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.

The ontology of person-centered healthcare: Theoretical essentials to reground medicine within its humanistic framework. Part I - A centered concept of personhood: Some tools to conceptualise subjectivity

2018 ◽  
Vol 6 (1) ◽  
pp. 146
Author(s):  
Thomas Frölich ◽  
F F Bevier ◽  
Alicja Babakhani ◽  
Hannah H Chisholm ◽  
Peter Henningsen ◽  
...  
Keyword(s):  
Graph Theory ◽  
Free Space ◽  
Rooted Tree ◽  
The Other ◽  
Discrete Mathematics ◽  
Soap Bubble ◽  
Soap Bubbles ◽  
In Series ◽  
The One ◽  
Individual Trees

To address subjectivity, as a generally rooted phenomenon, other ways of visualisation must be applied than in conventional objectivistic approaches. Using ‘trees’ as operational metaphors, as employed in Arthur Cayley’s ‘theory of the analytical forms called trees’, one rooted ‘tree’ must be set beneath the other and, if such ‘trees’ are combined, the resulting ‘forest’ is nevertheless made up of individual ‘trees’ and not of a deconstructed mix of ‘roots’, ‘branches’, ‘leaves’ or further categories, each understood as addressable both jointly and individually. The reasons for why we have chosen a graph theory and corresponding discrete mathematics as an approach and application are set out in this first of our three articles. It combines two approaches that, in combination, are quite uncommon and which are therefore not immediately familiar to all readers. But as simple as it is to imagine a tree, or a forest, it is equally simple to imagine a child blowing soap bubbles with the aid of a blow ring. A little more challenging, perhaps, is the additional idea of arranging such blow rings in series, transforming the size of the soap bubble in one ring after the other. To finally combine both pictures, the one of trees and the other of blow rings, goes beyond simple imagination, especially when we prolong the imagined blow ring becoming a tunnel, with a specific inner shape. The inner shape of the blow ring and its expansion as a tunnel are understood as determined by discrete qualities, each forming an internal continuity, depicted as a scale, with the scales combined in the form of a glyph plot. The different positions on these scales determine their length and if the endpoints of the spines are connected with an enveloping line then this corresponds to the free space left open in the tunnel to go through it. Using so many visualisation techniques at once is testing. Nevertheless, this is what we propose here and to facilitate such a visualisation within the imagination, we do it step by step. As the intended result of this ‘juggling of three balls’, as it were, we end up with a concept of how living beings elaborate their principal structure to enable controlled outside-inside communication.

Discrete Mathematics And Historical Analysis: A Study Of Magellan

1995 ◽  
Vol 88 (2) ◽  
pp. 106-112
Author(s):  
Arnold E. Perham ◽  
Bernadette H. Perham
Keyword(s):  
Game Theory ◽  
Graph Theory ◽  
Historical Analysis ◽  
Discrete Mathematics ◽  
Historical Narratives ◽  
Political Movements ◽  
Modeling Tools

Historical narratives often involve the lives of kings and queens, periods of exploration, or political movements. In these narratives, identifying the strategic elements and analyzing their interrelationships are interesting problems. Topics in discrete mathematics used to model conflict, like graph theory and game theory, could be helpful modeling tools of history.

Using Dynamic Geometry Software to Teach Graph Theory: Isomorphic, Bipartite, and Planar Graphs

1997 ◽  
Vol 90 (4) ◽  
pp. 328-332
Author(s):  
Anne Larson Quinn
Keyword(s):  
Graph Theory ◽  
Planar Graphs ◽  
Software Package ◽  
Dynamic Geometry ◽  
Bipartite Graphs ◽  
Dynamic Geometry Software ◽  
Discrete Mathematics ◽  
Geometer's Sketchpad ◽  
Mathematics Courses ◽  
Mathematics Course

I have always used concrete marupulatives, such as marshmallows and toothpicks, to create models for my geometry and discrete-mathematics courses. These models have come in handy when discussing volume, introducing the 4-cube, or illustrating isomorphic or bipartite graphs. However, after discovering what a dynamic geometry–software package could do for geometry teaching, which has been well documented by research (e.g., Battista and Clements [1995]), I realized that this type of technology also had much to offer for teaching graph theory in my discrete-mathematics course. Although this article discusses The Geometer's Sketchpad 3 (Jackiw 1995), any software that can draw, label, and drag figures can be substituted for Sketchpad.

scholarly journals Pengembangan Buku Ajar Kompilasi Teori Graf dengan Model Addie

2019 ◽  
Vol 3 (1) ◽  
pp. 137
Author(s):  
Ratih Puspasari
Keyword(s):  
Graph Theory ◽  
Small Groups ◽  
Development Model ◽  
Discrete Mathematics ◽  
Learning Design ◽  
Development Research ◽  
Test Results ◽  
Design Development ◽  
Analysis Design ◽  
Addie Model

