Transcendence of Certain Reciprocal Sums of Linear Recurrences

 Suppose that {R _n } _n ⩾ 0 is a sequence of integers satisfying a binary linear recurrence relation with suitable conditions. We prove the transcendency of the numbers

Remote asymmetric induction with vinylketene silyl n,o-acetal

A highly regio- and diastereoselective TiCl4-mediated vinylogous Mukaiyama aldol reaction using the chiral vinylketene silyl N,O-acetal has been developed. The present vinylogous Mukaiyama aldol reaction provides a unique and effective means of controlling remote asymmetric induction. The methyl group at the alpha-position is important in achieving a high level of stereoselectivity. From a synthetic point of view, this methodology can provide a one-step construction of delta-hydroxy-alpha,gamma-dimethyl-alpha,beta-unsaturated carbonyl unit that is seen in many natural polyketide products.     

Superconductivity and crystallographic properties of La2 − xMxCuO4 − δ (M = Na, K)

Superconductivity and crystallographic properties of La_{2 − x}M_xCuO_{4 − δ} (M = Na, K) are studied. In the La_{2 − x}M_xCuO_{4 − δ} system, superconductivity is detected for x 0.2. Oxygen content analysis shows that the system has more oxygen vacancies than the La_{2 − x}Sr_xCuO_{4 − δ} system. These oxygen vacancies may reduce the hole concentration, and high Na-doping is needed to produce superconductivity. In the La_{2 − x}K_xCuO_{4 − δ} system, superconductivity is observed for the first time. Resistivity and magnetic susceptibility measurements show that T_c(onset) is 40 K and the Meissner volume fraction is about 4% for x = 0.7. The system changes from orthorhombic to a tetragonal K₂NiF₄ structure at x ≈ 0.3 and only tetragonal samples show superconductivity.     

Synthesis and morphology of polyethylene‐block‐poly(methyl methacrylate) through the combination of metallocene catalysis with living radical polymerization

Polyethylene‐block‐poly(methyl methacrylate) (PE‐b‐PMMA) was successfully synthesized through the combination of metallocene catalysis with living radical polymerization. Terminally hydroxylated polyethylene, prepared by ethylene/allyl alcohol copolymerization with a specific zirconium metallocene/methylaluminoxane/triethylaluminum catalyst system, was treated with 2‐bromoisobutyryl bromide to produce terminally esterified polyethylene (PE‐Br). With the resulting PE‐Br as an initiator for transition‐metal‐mediated living radical polymerization, methyl methacrylate polymerization was subsequently performed with CuBr or RuCl₂(PPh₃)₃ as a catalyst. Then, PE‐b‐PMMA block copolymers of different poly(methyl methacrylate) (PMMA) contents were prepared. Transmission electron microscopy of the obtained block copolymers revealed unique morphological features that depended on the content of the PMMA segment. The block copolymer possessing 75 wt % PMMA contained 50–100‐nm spherical polyethylene lamellae uniformly dispersed in the PMMA matrix. Moreover, the PE‐b‐PMMA block copolymers effectively compatibilized homopolyethylene and homo‐PMMA at a nanometer level. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3965–3973, 2003     

Novelty Filtering Using Phase Conjugate Wave in Organic Dye-Doped Polymer Films

A real-time detection of a moving object was demonstrated by taking the subtraction between cross-polarized phase conjugate waves with fast and slow response times with two kinds of dye-doped phase conjugators. One consists of superposed films of an erythrosin-B-doped film and a methyl-orange-doped film, and the other is a film dispersed with both dyes. The relative phase between cross-polarized phase conjugate waves by the both dye-dispersed films was stable.     

Rhodium-catalyzed asymmetric addition of potassium organotrifluoroborates to N-sulfonyl ketimines

A rhodium-catalyzed asymmetric addition of readily available potassium organotrifluoroborates to both N-tosyl and N-nosyl ketimines has been developed. High enantioselectivity has been achieved by using a chiral diene ligand, and the nosyl group of the addition products can be easily removed while retaining the enantiomeric purity.     

Preparative purification of gentamicin components using high-speed counter-current chromatography coupled with electrospray mass spectrometry

We developed a useful and preparative method based on high-speed counter-current chromatography with mass spectrometry (HSCCC/MS) to purify gentamicin C1a, C2/2a and C1 from standard powder. The analytes were purified on the HSCCC model CCC-1000 (multi-layer coil planet centrifuge) with a volatile two-phase solvent system composed of n-butanol/10% aqueous ammonia solution (50:50, v/v) and detected on an LCMS-2020EV quadrupole mass spectrometer fitted with an electrospray ionization (ESI) source system in positive ionization following scan mode (m/z 100-500). The HSCCC/ESI-MS peaks indicated that gentamicin C1a (m/z 450: [M+H](+)), C2/2a (m/z 464: [M+H](+)) and C1 (m/z 478: [M+H](+)) have the peak resolution values of 1.3 and 1.7 from 30 mg of loaded gentamicin powder. The HSCCC yielded 3.9 mg of gentamicin C1a, 12.6 mg of gentamicin C2/2a and 12.0 mg of gentamicin C1. These purified substances were analyzed by LC/MS with scan positive-mode. Based on the LC/MS chromatograms and spectra of the fractions, analytes were estimated to be over 95% pure. These gentamicin isomers of C1a, C2/2a and C1 were evaluated for their antibacterial activities. The overall results indicate that this approach of HSCCC/MS is a powerful technique for the purification of gentamicin components.