scholarly journals Dimer–monomer model on the Towers of Hanoi graphs

2015 ◽  
Vol 29 (23) ◽  
pp. 1550173 ◽  
Author(s):  
Hanlin Chen ◽  
Renfang Wu ◽  
Guihua Huang ◽  
Hanyuan Deng
Keyword(s):  
Asymptotic Behavior ◽  
Lower Bounds ◽  
Statistical Physics ◽  
Upper And Lower Bounds ◽  
Recursion Relations ◽  
Sierpiński Graphs ◽  
Towers Of Hanoi ◽  
The Difference ◽  
Significant Figures

The number of dimer–monomers (matchings) of a graph [Formula: see text] is an important graph parameter in statistical physics. Following recent research, we study the asymptotic behavior of the number of dimer–monomers [Formula: see text] on the Towers of Hanoi graphs and another variation of the Sierpiński graphs which is similar to the Towers of Hanoi graphs, and derive the recursion relations for the numbers of dimer–monomers. Upper and lower bounds for the entropy per site, defined as [Formula: see text], where [Formula: see text] is the number of vertices in a graph [Formula: see text], on these Sierpiński graphs are derived in terms of the numbers at a certain stage. As the difference between these bounds converges quickly to zero as the calculated stage increases, the numerical value of the entropy can be evaluated with more than a hundred significant figures accuracy.

On a Voronoi aggregative process related to a bivariate Poisson process

1996 ◽  
Vol 28 (04) ◽  
pp. 965-981 ◽  
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.

scholarly journals Spectral Properties with the Difference between Topological Indices in Graphs

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Akbar Jahanbani ◽  
Roslan Hasni ◽  
Zhibin Du ◽  
Seyed Mahmoud Sheikholeslami
Keyword(s):  
Characteristic Polynomial ◽  
Lower Bounds ◽  
Adjacency Matrix ◽  
Spectral Properties ◽  
Main Tool ◽  
Topological Indices ◽  
Upper And Lower Bounds ◽  
New Energy ◽  
Energy Of Graph ◽  
The Difference

Let G be a graph of order n with vertices labeled as v1,v2,…,vn. Let di be the degree of the vertex vi, for i=1,2,…,n. The difference adjacency matrix of G is the square matrix of order n whose i,j entry is equal to di+dj−2−1/didj if the vertices vi and vj of G are adjacent or vivj∈EG and zero otherwise. Since this index is related to the degree of the vertices of the graph, our main tool will be an appropriate matrix, that is, a modification of the classical adjacency matrix involving the degrees of the vertices. In this paper, some properties of its characteristic polynomial are studied. We also investigate the difference energy of a graph. In addition, we establish some upper and lower bounds for this new energy of graph.

ON THE DIFFERENCE OF COEFFICIENTS OF OZAKI CLOSE-TO-CONVEX FUNCTIONS

2020 ◽  
pp. 1-8
Author(s):  
YOUNG JAE SIM ◽  
DEREK K. THOMAS
Keyword(s):  
Unit Disk ◽  
Lower Bounds ◽  
Convex Functions ◽  
Univalent Functions ◽  
Upper And Lower Bounds ◽  
The Difference

Let $f$ be analytic in the unit disk $\mathbb{D}=\{z\in \mathbb{C}:|z|<1\}$ and ${\mathcal{S}}$ be the subclass of normalised univalent functions given by $f(z)=z+\sum _{n=2}^{\infty }a_{n}z^{n}$ for $z\in \mathbb{D}$ . We give sharp upper and lower bounds for $|a_{3}|-|a_{2}|$ and other related functionals for the subclass ${\mathcal{F}}_{O}(\unicode[STIX]{x1D706})$ of Ozaki close-to-convex functions.

On a Voronoi aggregative process related to a bivariate Poisson process

1996 ◽  
Vol 28 (4) ◽  
pp. 965-981 ◽  
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.

scholarly journals EXACT UPPER AND LOWER BOUNDS ON THE DIFFERENCE BETWEEN THE ARITHMETIC AND GEOMETRIC MEANS

2015 ◽  
Vol 92 (1) ◽  
pp. 149-158 ◽  
Author(s):  
IOSIF PINELIS
Keyword(s):  
Convex Function ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Jensen Inequality ◽  
Geometric Means ◽  
The Difference

Exact upper and lower bounds on the difference between the arithmetic and geometric means are obtained. The inequalities providing these bounds may be viewed, respectively, as a reverse Jensen inequality and an improvement of the direct Jensen inequality, in the case when the convex function is the exponential.

scholarly journals The Mean Width of Circumscribed Random Polytopes

2010 ◽  
Vol 53 (4) ◽  
pp. 614-628 ◽  
Author(s):  
Károly J. Böröczky ◽  
Rolf Schneider
Keyword(s):  
Convex Body ◽  
Asymptotic Formula ◽  
Uniform Distribution ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Simplicial Polytope ◽  
Mean Width ◽  
The Mean ◽  
The Difference ◽  
Precise Asymptotic

