Article
On the Lower Bound of the HausdorffMeasure of the Koch Curve
Zhongshan University, 中山, Guangdong, China
Acta Mathematica Sinica (Impact Factor: 0.48). 10/2003; 19(4):715728. DOI: 10.1007/s1011400303102 ABSTRACT
This paper gives a lower bound of the Hausdorff measure of
the Koch curve by means of the mass distribution
principle.
the Koch curve by means of the mass distribution
principle.

 "We demonstrate the effectiveness of our algorithm for a synthetic but difficult problem, where the boundary between self and nonself is the wellknown Koch curve. The Koch curve is a fractal with a Hausdorff dimensionality of 1.26 [9]. In spite of its deceptively simple shape, the Koch curve has infinite length. "
Conference Paper: Procreating Vdetectors for nonself recognition: an application to anomaly detection in power systems.
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ABSTRACT: The artificial immune system approach for selfnonself discrimination and its application to anomaly detection problems in engineering is showing great promise. A seminal contribution in this area is the Vdetectors algorithm that can very effectively cover the nonself region of the feature space with a set of detectors. The detector set can be used to detect anomalous inputs. In this paper, a multistage approach to create an effective set of Vdetectors is considered. The first stage of the algorithm generates an initial set of Vdetectors. In subsequent stage, new detectors are grown from existing ones, by means of a mechanism called procreation. Procreating detectors can more effectively fill hardtoreach interstices in the nonself region, resulting in better coverage. The effectiveness of the algorithm is first illustrated by applying it to a wellknown fractal, the Koch curve. The algorithm is then applied to the problem of detecting anomalous behavior in power distribution systems, and can be of much use for maintenancerelated decisionmaking in electrical utility companies. 
Article: Fractal mechanics
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ABSTRACT: A mechanical theory of fractals and of nonsmooth objects in general is developed on the basis of the theory of differential spaces of Sikorski. Once the (generally infinite dimensional) configuration space is identified, an extended form of the principle of virtual work is used to define the concept of generalized force and stress. For the case of selfsimilar fractals, an appropriate integration based on the Hausdorff measure is introduced and applied to the numerical formulation of stiffness matrices of some common fractals, which can be used in a finite element implementation.  [Show abstract] [Hide abstract]
ABSTRACT: By means of the idea of [2] (Jia Baoguo, J.Math.Anal.Appl.In press) and the selfsimilarity of Sierpinski carpet, we obtain the lower and upper bounds of the Hausdorff Measure of Sierpinski carpet, which can approach the Hausdorff Measure of Sierpinski carpet infinitely.
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