The spin-half Heisenberg antiferromagnet on two Archimedian lattices: From the bounce lattice to the maple-leaf lattice and beyond

We investigate the ground state of the two-dimensional Heisenberg antiferromagnet on two Archimedean lattices, namely, the maple-leaf and bounce lattices as well as a generalized $J$-$J'$ model interpolating between both systems by varying $J'/J$ from $J'/J=0$ (bounce limit) to $J'/J=1$ (maple-leaf limit) and beyond. We use the coupled cluster method to high orders of approximation and also exact diagonalization of finite-sized lattices to discuss the ground-state magnetic long-range order based on data for the ground-state energy, the magnetic order parameter, the spin-spin correlation functions as well as the pitch angle between neighboring spins. Our results indicate that the "pure" bounce ($J'/J=0$) and maple-leaf ($J'/J=1$) Heisenberg antiferromagnets are magnetically ordered, however, with a sublattice magnetization drastically reduced by frustration and quantum fluctuations. We found that magnetic long-range order is present in a wide parameter range $0 \le J'/J \lesssim J'_c/J$ and that the magnetic order parameter varies only weakly with $J'/J$. At $J'_c \approx 1.45 J$ a direct first-order transition to a quantum orthogonal-dimer singlet ground state without magnetic long-range order takes place. The orthogonal-dimer state is the exact ground state in this large-$J'$ regime, and so our model has similarities to the Shastry-Sutherland model. Finally, we use the exact diagonalization to investigate the magnetization curve. We a find a 1/3 magnetization plateau for $J'/J \gtrsim 1.07$ and another one at 2/3 of saturation emerging only at large $J'/J \gtrsim 3$.Comment: 9 pages, 10 figure

Resolved Spectroscopy of the Narrow-Line Region in NGC 1068. II. Physical Conditions Near the NGC 1068 ``Hot-Spot''

The physical conditions near the optical continuum peak (``hot spot'') in the inner narrow line region (NLR) of the Seyfert 2 galaxy, NGC 1068. Spectra were taken with HST/STIS through the 0.1X52 arcsec slit, covering the full STIS 1200 to 10000 Angstrom waveband, and are from a region that includes the hot spot, extending 0.2, or ~ 14 pc (for H= 75 km/sec/Mpc). Perhaps the most striking feature of these spectra is the presence of strong coronal emission lines, including [S XII] 7611 which has hitherto only been identified in spectra of the solar corona. There is an apparent correlation between ionization energy and velocity of the emission lines with respect to the systemic velocity of the host galaxy, with the coronal lines blueshifted, most other high excitation lines near systemic, and some of the low ionization lines redshifted. From the results of our modeling, we find that the emission-line gas consists of three principal components: 1) one in which most of the strong emission-lines, such as [O III] 5007, [Ne V] 3426, C IV 1550, arise, 2) a more tenuous, highly ionized component, which is the source of the coronal-line emission, and 3) a component, which is not co-planar with the other two, in which the low ionization and neutral lines, such as [N II] 6548 and [O I] 6300, are formed. The first two components are directly ionized by the EUV-Xray continuum emitted by the central source, while the low ionization gas is ionized by a combination of highly absorbed continuum radiation and a small fraction of unabsorbed continuum scattered by free electrons associated with the hot spot. The combination of covering factor and Thomson optical depth of the high ionization components is insufficient to scatter the observed fraction of continuum radiation into our line-of-sight.Comment: 42 pages, Latex, includes 5 figures (postscript), to appear in the Astrophysical Journa

From structure topology to chemical composition. XX. Titanium silicates : The crystal structure of hejtmanite, Ba2Mn4Ti2(Si2O7)2O2(OH)2F2, a Group-II TS-block mineral

