Given a matrix A ∈ F(t)[D; δ] n×n over the ring of differential polynomials, we show how to compute the Hermite form H of A and a unimodular matrix U such that U A = H. The algorithm requires a polynomial number of operations in F in terms of n, deg D A, deg t A. When F = Q it require time polynomial in the bit-length of the rational coefficients as well.
Let F[∂; σ, δ] be the ring of Ore polynomials over a field (or skew field) F, where σ is a automor-phism of F and δ is a σ-derivation. Given a matrix A ∈ F[∂; σ, δ] n×n , we show how to compute the Hermite form H of A and a unimodular matrix U such that U A = H. The algorithm requires a polynomial number of operations in F in terms of n and the degrees (in… (More)
We reported well-integrated zinc oxide (ZnO) nanorod arrays (NRAs) on conductive textiles (CTs) and their structural and optical properties. The integrated ZnO NRAs were synthesized by cathodic electrochemical deposition on the ZnO seed layer-coated CT substrate in ultrasonic bath. The ZnO NRAs were regularly and densely grown as well as vertically aligned… (More)
We reported the enhancement of the structural and optical properties of electrochemically synthesized zinc oxide [ZnO] nanorod arrays [NRAs] using the multi-walled carbon nanotube [MWCNT]-composed seed layers, which were formed by spin-coating the aqueous seed solution containing MWCNTs on the indium tin oxide-coated glass substrate. The MWCNT-composed seed… (More)
We investigated the effect of gallium oxide hydroxide (GaOOH) nanorod arrays (NRAs) on the light extraction of InGaN/GaN multiple quantum well blue light-emitting diodes (LEDs). GaOOH NRAs were prepared on an indium tin oxide electrode (ITO) layer of LEDs by electrochemical deposition method. The GaOOH NRAs with preferred orientations were grown on the ITO… (More)