Abstract : Let be a 2nd order ODE. By Cartan equivalence method, we will study the local equivalence problem under the transformations group of time-fixed coordinates. We are going to solve this problem by an applicable method which has been recognized by R. Gardner, and classify them.   

This paper introduces a class of graphs deened as the models of a peculiar kind of linear bounded machines that read their input performing all computations on work tapes. It is proven that this class is closed, up to observational equivalence, under synchronized product. The rst{order theory of these graphs is investegated and shown to be undecidable. The latter result extends to any logic in ...

in welfare economic studies, because of the differences among households scale, we cannot consider household expenditures without attention to this factor. a simple method to consider household scale in welfare analysis is the usage of the per capita expenditure. but, the usage of per capita expenditure ignores economies of scale. in fact, per capita expenditure is a biased variable, and underv...