scholarly journals Application of Basic Graph Theory in Autonomous Motion of Robots

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 919
Author(s):  
Petr Coufal ◽  
Štěpán Hubálovský ◽  
Marie Hubálovská
Keyword(s):  
Graph Theory ◽  
Discrete Mathematics ◽  
Practical Implementation ◽  
Research Survey ◽  
Student Failure ◽  
And Mathematics ◽  
The Individual ◽  
University Course ◽  
Basic Graph ◽  
Educational Robots

Discrete mathematics covers the field of graph theory, which solves various problems in graphs using algorithms, such as coloring graphs. Part of graph theory is focused on algorithms that solve the passage through mazes and labyrinths. This paper presents a study conducted as part of a university course focused on graph theory. The course addressed the problem of high student failure in the mazes and labyrinths chapter. Students’ theoretical knowledge and practical skills in solving algorithms in the maze were low. Therefore, the use of educational robots and their involvement in the teaching of subjects in part focused on mazes and labyrinths. This study shows an easy passage through the individual areas of teaching the science, technology, engineering, and mathematics (STEM) concept. In this article, we describe the research survey and focus on the description and examples of teaching in a university course. Part of the work is the introduction of an easy transition from the theoretical solution of algorithms to their practical implementation on a real autonomous robot. The theoretical part of the course introduced the issues of graph theory and basic algorithms for solving the passage through the labyrinth. The contribution of this study is a change in the approach to teaching graph theory and a greater interconnection of individual areas of STEM to achieve better learning outcomes for science students.

scholarly journals Computing Topological Indices for Para-Line Graphs of Anthracene

2019 ◽  
Vol 17 (1) ◽  
pp. 955-962 ◽  
Author(s):  
Zhiqiang Zhang ◽  
Zeshan Saleem Mufti ◽  
Muhammad Faisal Nadeem ◽  
Zaheer Ahmad ◽  
Muhammad Kamran Siddiqui ◽  
...  
Keyword(s):  
Graph Theory ◽  
Chemical Compound ◽  
Line Graph ◽  
Molecular Graph ◽  
Chemical Properties ◽  
Molar Refraction ◽  
Chromatographic Behavior ◽  
Chemical Graph ◽  
Chemical Graph Theory ◽  
And Mathematics

AbstractAtoms displayed as vertices and bonds can be shown by edges on a molecular graph. For such graphs we can find the indices showing their bioactivity as well as their physio-chemical properties such as the molar refraction, molar volume, chromatographic behavior, heat of atomization, heat of vaporization, magnetic susceptibility, and the partition coefficient. Today, industry is flourishing because of the interdisciplinary study of different disciplines. This provides a way to understand the application of different disciplines. Chemical graph theory is a mixture of chemistry and mathematics, which plays an important role in chemical graph theory. Chemistry provides a chemical compound, and graph theory transforms this chemical compound into a molecular graphwhich further is studied by different aspects such as topological indices.We will investigate some indices of the line graph of the subdivided graph (para-line graph) of linear-[s] Anthracene and multiple Anthracene.

scholarly journals Self-similar resistive circuits as fractal-like structures

2017 ◽  
Vol 40 (1) ◽  
Author(s):  
Claudio Xavier Mendes dos Santos ◽  
Carlos Molina Mendes ◽  
Marcelo Ventura Freire
Keyword(s):  
Scale Invariance ◽  
Self Similarity ◽  
General Properties ◽  
Modern Physics ◽  
Resistive Networks ◽  
Self Similar ◽  
And Mathematics ◽  
Definition Of ◽  
The Individual

Fractals play a central role in several areas of modern physics and mathematics. In the present work we explore resistive circuits where the individual resistors are arranged in fractal-like patterns. These circuits have some of the characteristics typically found in geometric fractals, namely self-similarity and scale invariance. Considering resistive circuits as graphs, we propose a definition of self-similar circuits which mimics a self-similar fractal. General properties of the resistive circuits generated by this approach are investigated, and interesting examples are commented in detail. Specifically, we consider self-similar resistive series, tree-like resistive networks and Sierpinski’s configurations with resistors.

Finding Dead-Point Positions of Planar Pin-Connected Linkages Through Graph Theoretical Duality Principle

2005 ◽  
Vol 128 (3) ◽  
pp. 599-609 ◽  
Author(s):  
O. Shai ◽  
I. Polansky
Keyword(s):  
Graph Theory ◽  
Discrete Mathematics ◽  
Duality Principle ◽  
Mathematical Foundation ◽  
The Dead

The paper brings another view on detecting the dead-point positions of an arbitrary planar pin-connected linkage by employing the duality principle of graph theory. It is first shown how the dead-point positions are derived through the interplay between the linkage and its dual determinate truss—the relation developed in the previous works by means of graph theory. At the next stage, the process is shown to be performed solely upon the linkage by employing a new variable, the dual of potential, termed face force. Since the mathematical foundation of the presented method is discrete mathematics, the paper points to possible computerization of the method.

