scholarly journals On the Wiener Complexity and the Wiener Index of Fullerene Graphs

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1071 ◽  
Author(s):  
Andrey A. Dobrynin ◽  
Andrei Yu Vesnin
Keyword(s):  
Mathematical Models ◽  
Wiener Index ◽  
The Other ◽  
Graph Invariant ◽  
Calculation Results ◽  
Local Graph ◽  
Sum Of Distances ◽  
Fullerene Graphs

Fullerenes are molecules that can be presented in the form of cage-like polyhedra, consisting only of carbon atoms. Fullerene graphs are mathematical models of fullerene molecules. The transmission of a vertex v of a graph is a local graph invariant defined as the sum of distances from v to all the other vertices. The number of different vertex transmissions is called the Wiener complexity of a graph. Some calculation results on the Wiener complexity and the Wiener index of fullerene graphs of order n ≤ 232 and IPR fullerene graphs of order n ≤ 270 are presented. The structure of graphs with the maximal Wiener complexity or the maximal Wiener index is discussed, and formulas for the Wiener index of several families of graphs are obtained.

Measurement of Wiener kernels

1984 ◽  
Vol 16 (1) ◽  
pp. 11-12
Author(s):  
Yoshifusa Ito
Keyword(s):  
Differential Operator ◽  
Mathematical Models ◽  
White Noise ◽  
Linear Systems ◽  
Main Part ◽  
The Other ◽  
Linear Functionals ◽  
Wiener Kernels ◽  
Non Linear ◽  
Non Linear Systems

Since the late 1960s Wiener's theory on the non-linear functionals of white noise has been widely applied to the construction of mathematical models of non-linear systems, especially in the field of biology. For such applications the main part is the measurement of Wiener's kernels, for which two methods have been proposed: one by Wiener himself and the other by Lee and Schetzen. The aim of this paper is to show that there is another method based on Hida's differential operator.

Electron drift caused by rf field gradient creates many plasma phenomena: An attempt to distinguish the cause and the effect

2011 ◽  
Vol 78 (2) ◽  
pp. 165-174 ◽  
Author(s):  
C. L. XAPLANTERIS ◽  
E. D. FILIPPAKI ◽  
I. S. MISTAKIDIS ◽  
L. C. XAPLANTERIS
Keyword(s):  
Experimental Data ◽  
Steady State ◽  
Low Temperature ◽  
Mathematical Models ◽  
Field Gradient ◽  
Collision Frequency ◽  
The Other ◽  
Frequency Effect ◽  
Electron Drift ◽  
Plasma Parameters

AbstractMany experimental data along with their theoretical interpretations on the rf low-temperature cylindrical plasma have been issued until today. Our Laboratory has contributed to that research by publishing results and interpretative mathematical models. With the present paper, two issues are being examined; firstly, the estimation of electron drift caused by the rf field gradient, which is the initial reason for the plasma behaviour, and secondly, many new experimental results, especially the electron-neutral collision frequency effect on the other plasma parameters and quantities. Up till now, only the plasma steady state was taken into consideration when a theoretical elaboration was carried out, regardless of the cause and the effect. This indicates the plasma's complicated and chaotic configuration and the need to simplify the problem. In the present work, a classification about the causality of the phenomena is attempted; the rf field gradient electron drift is proved to be the initial cause.

scholarly journals Joins, coronas and their vertex-edge Wiener polynomials

2016 ◽  
Vol 47 (2) ◽  
pp. 163-178
Author(s):  
Mahdieh Azari ◽  
Ali Iranmanesh
Keyword(s):  
Generating Function ◽  
Connected Graph ◽  
Wiener Index ◽  
First Derivative ◽  
Sum Of Distances ◽  
Simple Connected Graph ◽  
Product Of Graphs ◽  
Corona Product

The vertex-edge Wiener index of a simple connected graph $G$ is defined as the sum of distances between vertices and edges of $G$. The vertex-edge Wiener polynomial of $G$ is a generating function whose first derivative is a $q-$analog of the vertex-edge Wiener index. Two possible distances $D_1(u, e|G)$ and $D_2(u, e|G)$ between a vertex $u$ and an edge $e$ of $G$ can be considered and corresponding to them, the first and second vertex-edge Wiener indices of $G$, and the first and second vertex-edge Wiener polynomials of $G$ are introduced. In this paper, we study the behavior of these indices and polynomials under the join and corona product of graphs. Results are applied for some classes of graphs such as suspensions, bottlenecks, and thorny graphs.

