E11E_{11}, Borcherds algebras and maximal supergravity

The dynamical $p$-forms of torus reductions of maximal supergravity theory have been shown some time ago to possess remarkable algebraic structures. The set ("dynamical spectrum") of propagating $p$-forms has been described as a (truncation of a) real Borcherds superalgebra \mf{V}_D that is characterized concisely by a Cartan matrix which has been constructed explicitly for each spacetime dimension $11 \geq D \geq 3.$ In the equations of motion, each differential form of degree $p$ is the coefficient of a (super-) group generator, which is itself of degree $p$ for a specific gradation (the \mf{V}-gradation). A slightly milder truncation of the Borcherds superalgebra enables one to predict also the "spectrum" of the non-dynamical $(D - 1)$ and $D$-forms. The maximal supergravity $p$-form spectra were reanalyzed more recently by truncation of the field spectrum of $E_{11}$ to the $p$-forms that are relevant after reduction from 11 to $D$ dimensions. We show in this paper how the Borcherds description can be systematically derived from the split ("maximally non compact") real form of $E_{11}$ for $D \geq 1.$ This explains not only why both structures lead to the same propagating $p$-forms and their duals for $p\leq (D - 2),$ but also why one obtains the same $(D - 1)$-forms and "top" $D$-forms. The Borcherds symmetries \mf{V}_2 and \mf{V}_1 are new too. We also introduce and use the concept of a presentation of a Lie algebra that is covariant under a given subalgebra.Comment: 39 pages. Version 2 contains improved presentation in particular an extra appendix B giving details on the infinite rank limit possibility. Version to appear in JHE

CO-PARENTING FACTORS THAT CONTRIBUTE TO ACADEMIC SUCCESS

This study assessed factors contributed from parents who live in two different households and that lead to academic success. Data were collected from undergraduates enrolled in a Midwestern satellite university. Academic success was defined by university enrollment, grade point average, and standardized testing scores. Co-parenting factors that were hypothesized to lead to academic success included the distance between parents homes (which further influenced time spent with the child, participation in child‘s activities, and participation in decision making) and financial stability (which also influenced participation in decision making and the level of conflict within the family). The original structural equation model revealed that the relationship linking the distance between homes and the time spent with the child was accurately described. Added to the model, after the Lagrange test, was a path from finances to participation in child‘s activities and time spent with the child. The financial stability of a family predicted the participation of the non-custodial parent in the child‘s activities, in the decision-making for the child, conflict, and the time spent with the child. Implications for practitioners who work with families with co-parenting responsibilities are discussed

CO-PARENTING FACTORS THAT CONTRIBUTE TO ACADEMIC SUCCESS

This study assessed factors contributed from parents who live in two different households and that lead to academic success. Data were collected from undergraduates enrolled in a Midwestern satellite university. Academic success was defined by university enrollment, grade point average, and standardized testing scores. Co-parenting factors that were hypothesized to lead to academic success included the distance between parents homes (which further influenced time spent with the child, participation in child‘s activities, and participation in decision making) and financial stability (which also influenced participation in decision making and the level of conflict within the family). The original structural equation model revealed that the relationship linking the distance between homes and the time spent with the child was accurately described. Added to the model, after the Lagrange test, was a path from finances to participation in child‘s activities and time spent with the child. The financial stability of a family predicted the participation of the non-custodial parent in the child‘s activities, in the decision-making for the child, conflict, and the time spent with the child. Implications for practitioners who work with families with co-parenting responsibilities are discussed

Tunable Conductivity and Conduction Mechanism in a UV light activated electronic conductor

A tunable conductivity has been achieved by controllable substitution of a novel UV light activated electronic conductor. The transparent conducting oxide system H-doped Ca12-xMgxAl14O33 (x = 0; 0.1; 0.3; 0.5; 0.8; 1.0) presents a conductivity that is strongly dependent on the substitution level and temperature. Four-point dc-conductivity decreases with x from 0.26 S/cm (x = 0) to 0.106 S/cm (x = 1) at room temperature. At each composition the conductivity increases (reversibly with temperature) until a decomposition temperature is reached; above this value, the conductivity drops dramatically due to hydrogen recombination and loss. The observed conductivity behavior is consistent with the predictions of our first principles density functional calculations for the Mg-substituted system with x=0, 1 and 2. The Seebeck coefficient is essentially composition- and temperature-independent, the later suggesting the existence of an activated mobility associated with small polaron conduction. The optical gap measured remains constant near 2.6 eV while transparency increases with the substitution level, concomitant with a decrease in carrier content.Comment: Submitted for publicatio

