In this we examine the concept of the dimension of fractals, extending the idea of integer dimension to fractals, which we define and investigate here in. Moving on we consider the Minkowski dimension, sometimes referred to as the "box dimension", of a fractal. We then continue to define and examine another type of dimension; the Hausdorff dimension. We then investigate under what conditions these are equal finally moving on to prove Hutchinsons Theorem,
Testing is both technically and economically an important part of high quality software production. It has been estimated that testing accounts for half of the expenses in software production. Much of the testing is done manually or using other labor-intensive methods. It is thus vital for the software industry to develop efficient, cost effective, and automatic means and tools for software testing. Researchers have proposed several methods over years to generate automatically solution which have different drawbacks. This study examines automatic software testing optimization by using genetic algorithm approaches. This study will cover two approaches: a) obtain the sequence of regression tests that cover the greatest amount of code and b) once it is achieved another genetic algorithm will eliminate tests cases that cover the same section of code on the basis of still get the maximum code coverage. The overall aim of this research is to reduce the number of test cases that need to be run with the greatest amount of code covered.
Research has made great strides in understanding the interactions of the elementary particles attractons and the corresponding vibrational energy released triggered by collision with humans, measured as cupids. During typical field work, researchers discovered a test subject with atypical behavioral traits that produced much higher volumes of cupids in other subjects than had been previously measured in labratory settings. Further research concluded that the traits of this subject produced an entirely new elementary particle, here referred to as valentons. This paper outlines the discoveries about the traits of this subject, the unique effects that these new particles produce, and an outline of how these new particles will affect the study of attractons, cupids, and valentons in future research.