: Nhon Do, Tuyen Trong Tran, Phan Hoai Truong

Abstract:

Nowadays e-Learning is more popular, in Vietnam especially. In e-learning, materials for studying are very important. It is necessary to design the knowledge base systems and expert systems which support for searching, querying, solving of problems. The ontology, which was called Computational Object Knowledge Base Ontology (COB-ONT), is a useful tool for designing knowledge base systems in practice. In this paper, a design method for knowledge base systems in education using COKB-ONT will be presented. We also present the design of a knowledge base system that supports studying knowledge and solving problems in higher mathematics.

Keywords: artificial intelligence, knowledge base systems, ontology, educational software.

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Authors: Kazuhisa Takagi

Abstract:

This paper is about movies and dynamic objects for mobile phones. Dynamic objects are the software programmed by JavaScript. They consist of geometric figures and work on HTML5-compliant browsers. Mobile phones are very popular among teenagers. They like watching movies and playing games on them. So, mathematics movies and dynamic objects would enhance teaching and learning processes. In the movies, manga characters speak with artificially synchronized voices. They teach trigonometry together with dynamic mathematical objects. Many movies are created. They are Windows Media files or MP4 movies. These movies and dynamic objects are not only used in the classroom but also distributed to students. By watching movies, students can study trigonometry before or after class.

Keywords: Dynamic mathematical object, JavaScript, Google drive, transfer jet.

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Authors: Truong Quang Dang Khoa, Masahiro Nakagawa

Abstract:

Chaos and fractals are novel fields of physics and mathematics showing up a new way of universe viewpoint and creating many ideas to solve several present problems. In this paper, a novel algorithm based on the chaotic sequence generator with the highest ability to adapt and reach the global optima is proposed. The adaptive ability of proposal algorithm is flexible in 2 steps. The first one is a breadth-first search and the second one is a depth-first search. The proposal algorithm is examined by 2 functions, the Camel function and the Schaffer function. Furthermore, the proposal algorithm is applied to optimize training Multilayer Neural Networks.

Keywords: learning and evolutionary computing, Chaos Optimization Algorithm, Artificial Neural Networks, nonlinear optimization, intelligent computational technologies.

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Authors: Elham Amini Boroujeni, Hamid Reza Momeni

Abstract:

Design of an observer based controller for a class of fractional order systems has been done. Fractional order mathematics is used to express the system and the proposed observer. Fractional order Lyapunov theorem is used to derive the closed-loop asymptotic stability. The gains of the observer and observer based controller are derived systematically using the linear matrix inequality approach. Finally, the simulation results demonstrate validity and effectiveness of the proposed observer based controller.

Keywords: Fractional order calculus, Fractional order observer, Linear matrix inequality, Nonlinear Systems, Observer based Controller.

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Authors: Hans H. Diel

Abstract:

A computer model of Quantum Theory (QT) has been developed by the author. Major goal of the computer model was support and demonstration of an as large as possible scope of QT. This includes simulations for the major QT (Gedanken-) experiments such as, for example, the famous double-slit experiment. Besides the anticipated difficulties with (1) transforming exacting mathematics into a computer program, two further types of problems showed up, namely (2) areas where QT provides a complete mathematical formalism, but when it comes to concrete applications the equations are not solvable at all, or only with extremely high effort; (3) QT rules which are formulated in natural language and which do not seem to be translatable to precise mathematical expressions, nor to a computer program. The paper lists problems in all three categories and describes also the possible solutions or circumventions developed for the computer model.

Keywords: Computability, Foundation of Quantum Mechanics, Measurement Process, Modeling.

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Authors: Chahid K. Ghaddar

Abstract:

The spreadsheet engine is exploited via a non-conventional mechanism to enable novel worksheet solver functions for computational calculus. The solver functions bypass inherent restrictions on built-in math and user defined functions by taking variable formulas as a new type of argument while retaining purity and recursion properties. The enabling mechanism permits integration of numerical algorithms into worksheet functions for solving virtually any computational problem that can be modelled by formulas and variables. Several examples are presented for computing integrals, derivatives, and systems of deferential-algebraic equations. Incorporation of the worksheet solver functions with the ubiquitous spreadsheet extend the utility of the latter as a powerful tool for computational mathematics.

Keywords: Calculus functions, nonlinear systems, differential algebraic equations, solvers, spreadsheet.

