a common method to determine the order of minimal realization of a continuous linear time invariant descriptor system is to decompose it into slow and fast subsystems using the weierstrass canonical form. the weierstrass decomposition should be avoided because it is generally an ill-conditioned problem that requires many complex calculations especially for high-dimensional systems. the present ...

We prove that, for low-order (n ≤ 4) stable polynomial segments or interval polynomials, there always exists a fixed polynomial such that their ratio is SPR-invariant, thereby providing a rigorous proof of Anderson’s claim on SPR synthesis for the fourth-order stable interval polynomials. Moreover, the relationship between SPR synthesis for low-order polynomial segments and SPR synthesis for lo...

We obtain exact analytical expressions for correlations between real zeros of the Kac random polynomial. We show that the zeros in the interval (−1, 1) are asymptotically independent of the zeros outside of this interval, and that the straightened zeros have the same limit translation invariant correlations. Then we calculate the correlations between the straightened zeros of the SO(2) random p...

We study determinantal translation-invariant random point processes on the real line. Under some technical assumptions on the correlation kernel, we prove that the smallest nearest spacings in a large interval have Poisson statistics as the length of the interval goes to infinity. 2000 Math. Subj. Class. 60G55, 60G70.

Introduction. An interesting but apparently neglected generalization due to Doob [l], of the ergodic theorem, is the generalization to transformations which are not necessarily one-to-one. In his paper [l], Doob showed that the transformation of the interval [0, l] into itself given by/(x) =nx (modulo 1), where n — 1 is a positive integer, is ergodic under Lebesgue measure and that the law of l...

"In single-time autonomous optimal control problems, the Hamiltonian is constant on evolution. In addition, if final time free, vanishes hole interval of The purpose this paper to extend some these results case multitime control. original include: anti-trace problem, weak and strong maximum principles, multitime-invariant systems change rate Hamiltonian, variational derivative volume integral, ...