Consistency conditions on the least squares estimator in single common factor analysis model

Summary This paper is concerned with the consistency of estimators in a single common factor analysis model when the dimension of the observed vector is not fixed. In the model several conditions on the sample sizen and the dimensionp are established for the least squares estimator (L.S.E.) to be consistent. Under some assumptions,p/n→0 is a necessary and sufficient condition that the L.S.E. converges in probability to the true value. A sufficient condition for almost sure convergence is also given.     

General Mechanism for Chiral Recognition by Native and Modified Cyclodextrins

A general mechanism for chiral recognition by native and modified cyclodextrins hasbeen proposed by reconsidering the data reported so far. Cyclodextrins in aqueoussolution adopt asymmetrically twisted structures, which seems to be the origin of chiralrecognition.     

Intensely Fluorescent Azobenzenes: Synthesis,Crystal Structures,Effects of Substituents,and Application to Fluorescent Vital Stain

2‐[Bis(pentafluorophenyl)boryl]azobenzenes bearing hydrogen, methoxy, dimethylamino, trifluoromethyl, fluoro, n‐butyl, and tert‐butyldimethylsiloxy groups at the 4′‐position or methoxy and bromo groups at the 4‐position have been synthesized. The 4‐bromo group of the 2‐boryl‐4‐bromoazobenzene derivative was converted to phenyl and diphenylamino groups by palladium‐catalyzed reactions. The absorption and fluorescence properties have been investigated using UV/Vis and fluorescence spectroscopy. The 2‐borylazobenzenes emitted an intense green, yellow, and orange fluorescence, in marked contrast to the usual azobenzene fluorescence. The 4′‐siloxy derivative showed the highest fluorescence quantum yield (0.90) among those reported for azobenzenes to date. The correlation between the substituent and the fluorescence properties was elucidated by studying the effect of the substituent on the relaxation process and from DFT and TD‐DFT calculations. An electron‐donating group at the 4′‐position was found to be important for an intense emission. Application of fluorescent azobenzenes as a fluorescent vital stain for the visualization of living tissues was also investigated by microinjection into Xenopus embryos, suggesting these compounds are nontoxic towards embryos.     

Versatile In Situ Generated N‐Boc‐Imines: Application to Phase‐Transfer‐Catalyzed Asymmetric Mannich‐Type Reactions

The efficient construction of nitrogen‐containing organic compounds is a major challenge in chemical synthesis. Imines are one of the most important classes of electrophiles for this transformation. However, both the available imines and applicable nucleophiles for them are quite limited given the existing preparative methods. Described herein are imine precursors which generate reactive imines with a wide variety of substituents under mild basic conditions. This approach enables the construction of various nitrogen‐containing molecules which cannot be accessed by the traditional approach. The utility of the novel imine precursor was demonstrated in the asymmetric Mannich‐type reaction under phase‐transfer conditions.     

Fast and Robust Nanocellulose Width Estimation Using Turbidimetry

The dimensions of nanocelluloses are important factors in controlling their material properties. The present study reports a fast and robust method for estimating the widths of individual nanocellulose particles based on the turbidities of their water dispersions. Seven types of nanocellulose, including short and rigid cellulose nanocrystals and long and flexible cellulose nanofibers, are prepared via different processes. Their widths are calculated from the respective turbidity plots of their water dispersions, based on the theory of light scattering by thin and long particles. The turbidity‐derived widths of the seven nanocelluloses range from 2 to 10 nm, and show good correlations with the thicknesses of nanocellulose particles spread on flat mica surfaces determined using atomic force microscopy.

     

Systematic study of protein detection mechanism of self-assembling 19F NMR/MRI nanoprobes toward rational design and improved sensitivity

(19)F NMR/MRI probe is expected to be a powerful tool for selective sensing of biologically active agents owing to its high sensitivity and no background signals in live bodies. We have recently reported a unique supramolecular strategy for specific protein detection using a protein ligand-tethered self-assembling (19)F probe. This method is based on a recognition-driven disassembly of the nanoprobes, which induced a clear turn-on signal of (19)F NMR/MRI. In the present study, we conducted a systematic investigation of the relationship between structure and properties of the probe to elucidate the mechanism of this turn-on (19)F NMR sensing in detail. Newly synthesized (19)F probes showed three distinct behaviors in response to the target protein: off/on, always-on, and always-off modes. We clearly demonstrated that these differences in protein response could be explained by differences in the stability of the probe aggregates and that "moderate stability" of the aggregates produced an ideal turn-on response in protein detection. We also successfully controlled the aggregate stability by changing the hydrophobicity/hydrophilicity balance of the probes. The detailed understanding of the detection mechanism allowed us to rationally design a turn-on (19)F NMR probe with improved sensitivity, giving a higher image intensity for the target protein in (19)F MRI.     

Catalytic asymmetric allylation of 3,4-dihydroisoquinolines and its application to the synthesis of isoquinoline alkaloids

A catalytic asymmetric allylation of 3,4-dihydroisoquinoline was carried out with allyltrimethoxylsilane-Cu as the nucleophile in the presence of DTBM-SEGPHOS as the chiral ligand to afford corresponding chiral 1-allyltetrahydroisoquinoline derivatives in good yield and stereoselectivity. The allyl adduct thus obtained was applied to the synthesis of several isoquinoline alkaloids such as crispine A and homolaudanosine. The reaction was further used for the synthesis of the isoquinoline moiety of schulzeine A.     

Rings of normal and nonnormal numbers

We construct an uncountable ring of real numbers all of whose nonzero elements are normal to baseb and nonnormal to baseab, wherea, b are and pair of integers greater than one with (a,b)=1. To the memory of Gerold Wagner     

Synthesis and properties of polyimide ionomers containing sulfoalkoxy and fluorenyl groups

A series of sulfopropylated and sulfobutylated polyimide copolymers containing fluorenyl groups, SPI‐4, were synthesized to investigate the effect of alkyl side chains on the properties (stability, mechanical strength, water uptake, and proton conductivity) of the polymimide electrolyte membranes. SPI‐4 showed much better hydrolytic stability (in 10% MeOH aq at 100 °C) than the main chain sulfonated polyimide, SPI‐1. Tough, flexible, and ductile membranes were obtained from these copolymers. At high relative humidity all the SPI‐4 membranes showed high mechanical properties (>34 MPa of the maximum stress) and proton conductivity (>0.1 Scm^?1). These properties are comparable to or even better than those of the perfluorosulfonic acid ionomer (Nafion 112). The new polyimide ionomers have proved to be a possible candidate as polymer electrolyte membrane for PEFCs and DMFCs. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 4439–4445, 2005