LP narrowing: A new strategy for finding all solutions of nonlinear equations

An efficient algorithm is proposed for finding all solutions of systems of n nonlinear equations. This algorithm is based on interval analysis and a new strategy called LP narrowing. In the LP narrowing strategy, boxes (n-dimensional rectangles in the solution domain) containing no solution are excluded, and boxes containing solutions are narrowed so that no solution is lost by using linear programming techniques. Since the LP narrowing is very powerful, all solutions can be found very efficiently. By numerical examples, it is shown that the proposed algorithm could find all solutions of systems of 5000-50,000 nonlinear equations in practical computation time.     

One-dimensional three-body problem via symbolic dynamics

Symbolic dynamics is applied to the one-dimensional three-body problem with equal masses. The sequence of binary collisions along an orbit is expressed as a symbol sequence of two symbols. Based on the time reversibility of the problem and numerical data, inadmissible (i.e., unrealizable) sequences of collisions are systematically found. A graph for the transitions among various regions in the Poincare section is constructed. This graph is used to find an infinite number of periodic sequences, which implies an infinity of periodic orbits other than those accompanying a simple periodic orbit called the Schubart orbit. Finally, under reasonable assumptions on inadmissible sequences, we prove that the set of admissible symbol sequences forms a Cantor set. (c) 2000 American Institute of Physics.     

Corrosion on continuous supercritical water oxidation for polychlorinated biphenyls

Abstract

The corrosion resistance of Hastelloy C-276 and titanium alloy G5 against C1 anion which was generated by supercritical water oxidation (scWO) of 3-chlorobiphenyl (3-PCB) in a flow reactor was investigated over a period of 336 hours at a constant pressure of 30 MPa. The condition of the scWO reaction zone was fixed at 750 K. The concentration of chlorine in the effluent collected after cooling to ambient temperature was about 850 wppm. The Hastelloy C-276 has a nominal ratio of approximately 3.7 Ni/l Cr. The Ni/Cr ratio in the effluent was the same with the nominal ratio, and the Hastelloy C-276 was proved to be corroded on the surface located between the bottom of the reactor and the cooling parts, which are under sub- and near- critical conditions of water. The corrosion rate was found to be 5 to 34mm/y in the zone where the temperature ranged from 543 K to 650 K and the corrosion spread over the whole surface of the alloy; however, one can hardly observe such a serious corrosion except the zone located in the between the reactor and the cooling part.     

Fabrication and characterization of silicon antireflection structures for infrared rays using a femtosecond laser

We focus on IR sensors with lower reflection for the wavelength around 10 μm, strongly awaited for detecting human bodies. A concave structure was designed as a more suitable reflection-free structure for IR light, and an optical system with a femtosecond laser was employed for verification of the effectiveness of the structure. The microstructures prepared through this process were fabricated and optically measured using SEM, FT-IR, and Raman spectroscopy. The measurement revealed that good reflection-free structures were realized for IR sensors with lower reflection for the wavelength of around 10 μm.     

4,5,6,7-tetradehyro-PG1, a stable and potent inhibitor of blood platelet aggregation

The titled compound, which is a stable and potent analog of PGI₂, was synthesized from easily available enone $\text{3}$ in two steps.     

Growth mechanism of stearic acid single crystals

Micro-morphological observation of the growth patterns on the (001) surfaces of large single crystals of stearic acid grown from solution under moderate growth conditions was carried out by optical and electron microscopy. Two typical growth features, namely, growth spiral steps and two-dimensional (2-D) nucleation-like steps, were identified optically. Then, these patterns were observed in more detail by the replica method of electron microscopy and it was found that the steps are usually two to four times the length of the bimolecular growth unit. These growth units also revealed spiral growth and 2-D nucleation growth patterns.     

Polymer effect on electron-donating character of polymeric donor. I. Formation of charge-transfer complex between polymers containing N,N-dimethylaniline group and maleic anhydride

The difference in electron-donating character between polymeric and monomeric donors in their charge-transfer-complex formation reactions was studied to clarify the so-called polymer effect in such reactions. Systems containing maleic anhydride and copolymers of N,N-dimethyl-p-aminostyrene (ASt) with styrene, which were prepared by a conventional free-radical polymerization technique, were found to be suitable for this purpose. In correlations between the mean sequence length μ_ASt of the ASt units in the copolymers and the lowest energy of their charge-transfer transition (λ_max) or the association constant of their complex formation K_CT, a bathochromic shift in λ_max and an increase in K_CT with increasing μ_ASt of copolymers are found. Moreover, there is a difference in their modes of μ_ASt dependence. It was concluded from these results that the electron-donating character of the dimethylaniline group increases with increasing number of groups attached on one polymer chain. Also, there is an interaction among neighboring functional groups on one polymer chain. The interaction may be regarded as a kind of polymer effect. In addition, the difference in μ_ASt dependence between λ_max and K_CT and also thermodynamics of the complex formation are discussed.     

Enantioselective borohydride reduction catalyzed by optically active cobalt complexes

The highly enantioselective borohydride reduction of aromatic ketones or imines to the corresponding alcohols was developed in the presence of a catalytic amount of an optically active cobalt(II) complex catalyst. This enantioselective reduction is carried out using a precisely premodified borohydride with alcohols such as tetrahydrofurfuryl alcohol, ethanol and methanol. High optical yields are obtained by choosing the appropriate alcohol as modifiers and a suitable beta-ketoiminato ligand of the catalyst. The enantioselective borohydride reduction has been successfully applied to the preparation of optically active 1,3-diols, the stereoselective reduction of diacylferrocenes, and dynamic and/or kinetic resolution of 1,3-dicarbonyl compounds.     

Two- and three-dimensional smectic ordering of single-handed helical polymers

Rodlike polymers with precisely defined architectures are ideal building blocks for self-assembled structures leading to novel nanometer-scale devices. We found that the living polymerization of a single isocyanide enantiomer bearing an l-alanine pendant with a long n-decyl chain simultaneously produced diastereomeric right- and left-handed helices with different molecular weights and narrow molecular weight distributions. Each single-handed, rodlike helical polymer with a controlled length and handedness isolated by a facile solvent fractionation method with acetone self-assembled to form well-defined two- and three-dimensional smectic ordering on the nanometer scale on a substrate and in a liquid crystalline state as evidenced by direct atomic force microscopic observations and X-ray diffraction measurements, respectively.