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Authors: Xu-xia Hu, Eric T. T. Wong

Abstract:

The simulation of external aerodynamics is one of the most challenging and important automotive CFD applications. With the rapid developments of digital computers, CFD is used as a practical tool in modern fluid dynamics research. It integrates fluid mechanics disciplines, mathematics and computer science. In this study, two different types of simulations were made, one for the flow around a simplified high speed passenger car with a rear-spoiler and the other for the flow without a rear-spoiler. The standard k-ε model is selected to numerically simulate the external flow field of the simplified Camry model with or without a rear-spoiler. Through an analysis of the simulation results, a new rear spoiler is designed and it shows a mild reduction of the vehicle aerodynamics drag. This leads to less vehicle fuel consumption on the road.

Keywords: CFD, vehicle rear-spoiler design.

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Authors: Phang Chang, Phang Piau

Abstract:

Wavelet transform or wavelet analysis is a recently developed mathematical tool in applied mathematics. In numerical analysis, wavelets also serve as a Galerkin basis to solve partial differential equations. Haar transform or Haar wavelet transform has been used as a simplest and earliest example for orthonormal wavelet transform. Since its popularity in wavelet analysis, there are several definitions and various generalizations or algorithms for calculating Haar transform. Fast Haar transform, FHT, is one of the algorithms which can reduce the tedious calculation works in Haar transform. In this paper, we present a modified fast and exact algorithm for FHT, namely Modified Fast Haar Transform, MFHT. The algorithm or procedure proposed allows certain calculation in the process decomposition be ignored without affecting the results.

Keywords: Fast Haar Transform, Haar transform, Wavelet analysis.

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Authors: Jyh-Yang Wu, Sheng-Gwo Chen

Abstract:

In this paper, we present a simple effective numerical geometric method to estimate the divergence of a vector field over a curved surface. The conservation law is an important principle in physics and mathematics. However, many well-known numerical methods for solving diffusion equations do not obey conservation laws. Our presented method in this paper combines the divergence theorem with a generalized finite difference method and obeys the conservation law on discrete closed surfaces. We use the similar method to solve the Cahn-Hilliard equations on evolving spherical surfaces and observe stability results in our numerical simulations.

Keywords: Conservation laws, diffusion equations, Cahn-Hilliard Equations, evolving surfaces.

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Authors: Nurettin Simsek, Özlem Cakır

Abstract:

The aim of this study is to point out whether personalization of mathematical word problems could affect student achievement or not. The research was applied on two-grades students at spring semester 2008-2009. Before the treatment, students personal data were taken and given to the computer. During the treatment, paper-based personalized problems and paper-based non personalized problems were prepared by computer as the same problems and then these problems were given to students. At the end of the treatment, students- opinion was taken. As a result of this research, it was found out that there were no significant differences between learners through personalized or non-personalized materials, and also there were no significant differences between gender through personalized and non-personalized problems. However, opinion of students was highly positive through the personalized problems.

Keywords: Personalization, word problem, computer aided personalization.

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Authors: Mona Taheri

Abstract:

For the purpose of finding the quotient structure of multiple algebras such as groups, Abelian groups and rings, we will state concepts of ( strong or weak ) equalities on multiple algebras, which will lead us to research on how ( strong or weak) are equalities defined on a multiple algebra over the quotients obtained from it. In order to find a quotient structure of multiple algebras such as groups, Abelian groups and loops, a part of this article has been allocated to the concepts of equalities (strong and weak) of the defined multiple functions on multiple algebras. This leads us to do research on how defined equalities (strong and weak) are made in the multiple algebra on its resulted quotient.

Keywords: Multiple algebra, mathematics, universal algebra.

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Authors: Pei Wen Liao, Tsung Hau Jen

Abstract:

the data of Taiwanese 8th grader in the 4th cycle of Trends in International Mathematics and Science Study (TIMSS) are analyzed to examine the influence of the science teachers- preference in experimental teaching on the relationships between the affective variables ( the perceived usefulness of science, ease of using science and science learning interest) and the academic achievement in science. After dealing with the missing data, 3711 students and 145 science teacher-s data were analyzed through a Hierarchical Linear Modeling technique. The major objective of this study was to determine the role of the experimental teaching moderates the relationship between perceived usefulness and achievement.

