• 대한수학회논문집
• /
• 제33권4호
• /
• pp.1357-1366
• /
• 2018

It is shown that the Mayer-Vietoris sequence holds for the cohomology of complexes of Lie algebroids which are defined on simplicial complexes and satisfy the compatibility condition concerning restrictions to the faces of each simplex. The Mayer-Vietoris sequence will be obtained as a consequence of the extension lemma for piecewise smooth forms defined on complexes of Lie algebroids.

• 한국지능시스템학회논문지
• /
• 제12권6호
• /
• pp.577-582
• /
• 2002

Neural network can be trained to approximate an arbitrary nonlinear function of multivariate data like the mini-mill crown values in Automatic Shape Control. The trained weights of neural network can evaluate or generalize the process data outside the training vectors. Sometimes, the blind modeling of the process data is necessary to compare with the scattered analytical model of mini-mill process in isolated electro-mechanical forms. To come up with a viable model, we propose the blind neural-based range-division domain-clustering piecewise-linear modeling scheme. The basic ideas are: 1) dividing the range of target data, 2) clustering the corresponding input space vectors, 3)training the neural network with clustered prototypes to smooth out the convergence and 4) solving the resulting matrix equations with a pseudo-inverse to alleviate the ill-conditioning problem. The simulation results support the effectiveness of the proposed scheme and it opens a new way to the data analysis technique. By the comparison with the statistical regression, it is evident that the proposed scheme obtains better modeling error uniformity and reduces the magnitudes of errors considerably. Approximatly 10-fold better performance results.