AbstractFor a given convex body K in ℝd, a random polytope K(n) is defined (essentially) as the intersection of n independent closed halfspaces containing K and having an isotropic and (in a specified sense) uniform distribution. We prove upper and lower bounds of optimal orders for the difference of the mean widths of K(n) and K as n tends to infinity. For a simplicial polytope P, a precise asymptotic formula for the difference of the mean widths of P(n) and P is obtained.

scholarly journals On the Difference of Coefficients of Starlike and Convex Functions

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1521
Author(s):  
Young Jae Sim ◽  
Derek K. Thomas
Keyword(s):  
Unit Disk ◽  
Lower Bounds ◽  
Convex Functions ◽  
Univalent Functions ◽  
Starlike Functions ◽  
Upper And Lower Bounds ◽  
Starlike And Convex Functions ◽  
The Difference

Let f be analytic in the unit disk D={z∈C:|z|<1}, and S be the subclass of normalized univalent functions given by f(z)=z+∑n=2∞anzn for z∈D. Let S*⊂S be the subset of starlike functions in D and C⊂S the subset of convex functions in D. We give sharp upper and lower bounds for |a3|−|a2| for some important subclasses of S* and C.

scholarly journals On the Difference of Inverse Coefficients of Univalent Functions

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2040
Author(s):  
Young Jae Sim ◽  
Derek Keith Thomas
Keyword(s):  
Unit Disk ◽  
Lower Bounds ◽  
Upper Bound ◽  
Convex Functions ◽  
Univalent Functions ◽  
Inverse Function ◽  
Starlike Functions ◽  
Upper And Lower Bounds ◽  
The Difference ◽  
Bazilevic Functions

Let f be analytic in the unit disk D={z∈C:|z|<1}, and S be the subclass of normalized univalent functions with f(0)=0, and f′(0)=1. Let F be the inverse function of f, given by F(z)=ω+∑n=2∞Anωn for some |ω|≤r0(f). Let S*⊂S be the subset of starlike functions in D, and C the subset of convex functions in D. We show that −1≤|A3|−|A2|≤3 for f∈S, the upper bound being sharp, and sharp upper and lower bounds for |A3|−|A2| for the more important subclasses of S* and C, and for some related classes of Bazilevič functions.

Estimates of the mean size of the subset image under composition of random mappings

2018 ◽  
Vol 28 (5) ◽  
pp. 331-338 ◽  
Author(s):  
Andrey M. Zubkov ◽  
Aleksandr A. Serov
Keyword(s):  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Random Mappings ◽  
Mean Size ◽  
The Mean ◽  
The Difference ◽  
Time Memory Tradeoff

Abstract Let XN be a set of N elements and F1, F2,… be a sequence of random independent equiprobable mappings XN → N. For a subset S0 ⊂ XN, |S0|=m, we consider a sequence of its images St=Ft(…F2(F1(S0))…), t=1,2… An approach to the exact recurrent computation of distribution of |St| is described. Two-sided inequalities forM{|St|||S0|=m} such that the difference between the upper and lower bounds is o(m)for m, t, N → ∞, mt=o(N) are derived. The results are of interest for the analysis of time-memory tradeoff algorithms.

scholarly journals On the enumeration of column-convex permutominoes

2011 ◽  
Vol DMTCS Proceedings vol. AO,... (Proceedings) ◽  
Author(s):  
Nicholas R. Beaton ◽  
Filippo Disanto ◽  
Anthony J. Guttmann ◽  
Simone Rinaldi
Keyword(s):  
Functional Equation ◽  
Asymptotic Behavior ◽  
Numerical Analysis ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Recursive Construction ◽  
Nous Obtenons ◽  
Comportement Asymptotique ◽  
Generating Trees ◽  
International Audience

International audience We study the enumeration of \emphcolumn-convex permutominoes, i.e. column-convex polyominoes defined by a pair of permutations. We provide a direct recursive construction for the column-convex permutominoes of a given size, based on the application of the ECO method and generating trees, which leads to a functional equation. Then we obtain some upper and lower bounds for the number of column-convex permutominoes, and conjecture its asymptotic behavior using numerical analysis. Nous étudions l'énumeration des \emphpermutominos verticalement convexes, c.à.d. les polyominos verticalement convexes définis par un couple de permutations. Nous donnons une construction recursive directe pour ces permutominos de taille fixée, basée sur une application de la méthode ECO et les arbres de génération, qui nous amène à une équat ion fonctionelle. Ensuite nous obtenons des bornes superieures et inférieures pour le nombre de ces permutominos convexes et nous conjecturons leur comportement asymptotique à l'aide d'analyses numériques.

Sign in / Sign up

Export Citation Format

Share Document