A mathematical model in graph theory for biological classification

1966 ◽  
Vol 12 (3) ◽  
pp. 297-310 ◽  
Author(s):  
G.F. Estabrook
Keyword(s):  
Mathematical Model ◽  
Graph Theory ◽  
Biological Classification

The Automatic Generation of a Mathematical Model for Machinery Systems

1973 ◽  
Vol 95 (2) ◽  
pp. 629-635 ◽  
Author(s):  
D. A. Smith ◽  
M. A. Chace ◽  
A. C. Rubens
Keyword(s):  
Mathematical Model ◽  
Graph Theory ◽  
Computer Program ◽  
Mechanical System ◽  
Input Data ◽  
Automatic Generation ◽  
Electrical Networks ◽  
Lagrange’S Equation ◽  
Detailed Explanation ◽  
Independent Loops

This paper presents a detailed explanation of a technique for automatically generating a mathematical model for machinery systems. The process starts from a relatively small amount of input data and develops the information required to model a mechanical system with Lagrange’s equation. The technique uses elements of graph theory which were developed for electrical networks. The basic identifications required for mechanical systems are: paths from ground to mass centers, the independent loops of parts, if any, and paths associated with applied force effects. The techniques described in this paper have been used successfully in a generalized computer program, DAMN.

scholarly journals Cryptographic Recursive Control of Integrity of Metadata Electronic Documents. Part 1. Mathematical Model

2020 ◽  
pp. 2-18
Author(s):  
Dmitry Tali ◽  
◽  
Oleg Finko ◽  
◽  
Keyword(s):  
Mathematical Model ◽  
Graph Theory ◽  
Information Systems ◽  
Control Method ◽  
Research Result ◽  
Document Management ◽  
Technical Solution ◽  
Electronic Document ◽  
Electronic Documents ◽  
Electronic Document Management

The purpose of the research is to increase the level of security of electronic document metadata in the face of destructive influences from authorized users (insiders). Research methods: new scientific results allowed using a combination of data integrity control method based on the «write once» method and of authentication of HMAС messages (hash-based message authentication, as well as graph theory methods. Research result: a method of cryptographic recursive 2-D control of the integrity of electronic documents metadata is proposed. The analysis of the object of the study was carried out, based on the results of which it was concluded that it is necessary to effectively protect the metadata of electronic documents processed by automated information systems of electronic document management. Developed and described a mathematical model of the proposed method, based on graph theory. The developed technical solution makes it possible to implement the functions of cryptographic recursive twodimensional control of the integrity of the metadata of electronic documents, as well as to provide the possibility of localizing modified (with signs of violation of integrity) metadata records, in conditions of destructive influences of authorized users (insiders). This, in turn, reduces the likelihood of collusion between trusted parties by introducing mutual control over the results of their actions. The proposed solution makes it possible to ensure control of the integrity of data processed by departmental automated information systems of electronic document management, where, due to the peculiarities of their construction, it is impossible to effectively use the currently popular blockchain technology.

scholarly journals Application of Linear and Nonlinear Graphs in Structural Synthesis of Kinematic Chains

1973 ◽  
Vol 95 (2) ◽  
pp. 525-532 ◽  
Author(s):  
M. Huang ◽  
A. H. Soni
Keyword(s):  
Mathematical Model ◽  
Graph Theory ◽  
Structural Analysis ◽  
Three Dimensional ◽  
Structural Synthesis ◽  
Kinematic Chains ◽  
Piston Cylinder ◽  
General Constraints ◽  
Analysis And Synthesis ◽  
Linear And Nonlinear

Using graph theory and Polya’s theory of counting, the present paper performs structural synthesis and analysis of planar and three-dimensional kinematic chains. The Section 2 of the paper develops a mathematical model that permits one to perform structural analysis and synthesis of planar kinematic chains with kinematic elements such as revolute pairs, cam pairs, springs, belt-pulley, piston-cylinder, and gears. The theory developed is applied to enumerate eight-link kinematic chains with these kinematic elements. The Section 3 of the paper develops a mathematical model that permits one to perform structural analysis and synthesis of multi-loop spatial kinematic chains with higher and lower kinematic pairs. The theory developed is applied to enumerate all possible two-loop kinematic chains with or without general constraints.

