scholarly journals Trigonometric series and self-similar sets

2021 ◽  
Author(s):  
Jialun Li ◽  
Tuomas Sahlsten
Keyword(s):  
Trigonometric Series ◽  
Self Similar

Hamiltonian System and Symmetries for Scale Invariant Wavefunctions

1998 ◽  
Vol 07 (06) ◽  
pp. 765-775 ◽  
Author(s):  
A. Ludu ◽  
J. P. Draayer ◽  
W. Greiner
Keyword(s):  
Hamiltonian System ◽  
Trigonometric Series ◽  
Algebraic Structure ◽  
Scaling Function ◽  
Scale Invariant ◽  
Invariant Functions ◽  
Infinite Dimensional ◽  
Nonlinear Lattices ◽  
Self Similar ◽  
Infinite Dimensional Hamiltonian System

The connection between scale invariant wavefunctions and solutions of some nonlinear equations (e.g., solitons and compactons) have been studied. Scale invariant functions are shown to have variational properties and a nonlinear algebraic structure. Any two-scale equation follows from Hamilton's equation of an infinite-dimensional Hamiltonian system, providing a self-similar formalism that is useful in studies of hierarchical and nonlinear lattices, soliton and compacton waves. The algebraic structure of any scaling function is shown to be a deformation of the trigonometric series generating algebra.

Self-similar collapse with non-radial motions

2006 ◽  
Vol 20 ◽  
pp. 1-4
Author(s):  
A. Nusser
Keyword(s):  
Self Similar

PREDICTING CHARACTERISTICS OF SELF SIMILAR TRAFFIC BY SPLINE-EXTRAPOLATION

2019 ◽  
Author(s):  
Irina Strelkovskay ◽  
Irina Solovskaya ◽  
Anastasija Makoganjuk ◽  
Nikolaj Severin
Keyword(s):  
Quality Characteristics ◽  
Traffic Prediction ◽  
Normative Values ◽  
Spline Functions ◽  
Network Nodes ◽  
Traffic Forecasting ◽  
Network Equipment ◽  
Self Similar ◽  
Accuracy Of Prediction

The problem of forecasting self-similar traffic, which is characterized by a considerable number of ripples and the property of long-term dependence, is considered. It is proposed to use the method of spline extrapolation using linear and cubic splines. The results of self-similar traffic prediction were obtained, which will allow to predict the necessary size of the buffer devices of the network nodes in order to avoid congestion in the network and exceed the normative values ​​of QoS quality characteristics. The solution of the problem of self-similar traffic forecasting obtained with the Simulink software package in Matlab environment is considered. A method of extrapolation based on spline functions is developed. The proposed method has several advantages over the known methods, first of all, it is sufficient ease of implementation, low resource intensity and accuracy of prediction, which can be enhanced by the use of quadratic or cubic interpolation spline functions. Using the method of spline extrapolation, the results of self-similar traffic prediction were obtained, which will allow to predict the required volume of buffer devices, thereby avoiding network congestion and exceeding the normative values ​​of QoS quality characteristics. Given that self-similar traffic is characterized by the presence of "bursts" and a long-term dependence between the moments of receipt of applications in this study, given predetermined data to improve the prediction accuracy, it is possible to use extrapolation based on wavelet functions, the so-called wavelet-extrapolation method. Based on the results of traffic forecasting, taking into account the maximum values ​​of network node traffic, you can give practical guidance on how traffic is redistributed across the network. This will balance the load of network objects and increase the efficiency of network equipment.

Self-similar traffic discrimination and generating methods based on fractal Brown motion

2013 ◽  
Vol 33 (4) ◽  
pp. 947-949
Author(s):  
Xueyuan ZHANG ◽  
Yonggang WANG ◽  
Qiong ZHANG
Keyword(s):  
Self Similar ◽  
Brown Motion
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