Latar belakang penelitian ini adalah selama proses perkuliahan Teori Graf berlangsung buku yang digunakan oleh mahasiswa mengacu pada berbagai buku teks yang beredar di pasaran namun urutan penyampaiannya tidak seragam dan terstruktur. Buku teks khusus teori graf sangat jarang sekali ada. Kalaupun ada, seringkali masuk pada sub bab matematika diskrit, sehingga dosen sering mengalami kesulitan untuk meramu materi yang sesuai dengan silabus dan RPS. Ketidaktersediaan buku Teori Graf yang dijadikan acuan sebagai sumber belajar menyebabkan mahasiswa sulit memahami konsep. Tujuan dari penelitian ini adalah menghasilkan buku ajar kompilasi Teori Graf yang berkualifikasi baik dan layak diterapkan dalam perkuliahan teori graf oleh dosen dan mahasiswa di STKIP PGRI Tulungagung. Penelitian ini merupakan penelitian dengan model ADDIE yang terdiri dari analisis, perancangan, pengembangan, implementasi, dan evaluasi. Metode pengumpulan data menggunakan kuesioner. Hasil validasi buku ajar teori graf menunjukkan bahwa ahli isi/materi menilai buku ajar berkualifikasi baik, ahli desain pembelajaran menilai buku ajar berkualifikasi baik, dan ahli media pembelajaran menilai buku ajar berkualifikasi baik. Rerata hasil uji pada kelompok kecil baik dosen maupun mahasiswa menunjukkan bahwa buku ajar yang dihasilkan berada pada kualifikasi baik. Hasil penelitian pengembangan adalah buku ajar kompilasi teori graf berkualifikasi baik, layak, dan siap digunakan oleh dosen dan mahasiswa di STKIP PGRI Tulungagung. Kata kunci: buku ajar kompilasi, teori graf, model ADDIE.   ABSTRACT The background of this research is, during the Graph Theory lecture, the books used by students are textbooks on the market which have an unstructured contents and order. Special textbooks on graph theory are very rare, even if they are often included in the sub-chapter of discrete mathematics, so that lecturers often have difficulty compiling material that is in accordance with the syllabus and lesson plans. The unavailability of the graph theory book as learning sources has made the lack of students’ understanding the concept. The purpose of this study is to produce good quality and feasible text theory compilation textbooks in lectures on graph theory by lecturers and students at STKIP PGRI Tulungagung. This research is a development research. The development model used in this study is the ADDIE model, which includes five steps: analysis, design, development, implementation, and evaluation. Data is collected using questionnaire. The results of the validation of graph theory textbooks are content/material experts assess textbooks as well qualified, learning design experts assess textbooks as well qualified, and learning media experts assess textbooks as well qualified. The average test results in small groups both lecturers and students indicate that the textbook is in good qualification. Thus the development research stated that the textbook compilation of qualified graph theory is good, feasible, and ready to be used by lecturers and students at STKIP PGRI Tulungagung. Keywords: compilation textbook, graph theory, ADDIE model.

Graph Applications to Data Structures

2012 ◽  
Vol 433-440 ◽  
pp. 3297-3301
Author(s):  
V. Manjula
Keyword(s):  
Graph Theory ◽  
Computer Science ◽  
Programming Languages ◽  
Data Structures ◽  
Applied Mathematics ◽  
Syntactic Analysis ◽  
Discrete Mathematics ◽  
Major Theme ◽  
Computer Algorithms ◽  
Mathematical Programs

This paper presents a topic on Graph theory and its application to data Structures which I consider basic and useful to students in APPLIED MATHEMATICS and ENGINEERING.This paper gives an elementary introduction of Graph theory and its application to data structures. Elements of Graph theory are indispensable in almost all computer Science areas .It can be used in Some areas such as syntactic analysis, fault detection, diagnosis in computers and minimal path problems. The computer representation and manipulation of graph are also discussed so that certain algorithms can be included .A major theme of this paper is to study Graph theory and its Application to data structures Furthermore I hope the students not only learn the course but also develop their analogy perceive, formulate and to solve mathematical programs Thus Graphs especially trees, binary trees are used widely in the representation of data structures this course one can develop mathematical maturity, ability to understand and create mathematical argumentsMethod of derivation is procedure given in the text books with necessary formulae and their application . Concepts and notations from discrete mathematics are useful in studying and describing objects and problems in branches of computer science, such as computer algorithms, programming languages.

scholarly journals Classification of Filiform Lie Algebras up to dimension 7 Over Finite Fields

2016 ◽  
Vol 24 (2) ◽  
pp. 185-204
Author(s):  
Óscar J. Falcón ◽  
Raúl M. Falcón ◽  
Juan Núñez ◽  
Ana M. Pacheco ◽  
M. Trinidad Villar
Keyword(s):  
Graph Theory ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Finite Fields ◽  
Discrete Mathematics ◽  
Main Interest ◽  
Filiform Lie Algebras ◽  
Suitable Technique ◽  
New Strategies