Semantic Product Requirement Network as Approaches for a Requirement Terminology and Tool for Linguistic Analysis of Requirements in Continuous Text

2008 ◽  
Author(s):  
Youssef Chahadi ◽  
Herbert Birkhofer
Keyword(s):  
Mathematical Model ◽  
Graph Theory ◽  
Sheet Metal ◽  
Collaborative Research ◽  
Linguistic Analysis ◽  
Customer Requirements ◽  
Identification Process ◽  
Metal Construction ◽  
Continuous Text ◽  
Branched Structures

The Collaborative Research Center 666 (CRC666) is concentrated on the research of methods and procedures for the optimized illustration of branched structures in integral sheet metal construction by regarding their functions and strains [1]. The virtual development of such branched structures emphasizes the found methods and procedures with regard to make them based on algorithms. This paper describes several approaches, which help to identify customer requirements based on algorithms. A standardized structure for the requirements is developed that builds the basis for a system of requirement terms. Product requirements can have relations among themselves. To make these relations directly and automatically available for the stakeholders during the identification process a semantic product requirement network was developed. This network helps the stakeholders to clearly identify and handle the requirements. This semantic product requirement network is based on the graph theory. A mathematical model for the access to the graph nodes (requirement) is introduced in the system for requirement terms that helps with the identification of requirements by using algorithms. Today requirements for a product are also collected in the form of a continuous text. For this case an approach is shows how requirements can be extracted from the continuous text by using linguistic procedures within the semantic product requirement network.

scholarly journals Research on folding suspension of multi-constrained rover based on the variation and fusion of rods and pairs

2017 ◽  
Vol 14 (4) ◽  
pp. 172988141772733
Author(s):  
Fei Yang ◽  
Honghao Yue ◽  
Meng Li ◽  
Jianguo Tao ◽  
Zongquan Deng
Keyword(s):  
Mathematical Model ◽  
Graph Theory ◽  
Functional Diversity ◽  
Structural Characteristics ◽  
Engineering Application ◽  
Cost Ratio ◽  
Planetary Rovers ◽  
Limited Space ◽  
Space Launch ◽  
Efficiency Cost

Planetary rovers with folding functions can solve the contradiction between the limited space of the vehicle and the functional diversity of the rover and greatly improve the efficiency–cost ratio of space launch activities. In this article, the multi-constrained quadrilateral suspension is considered based on the practical requirements of planetary detection. Based on graph theory and metamorphic theory, the structural characteristics and movement patterns of the rover are analyzed, the configuration transforming process of adding or decreasing the number of rods and kinematic pairs during folding is studied, and the corresponding mathematical model is established. The suspension of the rover is divided into three basic units, and the folding study is performed around each unit. The folding set of each unit type is given, and a feasible folding set is selected for each type of unit according to their structural characteristics and constraint conditions. At the same time, 15-folding schemes for the rover are given, and the optimal scheme is determined. According to the final folding scheme of the rover, the principle prototype of the rover is developed, and the functional experiment of the folding and unfolding is performed. The experimental results verify the feasibility and rationality of the folding scheme, indicating that the developed detection vehicle has a large fold ratio, which can fully adapt to the limited space inside the rocket. The theoretical and technical results can provide technical support for the engineering application of subsequent rovers with folding.

