The Asymptotic distribution of circles in the orbits of Kleinian groups

Let P be a locally finite circle packing in the plane invariant under a non-elementary Kleinian group Gamma and with finitely many Gamma-orbits. When Gamma is geometrically finite, we construct an explicit Borel measure on the plane which describes the asymptotic distribution of small circles in P, assuming that either the critical exponent of Gamma is strictly bigger than 1 or P does not contain an infinite bouquet of tangent circles glued at a parabolic fixed point of Gamma. Our construction also works for P invariant under a geometrically infinite group Gamma, provided Gamma admits a finite Bowen-Margulis-Sullivan measure and the Gamma-skinning size of P is finite. Some concrete circle packings to which our result applies include Apollonian circle packings, Sierpinski curves, Schottky dances, etc.Comment: 31 pages, 8 figures. Final version. To appear in Inventiones Mat

Partition Column Chromatography for Quantitating Effects of Fertilization on Plant Acids

A method for determining organic acid levels in biological materials by silica gel partition column chromatography (pcc) is described. It uses tetrabromophenolphthalein ethyl ester, which has a high molar absorbency, for quantitating the acids in the column effluent. The concentrations of several organic acids were determined in two species of crested wheatgrass, Nordan (Agropyron desertorum) and Fairway (A. cristatum), grown. under different conditions of K fertilization. For comparison, aconitic, citric, and malic acids were also determined by polarography, spectrophotometry, and fluorometry, respectively. Results obtained by these methods agreed with the data obtained by pcc. The concentration of trans-aconitic acid averaged about 96 and 21 mequiv/kg of dry matter in Nordan and Fairway, respectively, when grown in the greenhouse without K. K fertilization (312 kg/ha) approximately doubled the trans-aconitic acid concentration in both species. Fairway contained 363 mequiv/kg of malic acid, while Nordan contained 280 mequiv/kg. K fertilization increased these concentrations to 611 and 446 mequiv/kg, respectively. Citric acid was increased by K fertilization, but there was no significant difference between species and in no case was the citric acid concentration greater than 80 mequiv/kg of dry matter

Exchange coupling in CaMnO3_3 and LaMnO3_3: configuration interaction and the coupling mechanism

The equilibrium structure and exchange constants of CaMnO$_3$ and LaMnO$_3$ have been investigated using total energy unrestricted Hartree-Fock (UHF) and localised orbital configuration interaction (CI) calculations on the bulk compounds and Mn$_2$O$_{11}^{14-}$ and Mn$_2$O$_{11}^{16-}$ clusters. The predicted structure and exchange constants for CaMnO$_3$ are in reasonable agreement with estimates based on its N\'eel temperature. A series of calculations on LaMnO$_3$ in the cubic perovskite structure shows that a Hamiltonian with independent orbital ordering and exchange terms accounts for the total energies of cubic LaMnO$_3$ with various spin and orbital orderings. Computed exchange constants depend on orbital ordering. UHF calculations tend to underestimate exchange constants in LaMnO$_3$, but have the correct sign when compared with values obtained by neutron scattering; exchange constants obtained from CI calculations are in good agreement with neutron scattering data provided the Madelung potential of the cluster is appropriate. Cluster CI calculations reveal a strong dependence of exchange constants on Mn d e$_g$ orbital populations in both compounds. CI wave functions are analysed in order to determine which exchange processes are important in exchange coupling in CaMnO$_3$ and LaMnO$_3$.Comment: 25 pages and 9 postscript figure