Vocal Pedagogy in the Choral Rehearsal

2017 ◽  
Author(s):  
Duane Cottrell
Keyword(s):  
Scientific Research ◽  
Vocal Pedagogy ◽  
Practical Implementation ◽  
Vocal Production ◽  
Vocal Technique ◽  
Choral Conductors ◽  
Choral Singing ◽  
Choral Rehearsal ◽  
Choral Tone ◽  
The Individual

One of the primary endeavors of choral conductors is the facilitation of good choral tone, which is largely dependent upon the vocal technique of the individual singers. This chapter examines principles of historical vocal pedagogy, discussing their correlation with modern scientific research, and present suggestions for practical implementation of specific techniques in choral rehearsals. The chapter discusses four primary areas of vocal pedagogy in choral rehearsals: first, the significance of laryngeal position in choral singing; second, principles of resonance in singing and their impact on the choral sound; third, a discussion of breath support in choral singing; and fourth, principles of phonation and vocal production for singers in a choral setting. Each of these four discussions contain practical suggestions for the application of specific practices and exercises that will strengthen the vocal technique of choral singers.

scholarly journals Nursery School Cooperation with the Family in the Field of Media Education in Children

2021 ◽  
Vol 11 (2) ◽  
pp. 83-98
Author(s):  
Vladimíra Kocourková ◽  
Kamil Janiš ◽  
Veronika Woznicová
Keyword(s):  
Nursery School ◽  
Subject Area ◽  
Media Education ◽  
Negative Consequences ◽  
Specific Topic ◽  
School Teachers ◽  
Nursery Schools ◽  
Research Survey ◽  
The Family ◽  
The Individual

Abstract Introduction: The paper focuses on a narrowly specific topic of the family cooperation with an institution of pre-school education - the nursery school (or also just the nursery), concentrating on a specific topic of “media education”. It considers the determining factors and presents partial findings of a research survey aimed at the field of media education in nursery schools. Methods: The paper contains the results of our own questionnaire research, which was carried out online in nursery school teachers. It also contains a theoretical definition of media literacy and media education in the context of the target group. Results: The result is an analysis of the obtained findings and formulated proposals for measures in the given field, which are usable and applicable in practice. Discussion: The individual presented results are continuously discussed with regard to the findings from the field of media education in the nursery school. Today, the world of the media is a common part of life even for children of pre-school age, and therefore it is necessary to teach them to orient themselves in it, which should be one of the tasks of the nursery school. In the Czech Republic, this issue has not yet been addressed at a significant level or to an appropriate extent. Our results are therefore closely linked not only to the discussion comments, but also to the conclusions drawn from them. Limitations: The results of the empirical research may be influenced by the attitudes and prejudices of nursery school teachers in relation to media in pre-school children. Conclusion: An early intervention can teach children to use media for their benefit and prevent media from negatively affecting them. The negative consequences of unrestrained effects of e.g. the television or mobile phones have been empirically proven. This information about the negative consequences is very general, distorted or superficial for the general public (parents), though. We consider the implementation of media education into the “teaching” process in nursery schools to be inevitable, even with regard to a closer cooperation between the institution and parents. However, this also places increased demands on training pedagogical staff in nursery schools in the subject area, creating methodological materials, etc.

scholarly journals Parental Involvement and High School Dropout: Perspectives from Students, Parents, and Mathematics Teachers

2022 ◽  
Vol 11 (1) ◽  
pp. 469-480
Author(s):  
Giang-Nguyen T. ◽  
Byron Havard ◽  
Barbara Otto
Keyword(s):  
High School ◽  
High School Students ◽  
Parental Involvement ◽  
Drop Out ◽  
Negative Effects ◽  
School Students ◽  
Education Statistics ◽  
Using Data ◽  
And Mathematics ◽  
The Individual

<p>Students drop out of schools for many reasons, and it has negative effects on the individual and society. This paper reports a study using data published in 2015 from the Educational Longitudinal Study conducted by the National Center for Education Statistics to analyze the influence of parental involvement on low-achieving U.S. students’ graduation rates from high school. Findings indicate that both students and parents share the same perspective on the need for parental involvement in their academic progress. For low-achieving high school students, parental involvement in academic work is a positive factor influencing students’ graduation from high school.</p>

The Canterbury Tales and the Arabic Frame Tradition

PMLA ◽  
1983 ◽  
Vol 98 (2) ◽  
pp. 237-251 ◽  
Author(s):  
Katharine Slater Gittes
Keyword(s):  
Random Order ◽  
Canterbury Tales ◽  
Art Music ◽  
Arabic Literature ◽  
Confessio Amantis ◽  
Individual Unit ◽  
Music And Mathematics ◽  
And Mathematics ◽  
The Individual ◽  
The Canterbury Tales

The Canterbury Tales is the culmination of a frame tradition that originated and developed in Arabia, not in the West. The Arabic practice of enclosing tales within a frame may be explained by principles of organization peculiar to medieval Arabic literature, art, music, and mathematics: a preference for concreteness, a stress on autonomous elements, and a reliance on external organizing devices. Most Arabic literature emphasizes the individual unit; frames remain open-ended and inconclusive and rarely determine the subject or form of any included part. Although many Western characteristics are present in medieval European frame narratives like the Disciplina Clericalis, the Decameron, and the Confessio Amantis, those works, nonetheless, reveal themselves as continuations of the Arabic tradition. Even the Canterbury Tales, with all its subtle artistry, retains qualities typical of its Arabic ancestors, notably the controlling travelpilgrimage motif, the pointedly random order of tales, and the prominent authorial personality.

