Cut loci and conjugate loci on Liouville surfaces

In the earlier paper (Itoh and Kiyohara, Manuscr Math 114:247–264, 2004), we showed that the cut locus of a general point on two-dimensional ellipsoid is a segment of a curvature line and proved "Jacobi’s last geometric statement" on the singularities of the conjugate locus. In the present paper,we showthat a wider class of Liouville surfaces possess such simple cut loci and conjugate loci. The results include the determination of cut loci and the set of poles on two-sheeted hyperboloids and elliptic paraboloids

Perioperative use of eicosapentaenoic acid and patency of infrainguinal vein bypass: A retrospective chart review

AbstractBackground:A significant proportion of autogenous vein grafts fail in the long term. Currently, there is no treatment to improve graft patency.Objective:This study was designed to assess the effectiveness of eicosapentaenoic acid (EPA) to prevent late failure of an autogenous vein graft and other perioperative risk factors affecting long-term patency.Methods:A retrospective chart review was performed on grafts of patients who underwent infrainguinal bypass surgery using autogenous vein grafts for peripheral arterial disease in a lower limb. Patients were stratified by the perioperative use of EPA. The EPA group was those patients who administered EPA ≥1 time within 3 months of surgery. The non-EPA group was made up of those patients who did not administer EPA within 3 months of surgery. Primary, assisted primary, and secondary patency rates of the grafts in each group were calculated by the Kaplan-Meier method and compared by the log-rank test. To evaluate the effect of other perioperative risk factors, a Cox proportional hazards analysis was performed.Results:One hundred sixty-one grafts were analyzed from 159 patients who underwent surgery between July 1991 and July 2005. The primary patency rates of the EPA and non-EPA groups were 93% and 86%, 89% and 74%, and 83% and 68% at 1, 3, and 5 years, respectively. In terms of primary patency, the EPA group was significantly better than the non-EPA group (P=0.042). There was no significant difference between the groups in either assisted primary or secondary patency. A Cox proportional hazard analysis found that the minimum graft diameter and perioperative use of EPA were significant factors for primary patency (P=0.002 and P=0.004, respectively). Graft diameter was the only significant factor for assisted primary and secondary patency (P=0.021 and P=0.003, respectively).Conclusion:Although graft diameter was the most important factor for long-term patency of infrainguinal vein bypass grafts, the perioperative use of EPA significantly improved primary patency among these subjects

Proton incorporations and superconductivity in a cobalt oxyhydrate

We report the evidence of proton incorporations in a newly-discovered cobalt oxyhydrate superconductor. During the hydration process for Na$_{0.32}$CoO$_{2}$ by the direct reaction with water liquid, it was shown that substantial NaOH was gradually liberated, indicating that H$^{+}$ is incorporated into the hydrated compound. Combined with the thermogravimetric analysis, the chemical composition of the typical sample is Na$_{0.22}$H$_{0.1}$CoO$_{2}\cdot 0.85$H$_{2}$O, which shows bulk superconductivity at 4.4 K.Comment: 9 pages, 4 figure

On the Intuitionistic fuzzy topological (metric and normed) spaces

In this paper, we define precompact set in intuitionistic fuzzy metric spaces and prove that any subset of an intuitionistic fuzzy metric space is compact if and only if it is precompact and complete. Also we define topologically complete intuitionistic fuzzy metrizable spaces and prove that any $G_{\delta }$ set in a complete intuitionistic fuzzy metric spaces is a topologically complete intuitionistic fuzzy metrizable space and vice versa. Finally, we define intuitionistic fuzzy normed spaces and fuzzy boundedness for linear operators and so we prove that every finite dimensional intuitionistic fuzzy normed space is complete.Comment: 16 page

Possible observation of energy level quantization in an intrinsic Josephson junction

Energy level quantization (ELQ) is studied to clarify the macroscopic quantum dynamics of the d-wave Josephson junction (JJ). The influences of the nodal quasiparticles of d-wave superconductivity on the damping effect are numerically evaluated on the basis of a phenomenological model. The calculation, based on realistic parameters for a Bi2Sr2CaCu2O8+d (Bi2212) intrinsic JJ, shows that the observation of ELQ is possible when the sweep rate of the bias current exceeds 10 A/sec. High-sweep- rate measurements (121A/sec) performed on a Bi2212 intrinsic JJ result in the appearance of multiple peaks in the switching current distribution suggesting the realization of ELQ in the d-wave JJ.Comment: 5 pages, 3 figure

Tunneling properties at the interface between superconducting Sr2RuO4 and a Ru micro-inclusion

We have investigated the magnetic field and temperature dependence of the tunneling spectra of the eutectic system Sr2RuO4-Ru. Electric contacts to individual Ru lamellae embedded in Sr2RuO4 enable the tunneling spectra at the interface between ruthenate and a Ru microinclusion to be measured. A zero bias conductance peak (ZBCP) was observed in the bias voltage dependence of the differential conductance, suggesting that Andreev bound states are present at the interface. The ZBCP starts to appear at a temperature well below the superconducting transition temperature. The onset magnetic field of the ZBCP is also considerably smaller than the upper critical field when the magnetic field is parallel to the ab-plane. We propose that the difference between the onset of the ZBCP and the onset of superconductivity can be understood in terms of the existence of the single-component state predicted by Sigrist and Monien.Comment: 4 pages, 4 figures, to appear in J. Phys. Soc. Jpn. vol. 74 no.

Josephson current in s-wave superconductor / Sr_2RuO_4 junctions

The Josephson current between an s-wave and a spin-triplet superconductor Sr$_2$RuO$_4$ (SRO) is studied theoretically. In spin-singlet / spin-triplet superconductor junctions, there is no Josephson current proportional to $\sin \phi$ in the absence of the spin-flip scattering near junction interfaces, where $\phi$ is a phase-difference across junctions. Thus a dominant term of the Josephson current is proportional to $\sin 2\phi$ . The spin-orbit scattering at the interfaces gives rise to the Josephson current proportional to $\cos\phi$, which is a direct consequence of the chiral paring symmetry in SRO

Poly[bis­(acetone-κO)bis­{μ3-1-[(5-chloro-2-oxidophenyl)diazenyl]-2-naphtholato-κ4 O:O,O′:O′}­sodium(I)­chromium(III)]

The title compound, [CrNa(C16H9ClN2O2)2(C3H6O)2]n, is an azo-CrIII complex polymer that is used as a charge-control agent in electrophotography. The monomeric unit is composed of octa­hedral CrIII and NaI units, and is characterized by twofold rotation symmetry. The CrIII atom is chelated by two N and four O atoms from two [(5-chloro-2-oxidophen­yl)diazen­yl]-2-naphtholate ligands. The ligand anion exists in the cis form. The NaI atom is coordinated by two phen­oxy O atoms from a neighboring CrIII unit, two naphth­oxy O atoms from another neighboring CrIII unit and two O atoms from acetone mol­ecules. The dinuclear complex forms a one-dimensional polymer running along the c axis