Comments on the evolution of strongly degenerate neutrinos in the early universe

We reconsider the evolution of strongly degenerate neutrinos in the early universe. Our chief concern is the validity of the entropy conservation after the neutrino annihilation process has frozen out (so that the establishment of chemical equilibrium is not trivial). We argue that the entropy indeed conserves because elastic scattering keeps the neutrino and antineutrino distribution functions in the equilibrium form and the sum of their chemical potential keeps zero even after the neutrino annihilation freeze-out. We also simulate the evolution of the degenerate neutrino spectrum to support the argument. We conclude that the change in the neutrino degeneracy parameter when the relativistic degrees of freedom in the universe decreases is calculated using the entropy conservation and the lepton number conservation without worrying about at what temperature the neutrino annihilation process freezes out.     

Chiral amplification in macromolecular helicity assisted by noncovalent interaction with achiral amines and memory of the helical chirality

Poly[(4-carboxyphenyl)acetylene] (poly-1) exhibits an intense induced circular dichroism (ICD) in the UV-visible region upon complexation with excess (R)-1-(1-naphthyl)ethylamine ((R)-2), owing to the formation of a predominantly single-handed helical conformation of the polymer backbone. In the presence of a small amount of (R)-2, poly-1 showed a very weak ICD due to the lack of a single-handed helical conformation. However, we have found that the co-addition of the excess bulky, achiral 1-naphthylmethylamine (5) with a small amount of (R)-2 caused a dramatic increase in the ICD magnitude, comparable to the full ICD induced by excess (R)-2. This indicates that an almost single-handed helix can be induced on poly-1 upon complexation with a small amount of (R)-2 assisted by achiral 5. Furthermore, the induced single-handed helical poly-1 could be successfully memorized by the replacement of (R)-2 and 5 with achiral 2-aminoethanol or n-butylamine.     

On-line preconcentration using dual mini-columns for the speciation of chromium(III) and chromium(VI) and its application to water samples as studied by inductively coupled plasma-atomic emission spectrometry

On-line preconcentration system for the selective, sensitive and simultaneous determination of chromium species was investigated. Dual mini-columns containing chelating resin were utilized for the speciation and preconcentration of Cr(III) and Cr(VI) in water samples. In this system, Cr(III) was collected on first column packed with iminodiacetate resin. Cr(VI) in the effluent from the first column was reduced to Cr(III), which was collected on the second column packed with iminodiacetate resin. Hydroxyammonium chloride was examined as a potential reducing agent for Cr(VI) to Cr(III).The effects of pH, sample flow rate, column length, and interfering ions on the recoveries of Cr(III) were carefully studied. Five millilitres of a sample solution was introduced into the system. The collected species were then sequentially washed by 1 M ammonium acetate, eluted by 2 M nitric acid and measured by ICP-AES. The detection limit for Cr(III) and Cr(VI) was 0.08 and 0.15 μg l⁻¹, respectively. The total analysis time was about 9.4 min.The developed method was successfully applied to the speciation of chromium in river, tap water and wastewater samples with satisfied results.     

Effect of intramolecular pi-pi and CH-pi interactions between ligands on structure, electrochemical and spectroscopic properties of fac-[Re(bpy)(CO)3(PR3)]+(bpy = 2,2'-bipyridine; PR3= trialkyl or triarylphosphines)

