Y‐rotation in k‐minimal quadrangulations on the projective plane

Let G be a quadrangulation on a surface, and let f be a face bounded by a 4‐cycle abcd. A face‐contraction of f is to identify a and c (or b and d) to eliminate f. We say that a simple quadrangulation G on the surface is k‐minimal if the length of a shortest essential cycle is k(≥3), but any face‐contraction in G breaks this property or the simplicity of the graph. In this article, we shall prove that for any fixed integer k≥3, any two k‐minimal quadrangulations on the projective plane can be transformed into each other by a sequence of Y‐rotations of vertices of degree 3, where a Y‐rotation of a vertex v of degree 3 is to remove three edges vv₁, vv₃, vv₅ in the hexagonal region consisting of three quadrilateral faces vv₁v₂v₃, vv₃v₄v₅, and vv₅v₆v₁, and to add three edges vv₂, vv₄, vv₆. Actually, every k‐minimal quadrangulation (k≥4) can be reduced to a (k?1)‐minimal quadrangulation by the operation called Möbius contraction, which is mentioned in Lemma 13. © 2011 Wiley Periodicals, Inc. J Graph Theory 69: 301–313, 2012     

Evaluating glycogen signal contamination in muscle by (13)C MRS of the liver

To evaluate the contamination of glycogen signal synthesized in skeletal muscle by that in the liver, long-term monitoring of over 7 h of in vivo [1-¹³C] glycogen synthesis/degradation at the right abdomen and left shoulder was achieved using a 3.0-T clinical MR system. ¹³C MR spectra without localization were obtained from five healthy volunteers before and after oral administration of 85 g of d-glucose, including 10 g of 99% [1-¹³C] glucose. In all volunteers, the relative signal intensities at the abdomen to those at shoulder were about two- to fivefold, and those of time-course changes at the abdomen and shoulder were dissimilar. It is considered that the quantity of muscle-synthesized glycogen signal at the abdomen is less than that at the shoulder because of the lesser muscle volume at the abdomen, and it may be less affected for evaluating glycogen synthesis/degradation in the liver even without localization pulses.     

Selective formation of [Au23(SPhtBu)17]0, [Au26Pd(SPhtBu)20]0 and [Au24Pt(SC2H4Ph)7(SPhtBu)11]0 by controlling ligand-exchange reaction

To use atomically precise metal nanoclusters (NCs) in various application fields, it is essential to establish size-selective synthesis methods for the metal NCs. Studies on thiolate (SR)-protected gold NCs (Au_n(SR)_m NCs) revealed that the atomically precise Au_n(SR)_m NC, which has a different chemical composition from the precursor, can be synthesized size-selectively by inducing transformation in the framework structure of the metal NCs by a ligand-exchange reaction. In this study, we selected the reaction of [Au₂₅(SC₂H₄Ph)₁₈]⁻ (SC₂H₄Ph = 2-phenylethanethiolate) with 4-tert-butylbenzenethiol (^tBuPhSH) as a model ligand-exchange reaction and attempted to obtain new metal NCs by changing the amount of thiol, the central atom of the precursor NCs, or the reaction time from previous studies. The results demonstrated that [Au₂₃(SPh^tBu)₁₇]⁰, [Au₂₆Pd(SPh^tBu)₂₀]⁰ (Pd = palladium) and [Au₂₄Pt(SC₂H₄Ph)₇(SPh^tBu)₁₁]⁰ (Pt = platinum) were successfully synthesized in a high proportion. To best of our knowledge, no report exists on the selective synthesis of these three metal NCs. The results of this study show that a larger variety of metal NCs could be synthesized size-selectively than at present if the ligand-exchange reaction is conducted while changing the reaction conditions and/or the central atoms of the precursor metal NCs from previous studies.

This study succeeded in obtaining three new thiolate protected metal nanoclusters by changing the ligand-exchange condition from previous studies.     

Magnetic features of the Kondo system CeTSn (T=Ni,Pd, Pt) probed by positive muons

Zero-, longitudinal and transverseSR measurements are reported on CeNiSn, CePdSn and CePtSn. Below 1 K CeNiSn exhibits strong magnetic correlations, up to possible short range order, but a magnetic phase transition did not occur down to 0.033 K. CePdSn and CePtSn signal their transition into the ordered antiferromagnetic phase by a spontaneous spin precession signal. The second magnetic phase transition in CePtSn reveals itself by the onset of a more complex spin precession pattern. Most unusual is the formation of a paramagnetic state with frozen random spin structure in CePtSn about one Kelvin aboveT _N.This work was supported by the German Federal Minister for Research and Technology (Bundesminister für Forschung und Technologie [BMFT]) under Contract Nr. 03KA2-TUM-4.     