Keywords: TIMSS database, Science achievement, Experimental teaching, Perceived Usefulness, Perceived Ease of Use

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Authors: G.Mehdiyeva, V.Ibrahimov, M.Imanova

Abstract:

As is known, one of the priority directions of research works of natural sciences is introduction of applied section of contemporary mathematics as approximate and numerical methods to solving integral equation into practice. We fare with the solving of integral equation while studying many phenomena of nature to whose numerically solving by the methods of quadrature are mainly applied. Taking into account some deficiency of methods of quadrature for finding the solution of integral equation some sciences suggested of the multistep methods with constant coefficients. Unlike these papers, here we consider application of hybrid methods to the numerical solution of Volterra integral equation. The efficiency of the suggested method is proved and a concrete method with accuracy order p = 4 is constructed. This method in more precise than the corresponding known methods.

Keywords: Volterra integral equation, hybrid methods, stability and degree, methods of quadrature

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Authors: Yaşar Baykul, Musa Gürsel, Hacı Sulak, Erhan Ertekin, Ersen Yazıcı, Osman Dülger, Yasin Aslan, Kağan Büyükkarcı

Abstract:

The reliability of the tools developed to learn the learning styles is essential to find out students- learning styles trustworthily. For this purpose, the psychometric features of Grasha- Riechman Student Learning Style Inventory developed by Grasha was studied to contribute to this field. The study was carried out on 6th, 7th, and 8th graders of 10 primary education schools in Konya. The inventory was applied twice with an interval of one month, and according to the data of this application, the reliability coefficient numbers of the 6 sub-dimensions pointed in the theory of the inventory was found to be medium. Besides, it was found that the inventory does not have a structure with 6 factors for both Mathematics and English courses as represented in the theory.

Keywords: Learning styles, Grasha-Riechmann, reliability, validity.

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Authors: Feng Cheng Chang

Abstract:

A given polynomial, possibly with multiple roots, is factored into several lower-degree distinct-root polynomials with natural-order-integer powers. All the roots, including multiplicities, of the original polynomial may be obtained by solving these lowerdegree distinct-root polynomials, instead of the original high-degree multiple-root polynomial directly. The approach requires polynomial Greatest Common Divisor (GCD) computation. The very simple and effective process, “Monic polynomial subtractions" converted trickily from “Longhand polynomial divisions" of Euclidean algorithm is employed. It requires only simple elementary arithmetic operations without any advanced mathematics. Amazingly, the derived routine gives the expected results for the test polynomials of very high degree, such as p( x) =(x+1)1000.

Keywords: Polynomial roots, greatest common divisor, Longhand polynomial division, Euclidean GCD Algorithm.

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Authors: V. Vargas-Alejo, L. E. Montero-Moguel

Abstract:

Understanding the concept of function has been important in mathematics education for many years. In this study, the models built by a group of five business administration and accounting undergraduate students when carrying out a population growth activity are analyzed. The theoretical framework is the Models and Modeling Perspective. The results show how the students included tables, graphics, and algebraic representations in their models. Using technology was useful to interpret, describe, and predict the situation. The first model, the students built to describe the situation, was linear. After that, they modified and refined their ways of thinking; finally, they created exponential growth. Modeling the activity was useful to deep on mathematical concepts such as covariation, rate of change, and exponential function also to differentiate between linear and exponential growth.

Keywords: Covariation reasoning, exponential function, modeling, representations.

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Authors: Jiming Yang

Abstract:

A kind of singularly perturbed boundary value problems is under consideration. In order to obtain its approximation, simple upwind difference discretization is applied. We use a moving mesh iterative algorithm based on equi-distributing of the arc-length function of the current computed piecewise linear solution. First, a maximum norm a posteriori error estimate on an arbitrary mesh is derived using a different method from the one carried out by Chen [Advances in Computational Mathematics, 24(1-4) (2006), 197-212.]. Then, basing on the properties of discrete Green-s function and the presented posteriori error estimate, we theoretically prove that the discrete solutions computed by the algorithm are first-order uniformly convergent with respect to the perturbation parameter ε.

Keywords: Convergence analysis, green's function, singularly perturbed, equi-distribution, moving mesh.

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Authors: Nicoletta Adamo-Villani

Abstract:

The object of this research is the design and evaluation of an immersive Virtual Learning Environment (VLE) for deaf children. Recently we have developed a prototype immersive VR game to teach sign language mathematics to deaf students age K- 4 [1] [2]. In this paper we describe a significant extension of the prototype application. The extension includes: (1) user-centered design and implementation of two additional interactive environments (a clock store and a bakery), and (2) user-centered evaluation including development of user tasks, expert panel-based evaluation, and formative evaluation. This paper is one of the few to focus on the importance of user-centered, iterative design in VR application development, and to describe a structured evaluation method.

Keywords: 3D Animation, Virtual Reality, Virtual Learning Environments, User-Centered Design, User-centered Evaluation.

