Transitive maps in bitopological dynamical systems

This paper introduces fundamental ideas of bitopological dynamical systems. Here, notions of bitopological transitivity, point transitivity, pairwise iterated compactness, weakly bitopological transitivity, etc. are introduced. Later, it is shown that under pairwise homeomorphism, weakly point transitivity implies weakly bitopological transitivity. Moreover, under pairwise homeomorphism; pairwise compactness and pairwise iterated compactness are found to be equivalent. Later, we apply our results in the development process of a human embryo from the zygote until birth. During the process of biological application, we disprove conjecture 1 of Nada and Zohny [S. I. Nada, H. Zohny, An application of relative topology in biology. Chaos, Solitons and Fractals, 42 (2009) 202-204].

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On forward iterated Hausdorffness and development of embryo from zygote in bitopological dynamical systems

SERIES III - MATEMATICS, INFORMATICS, PHYSICS ◽

10.31926/but.mif.2020.13.62.2.3 ◽

2021 ◽

Vol 13(62) (2) ◽

pp. 399-410

Author(s):

Santanu Acharjee ◽

Kabindra Goswami ◽

Hemanta Kumar Sarmah

Keyword(s):

Dynamical System ◽

Cell Division ◽

Dynamical Systems ◽

Topological Space ◽

Development Process ◽

Hausdorff Space ◽

Topological Dynamical System ◽

Relative Topology ◽

Dynamical Properties

Topological dynamical system is an area of dynamical system to investigate dynamical properties in terms of a topological space. Nada and Zohny [Nada, S.I. and Zohny, H., An application of relative topology in biology, Chaos, Solitons and Fractals. 42 (2009), 202-204] applied topological dynamical system to explore the development process of an embryo from the zygote until birth and made three conjectures. In this paper, we disprove conjecture 3 of Nada and Zohny [Nada, S.I. and Zohny, H., An application of relative topology in biology, Chaos, Solitons and Fractals. 42 (2009), 202-204] by applying some of our mathematical results of bitopological dynamical system. Also, we introduce forward iterated Hausdorff space, backward iterated Hausdorff space, pairwise iterated Hausdor_ space and establish relations between them in bitopological dynamical system. We formulate the function that represents cell division (specially, mitosis) and using this function we show that in the development process of a human baby from the zygote until its birth, there is a stage where the developing stage is forward iterated Hausdorff

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Scanning Electron Microscopic Study of the Cell Surface

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100062087 ◽

1969 ◽

Vol 27 ◽

pp. 36-37 ◽

Cited By ~ 1

Author(s):

Toichiro Kuwabara

Keyword(s):

Tissue Fluid ◽

Biological Application ◽

Biological Structure ◽

Electron Microscopic ◽

Surface Appearance ◽

Minute Amount ◽

Scanning Electron Microscopic Study ◽

Scanning Electron Microscopic ◽

True Structure ◽

Scanning Electron

Although scanning electron microscopy has a great potential in biological application, there are certain limitations in visualization of the biological structure. Satisfactory techniques to demonstrate natural surfaces of the tissue and the cell have been reported by several investigators. However, it is commonly found that the surface cell membrane is covered with a minute amount of mucin, secretory substance or tissue fluid as physiological, pathological or artefactual condition. These substances give a false surface appearance, especially when the tissue is fixed with strong fixatives. It seems important to remove these coating substances from the surface of the cell for demonstration of the true structure.

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