scholarly journals COMB GRAPHS AND SPECTRAL DECIMATION

2009 ◽  
Vol 51 (1) ◽  
pp. 71-81 ◽  
Author(s):  
JONATHAN JORDAN
Keyword(s):  
Adjacency Matrix ◽  
Spectral Properties ◽  
Sierpinski Gasket ◽  
Self Similarity ◽  
Sierpiński Gasket ◽  
Spectral Similarity ◽  
Similarity Relationship ◽  
Adjacency Matrices ◽  
Similarity Operators ◽  
Math Phys

AbstractWe investigate the spectral properties of matrices associated with comb graphs. We show that the adjacency matrices and adjacency matrix Laplacians of the sequences of graphs show a spectral similarity relationship in the sense of work by L. Malozemov and A. Teplyaev (Self-similarity, operators and dynamics,Math. Phys. Anal. Geometry6(2003), 201–218), and hence these sequences of graphs show a spectral decimation property similar to that of the Laplacians of the Sierpiński gasket graph and other fractal graphs.

ECCENTRIC DISTANCE SUM OF SIERPIŃSKI GASKET AND SIERPIŃSKI NETWORK

Fractals ◽  
2019 ◽  
Vol 27 (02) ◽  
pp. 1950016 ◽  
Author(s):  
JIN CHEN ◽  
LONG HE ◽  
QIN WANG
Keyword(s):  
Asymptotic Formula ◽  
Complex Networks ◽  
Sierpinski Gasket ◽  
The Self ◽  
Self Similarity ◽  
Sierpiński Gasket ◽  
Similar Measure ◽  
Self Similar ◽  
Eccentric Distance

The eccentric distance sum is concerned with complex networks. To obtain the asymptotic formula of eccentric distance sum on growing Sierpiński networks, we study some nonlinear integral in terms of self-similar measure on the Sierpiński gasket and use the self-similarity of distance and measure to obtain the exact value of this integral.

From 1 → 3 dendritic designs to fractal supramacromolecular constructs: understanding the pathway to the Sierpiński gasket

2015 ◽  
Vol 44 (12) ◽  
pp. 3954-3967 ◽  
Author(s):  
George R. Newkome ◽  
Charles N. Moorefield
Keyword(s):  
Self Assembly ◽  
Sierpinski Gasket ◽  
Building Blocks ◽  
The Self ◽  
Self Similarity ◽  
Sierpiński Gasket

The potential to incorporate dendritic characteristics, such as self-similarity into new fractal-based materials is exemplified in the self-assembly of novel, polyterpyridine-based, building blocks.

scholarly journals SPECTRA OF SELF-SIMILAR LAPLACIANS ON THE SIERPINSKI GASKET WITH TWISTS

Fractals ◽  
2008 ◽  
Vol 16 (01) ◽  
pp. 43-68 ◽  
Author(s):  
ANNA BLASIAK ◽  
ROBERT S. STRICHARTZ ◽  
BARIS EVREN UGURCAN
Keyword(s):  
Sierpinski Gasket ◽  
Outer Approximation ◽  
Invariant Set ◽  
Self Similarity ◽  
Sierpiński Gasket ◽  
Constant Multiple ◽  
Self Similar ◽  
Definition Of ◽  
Two Parameter ◽  
Present Experimental Evidence

We study the spectra of a two-parameter family of self-similar Laplacians on the Sierpinski gasket (SG) with twists. By this we mean that instead of the usual IFS that yields SG as its invariant set, we compose each mapping with a reflection to obtain a new IFS that still has SG as its invariant set, but changes the definition of self-similarity. Using recent results of Cucuringu and Strichartz, we are able to approximate the spectra of these Laplacians by two different methods. To each Laplacian we associate a self-similar embedding of SG into the plane, and we present experimental evidence that the method of outer approximation, recently introduced by Berry, Goff and Strichartz, when applied to this embedding, yields the spectrum of the Laplacian (up to a constant multiple).

Self-similarity versus self-affinity: the Sierpinski gasket revisited

1986 ◽  
Vol 19 (16) ◽  
pp. L985-L989 ◽  
Author(s):  
A Lakhtakia ◽  
R Messier ◽  
V V Varadan ◽  
V K Varadan
Keyword(s):  
Sierpinski Gasket ◽  
Self Similarity ◽  
Sierpiński Gasket

scholarly journals Dimer Coverings on the Sierpinski Gasket

2008 ◽  
Vol 131 (4) ◽  
pp. 631-650 ◽  
Author(s):  
Shu-Chiuan Chang ◽  
Lung-Chi Chen
Keyword(s):  
Sierpinski Gasket ◽  
Sierpiński Gasket

scholarly journals Iterative Methods for the Computation of the Perron Vector of Adjacency Matrices

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1522
Author(s):  
Anna Concas ◽  
Lothar Reichel ◽  
Giuseppe Rodriguez ◽  
Yunzi Zhang
Keyword(s):  
Iterative Methods ◽  
Adjacency Matrix ◽  
Lanczos Method ◽  
Power Method ◽  
Arnoldi Method ◽  
Multiple Eigenvalues ◽  
Computer Storage ◽  
Adjacency Matrices ◽  
Lanczos Methods ◽  
Perron Vector

The power method is commonly applied to compute the Perron vector of large adjacency matrices. Blondel et al. [SIAM Rev. 46, 2004] investigated its performance when the adjacency matrix has multiple eigenvalues of the same magnitude. It is well known that the Lanczos method typically requires fewer iterations than the power method to determine eigenvectors with the desired accuracy. However, the Lanczos method demands more computer storage, which may make it impractical to apply to very large problems. The present paper adapts the analysis by Blondel et al. to the Lanczos and restarted Lanczos methods. The restarted methods are found to yield fast convergence and to require less computer storage than the Lanczos method. Computed examples illustrate the theory presented. Applications of the Arnoldi method are also discussed.

scholarly journals Metric approximations of spectral triples on the Sierpiński gasket and other fractal curves

2021 ◽  
Vol 385 ◽  
pp. 107771
Author(s):  
Therese-Marie Landry ◽  
Michel L. Lapidus ◽  
Frédéric Latrémolière
Keyword(s):  
Sierpinski Gasket ◽  
Sierpiński Gasket ◽  
Spectral Triples
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