ε-optimality criteria for convex programming problems via exact penalty functions

In this paper, we present-optimality criteria for convex programming problems associated with exact penalty functions. Several authors have given various criteria under the assumption that such convex problems and the associated dual problems can be solved. We assume the solvability of neither the convex problem nor the dual problem. To derive our criteria, we estimate the size of the penalty parameter in terms of an-solution for the dual problem.     

ESR Study of a Nitroxide Radical in Sol-Gel Glasses

A spin probe TEMPOL (4-hydroxy-2,2,6,6-tetramethylpiperidinyl-1-oxy) was dissolved in a tetraethyl orthosilicate sol-gel reaction system and measured by electron spin resonance spectroscopy at 295 K. The nitrogen hyperfine coupling constant was from 1.64–1.66 mT in the sol-gel solutions. The values were sensitive to the ethanol-to-water ratio of the solutions. The hyperfine coupling constant in the xerogels was 1.70 mT, which was almost the same as that in water, indicating that the probe molecules were trapped in silica pores with water adsorbed on the silica surfaces. The motion of TEMPOL in the xerogels was considerably slower than in the sol-gel solutions. The local viscosity estimated was from 70–90 cP. The ESR spectra of TEMPOL were altered during the sol-gel process, indicating that adsorbed water on the silicas surfaces has an important role for trapping organic molecules in sol-gel glasses.     

Chirality exchange from sp3 central chirality to axial chirality: benzannulation of optically active diaryl-2,2-dichlorocyclopropylmethanols to axially chiral alpha-arylnaphthalenes

Chirality exchange benzannulation of optically active (1S)-aryl(aryl')-2,2-dichlorocyclopropylmethanols (>99% ee) using TiCl4 successfully proceeded to give axially chiral (M)-alpha-arylnaphthalenes with excellent levels of stereo induction (>99% ee). This unique transformation involves the single-step chirality exchange from sp3 central chirality to axial chirality, that is, a type of excellent memory effect.     

A new theoretical approach to the empirical resonance energies of the aromatic hydrocarbons

In the framework of the Hückel MO approximation, the differences in total binding energy between a given molecule and the corresponding distorted Kekulé-type structure are calculated for a variety of benzenoid hydrocarbons. The total binding energy is assumed to be given by the sum of the -electron and -electron binding energies. It is shown that there is a good linear relationship between the calculated differences in total binding energy and the -electron delocalization energies (DE) as obtained by using the simple Hückel MO method. This provides a physical basis for the use of the -electron DE as a theoretical index to the empirical resonance energy (RE). Further, by examining the changes in -electron binding energy between a given molecule and the corresponding distorted Kekulé-type structure, it is concluded that in benzenoid hydrocarbons the main contributor to the RE is not the -electron DE but the compressional energy of bonds.     

Action Spectra for Photoinhibition of Sexual Development in Phycomyces blakesleeanus

The sexual development of the fungus Phycomyces is inhibited by light. The action spectra for this photoinhibitory effect were determined for 48 h continuous exposure between 350 and 700 nm wavelengths during the mating process. Effective wavelengths were shorter than 490 nm, but the most effective wavelengths depended on the stage of sexual development. In early stages of progametangium formation, the major peaks appeared near 360 nm with small shoulders at 410 nm, but in later stages, after gametangium formation, only single peaks were detected in the UVA range (350–390 nm). Low-fluence irradiation in the later stage, however, revealed inhibitory effectiveness at 370–410 nm, implying the existence of a dual photoresponse and multiple regulatiory systems in the mating process of Phycomyces.     

