This paper presents some results concerning the application of the fractal approach to the analysis of shape of white brain matter in the magnetic-resonance (MR) images. The fractal dimension of white brain matter was calculated using the box-counting algorithm.

In this paper, the fractal characteristics of goose down assembly are described by determining the pore area fractal dimension and the tortuosity fractal dimension. The goose down assembly, filled with mass of down fibers and pores, is loose and ductile. The pores are varying shapes and sizes, and distribute unevenly. Firstly, micro computed tomography is used to observe the internal microstruc...

Since Benoît Mandelbrot raised the question about the length of Britain’s coastline in 1967, it has become obvious that fractal geometry is appropriate for describing irregular forms. In 1996 Carl Bovill applied box-counting, a fractal analysis method, for the first time to architecture in order to quantify the characteristic visual complexity of facades. This paper presents an approach utilizi...

The fractal structure of a white cauliflower is investigated by using the box-counting method on its cross section. The capacity dimension of the cross section is 1.88 ± 0.02, independent of the direction. From the result, we predict that the capacity dimension of a cauliflower is about 2.8. The vertical cross section of a cauliflower is modeled into a self-similar set of a rectangular tree. We...

The rapid progress of many countries toward gender equality in education has been welldocumented. Of 106 countries, 83 achieved the Millennium Development target of parity in primary and secondary education by 2005; only 19 countries, most in sub-Saharan Africa, are off-track to meet the target of gender equality in primary and secondary school enrolment by 2015. While the progress on meeting t...

Recent changes to the criteria for engineering accreditation in Canada emphasize continuous curriculum improvement through outcomes-based assessment. In this article, the authors show how the CDIO (ConceiveDesign-Implement-Operate) approach not only enables continuous improvement, but can assist Canadian engineering programs with the overall graduate attributes assessment process through a case...

The first session of this semester’s Algorithms Reading Group dealt with the problem of parking cars on the streets of New York City. The goal is to analyze different parking behaviors and observe to what extent following some parking strategy can affect the maximum number of cars that can be parked on the street. Such analysis can be useful for finding out what parking patterns provide the max...

Let F ⊆ R denote the field of numbers which are constructible by means of ruler and compass. We prove that: (1) if x, y ∈ R (n > 1) and |x − y| is an algebraic number then there exists a finite set Sxy ⊆ R containing x and y such that each map from Sxy to R n preserving all unit distances preserves the distance between x and y; if x, y ∈ F then we can choose Sxy ⊆ F, (2) only algebraic distance...

Proof. If the edge (r, s) from the root to the sink is included in the spanning tree, then each of the principal branches of Tn may be assigned an oriented spanning tree independently, so there are t n−1 such spanning trees. On the other hand, if (r, s) is not included in the spanning tree, there is a directed path r → x1 → . . . → xn−1 → s in the spanning tree from the root to the sink. In thi...