scholarly journals Asymptotic Behavior of Boson Regge Trajectories

2021 ◽  
Vol 66 (2) ◽  
pp. 97
Author(s):  
A.A. Trushevsky
Keyword(s):  
Asymptotic Behavior ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Square Root ◽  
Asymptotic Growth ◽  
Regge Trajectories ◽  
Phase Representation

The asymptotic behavior of boson Regge trajectories is studied. Upper and lower bounds on the asymptotic growth of the trajectories are obtained using the phase representation for the trajectories and a number of physical requirements. It is shown that, within the assumptions made, the asymptotic behavior of the trajectories is a square root.

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.

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 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.

scholarly journals Asymptotic estimates on the von Neumann inequality for homogeneous polynomials

2018 ◽  
Vol 2018 (743) ◽  
pp. 213-227 ◽  
Author(s):  
Daniel Galicer ◽  
Santiago Muro ◽  
Pablo Sevilla-Peris
Keyword(s):  
Asymptotic Behavior ◽  
Lower Bounds ◽  
Homogeneous Polynomial ◽  
Asymptotic Estimates ◽  
Steiner Systems ◽  
Homogeneous Polynomials ◽  
Logarithmic Factor ◽  
Von Neumann ◽  
Asymptotic Growth ◽  
Commuting Operators

Abstract By the von Neumann inequality for homogeneous polynomials there exists a positive constant C_{k,q} (n) such that for every k-homogeneous polynomial p in n variables and every n-tuple of commuting operators ( T_{1} ,…, T_{n} ) with {\sum_{i=1}^{n}\|T_{i}\|^{q}\leq 1} we have \|p(T_{1},\ldots,T_{n})\|_{\mathcal{L}(\mathcal{H})}\leq C_{k,q}(n)\sup\Biggl{% \{}|p(z_{1},\ldots,z_{n})|:\sum_{i=1}^{n}|z_{i}|^{q}\leq 1\Biggr{\}}. For fixed k and q, we study the asymptotic growth of the smallest constant C_{k,q} (n) as n (the number of variables/operators) tends to infinity. For q = \infty , we obtain the correct asymptotic behavior of this constant (answering a question posed by Dixon in the 1970s). For 2 \leq q < \infty we improve some lower bounds given by Mantero and Tonge, and prove the asymptotic behavior up to a logarithmic factor. To achieve this we provide estimates of the norm of homogeneous unimodular Steiner polynomials, i.e. polynomials such that the multi-indices corresponding to the nonzero coefficients form partial Steiner systems.

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.

scholarly journals The Asymptotic Behavior of the Average $L^p-$Discrepancies and a Randomized Discrepancy

10.37236/378 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Stefan Steinerberger
Keyword(s):  
Asymptotic Behavior ◽  
Limit Theorem ◽  
Lower Bounds ◽  
Probabilistic Approach ◽  
Upper Bounds ◽  
Upper And Lower Bounds

This paper gives the limit of the average $L^p-$star and the average $L^p-$extreme discrepancy for $[0,1]^d$ and $0 < p < \infty$. This complements earlier results by Heinrich, Novak, Wasilkowski & Woźnia-kowski, Hinrichs & Novak and Gnewuch and proves that the hitherto best known upper bounds are optimal up to constants.We furthermore introduce a new discrepancy $D_{N}^{\mathbb{P}}$ by taking a probabilistic approach towards the extreme discrepancy $D_{N}$. We show that it can be interpreted as a centralized $L^1-$discrepancy $D_{N}^{(1)}$, provide upper and lower bounds and prove a limit theorem.

scholarly journals Bounds for eigenvalues of the Dirichlet problem for the logarithmic Laplacian

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Huyuan Chen ◽  
Laurent Véron
Keyword(s):  
Asymptotic Behavior ◽  
Fourier Transform ◽  
Dirichlet Problem ◽  
Lower Bounds ◽  
Upper Bounds ◽  
Upper And Lower Bounds ◽  
Laplacian Operator ◽  
Lower And Upper Bounds