Reduction of Cu2+ to Cu+ in Xerogels Prepared from (3-Aminopropyl)Trimethoxysilane

Silica gels doped with Cu²⁺ ions were prepared from the (3-aminopropyl) trimethoxysilane (APTMOS)/tetraethoxysilane (TEOS) systems. Sols showed a broad absorption peak at 640 nm, suggesting 3–5 coordination of the aminopropyl groups to Cu²⁺. For gels prepared from APTMOS and dried at room temperature, the 640 nm peak decreased and a red-shifted absorption appeared below 400 nm within a few months. The luminescence spectra of the xerogels showed emission bands at 430–470 and 510 nm. The former and latter bands are ascribed to Cu⁺ monomer and dimer emissions, respectively. These results indicate that Cu²⁺ ions are reduced to Cu⁺. When xerogels were prepared from APTMOS/TEOS = 1 (vol/vol), the color of xerogels was blue with an absorption peak at around 670 nm, indicating no reduction of Cu²⁺ ions.     

Vacuum birefringence in strong magnetic fields: (I) Photon polarization tensor with all the Landau levels

Photons propagating in strong magnetic fields are subject to a phenomenon called the “vacuum birefringence” where refractive indices of two physical modes both deviate from unity and are different from each other. We compute the vacuum polarization tensor of a photon in a static and homogeneous magnetic field by utilizing Schwinger’s proper-time method, and obtain a series representation as a result of double integrals analytically performed with respect to proper-time variables. The outcome is expressed in terms of an infinite sum of known functions which is plausibly interpreted as summation over all the Landau levels of fermions. Each contribution from infinitely many Landau levels yields a kinematical condition above which the contribution has an imaginary part. This indicates decay of a sufficiently energetic photon into a fermion–antifermion pair with corresponding Landau level indices. Since we do not resort to any approximation, our result is applicable to the calculation of refractive indices in the whole kinematical region of a photon momentum and in any magnitude of the external magnetic field.     

Rhodium-Catalyzed Enantioselective Synthesis,Structures, and Properties of Single and Double Azahelicene-Like Molecules

The enantioselective synthesis of aza[6] and [7]helicene-like molecules have been achieved by the cationic rhodium(I)/axially chiral biaryl bisphosphine complex-catalyzed intramolecular [2+2+2] cycloaddition of cyanodiynes. This protocol was successfully applied to the diastereo- and enantioselective synthesis of an S-shaped double aza[6]helicene-like molecule with a high ee value of 89 %. Although no epimerization and racemization were observed in the double carbo[6]helicene-like molecule at 80 °C, epimerization and racemization of the double aza[6]helicene-like molecule proceeded at 80 °C. This double aza[6]helicene-like molecule showed good fluorescent quantum yields and chiroptical responses under both neutral and acidic conditions.     

Isolation of Biphenyl and Polychlorinated Biphenyl-Degrading Bacteria and Their Degradation Pathway

Four strains of biphenyl-degrading bacteria were isolated from a sewage and identified from the Rhodococcus genus (SK-1, SK-3, and SK-4) and Aquamicrobium genus (SK-2) by 16S rRNA sequence. Among these strains, strain SK-2 was most suitable for biphenyl degradation. When 0.65, 1.3, 2.6, or 3.9 mM of biphenyl was used, the biphenyl was completely degraded within 24 and 96 h of culture, respectively. However, in the case of 6.5 and 9.75 mM of biphenyl, the biphenyl degradation yields were about 80 % and 46.7 % after 120 h of culture, respectively. The isolated strains could degrade a broad spectrum of aromatic compounds including high-chlorinated polychlorinated biphenyl (PCB) congeners in the presence of biphenyl. In addition, strain SK-2 could utilize PCB congeners containing one to six chlorine substituents such as 2,2′,4,4′,5,5′-hexachlorobiphenyl. The PCB utilization rate by the strain SK-2 was increased compared to that of other PCB congener-utilizing bacteria. The four isolates metabolized 4-chlorobiphenyl to 4-chlorobenzoic acid and 2-hydroxy-6-oxo-6-(4′-chlorophenyl)-hexa-2,4-dienoic acid. These results suggest the isolated strains might be good candidates for the bioremediation of PCB-contaminated soil, especially high-saline soils.