Our basic problem is to answer the question : when are two quadratic forms equivalent by a rational or integral change of basis? We shall temporarily suppose that all our forms are non-degenerate (i.e., have non-zero determinant), although degenerate forms really give no trouble, The answer in the rational case is given by the celebrated HasseMinkowski theorem, which is usually stated in the form:

In this paper, two quadratic observability normal forms dependent on output respectively correspondent to drift dominant term and forced dominant term are firstly discussed. Moreover characteristic numbers are studied in order to simplify the calculation of these two normal forms.

Diversity and accuracy are the two key factors that decide the ensemble generalization error. Constructing a good ensemble method by balancing these two factors is difficult, because increasing diversity is at the cost of reducing accuracy normally. In order to improve the performance of an ensemble while avoiding the difficulty derived of balancing diversity and accuracy, we propose a novel me...

Estimation of flexible functional forms for large consumer or producer demand systems is often precluded due to computational difficulties or due to a lack of degrees of freedom. We propose the concept of a semiflexible form, which is a special case of a flexible form but which requires fewer free parameters. Our proposed method of estimation allows the researcher to choose the degree of flexib...