Fractal geometry of the complement of Lagrange spectrum in Markov spectrum

Carlos Matheus; Carlos Gustavo Moreira

doi:10.4171/cmh/498

M∖L is Not Closed

International Mathematics Research Notices ◽

10.1093/imrn/rnaa096 ◽

2020 ◽

Author(s):

Davi Lima ◽

Carlos Matheus ◽

Carlos Gustavo Moreira ◽

Sandoel Vieira

Keyword(s):

Closed Subset ◽

Negative Answer ◽

Lagrange Spectrum ◽

Markov Spectrum

Abstract We show that $1+3/\sqrt{2}$ is a point of the Lagrange spectrum $L$ that is accumulated by a sequence of elements of the complement $M\!\setminus\! L$ of the Lagrange spectrum in the Markov spectrum $M$. In particular, $M\!\setminus\! L$ is not a closed subset of $\mathbb{R}$, so that a question by T. Bousch has a negative answer.

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Quadratic Irrationals in the Lower Lagrange Spectrum

Canadian Journal of Mathematics ◽

10.4153/cjm-1973-059-3 ◽

1973 ◽

Vol 25 (3) ◽

pp. 578-584 ◽

Cited By ~ 8

Author(s):

Nancy Davis ◽

J. R. Kinney

Keyword(s):

Lagrange Spectrum ◽

Markov Spectrum ◽

Image Position ◽

Positive Integers

We let , where the xi are positive integers and i ∈ N, the set of all integers. We define , where where . We let = [0; x1, x2, … ] whereWe letand defineThe range of L(ξ) is known as the Lagrange spectrum and the range of M(ξ) as the Markov spectrum. It is known that both are closed and that the Markov spectrum includes the Lagrange spectrum.

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Fractal geometry

10.1533/9780857099594 ◽

2002 ◽

Cited By ~ 3

Author(s):

J.M. Blackledge ◽

A.K. Evans ◽

M.J. Turner

Keyword(s):

Fractal Geometry

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Optimal Density Determination of Bouguer Anomaly Using Fractal Analysis (Case of study: Charak area,IRAN)

JOURNAL OF ADVANCES IN PHYSICS ◽

10.24297/jap.v1i1.2140 ◽

2005 ◽

Vol 1 (1) ◽

pp. 21-24

Author(s):

Hamid Reza Samadi

Keyword(s):

Surface Roughness ◽

Fractal Dimension ◽

Fractal Analysis ◽

Fractal Geometry ◽

Host Rock ◽

Bouguer Anomaly ◽

Research Area ◽

Density Difference ◽

Optimal Density

In exploration geophysics the main and initial aim is to determine density of under-research goals which have certain density difference with the host rock. Therefore, we state a method in this paper to determine the density of bouguer plate, the so-called variogram method based on fractal geometry. This method is based on minimizing surface roughness of bouguer anomaly. The fractal dimension of surface has been used as surface roughness of bouguer anomaly. Using this method, the optimal density of Charak area insouth of Hormozgan province can be determined which is 2/7 g/cfor the under-research area. This determined density has been used to correct and investigate its results about the isostasy of the studied area and results well-coincided with the geology of the area and dug exploratory holes in the text area

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An Exercise in a Transdisciplinary Approach for New Knowledge Paradigms

Human and Social Studies ◽

10.2478/hssr-2013-0042 ◽

2014 ◽

Vol 3 (3) ◽

pp. 114-143

Author(s):

Gabriel Crumpei ◽

Maricel Agop ◽

Alina Gavriluţ ◽

Irina Crumpei

Keyword(s):

Quantum Mechanics ◽

20Th Century ◽

Chaos Theory ◽

Fractal Geometry ◽

Science And Religion ◽

Transdisciplinary Approach ◽

Linear Dynamics ◽

New Knowledge ◽

Religious Perspectives ◽

Energy Information

Abstract In this paper, we aim at an exercise that is transdisciplinary, involving science and religion, and interdisciplinary, involving disciplines and theories which appeared in the second half of the 20th century (e.g., topology, chaos theory, fractal geometry, non-linear dynamics, all of which can be found in the theory of complex systems). The latter required the reformulation of quantum mechanics theories starting with the beginning of the century, based on the substance-energy-information triangle. We focus on information and we also attempt a transdisciplinary approach to the imaginary from a psychological - physical - mathematical perspective, but the religious perspectives find their place along with the philosophical or even philological vision

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COLONY OF THE FUNGUS Aspergillus oryzae AND SELF-AFFINE FRACTAL GEOMETRY OF GROWTH FRONTS

Fractals ◽

10.1142/s0218348x93000046 ◽

1993 ◽

Vol 01 (01) ◽

pp. 11-19 ◽

Cited By ~ 20

Author(s):

SHU MATSUURA ◽

SASUKE MIYAZIMA

Keyword(s):

Aspergillus Oryzae ◽

Environmental Conditions ◽

Fractal Geometry ◽

Nutrient Concentration ◽

Incubation Temperature ◽

Characteristic Exponent ◽

Growth Front ◽

Favorable Condition ◽

The Self ◽

The Mean

A variety of colony shapes of the fungus Aspergillus oryzae under varying environmental conditions such as the nutrient concentration, medium stiffness and incubation temperature are obtained, ranging from a homogeneous Eden-like to a ramified DLA-like pattern. The roughness σ(l, h) of the growth front of the band-shaped colony, where h is the mean front height within l of the horizontal range, satisfies the self-affine fractal relation under favorable environmental conditions. In the most favorable condition of our experiments, its characteristic exponent is found to be a little larger than that of the 2-dimensional Eden model.

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