Auslander–Gorenstein resolution

We introduce the notion of Auslander–Gorenstein resolution and show that a Noetherian ring is an Auslander–Gorenstein ring if it admits an Auslander–Gorenstein resolution over another Auslander–Gorenstein ring.     

Controlling the generation of high frequency electromagnetic pulses with relativistic flying mirrors using an inhomogeneous plasma

A method for the controlled generation of intense high frequency electromagnetic fields by a breaking Langmuir wave (relativistic flying mirrors) in a gradually inhomogeneous plasma is proposed. The wave breaking threshold depends on the local plasma density gradient. Compression, chirping and frequency multiplication of an electromagnetic wave reflected from relativistic mirrors is demonstrated using Particle-In-Cell simulations. Adjusting the shape of the density profile enables control of the reflected light properties.     

Kinetic Analysis of the Thermal Decomposition of Synthetic Malachite by CRTA

The kinetic behavior of the thermal decomposition of synthetic malachite was investigated by means of CRTA under different conditions of reduced pressure, flowing gases and quasi-isobaric atmospheres. The thermal decomposition was found to proceed at lower temperatures under the influence of the self-generated gases, CO₂ and H₂O. From a viewpoint of chemical equilibrium, the normal and opposite effects on the overall kinetics were observed for the self-generated CO₂ and H₂O, respectively. The complexity of the present reaction is also reflected by the variations of the apparent kinetic parameters which depend on the applied and self-generated atmospheric conditions. The practical usefulness of CRTA when applied to a complicated thermal decomposition is discussed as exemplified by the kinetic approaches to the present reaction. This revised version was published online in August 2006 with corrections to the Cover Date.     

Atomic electron-pair distances and subshell radii in position and momentum space

For the 53 neutral atoms from He to Xe in their ground states, the average distances < u> _{n l , n ′ l ′} in position space and < v> _{n l , n ′ l ′} in momentum space between an electron in a subshell nl and another electron in a subshell n ^′ l ^′ are studied, where n and l are the principal and azimuthal quantum numbers of an atomic subshell, respectively. Analysis of 1700 subshell pairs shows that the electron-pair distances < u> _{n l , n ′ l ′} in position space have an empirical but very accurate linear correlation with a one-electron quantity U _{n l , n ′ l ′}≡L _r +S _r ²/(3L _r ), where L _r and S _r are the larger and smaller of subshell radii < r> _{n l} and < r> _{n ′ l ′}, respectively. The correlation coefficients are never smaller than 0.999 for the 66 different combinations of two subshells appearing in the 53 atoms. The same is also true in momentum space, and the electron-pair momentum distances < > _{n l , n ′ l ′} have an accurate linear correlation with a one-electron momentum quantity V _{n l , n ′ l ′}≡L _p +S _p ²/(3L _p ), where L _p and S _p are the larger and smaller of average subshell momenta < p> _{n l} and < p> _{n ′ l ′}, respectively. Trends in the proportionality constants between < u> _{n l , n ′ l ′} and U _{n l , n ′ l ′} and between < > _{n l , n ′ l ′} and V _{n l , n ′ l ′} are discussed based on a hydrogenic model for the subshell radial functions. Received: 8 April 1998 / Accepted: 6 July 1998 / Published online: 18 September 1998     

Determination of ppt levels of atmospheric volatile organic compounds in Yakushima, a remote south-west island of Japan

An analytical method was utilized to detect ppt levels of VOCs in air. The method was based on the US-EPA method TO-14, consisting of canister sampling, three module enrichment and GC/MS analysis. Target compounds included chlorofluorocarbons (four kinds), benzene and its derivatives (14), halogenated hydrocarbons (20), and others (three). The minimum detection limits of the method for the target compounds ranged from 0.016 to 0.040 ppb (0.06–0.23 μg/m³). The recoveries of the target compounds ranged from 77 to 113% and relative coefficients of variation (n=4) were 3.0–9.0%. The sampled air was stable for at least 14 days after pressurizing with humidified nitrogen gas at 200 kPa (absolute pressure). The method was applied to analyze the VOCs in the air of Yakushima, a remote island of south-west Japan where no distinct local pollution source is considered.     

Characterization of amorphous hydrogenated carbon formed by low-pressure inductively coupled plasma enhanced chemical vapor deposition using multiple low-inductance antenna units