Abstract We provide bounds for the sequence of eigenvalues { λ i ⁢ ( Ω ) } i {\{\lambda_{i}(\Omega)\}_{i}} of the Dirichlet problem L Δ ⁢ u = λ ⁢ u ⁢  in  ⁢ Ω , u = 0 ⁢  in  ⁢ ℝ N ∖ Ω , L_{\Delta}u=\lambda u\text{ in }\Omega,\quad u=0\text{ in }\mathbb{R}^{N}% \setminus\Omega, where L Δ {L_{\Delta}} is the logarithmic Laplacian operator with Fourier transform symbol 2 ⁢ ln ⁡ | ζ | {2\ln\lvert\zeta\rvert} . The logarithmic Laplacian operator is not positively defined if the volume of the domain is large enough. In this article, we obtain the upper and lower bounds for the sum of the first k eigenvalues by extending the Li–Yau method and Kröger’s method, respectively. Moreover, we show the limit of the quotient of the sum of the first k eigenvalues by k ⁢ ln ⁡ k {k\ln k} is independent of the volume of the domain. Finally, we discuss the lower and upper bounds of the k-th principle eigenvalue, and the asymptotic behavior of the limit of eigenvalues.

scholarly journals Number of connected spanning subgraphs on the Sierpinski gasket

2009 ◽  
Vol Vol. 11 no. 1 (Combinatorics) ◽  
Author(s):  
Shu-Chiuan Chang ◽  
Lung-Chi Chen
Keyword(s):  
Lower Bounds ◽  
Sierpinski Gasket ◽  
Upper And Lower Bounds ◽  
Sierpiński Gasket ◽  
Growth Constant ◽  
Asymptotic Growth ◽  
Spanning Subgraphs ◽  
International Audience

Combinatorics International audience We study the number of connected spanning subgraphs f(d,b) (n) on the generalized Sierpinski gasket SG(d,b) (n) at stage n with dimension d equal to two, three and four for b = 2, and layer b equal to three and four for d = 2. The upper and lower bounds for the asymptotic growth constant, defined as zSG(d,b) = lim(v ->infinity) ln f(d,b)(n)/v where v is the number of vertices, on SG(2,b) (n) with b = 2, 3, 4 are derived in terms of the results at a certain stage. The numerical values of zSG(d,b) are obtained.

scholarly journals On the Generalized Distance Energy of Graphs

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 17 ◽  
Author(s):  
Abdollah Alhevaz ◽  
Maryam Baghipur ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Connected Graph ◽  
Distance Matrix ◽  
Wiener Index ◽  
Diagonal Matrix ◽  
Upper And Lower Bounds ◽  
Star Graph ◽  
Extremal Graphs ◽  
Generalized Distance

The generalized distance matrix D α ( G ) of a connected graph G is defined as D α ( G ) = α T r ( G ) + ( 1 − α ) D ( G ) , where 0 ≤ α ≤ 1 , D ( G ) is the distance matrix and T r ( G ) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy E D α ( G ) . Some new upper and lower bounds for the generalized distance energy E D α ( G ) of G are established based on parameters including the Wiener index W ( G ) and the transmission degrees. Extremal graphs attaining these bounds are identified. It is found that the complete graph has the minimum generalized distance energy among all connected graphs, while the minimum is attained by the star graph among trees of order n.

scholarly journals Hadamard k-fractional inequalities of Fejér type for GA-s-convex mappings and applications

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Hui Lei ◽  
Gou Hu ◽  
Zhi-Jie Cao ◽  
Ting-Song Du
Keyword(s):  
Lower Bounds ◽  
Hypergeometric Functions ◽  
Upper And Lower Bounds ◽  
Weighted Inequalities ◽  
Convex Mappings ◽  
Special Means

Abstract The main aim of this paper is to establish some Fejér-type inequalities involving hypergeometric functions in terms of GA-s-convexity. For this purpose, we construct a Hadamard k-fractional identity related to geometrically symmetric mappings. Moreover, we give the upper and lower bounds for the weighted inequalities via products of two different mappings. Some applications of the presented results to special means are also provided.

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