Let $R$ be a reversible ring which is $alpha$-compatible for an endomorphism $alpha$ of $R$ and $f(X)=a_0+a_1X+cdots+a_nX^n$ be a nonzero skew polynomial in $R[X;alpha]$. It is proved that if there exists a nonzero skew polynomial $g(X)=b_0+b_1X+cdots+b_mX^m$ in $R[X;alpha]$ such that $g(X)f(X)=c$ is a constant in $R$, then $b_0a_0=c$ and there exist nonzero elements $a$ and $r$ in $R$ such tha...

We explore the multifractality of steady state wave function in non-unitary random quantum dynamics one dimension. focus on two classes systems: hybrid Clifford circuit model and free fermion dynamics. In model, we map measurement driven transition to an Anderson localization effective graph space by using properties stabilizer state. show that volume law phase with nonzero rate is non-ergodic ...

The registration of preoperative CT to intra-operative reality systems is a crucial step in Computer Assisted Orthopedic Surgery (CAOS). The intra-operative sensors include 3D digitizers, fiducials, X-rays and Ultrasound (US). FAPBED is designed to process CT volumes for registration to tracked US data. Tracked US is advantageous because it is real time, noninvasive, and non-ionizing, but it is...

In this paper we introduce $(alpha,beta)-$linear connected spaces for nonzero cardinal numbers $alpha$ and $beta$. We show that $(alpha,beta)-$linear connectivity approach is a tool to classify the class of all linear connected spaces.

We prove the circular law for a class of non-Hermitian random block band matrices with genuinely sublinear bandwidth. Namely, we show that there exists ? ? (0, 1) so if bandwidth matrix X is at least n1?? and nonzero entries are iid variables mean zero slightly more than four finite moments, then limiting empirical eigenvalue distribution X, when properly normalized, converges in probability to...

The photon production due to conversion of two gluons into a photon, $gg\rightarrow\gamma$, in the presence background gauge fields is studied within specific mean-field approach QCD vacuum. In this approach, mean field confinement phase represented by statistical ensemble almost everywhere homogeneous abelian (anti-)self-dual gluon configurations, while deconfined can be characterized purely c...