Three-dimensional plasma enhanced chemical vapor deposition (CVD) of hydrogenated amorphous carbon (a-C:H) has been demonstrated using a new type high-density volumetric plasma source with multiple low-inductance antenna system. The plasma density in the volume of phi 200 mm x 100 mm is 5.1 x 10(10) cm(-3) within +/-5% in the lateral directions and 5.2 x 10(10)cm(-3) within +/-10% in the axial direction for argon plasma under the pressure of 0.1 Pa and the total power as low as 400 W. The uniformity of the thickness and refractive index is within +/-3.5% and +/-1%, respectively, for the a-C:H films deposited on the substrates placed on the six side walls, the top of the phi 60 mm x 80 mm hexagonal substrate holder in the pure toluene plasma under the pressure is as low as 0.04 Pa, and the total power is as low as 300 W. It is also found that precisely controlled ion bombardment by pulse biasing led to the explicit observation in Raman and IR spectra of the transition from polymer-like structure to diamond-like structure accompanied by dehydrogenation due to ion bombardment. Moreover, it is also concluded that the pulse biasing technique is effective for stress reduction without a significant degradation of hardness. The stress of 0.6 GPa and the hardness of 15 GPa have been obtained for 2.0 microm thick films deposited with the optimized deposition conditions. The films are durable for the tribology test with a high load of 20 N up to more than 20,000 cycles, showing the specific wear rate and the friction coefficient were 1.2 x 10(-7) mm3/Nm and 0.04, respectively.     

Average electron radii in many-electron atoms

In many-electron atoms, the average electron radius r represents the mean distance of a single electron from the nucleus when all the interelectronic interactions are averaged. If the electron-electron interaction is explicitly considered, the average radius r splits into two different radii, inner radius r(<) and outer radius r(>). For the 102 atoms He through Lr in their ground states, the radii r(<) and r(>) are systematically examined at the Hartree-Fock limit level. The effect of electron correlations on r(<) and r(>) is also discussed for the He atom and its isoelectronic ions.     

Influences of evolved gases on the thermal decomposition of zinc carbonate hydroxide evaluated by controlled rate evolved gas analysis coupled With TG

The influences of atmospheric CO₂ and H₂O on the kinetics of the thermal decomposition of zinc carbonate hydroxide, Zn₅(CO₃)₂(OH)₆, were investigated by means of controlled rate evolved gas analysis (CREGA) coupled with TG. Although CO₂ and H₂O were evolved simultaneously in a single mass-loss step of the thermal decomposition, different effects of those evolved gases on the kinetic rate behavior were observed. No distinguished effect of atmospheric CO₂ was detected within the possible range of self-generated CO₂ concentration. On the other hand, apparent acceleration effect by the increase in the concentration of atmospheric H₂O was observed as the reduction of reaction temperature during the course of constant rate thermal decomposition. The catalytic effect was characterized by the decrease in the apparent activation energy for the established reaction with increasing the concentration of atmospheric H₂O, accompanied by the partially compensating decrease in the pre-exponential factor.     

Thermal decomposition of copper(II) and zinc carbonate hydroxides by means of TG-MS

Summary For the quantitative analyses of evolved CO₂and H₂O during the thermal decomposition of solids, calibration curves, i.e. the amounts of evolved gases vs. the corresponding peak areas of mass chromatograms measured by TG-MS, were plotted as referenced by the reaction stoichiometry of the thermal decomposition of sodium hydrogencarbonate NaHCO₃. The accuracy and reliability of the quantitative analyses of the evolved CO₂and H₂O based on the calibration curves were evaluated by applying the calibration curves to the mass chromatograms for the thermal decompositions of copper(II) and zinc carbonate hydroxides. It was indicated from the observed ratio of evolved CO₂and H₂O that the compositions of copper(II) and zinc carbonate hydroxides examined in this study correspond to mineral malachite, Cu₂CO₃(OH)₂, and hydrozincate, Zn₅(CO₃)₂(OH)₆, respectively. Reliability of the present analytical procedure was confirmed by the fairly good agreement of the mass fraction of the evolved gases calculated from the analytical values with the total mass-loss during the thermal decompositions measured by TG.     

On the photolysis of homo- and copolymers of phenylisopropenylketone

Poly(phenylisopropenylketone (PPIK) and copolymers of PIK and methylmethacrylate (MMA) or styrene (St) were irradiated in benzene solution at 30° with 313 nm light (stationary irradiations) or with 347 nm light (flash photolysis experiments). Homo PPIK undergoes main chain degradation (β-scission) with ø(S) ≈ 0.05. The quantum yield for α-scission is ø(α) = 0.3. For copolymers of MMA and PIK (1 to 15 mol%), ø(S) is 0.04 independent of the copolymer composition. With copolymers of St and PIK, ø(S) was found to increase with decreasing PIK content and to approach 0.15 for very small PIK contents. The flash photolysis experiments showed: (a) the carbonyl triplet decay rate constant k_T(6 × 10⁶ sec^?1) for CP-MMA-PIK samples is independent of copolymer composition but is lower than for homo PPIK (1 × 10⁷ sec^?1). In CP-St-PIK samples k_T decreases with decreasing PIK content [from 8 × 10⁶ sec^?1 (12 mol% PIK) to 3 × 10⁶ sec^?1 (1 mol% PIK)]; (b) the transient spectra of triplet decay products indicate the formation of benzoyl radicals in the cases of PPIK and CP-MMA-PIK, and the formation of various different species in the case of CP-St-PIK.The results are consistent with the following concept. In homo PPIK and CP-MMA-PIK, α-scission (Norrish type I) is the dominant chemical route of triplet deactivation. In CP-St-PIK, however, type II processes become more and more important as the PIK content decreases.