Composite linear and quadratic systems produce three-wave coupling when stimulated by random-phase input sinusoids. Due to the non-linearity of the system the output frequencies are arithmetically related to the input. Using third order cumulant statistics and their associated bispectrum, techniques are devised based on phaseinsensitive matrix structures for detection and frequency estimation o...

In this paper, we establish the following two results: (1) a skew translation generalized quadrangle of even order is quadrangle, (2) does not admit point regular group automorphisms. The first result confirms conjecture Payne (1975) based on earlier work Ott (2021), and second Ghinelli (1992).

0 = d dt ‖x(t)‖ = 2x(t) ẋ(t) = 2x(t)Ax(t) = x(t) (A+ A )x(t) for all x(t), which occurs if and only A+A = 0, which is the same as A = −A, i.e., A is skew-symmetric. There are many other ways to see this. For example, the norm of the state will be constant provided the velocity vector is always orthogonal to the position vector, i.e., ẋ(t)x(t) = 0. This also leads us to A + A = 0. Another approa...

let $alpha$ be an endomorphism and $delta$ an $alpha$-derivationof a ring $r$.  in this paper we  study the relationship between an$r$-module $m_r$ and the  general polynomial module  $m[x]$ over theskew polynomial ring $r[x;alpha,delta]$. we introduce the notionsof skew-armendariz modules and skew quasi-armendariz modules whichare generalizations of $alpha$-armendariz modules and extend thecla...

for a ring endomorphism $alpha$ and an $alpha$-derivation $delta$, we introduce a concept, so called skew $pi$-armendariz ring, that is a generalization of both $pi$-armendariz rings, and $(alpha,delta)$-compatible skew armendariz rings. we first observe the basic properties of skew $pi$-armendariz rings, and extend the class of skew $pi$-armendariz rings through various ring extensions. we nex...

We construct a copula from the multivariate skew t-distribution of Azzalini and Capitanio (2003). This copula can capture asymmetric and extreme dependence between variables, and it is one of the few that is effective when the number of dimensions is high. However, two problems arise when estimating the parameters by maximum likelihood estimation. Here, we solve these problems and provide a con...

This paper provides a systematic and comprehensive treatment for obtaining general expressions of any order, the moments cumulants spherically elliptically symmetric multivariate distributions; results case t-distribution related skew-t distribution are discussed in some detail.

Uncertainty relation is a fundamental issue in quantum mechanics and information theory. By using modified generalized variance (MGV), Wigner–Yanase–Dyson skew (MGWYD), we identify the total uncertainty of channels. The elegant properties channels are explored detail. In addition, present trade-off between entanglement fidelity establish relationships entropy exchange/coherent information. Deta...

Using the skew-Hopf pairing, we obtain ℛ-matrix for two-parameter quantum algebra Uv,t. We further construct a strict monoidal functor