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The aim of this paper is the Ore extension of group-cograded Hopf coquasigroups. This paper first shows a categorical interpretation and some examples of group-cograded Hopf coquasigroups, and then gives a necessary and sufficient conditions for the Ore extensions of group-cograded Hopf coquasigroups to be group-cograded Hopf coquasigroups. Finally, a certain isomorphism between Ore extensions are considered., Comment: 15pages

In this paper, we generalizing the main result in Liu[10] to weak Hopf coquasigroups case. We first define and study group-cograded weak Hopf quasigroups, which generalize both group-cograded Hopf quasigroups and weak Hopf group-coalgebras. Then we introduce the notion of p-Yetter-Drinfeld weak quasimodule over group-cograded weak Hopf quasigroups H. If the antipode of H is bijective, we show that the category YDWQ(H) of Yetter-Drinfeld weak quasimodules over H is a crossed category, and the subcategory YD(H) of Yetter-Drinfeld modules is a braided crossed category., Comment: 19pages

We present studies on crystal structure and ionic diffusion behaviors of superionic Cu$_{2-\delta}$Se ($\delta$=0, 0.04, and 0.2) by utilizing neutron powder diffraction and quasi-elastic neutron scattering. In the superionic phase, the structural model with Cu ions occupying the Wyckoff sites of 8$c$ and 32$f$ provides the best description of the structure. As the content of Cu increasing in Cu$_{2-\delta}$Se, the Cu occupancy increases on the 32$f$ site, but decreases on the 8$c$ site . Fitting to the quasi-elastic neutron scattering spectra reveals two diffusion modes, the localized diffusion between the 8$c$ and 32$f$ sites and the long-range diffusion between the adjacent 8$c$ sites using the 32$f$ site as a bypass, respectively. Between 430 and 650 K, we measured that the compound with more Cu content exhibits a larger long-range diffusion coefficient. Temperature in this range does not affect the long-range diffusion process obviously. Our results suggest the two diffusion modes cooperative and thus provide a microscopic understanding of the ionic diffusion of the Cu ions in superionic Cu$_{2-\delta}$Se., Comment: 6 pages, 3 figures

For a class of $\Lambda$-Fleming-Viot processes with Brownian spatial motion in $\mathbb{R}^d$ whose associated $\Lambda$-coalescents come down from infinity, we obtain sharp global and local modulus of continuities for the ancestry processes recovered from the lookdown representations. As applications, we prove both global and local modulus of continuities for the $\Lambda$-Fleming-Viot support processes. In particular, if the $\Lambda$-coalescent is the Beta$(2-\beta,\beta)$ coalescent for $\beta\in(1,2]$ with $\beta=2$ corresponding to Kingman's coalescent, then for $h(t)=\sqrt{t\log (1/t)}$, the global modulus of continuity holds for the support process with modulus function $\sqrt{2\beta/(\beta-1)}h(t)$, and both the left and right local modulus of continuities hold for the support process with modulus function $\sqrt{2/(\beta-1)}h(t)$., Comment: 27 pages

Let $H$ be a crossed group-cograded Hopf quasigroup. We first introduce the notion of $p$-Yetter-Drinfeld quasimodule over $H$. If the antipode of $H$ is bijective, we show that the category $\mathscr Y\mathscr D\mathscr Q(H)$ of Yetter-Drinfeld quasimodules over $H$ is a crossed category, and the subcategory $\mathscr Y\mathscr D(H)$ of Yetter-Drinfeld modules is a braided crossed category., Comment: 19pages. Add a mirror structure and modify some typos. Comments are welcomed

A system of mutually interacting superprocesses with migration is constructed as the limit of a sequence of branching particle systems arising from population models. The uniqueness in law of the superprocesses is established using the pathwise uniqueness of a system of stochastic partial differential equations with non-Lipschitz coefficients, which is satisfied by the corresponding system of distribution-function-valued processes., Comment: 19 pages

