We evaluate several binomial transforms by using Euler's transform for power series. In this way we obtain various binomial identities involving power sums with harmonic numbers.

LFM signals are widely used in the fields of radar and communication etc., which make signals detection and parameters estimation a very important technology in multicomponent LFM signals. To solve the problems of error detection caused by the cross-terms in WVD-Hough methods and other modified WVD distribution methods, and low parameter estimation precision due to poor timefrequency concentrat...

The present material addresses several problems left open in the Trans. AMS paper ” Non-crossing cumulants of type B” of P. Biane, F. Goodman and A. Nica. The main result is that a type B non-commutative probability space can be studied in the framework of freeness with amalgamation. This view allows easy ways of constructing a version of the S-transform as well as proving analogue results to C...

Two basic tools of free probability are the R-transform and the S-transform. These transforms were introduced by Voiculescu in the 1980s, and are used to understand the addition and the multiplication of two free random variables respectively. The R-transform has a natural and very useful multi-variable extension describing the addition of two free k-tuples of random variables, but the problem ...

Recent observations on polynomial structures of AES-like round functions are analysed in this note. We present computational evidence that input/output bits of AESlike 2-round transform up to 40-bit, constructed with 8-bit AES S-boxes, do not satisfy any relations of degree 3. So it is very unlikely that actual AES 2-round transform admits any relations of degree ≤ 3.

In this paper we present two new texture segmentation algorithms based on local spectrum analysis with the two dimensional S-Transform. The effectiveness of these algorithms is demonstrated both on simple synthetic images, and complicated, real images of glacial sediment deposits. The S-Transform method is robust and is insensitive to changes in light intensity, and moisture variations. The eff...

. In the power quality analysis non-stationary nature of voltage distortions require some precise and powerful analytical techniques. The time-frequency representation (TFR) provides a powerful method for identification of the non-stationary of the signals. This paper investigates a comparative study on two techniques for analysis and visualization of voltage distortions with time-varying ampli...