Intramolecular pi-pi and CH-pi interactions between the bpy and PR3 ligands of fac-[Re(bpy)(CO)3(PR3)]+ affect their structure, and electrochemical and spectroscopic properties. Intramolecular CH-pi interaction was observed between the alkyl groups on the phosphine ligand (R =nBu, Et) and the bpy ligand, and intramolecular pi-pi and CH-pi interactions were both observed between the aryl group(s) on the phosphorus ligand (R =p-MeOPh, p-MePh, Ph, p-FPh, OPh) and the bpy ligand, while no such interactions were found in the trialkylphosphite complexes (R = OiPr, OEt, OMe). The intramolecular interactions distort the pyridine rings of the bpy ligand as long as 3.7 x 10(-2)A in crystals. Molecular orbital calculations of the bpy ligand suggest that this distortion decreases the energy gap between its pi and pi* orbitals. An absorption band attributed to the pi-pi*(bpy) transition of the distorted rhenium complexes, measured in a KBr pellet, was red-shifted by 1-5 nm compared to the complexes without the distorted bpy ligand. Even in solution, similar red shifts of the pi-pi*(bpy) absorption were observed. The redox potential E1/2(bpy/bpy*-) of the complexes with the trialkylphosphine and triarylphosphine ligand are shifted positively by 110-120 mV and 60-80 mV respectively, compared with those derived from the electron-attracting property of the phosphorus ligand. In contrast with these properties, three nu(CO) IR bands, which are sensitive to the electron density on the central rhenium because of pi-back bonding, were shifted to higher energy, and a Re(I/II)-based oxidation wave was observed at a more positive potential according to the electron-attracting property of the phosphorus ligand.     

First total synthesis of a new sesquiterpenoid natural product, (±)-3-(2,4-dihydroxybenzoyl)-4,5-dimethyl-5-(4,8-dimethyl-3(E),7(E)-nonadien-1-yl)tetrahydro-2-furanone

An efficient and stereodefined process is described for the first preparation of a new prenyl-benzoylfuranone type sesquiterpenoid, (±)-3-(2,4-dihydroxybenzoyl)-4,5-dimethyl-5-(4,8-dimethyl-3(E),7(E)-nonadien-1-yl)tetrahydro-2-furanone. The synthetic strategy is based on nucleophilic addition of organometallic reagents to the functionalized ketoamides elaborated from dihydroxyacetone dimer for the stereoselective construction of the key quaternary carbon center in the target compound.     

The structures of macbecin I and II : New antitumor antibiotics

Macbecin I 1, C₃₀H₄₂N₂O₈, and macbecin II 2, C₃₀H₄₄N₂O₈, were shown to be 2,6-disubstituted benzoquinone and hydroquinone derivatives by an oxidation-reduction relationship, UV. ¹H and ¹³C NMR spectra. Alkaline methanolysis of 1 gave a 2-aminobenzoquinone derivative 5, suggesting an ansa-structure for 1, and acid hydrolysis of 1 gave decarbamoyl products 9,10 and 11, indicative of the location of carbamoyloxy group in allylic position. Spin decoupling studies on 1,3 and 5clarified the partial structures [A], [B], [C] and [D]. From their mutual disposition two structures 1a and 1b, were proposed out of which 1a has been selected for the structure of 1 on the basis of the structure of oxidative degradation product 12. X-Ray analysis of the bromoacetyl derivative of 1 confirmed the above proposed structure and determined the absolute stereochemistry of 1 and 2.     

The determinant expressions of some theta constant identities

In this paper, we derive two interesting theta constant identities by considering determinant structures. One of the two identities which we obtained is given by the Pfaffian, and the other is expressed by the resultant.     

Synthesis and reversible hydration–dehydration system of copolymers bearing a vicinal tricarbonyl structure

Novel copolymers composed of a styrene (St) derivative bearing a vicinal tricarbonyl moiety and various vinyl monomers such as St, methyl methacrylate (MMA), and N‐vinylpyrrolidone (NVP) were synthesized by (1) radical copolymerization of a St derivative with a 1,3‐diketone structure with St, MMA, and NVP and (2) successive oxidation of the resulting copolymers with N‐bromosuccinimide in DMSO to convert their 1,3‐diketone moieties in the side chains into the corresponding vicinal tricarbonyl moieties. Their tricarbonyl moieties were readily hydrated in water‐containing acetone to generate the corresponding copolymers bearing geminal diol structures in the side chains. On the other hand, heating the resulting copolymers bearing the geminal diol structures in vacuo‐enabled successful recovery of the vicinal tricarbonyl moieties to demonstrate the reversible nature of this system. The hydration behavior in powdery state under air atmosphere saturated by water was also investigated. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012