SUPERRESOLUTION MULTISCALED IMAGING OF FRACTURE MEDIUM BASED ON A NEW METHOD OF FRACTAL STRUCTURE NATURAL EVOLUTION

Microstructural characteristics of A356 alloy prepared by low superheat pouring were researched, and the fractal dimensions of morphology of primary phase in the alloy was calculated. The results indicated that morphology of primary phase in A356 alloy belonged to fractal structure, and the microstructural characteristics in the alloy can be characterized by fractal dimension. There were the different fractal dimensions for the morphology of primary phase prepared by the different process.

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Injectivity of the Composition Operators of Étale Mappings

Algebra ◽

10.1155/2014/782973 ◽

2014 ◽

Vol 2014 ◽

pp. 1-11

Author(s):

Ronen Peretz

Keyword(s):

Topological Space ◽

Composition Operator ◽

Open Problem ◽

Fractal Structure ◽

Composition Operators ◽

New Method ◽

Jacobian Conjecture ◽

Two Dimensional ◽

New Approach ◽

Polynomial Mappings

Let X be a topological space. The semigroup of all the étale mappings of X (the local homeomorphisms X→X) is denoted by et(X). If G∈et(X), then the G-right (left) composition operator on et(X) is defined by RG LG:et(X)→et(X), RGF=F∘G (LGF=G∘F). When are the composition operators injective? The Problem originated in a new approach to study étale polynomial mappings C2→C2 and in particular the two-dimensional Jacobian conjecture. This approach constructs a fractal structure on the semigroup of the (normalized) Keller mappings and outlines a new method of a possible attack on this open problem (in preparation). The construction uses the left composition operator and the injectivity problem is essential. In this paper we will completely solve the injectivity problems of the two composition operators for (normalized) Keller mappings. We will also solve the much easier surjectivity problem of these composition operators.

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SELF-SIMILARITY IN COMPLEX NETWORKS: FROM THE VIEW OF THE HUB REPULSION

Modern Physics Letters B ◽

10.1142/s0217984913502011 ◽

2013 ◽

Vol 27 (28) ◽

pp. 1350201 ◽

Cited By ~ 14

Author(s):

HAIXIN ZHANG ◽

XIN LAN ◽

DAIJUN WEI ◽

SANKARAN MAHADEVAN ◽

YONG DENG

Keyword(s):

Fractal Dimension ◽

Complex Systems ◽

Complex Networks ◽

Fractal Structure ◽

The Self ◽

New Method ◽

Self Similarity ◽

Nature And Society ◽

Real Complex

Complex networks are widely used to model the structure of many complex systems in nature and society. Recently, fractal and self-similarity of complex networks have attracted much attention. It is observed that hub repulsion is the key principle that leads to the fractal structure of networks. Based on the principle of hub repulsion, the metric in complex networks is redefined and a new method to calculate the fractal dimension of complex networks is proposed in this paper. Some real complex networks are investigated and the results are illustrated to show the self-similarity of complex networks.

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Selective Sampling and Orientation of Non-Homogeneous Tissues

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100100238 ◽

1968 ◽

Vol 26 ◽

pp. 98-99

Author(s):

C. C. Clawson ◽

L. W. Anderson ◽

R. A. Good

Keyword(s):

Electron Microscopy ◽

Electron Microscope ◽

Light Microscopy ◽

Random Sampling ◽

New Method ◽

Microscope Examination ◽

Small Areas ◽

Selective Sampling ◽

Large Numbers ◽

Specific Orientation

Investigations which require electron microscope examination of a few specific areas of non-homogeneous tissues make random sampling of small blocks an inefficient and unrewarding procedure. Therefore, several investigators have devised methods which allow obtaining sample blocks for electron microscopy from region of tissue previously identified by light microscopy of present here techniques which make possible: 1) sampling tissue for electron microscopy from selected areas previously identified by light microscopy of relatively large pieces of tissue; 2) dehydration and embedding large numbers of individually identified blocks while keeping each one separate; 3) a new method of maintaining specific orientation of blocks during embedding; 4) special light microscopic staining or fluorescent procedures and electron microscopy on immediately adjacent small areas of tissue.

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