The crystal structure of hejtmanite, Ba2Mn4Ti2(Si2O7)2O2(OH)2F2, from Mbolve Hill, Mkushi River area, Central Province, Zambia (holotype material) has been refined on a twinned crystal to R1 = 1.88% on the basis of 4539 [|F| > 4\u3c3|F|] reflections. Hejtmanite is triclinic, C-1, a = 10.716(2), b = 13.795(3), c = 11.778 (2) \uc5, \u3b1 = 90.07(3), \u3b2 = 112.24(3),\u3b3= 90.03(3)\ub0, V = 1612(2) \uc53. Chemical analysis (electron microprobe) gives: Ta2O5 0.09, Nb2O5 1.27, ZrO2 0.65, TiO2 14.35, SiO2 23.13, BaO 26.68, SrO 0.19, FeO 11.28, MnO 15.12, Cs2O 0.05, K2O 0.33, F 3.82, H2Ocalc. 1.63, O = F-1.61, total 97.10 wt.%, where the H2O content was calculated from the crystal-structure refinement, with (OH + F) = 4 apfu. The empirical formula, calculated on the basis of 20 (O + F) anions, is of the form AP2 MO4 MH2 (Si2O7)2(XO)4(XP)2, Z=4: (Ba1.82K0.07 Sr0.02)\u3a31.91(Mn2.33Fe21 1:65Zr0.04Mg0.03)\u3a33.95(Ti1.88Nb0.10Zr0.02)\u3a32(Si2.02O7)2O2[(OH)1.89 F0.11]\u3a32F2. The crystal structure is a combination of a TS (Titanium Silicate) block and an I (intermediate) block. The TS block consists of HOH sheets (H-heteropolyhedral, O-octahedral). The topology of the TS block is as in Group-II TS-block minerals: Ti (+ Nb) = 2 apfu per (Si2O7)2 [as defined by Sokolova (2006)]. In the O sheet, five [6]MO sites are occupied mainly by Mn, less Fe2+ and minor Zr and Mg, with = 2.198 \uc5 (\u3c6 = O,OH), ideally giving Mn4 apfu. In the H sheet, two [6]MH sites are occupied mainly by Ti, with = 1.962 \uc5 (\u3c6 = O,F), ideally giving Ti2 apfu; four [4]Si sites are occupied by Si, with = 1.625 \uc5. TheMH octahedra and Si2O7 groups constitute the H sheet. The two [12]Ba-dominant AP(1,2) sites, with = 2.984 \uc5 (\u3c6 = O, F), ideally give Ba2 apfu. Two XOM(1,2) and two XOA (1,2) sites are occupied by O atoms and OH groups with minor F, respectively, ideally giving (XO)4 = (XM O)2 + (XAO)2=O2(OH)2 pfu. Two XP M(1,2) sites are occupied by F, giving F2 apfu. TS blocks link via a layer of Ba atoms which constitute the I block. Simplified and end-member formulae of hejtmanite are Ba2(Mn,Fe2+)4Ti2 (Si2O7)2O2(OH,F)2 F2 and Ba2Mn4Ti2(Si2O7)2O2(OH)2F2, Z = 4. Hejtmanite is a Mn-analogue of bafertisite, Ba2Fe2+4 Ti2(Si2O7)2O2(OH)2F2

Intergenerational change and familial aggregation of body mass index

The relationship between parental BMI and that of their adult offspring, when increased adiposity can become a clinical issue, is unknown. We investigated the intergenerational change in body mass index (BMI) distribution, and examined the sex-specific relationship between parental and adult offspring BMI. Intergenerational change in the distribution of adjusted BMI in 1,443 complete families (both parents and at least one offspring) with 2,286 offspring (1,263 daughters and 1,023 sons) from the west of Scotland, UK, was investigated using quantile regression. Familial correlations were estimated from linear mixed effects regression models. The distribution of BMI showed little intergenerational change in the normal range (\25 kg/m2), decreasing overweightness (25– \30 kg/m2) and increasing obesity (C30 kg/m2). Median BMI was static across generations in males and decreased in females by 0.4 (95% CI: 0.0, 0.7) kg/m2; the 95th percentileincreased by 2.2 (1.1, 3.2) kg/m2 in males and 2.7 (1.4, 3.9) kg/m2 in females. Mothers’ BMI was more strongly associated with daughters’ BMI than was fathers’ (correlation coefficient (95% CI): mothers 0.31 (0.27, 0.36), fathers 0.19 (0.14, 0.25); P = 0.001). Mothers’ and fathers’ BMI were equally correlated with sons’ BMI (correlation coefficient: mothers 0.28 (0.22, 0.33), fathers 0.27 (0.22, 0.33). The increase in BMI between generations was concentrated at the upper end of the distribution. This, alongside the strong parent-offspring correlation, suggests that the increase in BMI is disproportionally greater among offspring of heavier parents. Familial influences on BMI among middle-aged women appear significantly stronger from mothers than father

From structure topology to chemical composition. XXIII. Revision of the crystal structure and chemical formula of zvyaginite, Na2ZnTiNb2(Si2O7)2O2(OH)2(H2O)4, a seidozerite-supergroup mineral from the Lovozero alkaline massif, Kola peninsula, Russia