Abstract This paper tries to develop a recent research which consists in using Discrete Mathematics as a tool in the study of the problem of the classification of Lie algebras in general, dealing in this case with filiform Lie algebras up to dimension 7 over finite fields. The idea lies in the representation of each Lie algebra by a certain type of graphs. Then, some properties on Graph Theory make easier to classify the algebras. As main results, we find out that there exist, up to isomorphism, six, five and five 6-dimensional filiform Lie algebras and fifteen, eleven and fifteen 7-dimensional ones, respectively, over ℤ/pℤ, for p = 2, 3, 5. In any case, the main interest of the paper is not the computations itself but both to provide new strategies to find out properties of Lie algebras and to exemplify a suitable technique to be used in classifications for larger dimensions.

scholarly journals MATHEMATICAL METHODS IN CIBERNETIC SECURITY: GRAPHS AND THEIR APPLICATION IN INFORMATION AND CYBERNETIC SECURITY

2021 ◽  
Vol 1 (13) ◽  
pp. 133-144
Author(s):  
Svitlana Shevchenko ◽  
Yuliia Zhdanovа ◽  
Pavlo Skladannyi ◽  
Svitlana Spasiteleva
Keyword(s):  
Graph Theory ◽  
Cyber Security ◽  
Discrete Mathematics ◽  
Mathematical Methods ◽  
Security Systems ◽  
Professional Orientation ◽  
Modeling Analysis ◽  
Course Work ◽  
Software And Hardware ◽  
Current Stage

This article is devoted to the problem of applying graph theory in cybersecurity systems and is an overview. Widespread penetration of mathematical methods in the development of information technology characterizes the current stage of our society. Among the mathematical methods used in information and cyber security, a large niche is graph technology. A streamlined system of special terms and symbols of graph theory allows you to easily and easily describe complex and subtle things both geometrically and algebraically. A graph is a mathematical model of a wide variety of objects, phenomena, and the relationships between them. This justifies the choice and relevance of this study. The article outlines the main elements of graph theory, the wide scope of their implementation and provides a historical perspective on the development of this theory. The analysis of scientific works allowed to determine the main directions of application of properties, characteristics of graphs and graph algorithms in information and cyber security. Among them are studies related to the use of graphs in information systems and programming; with modeling, analysis and application of attack graphs; with cryptographic transformations; with the construction of a decision tree in decision-making tasks in conditions of risk and uncertainty. It is proved that the ability to operate with the methods of graph technologies contributes to the development of software and hardware for information protection. The considered approaches to the application of graph theory in information and cyber security can be implemented during the study of the discipline "Special methods in security systems: discrete mathematics" for students majoring in 125 Cybersecurity, as well as in training in research or course work or thesis. By increasing the professional orientation of training, future cybersecurity workers gain a thorough knowledge of fundamental disciplines.

scholarly journals Lai's Conditions for Spanning and Dominating Closed Trails

10.37236/4511 ◽  
2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Wei-Guo Chen ◽  
Zhi-Hong Chen ◽  
Mei Lu
Keyword(s):  
Graph Theory ◽  
Real Number ◽  
Connected Graph ◽  
Finite Family ◽  
Discrete Mathematics ◽  
Line Graphs ◽  
Connected Graphs ◽  
Supereulerian Graphs ◽  
The Family ◽  
Hamiltonian Line Graphs

A graph is supereulerian if it has a spanning closed trail. For an integer $r$, let ${\cal Q}_0(r)$ be  the family of 3-edge-connected nonsupereulerian graphs of order at most $r$. For a graph $G$, define $\delta_L(G)=\min\{\max\{d(u), d(v) \}| \  \mbox{ for any $uv\in E(G)$} \}$. For a given integer $p\ge 2$ and a given real number $\epsilon$,  a graph $G$ of order $n$ is said to satisfy a Lai's condition if $\delta_L(G)\ge \frac{n}{p}-\epsilon$.  In this paper, we show that  if $G$ is  a  3-edge-connected graph of order $n$ with $\delta_L(G)\ge \frac{n}{p}-\epsilon$, then there is an integer $N(p, \epsilon)$ such that when $n> N(p,\epsilon)$, $G$ is supereulerian if and only if $G$ is not  a graph obtained from a  graph $G_p$ in the finite family ${\cal Q}_0(3p-5)$ by replacing some vertices in $G_p$ with nontrivial graphs. Results on the best possible Lai's  conditions for Hamiltonian line graphs of 3-edge-connected graphs or 3-edge-connected supereulerian graphs are given,  which are improvements of the results in [J. Graph Theory 42(2003) 308-319] and in [Discrete Mathematics, 310(2010) 2455-2459].

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