A generalized stepping stone model with $\Xi$-resampling mechanism is a two dimensional probability-measure-valued stochastic process whose moment dual is similar to that of the classical stepping stone model except that Kingman's coalescent is replaced by $\Xi$-coalescent. We prove the existence of such a process by specifying its moments using the dual function-valued $\Xi$-coalescent process with geographical labels and migration, and then verifying a multidimensional Hausdorff moment problem. We also characterize the stationary distribution of the generalized stepping stone model and show that it is not reversible if the mutation operator is of uniform jump-type., Comment: 19 pages

The Progress in International Reading Literacy Study (PIRLS) is an international assessment of student performance in reading literacy at the fourth grade. PIRLS measures students in the fourth year of formal schooling because this is typically when students' learning transitions from a focus on "learning to read" to a focus on "reading to learn." PIRLS is a collaborative effort between participating countries and the International Association for the Evaluation of Educational Achievement (IEA). Administered every 5 years since 2001, PIRLS 2016 marks the survey's fourth administration. The current administration also provides the first results for ePIRLS: a computer-based extension of PIRLS designed to assess students' comprehension of online information. In 2016, some 58 education systems3 participated in the PIRLS assessment at the fourth year of formal schooling and 16 of these systems also participated in ePIRLS. The PIRLS framework focuses on two key content domains: purposes for reading and processes of comprehension. There are two key purposes for reading: reading for literary experience and reading to acquire and use information. The new ePIRLS is an innovative, computer-based assessment of online reading. It is designed to measure students' approaches to informational reading in an online environment. This report summarizes performance on PIRLS and ePIRLS 2016 from a U.S. perspective. PIRLS results are based on nationally representative samples of fourth-graders. The international data reported for PIRLS 2016 in this report cover 58 countries or other education systems, including the United States.

Two-dimensional (2D) layered materials emerge in recent years as a new platform to host novel electronic, optical or excitonic physics and develop unprecedented nanoelectronic and energy applications. By definition, these materials are strongly anisotropic between within the basal plane and cross the plane. The structural and property anisotropies inside their basal plane, however, are much less investigated. Herein, we report a rare chemical form of arsenic, called black-arsenic (b-As), as an extremely anisotropic layered semiconductor. We have performed systematic characterization on the structural, electronic, thermal and electrical properties of b-As single crystals, with particular focus on its anisotropies along two in-plane principle axes, armchair (AC) and zigzag (ZZ). Our analysis shows that b-As exhibits higher or comparable electronic, thermal and electric transport anisotropies between the AC and ZZ directions than any other known 2D crystals. Such extreme in-plane anisotropies are able to potentially implement novel ideas for scientific research and device applications.

We consider diploid bi-parental analogues of Cannings models: in a population of fixed size $N$ the next generation is composed of $V_{i,j}$ offspring from parents $i$ and $j$, where $V=(V_{i,j})_{1\le i\neq j \le N}$ is a (jointly) exchangeable (symmetric) array. Every individual carries two chromosome copies, each of which is inherited from one of its parents. We obtain general conditions, formulated in terms of the vector of the total number of offspring to each individual, for the convergence of the properly scaled ancestral process for an $n$-sample of genes towards a ($\Xi$-)coalescent. This complements M\"ohle and Sagitov's (2001) result for the haploid case and sharpens the profile of M\"ohle and Sagitov's (2003) study of the diploid case, which focused on fixed couples, where each row of $V$ has at most one non-zero entry. We apply the convergence result to several examples, in particular to two diploid variations of Schweinsberg's (2003) model, leading to Beta-coalescents with two-fold and with four-fold mergers, respectively., Comment: 41 pages, 1 figure

