Isogeny formulas for the Picard modular form and a three terms arithmetic geometric mean

In this paper we study the Picard modular forms and show a new three terms arithmetic geometric mean (AGM) system. This AGM system is expressed via the Appell hypergeometric function of two variables. The Picard modular forms are expressed via the theta constants, and they give the modular function for the family of Picard curves. Our theta constants are “Neben type” modular forms of weight 1 defined on the complex 2-dimensional hyperball with respect to an index finite subgroup of the Picard modular group. We define a simultaneous 3-isogeny for the family of Jacobian varieties of Picard curves. Our main theorem shows the explicit relations between two systems of theta constants which are corresponding to isogenous Jacobian varieties. This relation induces a new three terms AGM which is a generalization of Borweins' cubic AGM.     

New electron states that float on semiconductor and metal surfaces

We report first-principle electronic-structure calculations using the local density approximation in the density functional theory for Si(1 0 0) and Al(1 0 0) surfaces. We find a novel class of surface electron states that are distributed not near atomic arrays but float around with the maximum amplitudes being substantially separated from matters. We also find that the origin of the unusual character is quantum spill of electron density from matters and exchange-correlation effects among electrons.     

Errata to “Cyclic strength of imperfectly saturated sands and analysis of liquefaction”: [Proc. Jpn. Acad., Ser. B 80, No. 8, 372–391 (2004)]

The simplified method of analysis to assess liquefaction potential of a given sand deposit is briefly introduced in the first part of this paper. Then, recent advances in the laboratory testing for evaluating liquefaction resistance are described with a particular emphasis on the sand partly saturated with water. As a means to identify the degree of saturation which is applicable for both field deposits and laboratory samples, the use of the longitudinal wave (P-wave) is proposed based on a suite of data obtained from the triaxial tests in the laboratory. It is recommended that the non-destructive P-wave measurements be carried out first to determine the degree of saturation, and then the cyclic triaxial tests involving large destructive strains should be performed to determine the cyclic strength on the same sample of the sand. In order to demonstrate usefulness of the proposed approach, two sets of undisturbed samples were secured from two sites; one is located in Sakai-minato city which has suffered severe liquefaction at the time of the 2000 Tottoriken-Seibu earthquake and the other site is located in Koshigaya city, Saitama, where likelihood of liquefaction to occur in a future earthquake is of major concern. Penetration tests and in-situ velocity logging were also conducted at these two sites. By adjusting the P-wave velocity of the undisturbed samples in the laboratory so as to have the same velocity in the field, the in-situ state of saturation was reproduced in the laboratory samples. Then, the cyclic loading tests were conducted to determine the cyclic strength of intact samples. The results of the laboratory tests as above were incorporated into the simple method of liquefaction analysis described in the first section of this paper. The analysis seems to yield results which are in reasonably good agreement with what was observed at the time of the earthquake.     

Cationic ring‐opening copolymerization behavior of trioxane and seven‐membered cyclic carbonate

Cationic ring‐opening copolymerization behavior of trioxane (TOX) and a seven‐membered cyclic carbonate, 1,3‐dioxepan‐2‐one (7CC) is described. When TOX and 7CC were cationically copolymerized under various feed ratios using trifluoromethane sulfonic acid (TfOH) as an initiator in nitrobenzene at 30 °C, 7CC was consumed faster than TOX and the decarboxylation was accompanied to afford the corresponding polyacetal–polycarbonate type copolymers containing poly(oxytetramethylene) units. The copolymer composition could be controlled by the feed ratio of 7CC, whose increase resulted in the high copolymer composition of the 7CC unit. The solubility of the copolymers increased as the increase of the 7CC content. Thermogravimetric, size‐exclusion chromatographic, and X‐ray analyses of the copolymers suggest that the sequences of the copolymer chains consist of the segments containing the units originated from 7CC and those with TOX unit‐rich compositions. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 733–739, 2008     

New estimation methods of erase band width and track-edge noise in perpendicular magnetic recording

In order to realize higher track density, improving recording resolution and noise at track edge is one of the crucial issues. It has been considered that the erase band (EB), which appears at track-edge, can suppress the cross-talk noise from the adjacent track. On the other hand, the EB consists of a randomly magnetized area that may emanate track-edge noise. In this study, we estimated the accurate EB width by a newly proposed technique and derived analytical formula of the 747 curve with large EB noise. As a result, we found that the peak of track-edge noise was outside the EB and the EB was enough of a noise source at track edge and may be obstructive to the improvement of track density. A bump of 747 curve was produced in the case of little noise of EB. There is a close relationship between the shape of the 747 curve and the EB noise.     

