In this paper an improved multi_scale estimation method of signal is gaven.The detail signals on each scale are further more decomposed with wavelet transform.The subdetail signals and subsmoothing signals are processed with different threshold respectively. The smoothing signals on the coarsest scale are processed with Kalman fitering and reconstructed with the detail signal on each scale.At last the signal estimate value on the original scale is obtained.
A Class of rings is said to be weakly hereditary if 0≠I△R∈ implies 0≠I^n∈ for some positive integer n, which generalizes the concept of heredity but other than that of regularity. In §2 the properties of such class and its essential cover are studied. In §3 the upper radicals determined by them are investigated. At the same time the 'Problem 42, 44 and 55' of Szasz [7] are discussed. In §4 two examples are given, which show that the concept of weak heredity is independent of that of regularity.