Application of atomic stereomicroscope to surface science

A stereograph of atomic arrangement was displayed directly on the screen of display-type spherical-mirror analyzer without any computer-aided conversion process for the first time. This stereoscopic photograph enables viewing three-dimensional atomic arrangement. This technique was realized taking advantage of the phenomenon of circular dichroism in photoelectron angular distribution. The azimuthal shifts of forward focusing peaks in a photoelectron angular distribution taken with left and right helicity light in a special arrangement are the same as the parallaxes in a stereo view of atoms. Hence a stereoscopic recognition of three-dimensional atomic arrangement is possible, when the left eye and the right eye respectively view the two images obtained by left and right helicity light simultaneously.     

Regioselective reaction of quinones with Reformatsky reagent: (BrZnCH2CO2Et·THF)2

Reformatsky reactions of p-quinones with crystalline reagent (BrZnCH₂CO₂Et·THF)₂ were investigated and took place successfully, providing β-hydroxy esters in high yield. Notably, in the case of 2,6-disubstituted-p-quinones, regioselective Reformatsky reactions occurred to give corresponding β-hydroxy esters in good yields.     

Nearly planar nonsolvated monomeric silyl- and germyllithiums as a result of an intramolecular CH-Li agostic interaction

Pale-yellow crystals of the nonsolvated monomeric silyl- and germyllithiums, tris[di-tert-butyl(methyl)silyl]silyllithium 2a and tris[di-tert-butyl(methyl)silyl]germyllithium 2b, were obtained by one-electron reduction of the corresponding silyl and germyl radicals with lithium in hexane. The crystal structure analysis of both 2a and 2b showed almost planar geometry around the anionic centers, due to both intramolecular CH-Li agostic interactions and steric reasons. However, the free anions [(tBu2MeSi)3Si-][Li+(THF)4] 3a and [(tBu2MeSi)3Ge-][Li+(THF)n] (n = 3, 4) 3b no longer showed a planar geometry, because of the absence of the intramolecular CH-Li agostic interaction. A temperature-dependent 1H NMR study of 2a showed that the CH-Li interaction is weak.     

Stable mononuclear radical anions of heavier group 13 elements: [(tBu2MeSi)3E.-].[K+(2.2.2-Cryptand)] (E = Al, Ga)

The one-electron reduction of tris(di-tert-butylmethylsilyl)aluminum and -gallium with alkali metals (Li, Na, K) results in the formation of the corresponding radical anions [(tBu2MeSi)3Al*-] (3) and [(tBu2MeSi)3Ga]*- (4), which were isolated in the form of the potassium salt as extremely air- and moisture-sensitive deep red crystals, representing the first isolable mononuclear radical anions of heavier group 13 elements. The molecular structures of both 3.[K+(2.2.2-cryptand)] and 4.[K+(2.2.2-cryptand)] were established by X-ray crystallography, which showed a nearly planar geometry around the radical centers. The EPR spectra of 3 and 4 showed strong characteristic signals with g-values of 2.005 for 3 and 2.015 for 4 with hyperfine coupling constants of a(27Al) = 6.2 mT for 3, a(69Ga) = 12.3 mT, and a(71Ga) = 15.7 mT for 4, corresponding to a planar geometry of the radical center.     

Tetrasilyl-substituted cyclobutadiene dianion dilithium salt: synthesis and structure

The reaction of tetrakis(trimethylsilyl)cyclobutadienylcyclopentadienyl cobalt complex (Me₃Si)₄C₄CoCp with lithium metal in THF yielded the dilithium salt of cyclobutadiene dianion CBD^2– stabilized by four trimethylsilyl groups, Li⁺ ₂[(Me₃Si)₄C₄]^2–. The bridged CBD^2– dianion was also synthesized by a similar procedure starting from the bridged cobalt complex, which was prepared from the reaction of 2,2,5,5,8,8,11,11-octamethyl-2,5,8,11-tetrasilacyclododeca-1,6-diyne with CpCo(CO)₂ in refluxing octane. The aromaticity of the CBD^2– is discussed on the basis of the structural characteristics and magnetic properties.