The crystal structure and chemical formula of zvyaginite, ideally Na2ZnTiNb2(Si2O7)2O2(OH)2(H2O)4, a lamprophyllite-group mineral of the seidozerite supergroup from the type locality, Mt. Malyi Punkaruaiv, Lovozero alkaline massif, Kola Peninsula, Russia have been revised. The crystal structurewas refined with a new origin in space group C1, a = 10.769(2), b = 14.276(3), c = 12.101(2) \uc5, \u3b1 = 105.45(3), \u3b2 = 95.17(3), \u3b3 = 90.04(3)\ub0, V = 1785.3(3.2) \uc53, R1 = 9.23%. The electron-microprobe analysis gave the following empirical formula [calculated on 22 (O + F)]: (Na0.75Ca0.09K0.04 \u25a11.12)\u3c32 (Na1.12Zn0.88Mn0.17Fe2+ 0.04 \u25a10.79)\u3c33 (Nb1.68Ti1.25Al0.07)\u3c33 (Si4.03O14)O2 [(OH)1.11F0.89]\u3c32(H2O)4, Z = 4. Electron-diffraction patterns have prominent streaking along c 17and HRTEM images show an intergrowth of crystalline zvyaginite with two distinct phases, both of which are partially amorphous. The crystal structure of zvyaginite is an array of TS (Titanium-Silicate) blocks connected via hydrogen bonds between H2O groups. The TS block consists of HOH sheets (H = heteropolyhedral, O = octahedral) parallel to (001). In the O sheet, the [6]MH(1,5) sites are occupied mainly by Ti, Zn and Na and the [6]MO(2,3) sites are occupied by Na at less than 50%. In the H sheet, the [6]MH(1,2) sites are occupied mainly by Nb and the [8]AP(1) and [8]AP(2) sites are occupied mainly by Na and \u25a1. The MH and AP polyhedra and Si2O7 groups constitute the H sheet. The ideal structural formula is Na Nb2NaZnTi(Si2O7)2O2(OH)2(H2O)4. Zvyaginite is a Zn-bearing and Na-poor analogue of epistolite, ideally (Na)Nb2Na3Ti(Si2O7)2O2(OH)2(H2O)4. Epistolite and zvyaginite are related by the following substitution in the O sheet of the TS-block: (Na+ 2 )epi\u2194Zn2+ zvy +\u25a1zvy. The doubling of the t1 and t2 translations of zvyaginite relative to those of epistolite is due to the order of Zn and Na along a (t1) and b (t2) in the O sheet of zvyaginite

Transonic small-disturbance theory for lightly loaded cascades

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76863/1/AIAA-7841-736.pd

Relation between coronary risk and coronary mortality in women of the Renfrew and Paisley survey: comparison with men

Most epidemiological and intervention studies in patients with coronary artery disease have focused on men, the assumption being that such data can be extrapolated to women. However, there is little evidence to support this belief. We have completed a fifteen-year follow-up of 15 399 adults, including 8262 women, who lived in Renfrew and Paisley and were aged 45-64 years when screened between 1972 and 1976. We identified 490 deaths from coronary heart disease (CHD) in women and 878 in men. Women were more likely to have high cholesterol, to be obese, and to come from lower social classes than men, but they smoked less and had similar blood pressures. The relative risk--top to bottom quintile (95% Cl)--of cholesterol for coronary death after adjustment for all other risk markers was slightly greater in women (1[middle dot]77 [1[middle dot]45, 2[middle dot]16]) than in men (1[middle dot]56 [1[middle dot]32, 1[middle dot]85]), but absolute and attributable risk were lower. Thus, women in the top quintile for cholesterol had lower coronary mortality (6[middle dot]1 deaths per thousand patient years) than men in the bottom quintile (6[middle dot]8 deaths per thousand patient years). Moreover, it was estimated that there would have been only 103 (21 %) fewer CH D deaths in women, yet 211 (24%) fewer in men, if mortality had been the same for women and men in the lowest quintiles of cholesterol. Trends showing similar relative risks in these women, but lower absolute and attributable risks than in men, were present for smoking, diastolic blood pressure, and social class. There was no relation between obesity and coronary death after adjustment for other risks. Our results suggest that some other factors protect women against CHD. The potential for women to reduce their risk of CH D by changes in lifestyle may be less than for men.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/30146/1/0000523.pd

Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism

This essay examines the philosophical significance of $\Omega$-logic in Zermelo-Fraenkel set theory with choice (ZFC). The duality between coalgebra and algebra permits Boolean-valued algebraic models of ZFC to be interpreted as coalgebras. The modal profile of $\Omega$-logical validity can then be countenanced within a coalgebraic logic, and $\Omega$-logical validity can be defined via deterministic automata. I argue that the philosophical significance of the foregoing is two-fold. First, because the epistemic and modal profiles of $\Omega$-logical validity correspond to those of second-order logical consequence, $\Omega$-logical validity is genuinely logical, and thus vindicates a neo-logicist conception of mathematical truth in the set-theoretic multiverse. Second, the foregoing provides a modal-computational account of the interpretation of mathematical vocabulary, adducing in favor of a realist conception of the cumulative hierarchy of sets