Geniculo-Cortical Projection Diversity Revealed within the Mouse Visual Thalamus

This is the final version of the article. It was first available from PLOS via http://dx.doi.org/10.1371/journal.pone.0144846All dLGN cell co-ordinates, V1 injection sites, dLGN boundary coordinates, experimental protocols and analysis scripts are available for download from figshare at https://figshare.com/s/36c6d937b1844eec80a1.The mouse dorsal lateral geniculate nucleus (dLGN) is an intermediary between retina and primary visual cortex (V1). Recent investigations are beginning to reveal regional complexity in mouse dLGN. Using local injections of retrograde tracers into V1 of adult and neonatal mice, we examined the developing organisation of geniculate projection columns: the population of dLGN-V1 projection neurons that converge in cortex. Serial sectioning of the dLGN enabled the distribution of labelled projection neurons to be reconstructed and collated within a common standardised space. This enabled us to determine: the organisation of cells within the dLGN-V1 projection columns; their internal organisation (topology); and their order relative to V1 (topography). Here, we report parameters of projection columns that are highly variable in young animals and refined in the adult, exhibiting profiles consistent with shell and core zones of the dLGN. Additionally, such profiles are disrupted in adult animals with reduced correlated spontaneous activity during development. Assessing the variability between groups with partial least squares regression suggests that 4?6 cryptic lamina may exist along the length of the projection column. Our findings further spotlight the diversity of the mouse dLGN?an increasingly important model system for understanding the pre-cortical organisation and processing of visual information. Furthermore, our approach of using standardised spaces and pooling information across many animals will enhance future functional studies of the dLGN.Funding was provided by a Wellcome Trust grant jointly awarded to IDT and SJE (083205, www.wellcome.ac.uk), and by MRC PhD Studentships awarded to MNL and ACH (http://www.mrc.ac.uk/)

Production and Decay of D_1(2420)^0 and D_2^*(2460)^0

We have investigated $D^{+}\pi^{-}$ and $D^{*+}\pi^{-}$ final states and observed the two established $L=1$ charmed mesons, the $D_1(2420)^0$ with mass $2421^{+1+2}_{-2-2}$ MeV/c$^{2}$ and width $20^{+6+3}_{-5-3}$ MeV/c$^{2}$ and the $D_2^*(2460)^0$ with mass $2465 \pm 3 \pm 3$ MeV/c$^{2}$ and width $28^{+8+6}_{-7-6}$ MeV/c$^{2}$. Properties of these final states, including their decay angular distributions and spin-parity assignments, have been studied. We identify these two mesons as the $j_{light}=3/2$ doublet predicted by HQET. We also obtain constraints on {\footnotesize $\Gamma_S/(\Gamma_S + \Gamma_D)$} as a function of the cosine of the relative phase of the two amplitudes in the $D_1(2420)^0$ decay.Comment: 15 pages in REVTEX format. hardcopies with figures can be obtained by sending mail to: [email protected]

Measurement of the branching fraction for Υ(1S)→τ+τ−\Upsilon (1S) \to \tau^+ \tau^-

We have studied the leptonic decay of the $\Upsilon (1S)$ resonance into tau pairs using the CLEO II detector. A clean sample of tau pair events is identified via events containing two charged particles where exactly one of the particles is an identified electron. We find $B(\Upsilon(1S) \to \tau^+ \tau^-) = (2.61~\pm~0.12~{+0.09\atop{-0.13}})$. The result is consistent with expectations from lepton universality.Comment: 9 pages, RevTeX, two Postscript figures available upon request, CLNS 94/1297, CLEO 94-20 (submitted to Physics Letters B

Measurement of the Decay Asymmetry Parameters in Λc+→Λπ+\Lambda_c^+ \to \Lambda\pi^+ and Λc+→Σ+π0\Lambda_c^+ \to \Sigma^+\pi^0

We have measured the weak decay asymmetry parameters (\aLC ) for two \LC\ decay modes. Our measurements are \aLC = -0.94^{+0.21+0.12}_{-0.06-0.06} for the decay mode $\Lambda_c^+ \to \Lambda\pi^+$ and \aLC = -0.45\pm 0.31 \pm 0.06 for the decay mode $\Lambda_c \to \Sigma^+\pi^0$. By combining these measurements with the previously measured decay rates, we have extracted the parity-violating and parity-conserving amplitudes. These amplitudes are used to test models of nonleptonic charmed baryon decay.Comment: 11 pages including the figures. Uses REVTEX and psfig macros. Figures as uuencoded postscript. Also available as http://w4.lns.cornell.edu/public/CLNS/1995/CLNS95-1319.p