scholarly journals Modeling, Analysis, and Comparison of Nanotechnology System: A Graph-Theoretic Approach

2021 ◽  
Author(s):  
Tanvir Singh
Keyword(s):  
Graph Theory ◽  
Complete Analysis ◽  
Theoretic Model ◽  
Theoretic Approach ◽  
Graph Theoretic ◽  
Systems Model ◽  
System A ◽  
Modeling Analysis ◽  
Graph Theoretic Approach ◽  
Permanent Function

Abstract Nanotechnology can create many new nanomaterials and nanodevices with a vast range of applications, such as in medicine, electronics, biomaterials, and energy production, etc. An attempt is made to develop an integrated systems model for the structure of the nanotechnology system in terms of its constituents and interactions between the constituents and processes, etc. using graph theory and matrix algebra. The nanotechnology system is first modeled with the help of graph theory, secondly by variable adjacency matrix and thirdly by multinomial (which is known as a permanent function). The permanent function provides an opportunity to carry out a structural analysis of nanotechnology system in terms of its strength, weakness, improvement, and optimization, by correlating the different systems with its structure. The physical meaning has been associated with each term of the permanent function. Different structural attributes of the nanotechnology system are identified concurrently to reduce cost, time for design and development, and also to develop a graph-theoretic model, matrix model, and multinomial permanent model of nanotechnology system. The top-down approach for a complete analysis of any nanotechnology systems is given. The general methodology is presented for the characterization and comparison of two nanotechnology systems.

scholarly journals Modeling, Analysis, and Comparison of Nanotechnology System: A Graph-Theoretic Approach

2020 ◽  
Author(s):  
Tanvir Singh ◽  
V.P. Agrawal
Keyword(s):  
Graph Theory ◽  
Complete Analysis ◽  
Theoretic Model ◽  
Theoretic Approach ◽  
Graph Theoretic ◽  
Systems Model ◽  
System A ◽  
Modeling Analysis ◽  
Graph Theoretic Approach ◽  
Permanent Function

Nanotechnology can create many new nanomaterials and nanodevices with a vast range of applications, such as in medicine, electronics, biomaterials, and energy production, etc. An attempt is made to develop an integrated systems model for the structure of the nanotechnology system in terms of its constituents and interactions between the constituents and processes, etc. using graph theory and matrix algebra. The nanotechnology system is first modeled with the help of graph theory, secondly by variable adjacency matrix and thirdly by multinomial (which is known as a permanent function). The permanent function provides an opportunity to carry out a structural analysis of nanotechnology system in terms of its strength, weakness, improvement, and optimization, by correlating the different systems with its structure. The physical meaning has been associated with each term of the permanent function. Different structural attributes of the nanotechnology system are identified concurrently to reduce cost, time for design and development, and also to develop a graph-theoretic model, matrix model, and multinomial permanent model of nanotechnology system. The top-down approach for a complete analysis of any nanotechnology systems is given. The general methodology is presented for the characterization and comparison of two nanotechnology systems.

scholarly journals A Framework to Measure the Service Quality of Distributor with Fuzzy Graph Theoretic Approach

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Tarun Kumar Gupta ◽  
Vikram Singh
Keyword(s):  
Service Quality ◽  
Theory Approach ◽  
Theoretic Approach ◽  
Fuzzy Graph ◽  
Graph Theoretic ◽  
Graph Theoretic Approach ◽  
Manufacturing Supply Chain ◽  
Permanent Function ◽  
Numerical Index

A combination of fuzzy logic and graph theoretic approach has been used to find the service quality of distributor in a manufacturing supply chain management. This combination is termed as the fuzzy graph theoretic (FGT) approach. Initially the identified factors were grouped by SPSS (statistical package for social science) software and then the digraph approach was applied. The interaction and inheritance values were calculated by fuzzy graph theory approach in terms of permanent function. Then a single numerical index was calculated by using permanent function which indicates the distributor service quality. This method can be used to compare the service quality of different distributors.

scholarly journals A Graph-Theoretic Approach to Wilf's Conjecture

10.37236/9106 ◽  
2020 ◽  
Vol 27 (2) ◽  
Author(s):  
Shalom Eliahou
Keyword(s):  
Graph Theory ◽  
Numerical Semigroup ◽  
Numerical Semigroups ◽  
Theoretic Approach ◽  
Primitive Elements ◽  
Graph Theoretic ◽  
Graph Theoretic Approach ◽  
Wilf’S Conjecture ◽  
Open Question