Epistemic Opacity

2019 ◽  
pp. 98-131
Author(s):  
Johannes Lenhard
Keyword(s):  
Mathematical Models ◽  
Simulation Models ◽  
Scientific Understanding ◽  
The Other ◽  
Weak Version ◽  
Simulation Based ◽  
Lower Standard ◽  
Epistemic Standards ◽  
Epistemic Opacity ◽  
Experimental Runs

This chapter shows that—and how—simulation models are epistemically opaque. Nevertheless, it is argued, simulation models can provide a means to control dynamics. Researchers can employ a series of iterated (experimental) runs of the model and can learn to orient themselves within the model—even if the dynamics of the simulation remain (at least partly) opaque. Admittedly, such an acquaintance with the model falls short of the high epistemic standards usually ascribed to mathematical models. This lower standard is still sufficient, however, when the aim is controlled intervention in technological contexts. On the other hand, opacity has to be accepted if the option for control is to remain in any way open. This chapter closes by discussing whether epistemic opacity restricts simulation-based science to a pragmatic—“weak”—version of scientific understanding.

The second-minimum Wiener index of cacti with given cycles

2020 ◽  
pp. 2150039
Author(s):  
Hanyuan Deng ◽  
G. C. Keerthi Vasan ◽  
S. Balachandran
Keyword(s):  
Connected Graph ◽  
Wiener Index ◽  
Index Formula ◽  
Extremal Graphs ◽  
Unique Graph ◽  
Sum Of Distances ◽  
Appl Math

The Wiener index [Formula: see text] of a connected graph [Formula: see text] is the sum of distances between all pairs of vertices of [Formula: see text]. A connected graph [Formula: see text] is said to be a cactus if each of its blocks is either a cycle or an edge. Let [Formula: see text] be the set of all [Formula: see text]-vertex cacti containing exactly [Formula: see text] cycles. Liu and Lu (2007) determined the unique graph in [Formula: see text] with the minimum Wiener index. Gutman, Li and Wei (2017) determined the unique graph in [Formula: see text] with maximum Wiener index. In this paper, we present the second-minimum Wiener index of graphs in [Formula: see text] and identify the corresponding extremal graphs, which solve partially the problem proposed by Gutman et al. [Cacti with [Formula: see text]-vertices and [Formula: see text] cycles having extremal Wiener index, Discrete Appl. Math. 232 (2017) 189–200] in 2017.

The property market, property valuations and property performance measurement

1985 ◽  
Vol 112 (1) ◽  
pp. 19-60 ◽  
Author(s):  
David P. Hager ◽  
David J. Lord
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Performance Measurement ◽  
The Other ◽  
Property Market ◽  
Institutional Investment ◽  
Property Valuation ◽  
Valuation Method ◽  
Property Performance

1.1. The Institute has discussed papers on most aspects of institutional investment in recent years, with the notable exception of property. This is not due to the lack of importance of this investment sector to pension funds and life offices, but perhaps to the greater role of actuaries (rather than surveyors) in the other investment media and to the interest in mathematical models for gilts and equities.1.2. In this paper we have not tried to produce a mathematical model of the property market, a new valuation method for property or solutions to the extensive problems of property performance measurement and indices. We have, however, tried to pull together, in a single paper, the volumes of material on the property market and property valuation methods. We have also tried to set down some of the pitfalls of property performance measurement, which often tend to be overlooked in the relentless pursuit for more statistics in this important area.

scholarly journals Thermodynamic modeling of solid solubility in supercritical carbon dioxide: Comparison between mixing rules

