Unimodular integer circulants associated with trinomials

The n � n circulant matrix associated with the polynomial [image removed] (with d < n) is the one with first row (a0 ? ad 0 ? 0). The problem as to when such circulants are unimodular arises in the theory of cyclically presented groups and leads to the following question, previously studied by Odoni and Cremona: when is Res(f(t), tn-1) = �1? We give a complete answer to this question for trinomials f(t) = tm � tk � 1. Our main result was conjectured by the author in an earlier paper and (with two exceptions) implies the classification of the finite Cavicchioli?Hegenbarth?Repov? generalized Fibonacci groups, thus giving an almost complete answer to a question of Bardakov and Vesnin

Electron pockets and pseudogap asymmetry observed in the thermopower of underdoped cuprates

We calculate the diffusion thermoelectric power of high-Tc cuprates using the resonating-valence-bond spin-liquid model developed by Yang, Rice and Zhang (YRZ). In this model, reconstruction of the energy-momentum dispersion results in a pseudogap in the density of states that is heavily asymmetric about the Fermi level. The subsequent asymmetry in the spectral conductivity is found to account for the large magnitude and temperature dependence of the thermopower observed in underdoped cuprates. In addition we find evidence in experimental data for electron pockets in the Fermi surface, arising from a YRZ-like reconstruction, near the onset of the pseudogap in the slightly overdoped regime.Comment: 6 pages, 7 figures, accepted for publication in EP

Vortex Loop Phase Transitions in Liquid Helium, Cosmic Strings, and High-T_c Superconductors

The distribution of thermally excited vortex loops near a superfluid phase transition is calculated from a renormalized theory. The number density of loops with a given perimeter is found to change from exponential decay with increasing perimeter to algebraic decay as T_c is approached, in agreement with recent simulations of both cosmic strings and high-T_c superconductors. Predictions of the value of the exponent of the algebraic decay at T_c and of critical behavior in the vortex density are confirmed by the simulations, giving strong support to the vortex-folding model proposed by Shenoy.Comment: Version to appear in Phys. Rev. Lett, with a number of corrections and addition

The aspherical Cavicchioli-Hegenbarth-Repovš generalized Fibonacci groups

The Cavicchioli–Hegenbarth–Repovš generalized Fibonacci groups are defined by the presentations Gn (m, k) = 〈x 1, … , xn | xixi+m = xi+k (1 ⩽ i ⩽ n)〉. These cyclically presented groups generalize Conway's Fibonacci groups and the Sieradski groups. Building on a theorem of Bardakov and Vesnin we classify the aspherical presentations Gn (m, k). We determine when Gn (m, k) has infinite abelianization and provide sufficient conditions for Gn (m, k) to be perfect. We conjecture that these are also necessary conditions. Combined with our asphericity theorem, a proof of this conjecture would imply a classification of the finite Cavicchioli–Hegenbarth–Repovš groups

Spin Dynamics near the Superconductor-to-Insulator Transition in Impurity-Doped YBa2Cu4O8

We studied low-frequency spin dynamics near the impurity-induced superconductor-to-insulator transition for underdoped high-Tc superconductor YBa2(Cu1-xMx)4O8 (M=Ni, Zn) using the Cu nuclear quadrupole resonance (NQR) spin-echo technique. We observed remarkable suppression of the normal-state pseudo spin-gap and a loss of Cu NQR spectrum intensity at low temperatures around the critical impurity concentration.Comment: 6 pages, 4 figures. To be published in J. Phys. Soc. Jpn. Vol.70, No.7 (2001

Teenage Childbearing and Its Life Cycle Consequences: Exploiting a Natural Experiment

In this paper, we exploit a 'natural experiment' associated with human reproduction to identify the effect of teen childbearing on subsequent educational attainment, family structure, labor market outcomes and financial self-sufficiency. In particular, we exploit the fact that a substantial fraction of women who become pregnant experience a miscarriage (spontaneous abortion) and thus do not have a birth. If miscarriages were purely random and if miscarriages were the only way, other than by live births, that a pregnancy ended, then women, who had a miscarriage as a teen, would constitute an ideal control group with which to contrast teenage mothers. Exploiting this natural experiment, we devise an Instrumental Variables (IV) estimators for the consequences of teen mothers not delaying their childbearing, using data from the National Longitudinal Survey of Youth, 1979 (NLSY79). Our major finding is that many of the negative consequences of not delaying childbearing until adulthood are much smaller than has been estimated in previous studies. While we do find adverse consequences of teenage childbearing immediately following a teen mother's first birth, these negative consequences appear short- lived. By the time a teen mother reachers her late twenties, she appears to have only slightly more children, is only slightly more likely to be single mother, and has no lower levels of educational attainment than if she had delayed her childbearing to adulthood. In fact, by this age teen mothers appear to be better off in some aspects of their lives. Teenage childbearing appears to raise levels of labor supply, accumulated work experience and labor market earnings and appears to reduce the chances of living in poverty and participating in the associated social welfare programs. These estimated effects imply that the cost of teenage childbearing to U.S. taxpayers is negligible. In particular, our estimates imply that the widely held view that teenage childbearing imposes a substantial cost on government is an artifact of the failure to appropriately account for pre- existing socioeconomic differences between teen mothers and other women when estimating the causal effects of early childbearing. While teen mothers are very likely to live in poverty and experience other forms of adversity, our results imply that little of this would be changed just by getting teen mothers to delay their childbearing into adulthood.