Comparison of the Wiener and Kirchhoff Indices of Random Pentachains

Let G be a connected (molecule) graph. The Wiener index W G and Kirchhoff index K f G of G are defined as the sum of distances and the resistance distances between all unordered pairs of vertices in G , respectively. In this paper, explicit formulae for the expected values of the Wiener and Kirchhoff indices of random pentachains are derived by the difference equation and recursive method. Based on these formulae, we then make comparisons between the expected values of the Wiener index and the Kirchhoff index in random pentachains and present the average values of the Wiener and Kirchhoff indices with respect to the set of all random pentachains with n pentagons.

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A Singular Perturbation Problem and A Neutral Differential-Difference Equation

Canadian Mathematical Bulletin ◽

10.4153/cmb-1974-013-1 ◽

1974 ◽

Vol 17 (1) ◽

pp. 77-83

Author(s):

Edward Moore

Keyword(s):

Difference Equation ◽

Taylor Series Expansion ◽

Linear Difference Equation ◽

Constant Matrix ◽

Perturbation Problem ◽

Constant Coefficients ◽

Explicit Formulae ◽

Differential Difference Equation ◽

The Difference ◽

Image Position

Vasil’eva, [2], demonstrates a close connection between the explicit formulae for solutions to the linear difference equation with constant coefficients(1.1)where z is an n-vector, A an n×n constant matrix, τ>0, and a corresponding differential equation with constant coefficients(1.2)(1.2) is obtained from (1.1) by replacing the difference z(t—τ) by the first two terms of its Taylor Series expansion, combined with a suitable rearrangement of the terms.

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An improved generalized predictive control algorithm based on the difference equation CARIMA model for the SISO system with known strong interference

The Journal of Difference Equations and Applications ◽

10.1080/10236198.2018.1551384 ◽

2018 ◽

Vol 25 (9-10) ◽

pp. 1255-1269 ◽

Cited By ~ 2

Author(s):

Jianyuan Xu ◽

Xudong Pan ◽

Yuefeng Li ◽

Guanglin Wang ◽

R. Martínez

Keyword(s):

Difference Equation ◽

Predictive Control ◽

Control Algorithm ◽

Generalized Predictive Control ◽

Strong Interference ◽

The Difference ◽

Siso System

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On Boundedness of Solutions of the Difference Equation xn+1=(pxn+qxn−1)/(1+xn) for q>1+p>1

Advances in Difference Equations ◽

10.1155/2009/463169 ◽

2009 ◽

Vol 2009 ◽

pp. 1-11 ◽

Cited By ~ 2

Author(s):

Hongjian Xi ◽

Taixiang Sun ◽

Weiyong Yu ◽

Jinfeng Zhao

Keyword(s):

Difference Equation ◽

Boundedness Of Solutions ◽

The Difference

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An inequality with application to a difference equation

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700036285 ◽

2004 ◽

Vol 69 (3) ◽

pp. 519-528 ◽

Cited By ~ 4

Author(s):

Jong-Yi Chen ◽

Yunshyong Chow

Keyword(s):

Heat Conduction ◽

Difference Equation ◽

Heat Conduction Problem ◽

The Difference

In this paper we shall prove that for any 0 < d ≤ 2, holds for n ≥ 1.As an application, we shall then show that the following recursively defined sequence satisfies The difference equation above originates from a heat conduction problem studied by Myshkis (J. Difference Equ. Appl. 3(1997), 89–91).

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On a Voronoi aggregative process related to a bivariate Poisson process

Advances in Applied Probability ◽

10.1017/s0001867800027506 ◽

1996 ◽

Vol 28 (04) ◽

pp. 965-981 ◽

Cited By ~ 11

Author(s):

S. G. Foss ◽

S. A. Zuyev

Keyword(s):

Asymptotic Behavior ◽

Lower Bounds ◽

Distribution Functions ◽

Poisson Processes ◽

Upper And Lower Bounds ◽

Additive Functionals ◽

Second Moments ◽

Explicit Formulae ◽

Bivariate Poisson Process ◽

Sum Of Distances

We consider two independent homogeneous Poisson processes Π0 and Π1 in the plane with intensities λ0 and λ1, respectively. We study additive functionals of the set of Π0-particles within a typical Voronoi Π1-cell. We find the first and the second moments of these variables as well as upper and lower bounds on their distribution functions, implying an exponential asymptotic behavior of their tails. Explicit formulae are given for the number and the sum of distances from Π0-particles to the nucleus within a typical Voronoi Π1-cell.

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