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A topic for study derives from an interesting problem on the internet.Some significative conclusions about the problem of number ring transformation are made in the paper. Firstly, an assumption that a given starting number ring could be transformed to the end ring in finite degree is proved. Secondly, transformation degree is proved to be unconcerned with the order of the transformation. Furthermore, a function of computing transformation degree is worked out. Finally, the same end ring is gained with a given starting number ring transformed in different sequence.

Starting from the roots of the equation 3^x + 4^x = 5^x discussed in the Tenth Grade, we utilized the method, the algebraic extension of the rational number eld, to produce the ways to judge whether the roots of the basic exponential equation with a form as a^x+b^x = c^x are rational or not. For equations with more than two terms on the left side, as is the equation a_1^x+a_2^x+
···

+a_n^x = d^x, the determination of whether the root was irrational was comparatively dicult.Therefore, we provided a prevalent method for the examination of the root of a three-term equation as well as a conclusion that if the equation doesn't have integer roots, the roots won't be a rational number with a denominator of two. Finally, based on the method, the algebraic extension of the rational number eld, we concluded that under special occasions, the root of the equation can't be some rational numbers with certain denominators.

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Clothing is one of the symbol of modern fashion trends, research concerning clothing detail’s recognition still remains a hot topic in the field of computer. Existing research is mainly focused on relating clothing detail features and aesthetic styles, realizing the possibilities of auto clothing aesthetic appreciation. In this paper, based on existing data sets, we will introduce the ideology of Deep Learning into the association model between clothing visual features to improve the model’s effectiveness and accuracy. By calculating the distance between aesthetic words and seed words, we are able to map the most often used aesthetic words in a two-dimensional space, building a fashion semantic space. Later, we introduce the ideology of Deep Learning into the association model between clothing detail features, and designed experiments to prove the effectiveness of the model. In the research, we discussed how different parameters and structures in Deep Learning effect the outcome of the relating model, and by comparison we choose the best parameters of the model. Based on the work mentioned above, we analyze different styles of different categories’ clothing in shopping websites, which further confirms the effectiveness of our model.