Topology of multiple log transforms of 4-manifolds

Given a 4-manifold X and an imbedding of T^{2} x B^2 into X, we describe an algorithm X --> X_{p,q} for drawing the handlebody of the 4-manifold obtained from X by (p,q)-logarithmic transforms along the parallel tori. By using this algorithm, we obtain a simple handle picture of the Dolgachev surface E(1)_{p,q}, from that we deduce that the exotic copy E(1)_{p,q} # 5(-CP^2) of E(1) # 5(-CP^2) differs from the original one by a codimension zero simply connected Stein submanifold M_{p,q}, which are therefore examples of infinitely many Stein manifolds that are exotic copies of each other (rel boundaries). Furthermore, by a similar method we produce infinitely many simply connected Stein submanifolds Z_{p} of E(1)_{p,2} # 2(-CP^2)$ with the same boundary and the second Betti number 2, which are (absolutely) exotic copies of each other; this provides an alternative proof of a recent theorem of the author and Yasui [AY4]. Also, by using the description of S^2 x S^2 as a union of two cusps glued along their boundaries, and by using this algorithm, we show that multiple log transforms along the tori in these cusps do not change smooth structure of S^2 x S^2.Comment: Updated, with 17 pages 21 figure

Orbital Order Effect of Two-Dimensional Spin Gap System for CaV4O9

Effects of possible orbital order in magnetic properties of two-dimensional spin gap system for CaV$_4$O$_9$ are investigated theoretically. After analyzing experimental data, we show that single orbital models assumed in the literature are insufficient to reproduce the data. To understand the origin of the discrepancy, we assume that in $d^1$ state of V, $d_{xz}$ and $d_{yz}$ orbitals have substantial contributions in the lowest-energy atomic level which leads to a double-degeneracy. We study possible configurations of the orbital order. By exact diagonalization and perturbation expansion, we calculate the susceptibility, wavenumber dependence of low-lying excitations and equal-time spin-spin correlations which is related to integrated intensity of the neutron inelastic scattering. These quantities sensitively depend on the configuration of the orbital order. The calculated results for some configurations of the orbital order reproduce many experimental results much better than the previous single-orbital models. However some discrepancy still remains to completely reproduce all of the reported experimental results. To understand the origin of these discrepancies, we point out the possible importance of the partially occupied $d_{xy}$ orbital in addition to orbital order of partially filled $d_{xz}$ and $d_{yz}$ orbitals.Comment: 19 pages LATEX, 15 postscript figures, using jpsj.sty,to be published in J.Phys.Soc.Jpn. Vol.67 No.2 (1998

The Association Between Social Networks and Self-rated risk of HIV Infection among Secondary School Students in Moshi Municipality, Tanzania.

Abstract This study describes the social networks of secondary school students in Moshi Municipality, and their association with self-rated risk of human immunodeficiency virus (HIV) infection. A cross-sectional analytical study was conducted among 300 students aged 15-24 years in 5 secondary schools in Moshi, Tanzania. Bonding networks were defined as social groupings of students participating in activities within the school, while bridging networks were groups that included students participating in social groupings from outside of the school environs. A structured questionnaire was used to ask about participation in bonding and bridging social networks and self-rated HIV risk behavior. More participants participated in bonding networks (72%) than in bridging networks (29%). Participation in bridging networks was greater among females (25%) than males (12%, p < .005). Of 300 participants, 88 (29%) were sexually experienced, and of these 62 (70%) considered themselves to be at low risk of HIV infection. Factors associated with self-rated risk of HIV included: type of school (p < .003), family structure (p < .008), being sexually experienced (p < .004), having had sex in the past three months (p < .009), having an extra sexual partner (p < .054) and non-condom use in last sexual intercourse (p < .001), but not the presence or type of social capital. The study found no association between bonding and bridging social networks on self-rated risk of HIV among study participants. However, sexually experienced participants rated themselves at low risk of HIV infection despite practicing unsafe sex. Efforts to raise adolescents' self-awareness of risk of HIV infection through life skills education and HIV/acquired immunodeficiency syndrome risk reduction strategies may be beneficial to students in this at-risk group

Hole dynamics and photoemission in a t-J model for SrCu_2(BO_3)_2

The motion of a single hole in a t-J model for the two-dimensional spin-gap compound SrCu_2(BO_3)_2 is investigated. The undoped Heisenberg model for this system has an exact dimer eigenstate and shows a phase transition between a dimerized and a Neel phase at a certain ratio of the magnetic couplings. We calculate the photoemission spectrum in the disordered phase using a generalized spin-polaron picture. By varying the inter-dimer hopping parameters we find a cross-over between a narrow quasiparticle band regime known from other strongly correlated systems and free-fermion behavior. The hole motion in the Neel-ordered phase is also briefly considered.Comment: 4 pages, 3 fig