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Authors: Saipunidzam Mahamad, Mohammad Noor Ibrahim, Mohamad Izzriq Ab Malek Foad, ShakirahMohd Taib

Abstract:

With the proliferation of the mobile device technologies, mobile learning can be used to complement and improve traditional learning problems. Both students and teachers need a proper and handy system to monitor and keep track the performance of the students. This paper presents an implementation of M-learning for primary school in Malaysia by using an open source technology. It focuses on learning mathematics using handheld devices for primary schools- students aged 11 and 12 years old. Main users for this system include students, teachers and the administrator. This application suggests a new mobile learning environment with mobile graph for tracking the students- progress and performance. The purpose of this system is not to replace traditional classroom but to complement the learning process. In a testing conducted, students who used this system performed better in their examination.

Keywords: M-Learning, Automated Mobile Graph.

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Authors: Tai-Hwa Emily Lu

Abstract:

This study was a part of the three-year longitudinal research on setting up an math learning model for the disadvantaged students in Taiwan. A target 2nd grade class with 10 regular students and 6 disadvantaged students at a disadvantaged area in Taipei participated in this study. Two units of a market basal math textbook concerning fractions, three-dimensional figures, weight and capacity were adapted to enhance their math learning motivations, confidences and effects. The findings were (1) curriculum adaptation was effective on enhancing students- learning motivations, confidences and effects; (2) story-type problems and illustrations decreased difficulties on understanding math language for students from new immigrant families and students with special needs; (3) “concrete – semiconcrete – abstract" teaching strategies and hands-on activities were essential to raise students learning interests and effects; and (4) curriculum adaptation knowledge and skills needed to be included in the pre- and in-service teacher training programs.

Keywords: curriculum adaptations, mathematics, disadvantaged students, inclusive classroom

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Authors: Rudy Agustriyanto, Akbarningrum Fatmawati

Abstract:

The utilization of cheese whey as a fermentation substrate to produce bio-ethanol is an effort to supply bio-ethanol demand as a renewable energy. Like other process systems, modeling is also required for fermentation process design, optimization and plant operation. This research aims to study the fermentation process of cheese whey by applying mathematics and fundamental concept in chemical engineering, and to investigate the characteristic of the cheese whey fermentation process. Steady state simulation results for inlet substrate concentration of 50, 100 and 150 g/l, and various values of hydraulic retention time, showed that the ethanol productivity maximum values were 0.1091, 0.3163 and 0.5639 g/l.h respectively. Those values were achieved at hydraulic retention time of 20 hours, which was the minimum value used in this modeling. This showed that operating reactor at low hydraulic retention time was favorable. Model of bio-ethanol production from cheese whey will enhance the understanding of what really happen in the fermentation process.

Keywords: Cheese whey, ethanol, fermentation, modeling.

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Authors: Mohamed Chabi, Mohammad Shahid Jamil, Mahmoud I Syam

Abstract:

The purpose of this study is to determine whether paper assessment especially in the subject mathematics will ever be completely replaced by online assessment using Learning Management System and Content Management System such as blackboard. Testing students has moved from the traditional scribbling and sketching on paper towards working online on a screen and keyboard. It is found that online assessment by using selective types of questions like multiple choices, true or false and final answer questions don’t reflect the actual understanding of students in solving the problems and teachers can’t determine the weakness points of students. In addition, it is showed that OBMCQs are a very good tool for self-assessment and when teachers are testing for knowledge and facts. But when it comes to the skills, OBMCQs are poor tools for measuring the ability to apply knowledge to complex math problem. 

Keywords: Paper assessment, online assessment, learning management system, content management system.

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Authors: Mihai Rebenciuc, Simona Mihaela Bibic

Abstract:

Branch of modern mathematics, graphs represent instruments for optimization and solving practical applications in various fields such as economic networks, engineering, network optimization, the geometry of social action, generally, complex systems including contemporary urban problems (path or transport efficiencies, biourbanism, & c.). In this paper is studied the interconnection of some urban network, which can lead to a simulation problem of a digraph through another digraph. The simulation is made univoc or more general multivoc. The concepts of fragment and atom are very useful in the study of connectivity in the digraph that is simulation - including an alternative evaluation of k- connectivity. Rough set approach in (bi)digraph which is proposed in premier in this paper contribute to improved significantly the evaluation of k-connectivity. This rough set approach is based on generalized rough sets - basic facts are presented in this paper.

Keywords: (Bi)digraphs, rough set theory, systems of interacting agents, complex systems.

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