Further results on graph equations for line graphs and n-th power graphs

We present solutions of seven graph equations involving the line graph, complement and n-th power operations. One such equation $\text{L(G)}{}^{\mathrm{n}}\text{=}\text{G}\text{?}$ generalizes a result of M. Aigner. In addition, some comments are made about graphs satisfying $\text{G}{}^{\mathrm{n}}\text{=}\text{G}\text{?}$.     

Solid-state polymerization of N-carboxy-L-leucine anhydride crystals in n-hexane

4-Isobutyloxazolidinedione, L -leucine N-carboxy anhydride, was polymerized to produce high molecular weight polymer with triethylamine in n-hexane which is not a solvent for the N-carboxy anhydride and poly-L -leucine. It was found that as the crystal size became smaller, the total surface area was increased, the initial rate of polymerization was increased, and inherent viscosity of the formed polymer was decreased.     

Asymmetric information and macroeconomic dynamics

We show how macroeconomic dynamics can be derived from asymmetric information. As an illustration of the utility of this approach we derive the equilibrium density, non-equilibrium densities and the equation of motion for the response to a demand shock for productivity in a simple economy. Novel consequences of this approach include a natural incorporation of time dependence into macroeconomics and a common information-theoretic basis for economics and other fields seeking to link micro-dynamics and macro-observables.     

Stable 10 W Er:ZBLAN fiber laser operating at 2.71-2.88 μm

We have developed a diode-pumped tunable 3 μm fiber laser with a cw output power of the order of 10 W with the use of an erbium-doped ZBLAN fiber. A tunability range of 110 nm (2770 to 2880 nm) with an output power between 8 and 11 W was demonstrated. As the pump power was increased, the center of the wavelength range was shifted toward longer wavelengths, but the width of the wavelength range was largely unaffected. The total tunability range for various pump power levels was 170 nm (2710 to 2880 nm). To our knowledge, this is the highest performance (output power and tunability) obtained from a tunable 3 μm fiber laser.     

Uncertainty relations for joint measurements of noncommuting observables

Universally valid uncertainty relations are proven in a model independent formulation for inherent and unavoidable extra noises in arbitrary joint measurements on single systems, from which Heisenberg's original uncertainty relation is proven valid for any joint measurements with statistically independent noises.     

Second-order necessary conditions for domain optimization problems in elastic structures,part 1: Surface traction given as a field

In this paper, domain optimization problems for both linear and nonlinear elastic structures are studied. The first variation and the second variation of the objective function are calculated in terms of the solution, of the first variation of the solution for the primal elastic system, and of the adjoint variables introduced. The adjoint variables obey a (fictitious) linear elastic system in contrast with the nonlinear adjoint systems introduced by Dems and Mróz, and by Dems and Haftka. From these results, the first-order and the second-order necessary conditions that an optimal domain should satisfy are immediately derived.Portions of this paper were presented at the 5th IFAC Symposium on Control of Distributed Parameter Systems, Perpignan, France, 1989. The authors would like to express their sincere thanks to the referees for their critical readings.     

Theoretical Study on Redox Potential Control of Iron-Sulfur Cluster by Hydrogen Bonds: A Possibility of Redox Potential Programming

The effect of hydrogen bonds around the active site of Anabaena [2Fe-2S] ferredoxin (Fd) on a vertical ionization potential of the reduced state (IP(red)) is examined based on the density functional theory (DFT) calculations. The results indicate that a single hydrogen bond increases the relative stability of the reduced state, and shifts IP(red) to a reductive side by 0.31–0.33 eV, regardless of the attached sulfur atoms. In addition, the IP(red) value can be changed by the number of hydrogen bonds around the active site. The results also suggest that the redox potential of [2Fe-2S] Fd is controlled by the number of hydrogen bonds because IP(red) is considered to be a major factor in the redox potential. Furthermore, there is a possibility that the redox potentials of artificial iron-sulfur clusters can be finely controlled by the number of the hydrogen bonds attached to the sulfur atoms of the cluster.