in this work are studied the jacobians of certain singular transformations and the corresponding measures which support the jacobian computations.

In this paper, we present a new computational method to solve Volterra integral equations of the first kind based on Bernstein polynomials. In this method, using operational matrices turn the integral equation into a system of equations. The computed operational matrices are exact and new. The comparisons show this method is acceptable. Moreover, the stability of the proposed method is studied.

A generalized structure of complementary matrices involved in the input-state-output Inclusion Principle for linear time-invariant systems (LTI) including contractibility conditions for static state feedback controllers is well known. In this paper, it is shown how to further extend this structure in a systematic way when considering contractibility of dynamic controllers. Necessary and suffici...

It is known that two normal matrices can be diagonalized by the same unitary transformation if and only if they commute ; this theorem is ordinarily stated for hermitian matrices. Some generalizations of this theorem are known. According to a theorem due to Eckert and Young, if A and B are two rXs matrices, there are two unitary matrices U and V such that UAV=DX and UBV=D2, D\ and D2 diagonal m...