• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.535-540
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• 2006

In this paper, characterizations of difference quotient transformation in the Krein space which is contained continuously and contractively in the krein space of square summable power series C (z) is obtained from the complementation theory.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제16권3호
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• pp.157-162
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• 2016

In this paper, a yield prediction model based on relevance vector machine (RVM) and a granular computing model (quotient space theory) is presented. With a granular computing model, massive and complex meteorological data can be analyzed at different layers of different grain sizes, and new meteorological feature data sets can be formed in this way. In order to forecast the crop yield, a grey model is introduced to label the training sample data sets, which also can be used for computing the tendency yield. An RVM algorithm is introduced as the classification model for meteorological data mining. Experiments on data sets from the real world using this model show an advantage in terms of yield prediction compared with other models.

• Journal of Information Processing Systems
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• 제16권3호
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• pp.663-676
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• 2020

Plant leaf classification is a significant application of image processing techniques in modern agriculture. In this paper, a multi-granular angle description method is proposed for plant leaf classification and retrieval. The proposed method can describe leaf information from coarse to fine using multi-granular angle features. In the proposed method, each leaf contour is partitioned first with equal arc length under different granularities. And then three kinds of angle features are derived under each granular partition of leaf contour: angle value, angle histogram, and angular ternary pattern. These multi-granular angle features can capture both local and globe information of the leaf contour, and make a comprehensive description. In leaf matching stage, the simple city block metric is used to compute the dissimilarity of each pair of leaf under different granularities. And the matching scores at different granularities are fused based on quotient space theory to obtain the final leaf similarity measurement. Plant leaf classification and retrieval experiments are conducted on two challenging leaf image databases: Swedish leaf database and Flavia leaf database. The experimental results and the comparison with state-of-the-art methods indicate that proposed method has promising classification and retrieval performance.

• 대한수학회보
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• 제50권4호
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• pp.1193-1200
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• 2013

The center of the Lie group $SU(n)$ is isomorphic to $\mathbb{Z}_n$. If $d$ divides $n$, the quotient $SU(n)/\mathbb{Z}_d$ is also a Lie group. Such groups are locally isomorphic, and their Weyl groups $W(SU(n)/\mathbb{Z}_d)$ are the symmetric group ${\sum}_n$. However, the integral representations of the Weyl groups are not equivalent. Under the mod $p$ reductions, we consider the structure of invariant rings $H^*(BT^{n-1};\mathbb{F}_p)^W$ for $W=W(SU(n)/\mathbb{Z}_d)$. Particularly, we ask if each of them is a polynomial ring. Our results show some polynomial and non-polynomial cases.