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.     

Mechanical property changes in sapphire by nickel ion implantation and their dependence on implantation temperature

Sapphire plates, cut parallel to an {0001} plane, have been implanted with 300 keV nickel ions to doses ranging from 5×10¹² to 1×10¹⁷ Ni cm^–2 at specimen temperatures of 100, 300 and 523 K, in order to investigate the effect of implantation temperature on the mechanical property changes in sapphire caused by ion implantation. The measured changes in surface hardness, surface fracture toughness and bulk flexural strength were found to depend strongly on the implantation temperature, and were largely correlated with the residual surface compressive stress measured by using a cantilever beam technique. The surface amorphization that occurred only by the implantation at 100 K and at doses larger than 2×10s15 Ni cm^–2 reduced the hardness to 0.6 relative to the value of the unimplanted sapphire, and considerably increased the surface plasticity. Furthermore, the amorphization was found to involve a large volume expansion of 30% and to change drastically the apparent shape and size of a Knoop indentation flaw made prior to implantation. This effect was suggested to reduce stress concentrations at surface flaws and hence to increase the flexural strength.     

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.     

Living cationic polymerization of isobutyl vinyl ether by the diphenyl phosphate/zinc iodide initiating system

Summary The first example of the living cationic polymerization of isobutyl vinyl ether via the phosphate counteranion has been achieved in toluene below 0°C with a new initiating system that consists of diphenyl phosphate and zinc iodide, (C₆H₅0)₂P(0)0H/ZnI₂. The number-average molecular weight of the polymers increased in direct proportion to monomer conversion, and was in excellent agreement with the calculated value assuming that one polymer chain forms per unit diphenyl phosphate. On addition of a fresh feed of monomer at the end of the polymerization, the added feed was smoothly polymerized at nearly the same rate as in the first stage, and the polymer molecular weight further increased in direct proportion to monomer conversion. Throughout the reaction, the molecular weight distribution of the polymers stayed very narrow (¯M/¯M_n 1.1). At room temperature (+25 °C), however, the molecular weight distribution of the polymers slightly broadened (¯M_w/¯M_n 1.2) at high conversions where the polymer molecular weight became smaller than the calculated value. Evidently, the (C₆H₅0)₂-P(0)0H/ZnI₂ system indeed generates a propagating species of a long life-time at room temperature, but the perfectly living polymerization by this system operates below 0°C.Living cationic polymerization of vinyl ethers by electrophile     

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).