A study of C-F...M(+) interaction: metal complexes of fluorine-containing cage compounds

The C-F...M(+) interaction was investigated by observation of the NMR spectroscopic changes and complexation studies between metal cations and the cage compounds 1 and 2 which have fluorobenzene units as donor atoms. As a result, the interaction was detected with all of the metal cations which form complexes with 1 and 2. The stability of the complexes of 1 and 2 was determined by the properties of the metal cations (ionic radii and degree of hydrolysis), not by the hard-soft nature of the cations. Crystallographic analyses of Tl(+) subset 1 and La(3+) subset 2 provided structural information (interatomic distances and bond angles), and the bond strengths, C-F...M(+), O...M(+), and N...M(+), were estimated by Brown's equation based on the structural data. Short C-F...Tl(+) (2.952-3.048 A) distances were observed in the complex Tl(+) subset 1. The C-F bond lengths in the complexes, Tl(+) subset 1 and La(3+) subset 2, are elongated compared to those of the metal-free compounds. Interestingly, no solvent molecules including water molecules were coordinated to La(3+) in the La(3+) subset 2. The stabilization energy of cation-dipole interaction was calculated on the basis of the data from X-ray crystallographic analysis, and it is roughly consistent with the (-)Delta H values estimated in solution. Thus, the C-F...M(+) interaction can be expressed by the cation-dipole interaction. This result explains the fact that compound 1 which has fluorine atom as hard donor strongly binds soft metals such as Ag(+) and Tl(+). Furthermore, it was concluded that the fluorobenzene unit has a poor electron-donating ability compared to that of ether oxygen or amine nitrogen, and thus the ratio of the coordination bond in C-F...M(+) is small. The specific and remarkable changes in the (1)H, (13)C, and (19)F NMR spectra were observed accompanied by the complexation between M(+) and the hosts 1 and 2. These spectral features are important tools for the investigation of the C-F...M(+) interaction. Furthermore, F.Tl(+) spin couplings were observed at room temperature in the Tl(+) subset 1, 2 (J(F-Tl) = 2914 Hz for Tl(+) subset 1 and 4558 Hz for Tl(+) subset 2), and these are clear and definitive evidence of the interaction.     

Markov degree of the Birkhoff model

We prove the conjecture by Diaconis and Eriksson (J. Symbolic Comput. 41(2):182–195, 2006) that the Markov degree of the Birkhoff model is three. In fact, we prove the conjecture in a generalization of the Birkhoff model, where each voter is asked to rank a fixed number, say r, of candidates among all candidates.     

Synthesis of (±)-chamobtusin A by a presumed biomimetic aza-cyclization

A total synthesis of (±)-chamobtusin A has been accomplished on the basis of our presumed biosynthetic pathway: the imine formation of keto aldehyde followed by intramolecular aza-Michael addition.     

Mimicking an antimicrobial peptide polymyxin B by use of cyclodextrin

Cyclodextrin derivatives prepared to mimic a membrane active antibacterial peptide polymyxin B strongly permeabilized bacterial membrane and inhibited bacterial proliferation.     

The law of the iterated logarithm in game-theoretic probability with quadratic and stronger hedges

We prove both the validity and the sharpness of the law of the iterated logarithm in game-theoretic probability with quadratic and stronger hedges.     

Ab initio evidence for strong correlation associated with Mott proximity in iron-based superconductors

We predict that iron-based superconductors discovered near d(6) configuration (5 Fe 3d orbitals filled by 6 electrons) is located on the foot of an unexpectedly large dome of correlated electron matter centered at the Mott insulator at d(5) (namely, half filling). This is based on the many-variable variational Monte Carlo results for ab initio low-energy models derived by the downfolding. The d(5) Mott proximity extends to subsequent emergence of incoherent metals, orbital differentiations due to the Mott physics, and Hund's rule coupling, followed by antiferromagnetic quantum criticality, in quantitative accordance with available experiments.     

On sum of 0–1 random variables I. Univariate case

Summary Distribution of sum of 0–1 random variables is considered. No assumption is made on the independence of the 0–1 variables. Using the notion of “central binomial moments” we derive distributional properties and the conditions of convergence to standard distributions in a clear and unified manner.     

Reflective thermal lens detection device

A reflective thermal lens detection device was developed for realizing a portable and sensitive detector for a microsystem. An aluminum mirror was formed on the main plate of a microchip, and a reflected probe beam was detected with a single pick-up unit. The background signal due to light absorption of the aluminum mirror was 60 times reduced when the microchannel and the mirror were separated with an interval of 600 microm. The tilt angle of the microchip significantly affected the precision of the measurement. Then a quadrant photodiode was used to detect the center of gravity of the reflected probe beam to regulate the tilt angle within +/-0.05 degrees , and this value was enough to achieve 1% CV (coefficient of variance) precision in the measurements. The limit of detection (LOD) was 60 nM for xylene cyanol solution, and the absorbance was 9.4 x 10(-6) AU. About 40 times higher sensitivity was obtained in comparison with a spectrophotometer.     

Arrangements and Ranking Patterns

In the unidimensional unfolding model, given m objects in general position on the real line, there arise 1 + m(m − 1)/2 rankings. The set of rankings is called the ranking pattern of the m given objects. Change of the position of these m objects results in change of the ranking pattern. In this paper we use arrangement theory to determine the number of ranking patterns theoretically for all m and numerically for m ≤ 8. We also consider the probability of the occurrence of each ranking pattern when the objects are randomly chosen. Received March 5, 2005