Smooth empirical Bayes estimation of observation error variances in linear systems

A smooth empirical Bayes estimator was developed for estimating the unknown random scale component of each of a set of observation error variances. It is shown that the estimator possesses a smaller average squared error loss than other estimators for a discrete time linear system

Phase diagrams of period-4 spin chains consisting of three kinds of spins

We study a period-4 antiferromagnetic mixed quantum spin chain consisting of three kinds of spins. When the ground state is singlet, the spin magnitudes in a unit cell are arrayed as (s-t, s, s+t, s) with integer or half-odd integer s and t (0 <= t < s). The spin Hamiltonian is mapped onto a nonlinear sigma model (NLSM) in a previously developed method. The resultant NLSM includes only two independent parameters originating from four exchange constants for fixed s and t. The topological angle in the NLSM determines the gapless phase boundaries between disordered phases in the parameter space. The phase diagrams for various s and t shows rich structures. We systematically explain the phases in the singlet-cluster-solid picture.Comment: 8 pages (16 figures included

The mass-metallicity relation of Lyman-break analogues and its dependence on galaxy properties

We investigate the mass-metallicity relation and its dependence on galaxy physical properties with a sample of 703 Lyman-break analogues (LBAs) in local Universe, which have similar properties to high redshift star-forming galaxies. The sample is selected according to \ha luminosity, L(\ha)>10^{41.8}\,{\rm erg\,s^{-1}}, and surface brightness, I(\ha)>10^{40.5}\,{\rm erg\,s^{-1}\,kpc^{-2}}, criteria. The mass-metallicity relation of LBAs harmoniously agrees with that of star-forming galaxies at $z \sim$ 1.4-1.7 in stellar mass range of $10^{8.5}M_{\odot}<M_{*}<10^{11}M_{\odot}$. The relation between stellar mass, metallicity and star formation rate of our sample is roughly consistent with the local fundamental metallicity relation. We find that the mass-metallicity relation shows a strong correlation with the 4000\AA\, break; galaxies with higher 4000\AA\, break typically have higher metallicity at a fixed mass, by 0.06 dex in average. This trend is independent of the methodology of metallicity. We also use the metallicity estimated by $T_{\rm e}$-method to confirm it. The scatter in mass-metallicity relation can be reduced from 0.091 to 0.077 dex by a three-dimensional relation between stellar mass, metallicity and 4000\AA\, break. The reduction of scatter in mass-metallicity relation suggests that the galaxy stellar age plays an important role as the second parameter in the mass-metallicity relation of LBAs.Comment: 10 pages,8 figure

The structure of the Kac-Wang-Yan algebra

The Lie algebra $\mathcal{D}$ of regular differential operators on the circle has a universal central extension $\hat{\mathcal{D}}$. The invariant subalgebra $\hat{\mathcal{D}}^+$ under an involution preserving the principal gradation was introduced by Kac, Wang, and Yan. The vacuum $\hat{\mathcal{D}}^+$-module with central charge $c\in\mathbb{C}$, and its irreducible quotient $\mathcal{V}_c$, possess vertex algebra structures, and $\mathcal{V}_c$ has a nontrivial structure if and only if $c\in \frac{1}{2}\mathbb{Z}$. We show that for each integer $n>0$, $\mathcal{V}_{n/2}$ and $\mathcal{V}_{-n}$ are $\mathcal{W}$-algebras of types $\mathcal{W}(2,4,\dots,2n)$ and $\mathcal{W}(2,4,\dots, 2n^2+4n)$, respectively. These results are formal consequences of Weyl's first and second fundamental theorems of invariant theory for the orthogonal group $\text{O}(n)$ and the symplectic group $\text{Sp}(2n)$, respectively. Based on Sergeev's theorems on the invariant theory of $\text{Osp}(1,2n)$ we conjecture that $\mathcal{V}_{-n + 1/2}$ is of type $\mathcal{W}(2,4,\dots, 4n^2+8n+2)$, and we prove this for $n=1$. As an application, we show that invariant subalgebras of $\beta\gamma$-systems and free fermion algebras under arbitrary reductive group actions are strongly finitely generated.Comment: Final versio

Tunneling Conductance Between Parallel Two Dimensional Electron Systems

We derive and evaluate expressions for the low temperature {\it dc} equilibrium tunneling conductance between parallel two-dimensional electron systems. Our theory is based on a linear-response formalism and on impurity-averaged perturbation theory. The disorder broadening of features in the dependence of tunneling conductance on sheet densities and in-plane magnetic field strengths is influenced both by the finite lifetime of electrons within the wells and by non-momentum-conserving tunneling events. Disorder vertex corrections are important only for weak in-plane magnetic fields and strong interwell impurity-potential correlations. We comment on the basis of our results on the possibility of using tunneling measurements to determine the lifetime of electrons in the quantum wells.Comment: 14 pages, 5 Fig. not included, revtex, IUcm92-00

The Impact of Perceived Lottery Knowledge on Problem Lottery Playing: A Moderated Mediation Model

The study explored the mechanism of perceived lottery knowledge in predicting problem in lottery playing through a Moderated Mediation Model centering on overconfidence. A total of 972 Chinese football bettors from nine provinces completed a questionnaire survey. The result showed that: (1) perceived lottery knowledge could positively predict problem lottery playing; (2) perceived lottery knowledge influenced problem lottery playing directly and indirectly through overconfidence; (3) risk perception moderated the mediated path. The indirect effect was stronger for football bettors with low-risk perception than for those with high-risk perception. Implications of consumption and intervention for problem lottery players were discussed. &nbsp; &nbsp; Keywords: football bettors, problem lottery playing, perceived lottery knowledge, overconfidence, risk perceptio

Effect of fluctuating hydraulic retention time (HRT) on denitrification in the UASB reactors

© 2017 Elsevier B.V. This study cultivated denitrifying granular sludge in three up-flow anaerobic sludge blanket (UASB) reactors using different fluctuation hydraulic retention time (HRT) strategies (reactor 1 (RC): constant HRT (C-HRT); reactor 2 (RDF): downward fluctuation HRT (DF-HRT); and reactor 3 (RUF): upward fluctuation HRT (UF-HRT)). The results verified that these fluctuation HRT strategies could enhance microbial diversity, while robust against fluctuations in nutrient load of the denitrifying granular sludge. Microbial aggregates appeared in RC, RUF and RDF on days 22, 12 and 7, respectively. The sludge in RUF and RDF achieved complete granulation on days 22 and 14, respectively. Compared to the results of RC and RUF, the acyl homoserine lactones (AHLs) concentration rapidly increased, and changed the components of extracellular polymeric substances (EPS) resulted in the rapid formation of denitrifying granular sludge in RDF. These results demonstrate that microbial community, AHLs, EPS, and the denitrifying sludge granulation process were associated with each other. Informed from quorum sensing system, a mechanism for the granulation of denitrifying sludge using the DF-HRT strategy was proposed. The DF-HRT strategy is an economical and fast method to cultivate denitrifying granular sludge. We hope that the results of our research would provide some theoretical support for wastewater producing unstable plants