2013 ◽  
Vol 19 (3) ◽  
pp. 389-398 ◽  
Author(s):  
Hadi Baseri ◽  
Ali Haghighi-Asl ◽  
Nader Lotfollahi
Keyword(s):  
Carbon Dioxide ◽  
Supercritical Carbon Dioxide ◽  
Thermodynamic Modeling ◽  
Pressure Range ◽  
The Other ◽  
Mixing Rules ◽  
Calculation Results ◽  
Temperature And Pressure ◽  
Robinson Equation ◽  
Supercritical Carbon

In this paper, Peng Robinson equation of state is used for thermodynamic modeling of the solubility of various solid components in the supercritical carbon dioxide. Moreover, the effects of three mixing rules of Van der Waals mixing rules, Panagiotopoulos and Reid mixing rules and modified Kwak and Mansoori mixing rules on the accuracy of calculation results were studied. Good correlations between calculated and experimental data were obtained in the wide temperature and pressure range. A comparison between used models shows that modified Kwak and Mansoori mixing rules give better correlations in comparison with the other mixing rules.

scholarly journals On the Wiener index and variants of the Szeged index of single-walled titania nanotubes TiO2(m,n)

2017 ◽  
Vol 95 (1) ◽  
pp. 68-86 ◽  
Author(s):  
Muhammad Imran ◽  
Sabeel-e Hafi
Keyword(s):  
Physicochemical Properties ◽  
Strain Energy ◽  
Chemical Compounds ◽  
Wiener Index ◽  
Exact Expression ◽  
Topological Indices ◽  
Titania Nanotubes ◽  
Graph Invariant ◽  
Szeged Index ◽  
Cut Method

Topological indices are numerical parameters of a graph that characterize its topology and are usually graph invariant. There are certain types of topological indices such as degree-based topological indices, distance-based topological indices, and counting-related topological indices. These topological indices correlate certain physicochemical properties such as boiling point, stability, and strain energy of chemical compounds. In this paper, we compute an exact expression of Wiener index, vertex-Szeged index, edge-Szeged index, and total-Szeged index of single-walled titania nanotubes TiO2(m, n) by using the cut method for all values of m and n.

scholarly journals Exact Formula for Computing the Hyper-Wiener Index on Rows of Unit Cells of the Face-Centred Cubic Lattice

2018 ◽  
Vol 26 (1) ◽  
pp. 169-187 ◽  
Author(s):  
Hamzeh Mujahed ◽  
Benedek Nagy
Keyword(s):  
Wiener Index ◽  
Exact Formula ◽  
Mathematical Induction ◽  
Binomial Coefficients ◽  
Integer Sequences ◽  
Cubic Lattice ◽  
Unit Cells ◽  
The Face ◽  
The Given ◽  
Sum Of Distances

Abstract Similarly to Wiener index, hyper-Wiener index of a connected graph is a widely applied topological index measuring the compactness of the structure described by the given graph. Hyper-Wiener index is the sum of the distances plus the squares of distances between all unordered pairs of vertices of a graph. These indices are used for predicting physicochemical properties of organic compounds. In this paper, the graphs of lines of unit cells of the face-centred cubic lattice are investigated. The graphs of face-centred cubic lattice contain cube points and face centres. Using mathematical induction, closed formulae are obtained to calculate the sum of distances between pairs of cube points, between face centres and between cube points and face centres. The sum of these formulae gives the hyper-Wiener index of graphs representing face-centred cubic grid with unit cells connected in a row. In connection to integer sequences, a recurrence relation is presented based on binomial coefficients.

scholarly journals On the Wiener Indices of Trees Ordering by Diameter-Growing Transformation Relative to the Pendent Edges

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Xiaoxin Xu ◽  
Yubin Gao ◽  
Yanbin Sang ◽  
Yueliang Liang
Keyword(s):  
Graph Transformation ◽  
Wiener Index ◽  
Sum Of Distances

The Wiener index of a graph is defined as the sum of distances between all unordered pairs of its vertices. We found that finite steps of diameter-growing transformation relative to vertices can not always enable the Wiener index of a tree to increase sharply. In this paper, we provide a graph transformation named diameter-growing transformation relative to pendent edges, which increases Wiener index W(T) of a tree sharply after finite steps. Then, twenty-two trees are ordered by their Wiener indices, and these trees are proved to be the first twenty-two trees with the first up to sixteenth smallest Wiener indices.

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