Deformation of LeBrun's ALE metrics with negative mass

In this article we investigate deformations of a scalar-flat K\"ahler metric on the total space of complex line bundles over CP^1 constructed by C. LeBrun. In particular, we find that the metric is included in a one-dimensional family of such metrics on the four-manifold, where the complex structure in the deformation is not the standard one.Comment: 20 pages, no figure. V2: added two references, filled a gap in the proof of Theorem 1.2. V3: corrected a wrong statement about Kuranishi family of a Hirzebruch surface stated in the last paragraph in the proof of Theorem 1.2, and fixed a relevant error in the proof. Also added a reference [24] about Kuranishi family of Hirzebruch surface

High-field phase diagram of the Haldane-gap antiferromagnet Ni(C5H14N2)2N3(PF6)Ni (C_5 H_{14} N_2)_2 N_3 (PF_6)

We have determined the magnetic phase diagram of the quasi-one-dimensional $S=$ 1 Heisenberg antiferromagnet $Ni (C_5 H_{14} N_2)_2 N_3 (PF_6)$ by specific heat measurements to 150 mK in temperature and 32 T in magnetic field. When field is applied along the spin-chain direction, a new phase appears at $H_{c2}\approx 14$ T. For the previously known phases of field-induced order, accurate determination is made of the power-law exponents of the ordering temperature near the zero-temperature critical field $H_c$, owing to the four-fold improvement of the minimum temperature over the previous work. The results are compared with the predictions based on the Bose-Einstein condensation of triplet excitations. Substituting deuterium for hydrogen is found to slightly reduce the interchain exchange.Comment: 6 pages, 6 figure

Behavior of Li abundances in solar-analog stars II. Evidence of the connection with rotation and stellar activity

We previously attempted to ascertain why the Li I 6708 line-strengths of Sun-like stars differ so significantly despite the superficial similarities of stellar parameters. We carried out a comprehensive analysis of 118 solar analogs and reported that a close connection exists between the Li abundance A_Li and the line-broadening width (v_r+m; mainly contributed by rotational effect), which led us to conclude that stellar rotation may be the primary control of the surface Li content. To examine our claim in more detail, we study whether the degree of stellar activity exhibits a similar correlation with the Li abundance, which is expected because of the widely believed close connection between rotation and activity. We measured the residual flux at the line center of the strong Ca II 8542 line, r_0(8542), known to be a useful index of stellar activity, for all sample stars using newly acquired spectra in this near-IR region. The projected rotational velocity (v_e sin i) was estimated by subtracting the macroturbulence contribution from v_r+m that we had already established. A remarkable (positive) correlation was found in the A_Li versus (vs.) r_0(8542) diagram as well as in both the r_0(8542) vs. v_e sin i and A_Li vs. v_e sin i diagrams, as had been expected. With the confirmation of rotation-dependent stellar activity, this clearly shows that the surface Li abundances of these solar analogs progressively decrease as the rotation rate decreases. Given this observational evidence, we conclude that the depletion of surface Li in solar-type stars, probably caused by effective envelope mixing, operates more efficiently as stellar rotation decelerates. It may be promising to attribute the low-Li tendency of planet-host G dwarfs to their different nature in the stellar angular momentum.Comment: 12 pages, 9 figures; accepted for publication in Astron. Astrophys

Multiscale expansion of the lattice potential KdV equation on functions of infinite slow-varyness order

We present a discrete multiscale expansion of the lattice potential Korteweg-de Vries (lpKdV) equation on functions of infinite order of slow-varyness. To do so we introduce a formal expansion of the shift operator on many lattices holding at all orders. The lowest secularity condition from the expansion of the lpKdV equation gives a nonlinear lattice equation, depending on shifts of all orders, of the form of the nonlinear Schr\"odinger (NLS) equationComment: 9 pages, submitted to Journ. Phys.