Asymptotic behavior of Fredholm determinants of truncated integral operators with matrix-valued kernels depending on the difference of the arguments

1986 ◽  
pp. 83-89
Author(s):  
L. V. Mikaelyan
Keyword(s):  
Asymptotic Behavior ◽  
Integral Operators ◽  
Fredholm Determinants ◽  
The Difference

scholarly journals Asymptotic Behavior of Singular and Entropy Numbers for Some Riemann–Liouville Type Operators

2001 ◽  
Vol 8 (2) ◽  
pp. 323-332
Author(s):  
A. Meskhi
Keyword(s):  
Asymptotic Behavior ◽  
Integral Operators ◽  
Integral Transforms ◽  
Singular Value ◽  
Entropy Numbers ◽  
Liouville Type ◽  
Singular Value Decompositions

Abstract The asymptotic behavior of the singular and entropy numbers is established for the Erdelyi–Köber and Hadamard integral operators (see, e.g., [Samko, Kilbas and Marichev, Integrals and derivatives. Theoryand Applications, Gordon and Breach Science Publishers, 1993]) acting in weighted L 2 spaces. In some cases singular value decompositions are obtained as well for these integral transforms.

Winding angle and maximum winding angle of the two-dimensional random walk

1991 ◽  
Vol 28 (4) ◽  
pp. 717-726 ◽  
Author(s):  
Claude Bélisle ◽  
Julian Faraway
Keyword(s):  
Asymptotic Behavior ◽  
Brownian Motion ◽  
Random Walk ◽  
Random Walks ◽  
Computer Simulations ◽  
Asymptotic Distributions ◽  
Two Dimensional ◽  
Exact Distributions ◽  
The Difference ◽  
Winding Angle

Recent results on the winding angle of the ordinary two-dimensional random walk on the integer lattice are reviewed. The difference between the Brownian motion winding angle and the random walk winding angle is discussed. Other functionals of the random walk, such as the maximum winding angle, are also considered and new results on their asymptotic behavior, as the number of steps increases, are presented. Results of computer simulations are presented, indicating how well the asymptotic distributions fit the exact distributions for random walks with 10m steps, for m = 2, 3, 4, 5, 6, 7.

A generalized class of integral operators

2020 ◽  
Vol 36 (3) ◽  
pp. 423-431
Author(s):  
VIJAY GUPTA
Keyword(s):  
Large Class ◽  
Present Note ◽  
Integral Operators ◽  
Basis Functions ◽  
Unified Approach ◽  
Quantitative Estimates ◽  
Special Cases ◽  
Discrete Operators ◽  
Durrmeyer Type Operators ◽  
The Difference

We introduce in the present note a unified approach to define integral operators, which include many well-known operators viz. Durrmeyer type operators, mixed hybrid operators as special cases. We also obtain the quantitative estimates between the difference of such integral operators with the discrete operators having same and different basis functions. Our operators proposed here give a very large class of integral operators, which have been discussed and proposed by several researchers in past seven decades.

scholarly journals Global Behavior of a Discrete Anticompetitive System in the Plane

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Lin-Xia Hu
Keyword(s):  
Asymptotic Behavior ◽  
Open Problem ◽  
Global Attractivity ◽  
Global Behavior ◽  
Initial Condition ◽  
Difference System ◽  
Rational Systems ◽  
The Difference

The main goal of this paper is to investigate the global asymptotic behavior of the difference system xn+1=γ1yn/A1+xn,  yn+1=β2xn/B2+yn,  n=0,1,2,…. with γ1,β2,A1,B2∈(0,∞) and the initial condition (x0,y0)∈[0,∞)×[0,∞). We obtain some global attractivity results of this system for different values of the parameters, which answer the open problem proposed in “Rational systems in the plane, J. Difference Equ. Appl. 15 (2009), 303-323”.

ASYMPTOTIC BEHAVIOR OF THE SPECTRUM OF WEAKLY POLAR INTEGRAL OPERATORS

1970 ◽  
Vol 4 (5) ◽  
pp. 1151-1168 ◽  
Author(s):  
M Š Birman ◽  
M Z Solomjak
Keyword(s):  
Asymptotic Behavior ◽  
Integral Operators

Carleman integral operators with kernels depending on the difference and sum of the arguments

1977 ◽  
Vol 18 (1) ◽  
pp. 1-15 ◽  
Author(s):  
E. L. Aleksandrov ◽  
B. I. Kirichenko
Keyword(s):  
Integral Operators ◽  
The Difference

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.

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