Preparations and reactions of 2-trifluoromethylketenimines

Preparations and reactions of a series of 2-trifluoromethylketenimines are described. Trifluoromethylketenimines were prepared from trifluoropropanoic acids via corresponding imidoyl chlorides in good yields. 2-Trifluoromethylketenimine was functionalized at its β-position by electrophilic addition of halide, followed by dehydrohalogenation. Addition of nucleophile at α-position gave trifluoroethylated β-amino acid derivative via 1,3-proton shift.     

Measurement of Strain Distributions in Mouse Femora with 3D-Digital Speckle Pattern Interferometry

Bone is a mechanosensitive tissue that adapts its mass, architecture and mechanical properties to external loading. Appropriate mechanical loads offer an effective means to stimulate bone remodeling and prevent bone loss. A role of in situ strain in bone is considered essential in enhancement of bone formation, and establishing a quantitative relationship between 3D strain distributions and a rate of local bone formation is important. Digital speckle pattern interferometry (DSPI) can achieve whole-field, non-contacting measurements of microscopic deformation for high-resolution determination of 3D strain distributions. However, the current system does not allow us to derive accurate strain distributions because of complex surface contours inherent to biological samples. Through development of a custom-made piezoelectric loading device as well as a new DSPI-based force calibration system, we built an advanced DSPI system and integrated local contour information to deformation data. Using a mouse femur in response to a knee loading modality as a model system, we determined 3D strain distributions and discussed effectiveness and limitations of the described system.     

Effect of uniaxial stress cooling on the neutron magnetic scattering in a ZnCr2O4 single crystal

For the determination of the magnetic structure, elimination of the magnetic domains is indispensable and the appropriate stress will be effective when the crystal has a structural transformation at T_N. The effect of uniaxial stress cooling on the neutron magnetic scattering in a ZnCr₂O₄ single crystal was studied. The pressure axis was set parallel to the [1 0 0] or [0 0 1], parallel or perpendicular to the diffraction plane, (0 0 1). The [1 0 0] pressure cooling increases one half-integer spots along the [1 0 0], whereas decreases others. The [0 0 1] pressure cooling increases two half-integer spots in the (0 0 1) plane, whereas decreases one half-integer spots.     

Rotational spectra of gauche perfluoro-n-butane, C4F10; perfluoro-iso-butane, (CF3)3CF; and tris(trifluoromethyl)methane, (CF3)3CH

The microwave spectra of the gauche conformer of perfluoro-n-butane, n-C₄F₁₀, of perfluoro-iso-butane, (CF₃)₃CF, and of tris(trifluoromethyl)methane, (CF₃)₃CH, have been observed and assigned. The rotational and centrifugal distortion constants for gauche n-C₄F₁₀ are: A = 1058.11750(7) MHz, B = 617.6832(1) MHz, C = 552.18794(1) MHz, Δ_J = 0.0257(5) kHz, δ_J = 0.0052(3) kHz. A C-C-C-C dihedral angle, ω, of ∼55° has been determined. These values agree well with those obtained from a coupled cluster (CCSD/cc-PVTZ) calculation. The rotational and centrifugal distortion constants for iso-C₄F₁₀ and iso-C₄HF₉ are: B_o = 816.4519(4) MHz, D_J = 0.023(2) kHz, and B_o = 903.6985(25) MHz, D_J = 0.043(4) kHz, respectively. The dipole moment of iso-C₄F₁₀ and iso-C₄HF₉ have been measured and found to be 0.0338(8) and 1.69(9) D, respectively.