Semi-local units modulo Gauss sums

For thep-th cyclotomic fieldk, Iwasawa proved thatp does not divide the class number of its maximal real subfield if and only if the odd part of the group of local units coincides with its subgroup generated by Jacobi sums related tok. We refine and give a quantitative version of this result for more general imaginary abelian fields. Our result is an analogy of the famous result on “semi-local units modulo cyclotomic units”. Partially supported by Grant-in-Aid for Scientific Research (C), Grant 09640054.     

On the parity of the class number of an imaginary abelian field of conductor 2<Superscript><Emphasis Type="Italic">a</Emphasis></Superscript><Emphasis Type="Italic">p</Emphasis><Superscript><Emphasis Type="Italic">b</Emphasis></Superscript>

Let p be an odd prime number, and p^n₀{p^{n_0}} the highest power of p dividing 2 ^p−1 − 1. Let K_n=Q(z_pⁿ⁺¹){K_n={\bf Q}(\zeta_{p^{n+1}})} and L_n,j=K_n⁺(z_2^j+2){L_{n,j}=K_n^+(\zeta_{2^{j+2}})} for j ≥ 0. Let h_n^*{h_n^*} be the relative class number of K _n , and h _n,j the class number of L _n,j , respectively. Let n be an integer with n ≥ n ₀. We prove that if the ratio h_n^*/h_n-1^*{h_n^*/h_{n-1}^*} is odd, then h _n,j /h _n−1,j is odd for any j ≥ 0.     

Detection of diminished response to cold pressor test in smokers: Assessment using phase-contrast cine magnetic resonance imaging of the coronary sinus

Purpose

The purposes of this study were to evaluate the reproducibility for measuring the cold pressor test (CPT)-induced myocardial blood flow (MBF) alteration using phase-contrast (PC) cine MRI, and to determine if this approach could detect altered MBF response to CPT in smokers.

Materials and methods

After obtaining informed consent, ten healthy male non-smokers (mean age: 28 ± 5 years) and ten age-matched male smokers (smoking duration ≥ 5 years, mean age: 28 ± 3 years) were examined in this institutional review board approved study. Breath-hold PC cine MR images of the coronary sinus were obtained with a 3 T MR imager with 32 channel coils at rest and during a CPT performed after immersing one foot in ice water. MBF was calculated as coronary sinus flow divided by the left ventricular (LV) mass which was given as a total LV myocardial volume measured on cine MRI multiplied by the specific gravity (1.05 g/mL).

Results

In non-smokers, MBF was 0.86 ± 0.25 mL/min/g at rest, with a significant increase to 1.20 ± 0.36 mL/min/g seen during CPT (percentage change of MBF (?MBF (%)); 39.2% ± 14.4%, p < 0.001). Inter-study reproducibility for ?MBF (%) measurements by different MR technologist was good, as indicated by the intraclass correlation coefficient of 0.93 and reproducibility coefficient of 10.5%. There was no significant difference between smokers and non-smokers for resting MBF (0.85 ± 0.32 mL/min/g, p = 0.91). However, ?MBF (%) in smokers was significantly reduced (-4.0 ± 32.2% vs. 39.2 ± 14.4%, p = 0.011).

Conclusion

PC cine MRI can be used to reproducibly quantify MBF response to CPT and to detect impaired flow response in smokers. This MR approach may be useful for monitoring the sequential change of coronary blood flow in various potentially pathologic conditions and for investigating its relationship with cardiovascular risk.     

Observation of the effects of radially sheared electric fields on the suppression of turbulent vortex structures and the associated transverse loss in GAMMA 10

Vortexlike turbulent structures in hot-ion mode plasmas with several keV are observed in the case with a radially produced weak shear of electric fields E(r). However, a strong E(r) shear formation due to a high ion-confining potential phi(c) production clears up these vortices together with plasma-confinement improvement and disappearance of both drift-wave and turbulencelike Fourier spectral signals. These findings are based on three-time progress in phi(c) in comparison to phi(c) attained 1992-2002. The significant advance of phi(c) is well extended in line with proposed potential-formation physics scalings.     

Preparation of water-soluble photoresist derived from poly(vinyl alcohol)

The reaction of PVA with 2,2-dialkoxyethoxystyrylpyridinium or quinolinium salts is described. The resultant water-soluble polymers, which contain small amounts of the styrylpyridinium- or quinolinium group, exhibited high photosensitivity. Among the polymers prepared PVA-bearing 4-oxystyrylquinolinium group was photoinsolubilized with visible light that corresponded to an argon laser.     

Observation of "partial coherence" in an Aharonov-Bohm interferometer with a quantum dot

We report experiments on the interference through spin states of electrons in a quantum dot (QD) embedded in an Aharonov-Bohm (AB) interferometer. We have picked up a spin-pair state, for which the environmental conditions are ideally similar. The AB amplitude is traced in a range of gate voltage that covers the pair. The behavior of the asymmetry in the amplitude around the two Coulomb peaks agrees with the theoretical prediction that the spin-flip process in a QD is related to the quantum dephasing of electrons. These results constitute evidence of "partial coherence" due to an entanglement of spins in the QD and in the interferometer.     

Redox-controlled, reversible rearrangement of a tris(2-pyridylthio)methyl ligand on nickel to an isomer with an “N,S-confused” 2-pyridylthiolate arm

Interchange between the nickel +2 and +3 oxidation states precisely controls the reversible rearrangement of the tris(2-pyridylthio)methanide (tptm) ligand in the organometallic nickel(II) complex [{Ni(μ-Br)-(tptm)}(2)] (2). Oxidation of 2 first gives the corresponding Ni(III) complex [{Ni(μ-Br)(tptm)}(2)][PF(6)](2) (4). However, in solution the tptm ligand in 4 slowly undergoes a rearrangement, in which the N and S atoms of one of the pyridylthiolate arms exchange Ni and C bonding partners, thereby resulting in an "N,S-confused" isomer of tptm in the product, [NiBr(bpttpm)]PF(6) (5; bpttpm= bis(2-pyridylthio)(2-thiopyridinium)-methyl). Reduction of 5 reverses this ligand rearrangement and 2 is reformed quantitatively. The individual steps involved in these unusual ligand rearrangements were investigated by a number of methods, including voltammetric analysis, and a mechanism for this process is proposed. X-ray crystal structure determinations of the key compounds 2, 4 and 5 have been obtained.     

Novel method for preparation of photocrosslinkable poly(vinyl alcohol)

A convenient procedure to prepare photosensitive poly(vinyl alcohol) by acetalization with 1-methyl-4-(p-formylstyryl)pyridinium methosulfate in heterogeneous condition is described. The reaction of fully saponified poly(vinyl alcohol) was carried out in suspension in acidic aqueous solution, while partially saponified poly(vinyl alcohol) was acetalized in acidic aqueous organic solvent. The photosensitive poly(vinyl alcohol) thus prepared was purified by filtration and successive washing out with methanol. The effect of the preparative condition on the electronic absorption spectra of the styrylpyridinium group attached to poly(vinyl alcohol) is discussed.     

Direct conversion to 2-phenyl-4-quinolones via a 4-alkoxyflavylium salt from a naturally occurring flavanone

A flavanone, in which a hydroxyl group at the 5-position was protected with a methyl group, converted to the corresponding 5-methoxy-2-phenyl-4-quinolone via flavylium salt under mild conditions. Flavanone-O-rhamnoglucoside, naringin, was also converted to 5-methoxy-2-phenyl-4-quinolon-7-O-rhamnoglucoside in the same way in an overall 25% yield.