ALMA Observations of a Quiescent Molecular Cloud in the Large Magellanic Cloud

We present high-resolution (sub-parsec) observations of a giant molecular cloud in the nearest star-forming galaxy, the Large Magellanic Cloud. ALMA Band 6 observations trace the bulk of the molecular gas in $^{12}$CO(2-1) and high column density regions in $^{13}$CO(2-1). Our target is a quiescent cloud (PGCC G282.98-32.40, which we refer to as the "Planck cold cloud" or PCC) in the southern outskirts of the galaxy where star-formation activity is very low and largely confined to one location. We decompose the cloud into structures using a dendrogram and apply an identical analysis to matched-resolution cubes of the 30 Doradus molecular cloud (located near intense star formation) for comparison. Structures in the PCC exhibit roughly 10 times lower surface density and 5 times lower velocity dispersion than comparably sized structures in 30 Dor, underscoring the non-universality of molecular cloud properties. In both clouds, structures with relatively higher surface density lie closer to simple virial equilibrium, whereas lower surface density structures tend to exhibit super-virial line widths. In the PCC, relatively high line widths are found in the vicinity of an infrared source whose properties are consistent with a luminous young stellar object. More generally, we find that the smallest resolved structures ("leaves") of the dendrogram span close to the full range of line widths observed across all scales. As a result, while the bulk of the kinetic energy is found on the largest scales, the small-scale energetics tend to be dominated by only a few structures, leading to substantial scatter in observed size-linewidth relationships.Comment: Accepted by ApJ; 21 pages in AASTeX two-column styl

Dust and gas in the magellanic clouds from the heritage Herschel Key Project. I. Dust properties and insights into the origin of the submillimeter excess emission

The dust properties in the Large and Small Magellanic clouds (LMC/SMC) are studied using the HERITAGE Herschel Key Project photometric data in five bands from 100 to 500 μm. Three simple models of dust emission were fit to the observations: a single temperature blackbody modified by a power-law emissivity (SMBB), a single temperature blackbody modified by a broken power-law emissivity (BEMBB), and two blackbodies with different temperatures, both modified by the same power-law emissivity (TTMBB). Using these models, we investigate the origin of the submillimeter excess, defined as the submillimeter emission above that expected from SMBB models fit to observations <200 μm. We find that the BEMBB model produces the lowest fit residuals with pixel-averaged 500 μm submillimeter excesses of 27% and 43% for the LMC and SMC, respectively. Adopting gas masses from previous works, the gas-to-dust ratios calculated from our fitting results show that the TTMBB fits require significantly more dust than are available even if all the metals present in the interstellarmedium (ISM) were condensed into dust. This indicates that the submillimeter excess ismore likely to be due to emissivity variations than a second population of colder dust. We derive integrated dust masses of (7.3 ± 1.7) × 105 and (8.3 ± 2.1) × 104 M⊙ for the LMC and SMC, respectively. We find significant correlations between the submillimeter excess and other dust properties; further work is needed to determine the relative contributions of fitting noise and ISM physics to the correlation

Dust and gas in the magellanic clouds from the heritage herschel key project. II. Gas-to-dust ratio variations across interstellar medium phases

The spatial variations of the gas-to-dust ratio (GDR) provide constraints on the chemical evolution and lifecycle of dust in galaxies. We examine the relation between dust and gas at 10-50 pc resolution in the Large and Small Magellanic Clouds (LMC and SMC) based on Herschel far-infrared (FIR), HI 21 cm, CO, and Hiα observations. In the diffuse atomic interstellar medium (ISM), we derive the GDR as the slope of the dust-gas relation and find GDRs of 380-130+250 ± 3 in the LMC, and 1200-420+1600 ± 120 in the SMC, not including helium. The atomic-to-molecular transition is located at dust surface densities of 0.05 M⊙ pc-2 in the LMC and 0.03 M⊙ pc-2 in the SMC, corresponding to AV ∼ 0.4 and 0.2, respectively. We investigate the range of CO-to-H2 conversion factor to best account for all the molecular gas in the beam of the observations, and find upper limits on XCO to be 6 × 1020 cm-2 K-1 km-1 s in the LMC (Z = 0.5 Z⊙) at 15 pc resolution, and 4 × 1021 cm-2 K-1 km-1 s in the SMC (Z = 0.2 Z⊙) at 45 pc resolution. In the LMC, the slope of the dust-gas relation in the dense ISM is lower than in the diffuse ISM by a factor ∼2, even after accounting for the effects of CO-dark H2 in the translucent envelopes of molecular clouds. Coagulation of dust grains and the subsequent dust emissivity increase in molecular clouds, and/or accretion of gas-phase metals onto dust grains, and the subsequent dust abundance (dust-to-gas ratio) increase in molecular clouds could explain the observations. In the SMC, variations in the dust-gas slope caused by coagulation or accretion are degenerate with the effects of CO-dark H2. Within the expected 5-20 times Galactic XCO range, the dust-gas slope can be either constant or decrease by a factor of several across ISM phases. Further modeling and observations are required to break the degeneracy between dust grain coagulation, accretion, and CO-dark H2. Our analysis demonstrates that obtaining robust ISM masses remains a non-trivial endeavor even in the local Universe using state-of-the-art maps of thermal dust emissio