New definitions of determinant functionals over the quaternion skew field are given in this paper. The inverse matrix over the quaternion skew field is represented by analogues of the classical adjoint matrix. Cramer rule for right and left quaternionic systems of linear equations have been obtained.

Process-variation induced skew has become one of the major contributors to the clock-skew in advanced technologies. Since process-variation induced skew is roughly proportional to clock-delay, it is preferable to design zero-skew clock-trees and have minimum clock-delay to reduce both unintentional and process-variation induced skews. In this paper, we propose a zero-skew buffered clock-tree sy...

We construct chain maps between the bar and Koszul resolutions for a quantum symmetric algebra (skew polynomial ring). This construction uses a recursive technique involving explicit formulae for contracting homotopies. We use these chain maps to compute the Gerstenhaber bracket, obtaining a quantum version of the Schouten-Nijenhuis bracket on a symmetric algebra (polynomial ring). We compute b...

In time-of-flight range imagers, as the range resolution increases, a gating clock skew becomes a serious problem. This paper describes two skew calibration techniques implemented in column-parallel circuits for TOF range imagers. Skew calibration technique with optical response is simple but the long calibration time is required. To reduce the calibration time, self-calibration technique with ...

let r be a ring, m a right r-module and (s,≤) a strictly ordered monoid. in this paper we will show that if (s,≤) is a strictly ordered monoid satisfying the condition that 0 ≤ s for all s ∈ s, then the module [[ms,≤]] of generalized power series is a uniserial right [[rs,≤]] ]]-module if and only if m is a simple right r-module and s is a chain monoid.