• Journal of the Chungcheong Mathematical Society
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• v.21 no.3
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• pp.371-376
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• 2008

Let $P(M,G,{\pi})=:P$ be a principal fibre bundle with structure Lie group G over a base manifold M. In this paper we get the following facts: 1. The tangent bundle TG of the structure Lie group G in $P(M,G,{\pi})=:P$ is a Lie group. 2. The Lie algebra ${\mathcal{g}}=T_eG$ is a normal subgroup of the Lie group TG. 3. $TP(TM,TG,{\pi}_*)=:TP$ is a principal fibre bundle with structure Lie group TG and projection ${\pi}_*$ over base manifold TM, where ${\pi}_*$ is the differential map of the projection ${\pi}$ of P onto M. 4. for a Lie group $H,\;TH=H{\circ}T_eH=T_eH{\circ}H=TH$ and $H{\cap}T_eH=\{e\}$, but H is not a normal subgroup of the group TH in general.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.33B no.11
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• pp.140-149
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• 1996

Cursive characters are written on an economical principle to reduce the motion of a pen in the limit of distinction between characters. That is, the pen is not lifted up to move for writing a next stroke, the pen is not moved at all, or connected two strokes chance their shapes to a similar and simple shape which is easy to be written. For these reasons, strokes and korean alphabets are not only easy to be changed, but also difficult to be splitted. In this paper, we propose a curvature stroke modeling method for splitting and matching by using a structural primitive. A curvature stroke is defined as a substroke which does not change its curvanture. Input strokes handwritten in a cursive style are splitted into a sequence of curvature strokes by segmenting the points which change the direction of rotation, which occur a sudden change of direction, and which occur an excessive rotation Each reference of korean alphabets is handwritten in a printed style and is saved as a sequence of curvature strikes which is generated by splitting process. And merging process is used to generate various sequences of curvature strikes for matching. Here, it is also considered that imaginary strokes can be written or omitted. By using a curvature stroke as a unit of recognition, redundant splitting points in input characters are effectively reduced and exact matching is possible by generating a reference curvature stroke, which consists of the parts of adjacent two korean alphasbets, even when the connecting points between korean alphabets are not splitted. The results showed 83.6% as recognition rate of the first candidate and 0.99sec./character (CPU clock:66MHz) as processing time.