THEORY AND VOCATION OF THE POLICE IN MODERN STATE STUDIES: INTERPRETATION OF M. FОUCAULT

2021 ◽  
Vol 2 (2) ◽  
pp. 39-48
Author(s):  
Oleh Turenko ◽  
Keyword(s):  
A Priori ◽  
Social Institutions ◽  
Modern Society ◽  
Modern Concept ◽  
Practical Implementation ◽  
Regulatory Body ◽  
Continuous Control ◽  
State Laws ◽  
Theoretical Substantiation ◽  
The Individual

The Foucault’s interpretation of the police, its theoretical substantiation, the range of powers and managerial tasks in modernist discourses. The French philosopher emphasized it should the modern concept of “police” does not coincide with its original theories of modern times. The doctrines of modern political scientists idealized the vocation of the police and identified it with the entire government, providing it with universal means of implementing the state interest. Considering the police from the perspective of “history of thought” Foucault notes that it is the unlimited nature of police functions gave the modern government to approve a disciplinary society, a new form of government - bio-power. This form of power totally controlled the individual, “took care of him” at all levels of biological life and, above all, the depths of consciousness - artificially created his authenticity. At the same time, in the theories of political scientists, the police received the status of a self-regulatory body, whose activities were not strictly controlled by state laws. In this case, the police, in the imaginary sense, is the living embodiment of state interest, morality and integrity, the formative and corrective body of state power. In order to form a disciplined and productive life, the police must direct individuals to regulation, to their temporal and hierarchical repetition. The a priori qualities of the police and its all-encompassing powers form the basis for the assertion of the idea of a “police state” and its radical form of panopticon. It is thanks to the idea of panopticon, its practical implementation by the police in modern society - the formation of disciplinary practice of continuous control in the social institutions of modernism.

Educational Robotics in Smart Learning

2019 ◽  
pp. 244-255
Author(s):  
Saravanan Venkataraman ◽  
Sunil Kumar Sharma
Keyword(s):  
Learning Process ◽  
Educational Robotics ◽  
Technological Advancement ◽  
Science Concept ◽  
Teaching Approaches ◽  
Smart Learning ◽  
And Mathematics ◽  
Teaching Learning ◽  
Educational Robots ◽  
Mathematics And Science

Science, technology, engineering, and mathematics (STEM) are the key courses for the students in the 21st century. There are several teaching approaches to improve the average scores in STEM education. Involvement of robots in the teaching-learning process plays an important role to transform and enhance the learning process. The technological advancement helps the students to translate the typical mathematics and science concept into real-word applications. In this chapter, some concepts of STEM have been implemented with the help of Bioloid educational robots. The educational robotics enhance the academic achievement of the students. The programming of the BioLoid robots is carried out using RoboPlus software, and the outcomes of the concrete mathematics concepts are shown physically.

Numerical Implementation

1994 ◽  
Author(s):  
Nhan Phan-Thien ◽  
Sangtae Kim
Keyword(s):  
Boundary Element ◽  
Numerical Integration ◽  
Integral Equations ◽  
Large Scale ◽  
Boundary Integral Equations ◽  
Numerical Technique ◽  
Boundary Integral ◽  
Practical Implementation ◽  
Computing Environment ◽  
The Individual

Analytical solutions to a set of boundary integral equations are rare, even with simple geometries and boundary conditions. To make any reasonable progress, a numerical technique must be used. There are basically four issues that must be discussed in any numerical scheme dealing with integral equations. The first and most basic one is how numerical integration can be effected, together with an effective way of dealing with singular kernels of the type encountered in elastostatics. Numerical integration is usually termed numerical quadrature, meaning mathematical formulae for numerical integration. The second issue is the boundary discretization: when integration over the whole boundary is replaced by a sum of the integrations over the individual patches on the boundary. Each patch would be a finite element, or in our case, a boundary element on the surface. Obviously a high-order integration scheme can be devised for the whole domain, thus eliminating the need for boundary discretization. Such a scheme would be problem dependent and therefore would not be very useful to us. The third issue has to do with the fact that we are constrained by the very nature of the numerical approximation process to search for solutions within a certain subspace of L2, say the space of piecewise constant functions in which the unknowns are considered to be constant over a boundary element. It is the order of this subspace, together with the order and the nature of the interpolation of the geometry, that gives rise to the names of various boundary element schemes. Finally, one is faced with the task of solving a set of linear algebraic equations, which is usually dense (the system matrix is fully populated) and potentially ill-conditioned. A direct solver such as Gauss elimination may be very efficient for small- to medium-sized problems but will become stuck in a large-scale simulation, where the only feasible solution strategy is an iterative method. In fact, iterative solution strategies lead naturally to a parallel algorithm under a suitable parallel computing environment. This chapter will review various issues involved in the practical implementation of the CDL-BIEM on a serial computer and on a distributed computing environment.

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