Let $S \subseteq \mathbb{N}$ be a numerical semigroup with multiplicity $m = \min(S \setminus \{0\})$ and conductor $c=\max(\mathbb{N} \setminus S)+1$. Let $P$ be the set of primitive elements of $S$, and let $L$ be the set of elements of $S$ which are smaller than $c$. A longstanding open question by Wilf in 1978 asks whether the inequality $|P||L| \ge c$ always holds. Among many partial results, Wilf's conjecture has been shown to hold in case $|P| \ge m/2$ by Sammartano in 2012. Using graph theory in an essential way, we extend the verification of Wilf's conjecture to the case $|P| \ge m/3$. This case covers more than $99.999\%$ of numerical semigroups of genus $g \le 45$.

scholarly journals Clinical Decision-Making: Developing a 4 C Model Using Graph Theoretic Approach

2020 ◽  
Vol 7 (1) ◽  
pp. 30
Author(s):  
Rajesh P. Mishra ◽  
Nidhi Mundra ◽  
Girish Upreti ◽  
Marcela Villa-Marulanda
Keyword(s):  
Decision Making ◽  
Clinical Decision Making ◽  
Clinical Decision ◽  
Theoretic Model ◽  
Specific Situation ◽  
Theoretic Approach ◽  
Graph Theoretic ◽  
Treatment Processes ◽  
Graph Theoretic Approach ◽  
Major Factors

The purpose of this paper is to propose a graph-theoretic mathematical model to measure how conducive the environment of a hospital is for decision-making. We propose a 4-C model, developed from four interacting factors: confidence, complexity, capability, and customer. In this graph-theoretic model, abstract information regarding the system is represented by the directed edges of a graph (or digraph), which together depict how one factor affects another. The digraph yields a matrix model useful for computer processing. The net effect of different factors and their interdependencies on the hospital's decision-making environment is quantified and a single numerical index is generated. This paper categorizes all the major factors that influence clinical decision-making and attempts to provide a tool to study and measure their interactions with each other. Each factor and each interaction among factors are to be quantified by healthcare experts according to their best judgment of the magnitude of its effect in a local hospital environment.A hospital case study is used to demonstrate how the 4-C model works. The graph-theoretic approach allows for the inclusion of new factors and generation of alternative environments by a combination of both qualitative and quantitative modeling. The 4-C model can be used to create both a database and a simple numerical scale that help a hospital set customized guidelines, ranging from patient admittance procedures to diagnostic and treatment processes, according to its specific situation. Implementing this methodology systematically can allow a hospital to identify factors that will lead to improved decision-making as well as identifying operational factors that present roadblocks.

scholarly journals Physically feasible decomposition of Engino® toy models: A graph-theoretic approach

2018 ◽  
Vol 30 (2) ◽  
pp. 278-297
Author(s):  
E. N. ANTONIOU ◽  
A. ARAÚJO ◽  
M. D. BUSTAMANTE ◽  
A. GIBALI
Keyword(s):  
Graph Theory ◽  
Building Blocks ◽  
Study Group ◽  
Theoretic Approach ◽  
European Study ◽  
Graph Theoretic ◽  
European Study Group ◽  
Graph Theoretic Approach ◽  
Assembly Instructions ◽  
Algorithmic Procedure

During the 125th European Study Group with Industry held in Limassol, Cyprus, 5–9 December 2016, one of the participating companies, Engino.net Ltd, posed a very interesting challenge to the members of the study group. Engino.net Ltd is a Cypriot company, founded in 2004, that produces a series of toy sets – the Engino® toy sets – consisting of a number of building blocks, which can be assembled by pupils to compose toy models. Depending on the contents of a particular toy set, the company has developed a number of models that can be built utilizing the blocks present in the set; however, the production of a step-by-step assembly manual for each model could only be done manually. The goal of the challenge posed by the company was to implement a procedure to automatically generate the assembly instructions for a given toy. In the present paper, we propose a graph-theoretic approach to model the problem and provide a series of results to solve it by employing modified versions of well-established algorithms in graph theory. An algorithmic procedure to obtain a hierarchical, physically feasible decomposition of a given toy model, from which a series of step-by-step assembly instructions can be recovered, is proposed.

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