Qualitative properties of generalized principal eigenvalues for superquadratic viscous Hamilton–Jacobi equations

This paper is concerned with the ergodic problem for superquadratic viscous Hamilton–Jacobi equations with exponent \(m>2\). We prove that the generalized principal eigenvalue of the equation converges to a constant as \(m\rightarrow \infty \), and that the limit coincides with the generalized principal eigenvalue of an ergodic problem with gradient constraint. We also investigate some qualitative properties of the generalized principal eigenvalue with respect to a perturbation of the potential function. It turns out that different situations take place according to \(m=2\), \(2<m<\infty \), and the limiting case \(m=\infty \).     

Hyperbolic sections in surface bundles

We give conditions assuring that the given section in a surface bundle over the circle is hyperbolic in terms of the ‘‘projection" in the fiber surface according to the Nielsen-Thurston types of the monodromies.     

Photon angular distribution of Radiative Electron Capture into the M shell of He-like uranium ions at 110–140 MeV/u

Measurements of the photon angular distribution of Radiative Electron Capture into the M shell have been performed with He-like uranium ions in the range 110–140 MeV/u. In addition, L REC was studied at a projectile energy of 140 MeV/u. In both cases, the experimental data show an asymmetry around 90° and agree well with a fully relativistic theory.     

Designing magnetics of capped perpendicular media with minor-loop analysis

A novel method of analyzing the switching field distribution (SFD) and magnetic correlation length of perpendicular magnetic recording media that uses major and minor magnetization loops is proposed. By applying the analysis to a series of capped perpendicular media, we found that a thick capping layer with a low saturation magnetization effectively reduced SFD without rapidly increasing the magnetic correlation length. Transmission electron microscope observation suggests that the SFD is narrowed by the increased uniformity of intergranular exchange coupling via the thick capping layer. Evaluations of recording characteristics demonstrated a close correlation between narrower SFDs and improved recording performance. Reducing exchange coupling dispersion is a clear solution for improving the performance of recording media.     

Fast polarimetry system for the application to spin quantum non-demolition measurement

We report the development of a fast pulse polarimeter for the application to quantum non-demolition measurement of atomic spin (spin QND). The developed system was tunable to the atomic resonance of a ytterbium atom and has narrow laser line width suitable for spin QND. Using the developed polarimeter, we successfully demonstrated the measurement of the vacuum noise, with 10⁶ to 10⁷ photon number per pulse. PACS 42.25.Ja; 42.50.Lc; 42.55.Px     

Paramagnetic Faraday rotation with spin-polarized ytterbium atoms

We report the observation of paramagnetic Faraday rotation of spin-polarized ytterbium (Yb) atoms. As the atomic samples, we used an atomic beam, released atoms from a magneto-optical trap (MOT), and trapped atoms in a far-off-resonant trap (FORT). Since Yb is diamagnetic and includes a spin-1/2 isotope, it is an ideal sample for spin physics, such as quantum non-demolition measurement of spin (spin QND), for example. From the results of the rotation angle, we confirmed that the atoms were almost perfectly polarized. PACS 32.80.Bx; 32.80.Pj; 42.25.Lc     

Limit Theorem for Controlled Backward SDEs and Homogenization of Hamilton–Jacobi–Bellman Equations

We prove a convergence theorem for a family of value functions associated with stochastic control problems whose cost functions are defined by backward stochastic differential equations. The limit function is characterized as a viscosity solution to a fully nonlinear partial differential equation of second order. The key assumption we use in our approach is shown to be a necessary and sufficient assumption for the homogenizability of the control problem. The results generalize partially homogenization problems for Hamilton–Jacobi–Bellman equations treated recently by Alvarez and Bardi by viscosity solution methods. In contrast to their approach, we use mainly probabilistic arguments, and discuss a stochastic control interpretation for the limit equation.     

Asymmetric total synthesis of sperabillins B and D via lithium amide conjugate addition

Diastereoselective conjugate addition of homochiral lithium (R)-N-allyl-N-alpha-methylbenzylamide to methyl (2E,5E)-hepatadienoate, followed by protecting group manipulation and subsequent iodocyclocarbamation allows a concise route to the core fragment, methyl (3R,5R,6R)-3,6-diamino-5-hydroxyheptanoate, of sperabillins B and D. Differentiation between the C-3 and C-6 primary amino groups of this core amino acid was readily achieved by treatment with acetone, giving the 5,6-isopropylidene and C-3-imine protected diamine, with subsequent regioselective acylation of the C-6-nitrogen facilitating the total synthesis of sperabillin D in 10.8% overall yield, and the first asymmetric synthesis of sperabillin B in 5.8% overall yield.     

Study of the dissociation of a charge-reduced phosphopeptide formed by electron transfer from an alkali metal target

Doubly protonated phosphopeptide (YGGMHRQET(p)VDC) ions obtained by electrospray ionization were collided with Xe and Cs targets to give singly and doubly charged positive ions via collision-induced dissociation (CID). The resulting ions were analyzed and detected by using an electrostatic analyzer (ESA). Whereas doubly charged fragment ions resulting from collisionally activated dissociation (CAD) were dominant in the CID spectrum with the Xe target, singly charged fragment ions resulting from electron transfer dissociation (ETD) were dominant in the CID spectrum with the Cs target. The most intense peak resulting from ETD was estimated to be associated with the charge-reduced ion with H2 lost from the precursor. Five c-type fragment ions with amino acid residues detached consecutively from the C-terminal were clearly observed without a loss of the phosphate group. These ions must be formed by N--Calpha bond cleavage, in a manner similar to the cases of electron capture dissociation (ECD) and ETD from negative ions. Although the accuracy in m/z of the CID spectra was about +/-1 Th because of the mass analysis using the ESA, it is supposed from the m/z values of the c-type ions that these ions were accompanied by the loss of a hydrogen atom. Four z-type (or y--NH3, or y--H2O) ions analogously detached consecutively from the N-terminal were also observed. The fragmentation processes took place within the time scale of 4.5 micros in the high-energy collision. The present results demonstrated that high-energy ETD with the alkali metal target allowed determination of the position of phosphorylation and the amino acid sequence of post-translational peptides.