Hydrostatic pressure applied using diamond anvil cells (DAC) has been widely explored to modulate physical properties of materials by tuning their lattice degree of freedom. Independently, electrical field is able to tune the electronic degree of freedom of functional materials via, for example, the field-effect transistor (FET) configuration. Combining these two orthogonal approaches would allow discovery of new physical properties and phases going beyond the known phase space. Such experiments are, however, technically challenging and have not been demonstrated. Herein, we report a feasible strategy to prepare and measure FETs in a DAC by lithographically patterning the nanodevices onto the diamond culet. Multiple-terminal FETs were fabricated in the DAC using few-layer MoS2 and BN as the channel semiconductor and dielectric layer, respectively. It is found that the mobility, conductance, carrier concentration, and contact conductance of MoS2 can all be significantly enhanced with pressure. We expect that the approach could enable unprecedented ways to explore new phases and properties of materials under coupled mechano-electrostatic modulation., Comment: 15 pages, 5 figures

On a compact foliated Riemannian manifold with some transversal curvature conditions, there are no nontrivial basic harmonic forms (M. Min-Oo et al., J. Reine Angew. Math. 415 (1991). In this paper, we extend the above facts to a complete foliated Riemannian manifold., Comment: 10 pages

In this article, we study the L2-transverse conformal Killing forms on complete foliated Riemannian manifolds and prove some vanishing theorems. Also, we study the same problems on Kahler foliations with a complete bundle-like metric., Comment: arXiv admin note: text overlap with arXiv:1408.6907

For a class of $\Lambda$-Fleming-Viot processes with underlying Brownian motion whose associated $\Lambda$-coalescents come down from infinity, we prove a one-sided modulus of continuity result for their ancestry processes recovered from the lookdown construction of Donnelly and Kurtz. As applications, we first show that such a $\Lambda$-Fleming-Viot support process has one-sided modulus of continuity (with modulus function $C\sqrt{t\log(1/t)}$) at any fixed time. We also show that the support is compact simultaneously at all positive times, and given the initial compactness, its range is uniformly compact over any finite time interval. In addition, under a mild condition on the $\Lambda$-coalescence rates, we find a uniform upper bound on Hausdorff dimension of the support and an upper bound on Hausdorff dimension of the range., Comment: arXiv admin note: text overlap with arXiv:1208.4152

The (\Xi, A)-Fleming-Viot process with mutation is a probability-measure-valued process whose moment dual is similar to that of the classical Fleming-Viot process except that the Kingman's coalescent is replaced by the \Xi-coalescent, the coalescent with simultaneous multiple collisions. We first prove the existence of such a process for general mutation generator A. We then investigate its reversibility. We also study both the weak and strong uniqueness of solution to the associated stochastic partial differential equation.

Using the lookdown construction of Donnelly and Kurtz we prove that, at any fixed positive time, the $\Lambda$-Fleming-Viot process with underlying Brownian motion has a compact support provided that the corresponding $\Lambda$-coalescent comes down from infinity not too slowly. We also find both upper bound and lower bound on the Hausdorff dimension for the support., Comment: 21 pages

In a joint work with Saji, the second and the third authors gave an intrinsic formulation of wave fronts and proved a realization theorem of wave fronts in space forms. As an application, we show that the following four objects are essentially same; * conformally flat n-manifolds (n>=3) with admissible singular points (i.e. admissible GCF-manifolds), * frontals as hypersurfaces in the lightcone Q^{n+1}_+, * frontals as hypersurfaces in the hyperbolic space H^{n+1}, * sapacelike frontals as hypersurfaces in the de Sitter space S^{n+1}_1. Recently, the duality of conformally flat Riemannian manifolds was found by several geometers. In our setting, this duality can be explained via the existence of a two-fold map of the congruent classes of admissible GCF-manifolds into that of frontals in H^{n+1}. It should be remarked that the dual conformally flat metric may have degenerate points even when the original conformally flat metric is positive definite. This is the reason why we consider conformally flat manifolds with singular points. In fact, the duality is an involution on the set of admissible GCF-manifolds. The case n=2 requires an exceptional treatment, since any Riemannian 2-manifolds are conformally flat. At the end of this paper, we also determine the moduli space of isometric immersions of a given simply connected Riemannian 2-manifold into the lightcone Q^{3}_+., Comment: 16 pages; Version 4