Re-revision of the stereo structure of piperidine lactone,an intermediate in the synthesis of febrifugine

The stereo structure of piperidine lactone (3), an intermediate of the antimalarial agent febrifugine ((+)-1) prepared by a synthetic method, was re-revised to the cis-form from the trans-form.     

Innovative instrumental analysis of heartbeat signals and its clinical application

A new apparatus has been built that annexes a normal electrocardiograph, ECG, with the aim to enhance its capacity. It adds the normal ECG power to superpose multiple records of ECG altogether and averages out them and, further, makes sophisticated analysis, such as normalizing the peak heights, evaluating the half-line widths of the peaks, or that of the standard deviations of measurements like the inter peak distances. The results of the said calculations have not been obtainable using the former instruments, and are expected to be useful for clinicians.     

A characterization of Hyers-Ulam stability of first order linear differential operators

Let X be a complex Banach space and a continuous function. Let be the linear differential operator defined by T_hu=u′+hu. We give a necessary and sufficient condition in order that the operator T_h has the Hyers-Ulam stability.     

Many different covering numbers of Yorioka’s ideals

For ${b \in {^{\omega}}{\omega}}$ , let ${\mathfrak{c}^{\exists}_{b, 1}}$ be the minimal number of functions (or slaloms with width 1) to catch every functions below b in infinitely many positions. In this paper, by using the technique of forcing, we construct a generic model in which there are many coefficients ${\mathfrak{c}^{\exists}_{{b_\alpha}, 1}}$ with pairwise different values. In particular, under the assumption that a weakly inaccessible cardinal exists, we can construct a generic model in which there are continuum many coefficients ${\mathfrak{c}^{\exists}_{{b_\alpha}, 1}}$ with pairwise different values. In conjunction with these results, we give a generic model in which there are many Yorioka’s ideals ${\mathcal{I}_{f_\alpha}}$ with pairwise different covering numbers.     

Formal (3+3) cycloaddition of silyl enol ethers catalyzed by trifric imide: domino Michael addition-claisen condensation accompanied with isomerization of silyl enol ethers

We describe here a Tf?NH-catalyzed formal (3+3) cycloaddition of silyl enol ethers with acrylates as a new domino reaction. In the domino sequence, the catalyst activates Michael addition, deprotonation of the resulting silyloxonium cation and intramolecular Claisen condensation. It was found that reaction modes significantly depend on the reaction temperature. We also examined the mechanistic detail of the reaction by 1H-NMR experiment.     

Determination of the Avogadro constant by counting the atoms in a 28Si crystal

The Avogadro constant links the atomic and the macroscopic properties of matter. Since the molar Planck constant is well known via the measurement of the Rydberg constant, it is also closely related to the Planck constant. In addition, its accurate determination is of paramount importance for a definition of the kilogram in terms of a fundamental constant. We describe a new approach for its determination by counting the atoms in 1 kg single-crystal spheres, which are highly enriched with the 28Si isotope. It enabled isotope dilution mass spectroscopy to determine the molar mass of the silicon crystal with unprecedented accuracy. The value obtained, NA = 6.022,140,78(18) × 10(23) mol(-1), is the most accurate input datum for a new definition of the kilogram.