The finite systems scheme: An abstract theorem and a new example

CRM Proceedings and Lecture Notes - Measure-Valued Processes, Stochastic Partial Differential Equations, and Interacting Systems ◽

10.1090/crmp/005/04 ◽

1994 ◽

pp. 55-67 ◽

Cited By ~ 2

Author(s):

John Cox ◽

Andreas Greven

Keyword(s):

Abstract Theorem ◽

Finite Systems

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Interpretation of apparent thermal conductivity in finite systems from equilibrium molecular dynamics simulations

Physical Review B ◽

10.1103/physrevb.103.035417 ◽

2021 ◽

Vol 103 (3) ◽

Author(s):

Haikuan Dong ◽

Shiyun Xiong ◽

Zheyong Fan ◽

Ping Qian ◽

Yanjing Su ◽

...

Keyword(s):

Thermal Conductivity ◽

Molecular Dynamics ◽

Molecular Dynamics Simulations ◽

Finite Systems ◽

Apparent Thermal Conductivity ◽

Dynamics Simulations

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A Concretization of an Approximation Method for Non-Affine Fractal Interpolation Functions

Mathematics ◽

10.3390/math9070767 ◽

2021 ◽

Vol 9 (7) ◽

pp. 767

Author(s):

Alexandra Băicoianu ◽

Cristina Maria Păcurar ◽

Marius Păun

Keyword(s):

Approximation Method ◽

Finite System ◽

Countable System ◽

Fractal Interpolation ◽

Interpolation Function ◽

Finite Systems ◽

Fractal Interpolation Function ◽

Fractal Interpolation Functions ◽

Finite Set ◽

Interpolation Functions

The present paper concretizes the models proposed by S. Ri and N. Secelean. S. Ri proposed the construction of the fractal interpolation function(FIF) considering finite systems consisting of Rakotch contractions, but produced no concretization of the model. N. Secelean considered countable systems of Banach contractions to produce the fractal interpolation function. Based on the abovementioned results, in this paper, we propose two different algorithms to produce the fractal interpolation functions both in the affine and non-affine cases. The theoretical context we were working in suppose a countable set of starting points and a countable system of Rakotch contractions. Due to the computational restrictions, the algorithms constructed in the applications have the weakness that they use a finite set of starting points and a finite system of Rakotch contractions. In this respect, the attractor obtained is a two-step approximation. The large number of points used in the computations and the graphical results lead us to the conclusion that the attractor obtained is a good approximation of the fractal interpolation function in both cases, affine and non-affine FIFs. In this way, we also provide a concretization of the scheme presented by C.M. Păcurar .

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