A general steady state mathematical model for fin-and-tube heat exchanger based on graph theory

2004 ◽  
Vol 27 (8) ◽  
pp. 965-973 ◽  
Author(s):  
Jian Liu ◽  
WenJian Wei ◽  
GouLiang Ding ◽  
Chunlu Zhang ◽  
Masaharu Fukaya ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Graph Theory ◽  
Steady State ◽  
Heat Exchanger ◽  
Tube Heat Exchanger

scholarly journals RESEARCH OF GENETIC ALGORITHMS FOR SEARCHING OPTIMAL WAYS IN THE SYSTEM OF CONDUCTING METROMARATHONS

2019 ◽  
Vol 2 (93) ◽  
pp. 53-58
Author(s):  
О. О. Mazurova ◽  
Т. О. Gordienko
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Experimental Study ◽  
Genetic Algorithms ◽  
Graph Theory ◽  
Different Dimensions ◽  
Subway Stations ◽  
Genome Representation

The work is devoted to the study of genetic algorithms on the example of the search for the best ways to support“Transit challenge” or “Subway Challenge” system. Based on the rules of “Transit challenge” and the tasks of thesalesman, the problem of stations was formulated - the search for the best way to visit all subway stations in the shortestpossible time. Based on the graph theory, a mathematical model of the metrophone system was developed. To solve thestation problem, a genetic algorithm has been developed: the method of genome representation, population mutationand genome crossing rules have been chosen. On the basis of the experimental study of the genetic algorithm the mosteffective parameters were selected and recommendations on the solution of the station problem for “Transit challenge”of different dimensions were developed.

scholarly journals Analysis of the preparation technology of a row seeder for work

2020 ◽  
Vol 193 ◽  
pp. 01035
Author(s):  
A. Yu. Popov ◽  
Noureldin Sharaby ◽  
V.V. Zhurba ◽  
Е.А. Chaika
Keyword(s):  
Mathematical Model ◽  
Graph Theory ◽  
Crop Yields ◽  
Initial Conditions ◽  
Critical Path ◽  
Economic Factors ◽  
Agricultural Crop ◽  
Preparation Technology ◽  
Urgent Task ◽  
Relationship Of

The level of preparation of a row seeder for work and its adaptability to adjustments and settings affects the efficiency of sowing. Analysis of the designs of modern row seeders shows that after-sales service remains a reserve for improving the efficiency of their use, and, therefore, increasing the agricultural crop yields. However, the technologies for the preparation and adjustment row seeders remain poorly understood, and the search for ways to reduce the complexity of maintenance for sowing units is an urgent task. The aim of the study is to build a mathematical model of the technology for checking, adjusting and tuning a row seeder on the basis of graph theory, determining a way to reduce the complexity of servicing maintenance a row seeder in preparation for sowing and justifying a rational way of organizing the seeder setting. Taking into account a number of assumptions and initial conditions, a list of operations for adjusting and setting the seeder is developed. A digraph of a row seeder preparation technology is constructed, which displays the sequence and relationship of the operations of preparation, adjusting and sitting its nodes and mechanisms. The critical path with the greatest time spent on seeder maintenance is determined. The methods for reducing the complexity of maintenance of a row seeder were established and it is recommended that further modernization of the units and mechanisms of the seeder by indicators in terms of suitability for verification, adjustment and setup. The methods of preparing the seeder for work by one performer are considered. The influence of economic factors on the number of performers during maintenance of the seeder before sowing is shown.

Mathematical Models for VLSI Placement with Rectilinear Embedding

2013 ◽  
Vol 744 ◽  
pp. 536-539
Author(s):  
Li Yan Pan ◽  
Yan Pei Liu
Keyword(s):  
Mathematical Model ◽  
Graph Theory ◽  
Generating Functions ◽  
Functional Equations ◽  
Theoretical Foundation ◽  
Outerplanar Graph ◽  
Lagrangian Inversion ◽  
Multiple Parameters ◽  
Placement Optimization ◽  
Explicit Formulae

Based on the theory of functional equations in rectilinear embedding, a mathematical model of VLSI placement design was established in this paper. The cell on the plane is conceived as a point, while the wire links the cells is assumed as lines, then the VLSI placement is transformed into quadrangulation by using graph theory. First of all, we obtained generating functions for two types of quadrangulations (quartic graphs) with graph multiple parameters and secondly derived explicit formulae by employing Lagrangian inversion. Furthermore, we found a relation between outerplanar graph and Hamilton graph, and then got the counting result of Hamilton quadrangulation. The quadrangulation calculations could provide a theoretical foundation for computerized algorithm, which can be widely used for VLSI placement optimization.

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