197Au and125Te Mössbauer spectroscopic study on the low temperature phases of Ag3AuX2 (X=S,Se, and Te)

¹⁹⁷Au and¹²⁵Te Mössbauer spectroscopy has been applied for the low-temperature β-phases of Ag₃AuX₂ (X=S, Se, and Te). The values of I. S. and Q. S. for¹⁹⁷Au suggest that the gold atoms, linearly coordinated by two chalcogen atoms in these phases, exist as monovalent cations. The¹²⁵Te Mössbauer spectra suggest that the tellurium atoms are substantially ionic for both Ag₂Te and Ag₃AuTe₂. The nature of X-Au-X bonds is discussed on the basis of the Mössbauer data and the bond distances.     

On orders of approximation of plane curves by parametric cubic splines

The aim of the present paper is to show that the convergence rate of the parametric cubic spline approximation of a plane curve is of order four instead of order three. For the first and second derivatives, the rates are of order three and two, respectively. Finally some numerical examples are given to illustrate the predicted error behaviour.     

Mechanical fabrication of metal nano-contacts showing conductance quantization under electrochemical potential control

We have mechanically fabricated Ni and Cu nano-constrictions in solution to study their quantized conductance behavior under electrochemical potential control. Conductance quantization was observed at both metals in solution at room temperature for the first time. The conductance of Cu nano-constriction was quantized in units of G₀(=2e²/h). A sharp 1G₀ peak was observed in the conductance histogram. For Ni, a rather broad peak at 1–1.5G₀ was observed in the histogram. The conductance quantization behavior was discussed by comparing previously documented results of nano-constrictions fabricated in air or ultra-high vacuum conditions, with those fabricated in solution.     

Electroorganic synthesis in oil-in-water (O/W) nanoemulsion: TEMPO-mediated electrooxidation of amphiphilic alcohols in water

Oil-in-water nanoemulsion which consisted of TEMPO, amphiphilic alcohols, and water offered unique reaction environments for electrooxidation of the alcohols to give the corresponding carboxylic acids in good to excellent yields.     

Quasienergy anholonomy and its application to adiabatic quantum state manipulation

The parametric dependence of a quantum map under the influence of a rank-1 perturbation is investigated. While the Floquet operator of the map and its spectrum have a common period with respect to the perturbation strength lambda, we show an example in which none of the quasienergies nor the eigenvectors obey the same period: After a periodic increment of lambda, the quasienergy arrives at the nearest higher one, instead of the initial one, exhibiting an anholonomy, which governs another anholonomy of the eigenvectors. An application to quantum state manipulations is outlined.     

C‐Selective and Diastereoselective Alkyl Addition to β,γ‐Alkynyl‐α‐imino Esters with Zinc(II)ate Complexes

Since umpolung α‐imino esters contain three electrophilic centers, regioselective alkyl addition with traditional organometallic reagents has been a serious problem in the practical synthesis of versatile chiral α‐amino acid derivatives. An unusual C‐alkyl addition to α‐imino esters using a Grignard reagent (RMgX)‐derived zinc(II)ate was developed. Zinc(II)ate complexes consist of a Lewis acidic [MgX]⁺ moiety, a nucleophilic [R₃Zn]^? moiety, and 2 [MgX₂]. Therefore, the ionically separated [R₃Zn]^? selectively attacks the imino carbon atom ,which is most strongly activated by chelation of [MgX]⁺. In particular, chiral β,γ‐alkynyl‐α‐imino esters can strongly promote highly regio‐ and diastereoselective C‐alkylation because of structural considerations, and the corresponding optically active α‐quaternary amino acid derivatives are obtained within 5 minutes in high to excellent yields.     

Equality statements for Schwarz–Pick type estimates and the pseudo-hyperbolic distance

In the present article we demonstrate that the conclusion on the case of equality for the estimate of Schwarz–Pick type is a property of a distance-nonincreasing holomorphic mapping which is locally defined. Also, while considering existence of branch points, we deal with the topics in terms of the pseudo-hyperbolic distance.