Bilateral polynomial matrix equations in two indeterminates

Two special cases of the bilateral 2-D polynomial matrix equationDU +VN=C whenC=I andC=I with being a -stable 2-D polynomial, which are related respectively to deadbeat and asymptotic control problems of 2-D systems, are first considered. By generalizing the concepts of factor coprimeness, zero coprimeness and zero skew primeness in the 2-D polynomial ring to the ring of causal -stable 2-D rational functions, a constructive solution of these two problems mentioned is proposed. Based on these results, we derive a solvability condition for the bilateral equiation whereC is a general 2-D polynomial matrix. The general solutions are investigated as well.     

Sialon formation by Si+ and N2 + ion implantation into sapphire

Single-crystal alumina was implanted firstly with 400 keV Si⁺ and subsequently with N₂ ⁺ ions and then annealed at 1673 K in an No atmosphre. The implanted layers were characterized by means of X-ray diffraction, Rutherford backscattering-channelling of 2 MeV He⁺ ions, and the resonance nuclear reaction¹⁵N(p,)¹²C. The annealing of sapphire implanted at ambient temperature resulted in the formation of-sialon, a solid solution of-silicon nitride and alumina in the subsurface layer, while implantation at 100 K resulted in the formation of aluminium oxynitride in the surface layer. In the latter case, the implanted silicon atoms were believed not to react vxi1h the implanted nitrogen atoms but with the substrate oxygen atoms. These crystalline precipitates were found to have epitaxial relations with the sapphire substrate.     

Two-wavelength laser diode interferometer with time-sharing sinusoidal phase modulation

We describe an interferometer system that uses two separate wavelengths to measure step height. The overlapping interference images detected by a CCD camera are easily separated by an ordinary integrating-bucket method and time-sharing sinusoidal phase modulation, in which two laser diodes are alternately modulated with a sinusoidal signal. A phase map is obtained only for the laser diode into which the modulation signal is injected. In this instance, a 1-microm step height was accurately detected.     

Disturbance-free high-speed sinusoidal phase-modulating laser diode interferometer

A surface profiler that incorporates a feedback controller to eliminate external disturbances is proposed and demonstrated. Its overall performance is dependent on the frequency response of the feedback loop. The frequency of the modulating signal strongly influences the response of the feedback controller. When we used the integrating-bucket method, the CCD camera had to be operated at a low-frequency video rate. Our technique uses a CCD camera equipped with an electronic shutter. The shutter function enables us to apply high-speed sinusoidal phase modulation to the conventional integrating-bucket method under the standard video rate.     

Photo-Induced Effect of the Electron-Spin Resonance on the Charge-Ordered State in Pr0.65Ca0.35MnO3

Electron-spin resonance (ESR) for the charge-ordered state in well-characterized Pr_0.65Ca_0.35MnO₃ exhibited significant change of both the absorption profile and the effective spin susceptibility upon injection of laser light with photon energy of 1.17 eV provided by Nd-YAG laser. The increase of the effective spin susceptibility was clearly found out thanks to the injection of photons in the temperature range 90 K–80 K, which is below the transition temperature from the antiferromagnetic charge ordered state to the canted antiferromagnetic spin alternation state, T _CAF125 K. The temperature dependence of the change of the ESR profile excludes the possibility of heating by laser light. The present result suggests that a kind of photo-induced insulator–metal transition may occur due to propagation of the delocalized carriers via probable double exchange interaction in the charge-ordering collapsed state created by the injection of photons.     

Electron Spin Resonance in Pr0.65Ca0.35MnO3

The magnetic behavior of the distorted perovskite manganese, Pr_0.65Ca_0.35MnO₃ was studied by X-band electron spin resonance for powder samples. We observed the onset of the charge-ordered state at T _CO215 K, the antiferromagnetic transition with the peak of the ESR linewidth, H _p–p at T _AF180 K and the canted antiferromagnetic transition at T _CAF125 K associated with the abrupt increase of both the effective magnetization and H _p–p . Below 90 K, the absorption intensity profile becomes weakened with decreasing temperature suggesting the existence of some kind of magnetic disorder below 90 K, which is responsible for a part of evidence of the existence of the spin-glass state as has been proposed by Yoshizawa et al., Phys. Rev. B 52, 1689 (1996).     

2D Model-Following Servo System

This paper gives, in view of the feature of practical 2D (2-dimensional) systems, a formulation of the 2D model-following servo problem for the case where one of the independent variables of the considered 2D systems is unbounded and the other one is bounded. That is, to determine a control input such that the outputs of a given 2D plant asymptotically track, with tracking error as small as possible, the (step) response of a given 2D model system as the unbounded variable approaches infinite. It is shown that this problem under a specified quadratic performance index can be transformed into a 1D LQR problem, and thus can be solved by the well-known 1D approaches. The relation between the solvability condition obtained for the equivalent 1D LQR problem and the practical stabilizability and detectability of the original 2D plant is clarified. Its application to the design of non-unit memory linear multipass processes is also shown. Finally, a numerical example for metal rolling process is given to verify the effectiveness.     

Thermal proof testing of ceramics

The possibility of thermal proof testing with thermal stress induced by quenching was examined. For this purpose, the bending strength and the critical temperature difference for quenching into water and quench oil for soda-lime-silica glass were measured before and after proof testing by quenching the specimens into water, ethyl alcohol, silicon oil and quench oil. Proof testing by water, ethyl alcohol and silicon oil quenching modified the distribution of the critical temperature difference as expected, but not that of the bending strength at all. It is suggested that proof testing by rapid quenching is a useful method for truncating the critical temperature difference distribution of ceramic components of heat engines and so on.