Approximate solutions to large nonsymmetric differential Riccati problems with applications to transport theory

In the present paper, we consider large scale nonsymmetric differential matrix Riccati equations with low rank right hand sides. These matrix equations appear in many applications such as control theory, transport theory, applied probability and others. We show how to apply Krylov-type methods such as the extended block Arnoldi algorithm to get low rank approximate solutions. The initial problem is projected onto small subspaces to get low dimensional nonsymmetric differential equations that are solved using the exponential approximation or via other integration schemes such as Backward Differentiation Formula (BDF) or Rosenbrok method. We also show how these technique could be easily used to solve some problems from the well known transport equation. Some numerical experiments are given to illustrate the application of the proposed methods to large-scale problem

Recovery of an embedded obstacle and the surrounding medium for Maxwell's system

In this paper, we are concerned with the inverse electromagnetic scattering problem of recovering a complex scatterer by the corresponding electric far-field data. The complex scatterer consists of an inhomogeneous medium and a possibly embedded perfectly electric conducting (PEC) obstacle. The far-field data are collected corresponding to incident plane waves with a fixed incident direction and a fixed polarisation, but frequencies from an open interval. It is shown that the embedded obstacle can be uniquely recovered by the aforementioned far-field data, independent of the surrounding medium. Furthermore, if the surrounding medium is piecewise homogeneous, then the medium can be recovered as well. Those unique recovery results are new to the literature. Our argument is based on low-frequency expansions of the electromagnetic fields and certain harmonic analysis techniques.Comment: 15 page

Public involvement in setting a national research agenda

<p>(A) Graphical map of the BLAST results showing nucleotide identity between <i>A</i>. <i>fasciata</i> mitogenome and 15 related species listed in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0136297#pone.0136297.t001" target="_blank">Table 1</a>, as generated by the CGView comparison tool (CCT). CCT arranges BLAST result in an order where sequence that is most similar to the reference (<i>A</i>. <i>fasciata</i>) is placed closer to the outer edge of the map. The rings labelled 1 to17 indicate BLAST results of <i>A</i>. <i>fasciata</i> mitogenome against <i>A</i>. <i>chrysaetos</i>, <i>N</i>. <i>nipalensis</i>, <i>N</i>. <i>alboniger</i>, <i>S</i>. <i>cheela</i>, <i>A</i>. <i>monachus</i>, <i>B</i>. <i>lagopus</i>, <i>B</i>. <i>buteo</i>, <i>B</i>. <i>buteo burmanicus</i>, <i>A</i>. <i>soloensis</i>, <i>A</i>. <i>virgatus</i>, <i>A</i>. <i>gentilis</i>, <i>A</i>. <i>nisus</i>, <i>P</i>. <i>haliaetus</i>, <i>S</i>. <i>serpentarius</i>, <i>C</i>. <i>aura</i>, <i>P</i>. <i>badius</i>, and <i>S</i>. <i>leptogrammica</i>, respectively. (B) Nucleotide-based phylogenetic tree of 16 Accipitriformes species, with two Strigiformes birds as outgroups. This analysis is based on 13PCGs. Both ML and Bayesian analyses produced identical tree topologies. The ML bootstrap and Bayesian posterior probability values for each node are indicated.</p

Visible-Light Photocatalytic Removal of NO in Air over BiOX (X = Cl, Br, I) Single-Crystal Nanoplates Prepared at Room Temperature

Well-crystallized layered two-dimensional bismuth oxyhalide (BiOX; X = Cl, Br, I) single-crystal nanoplates were synthesized via a facile and low-cost method at room temperature. The as-synthesized samples were analyzed by various characterization techniques. The photocatalytic activity of the samples was evaluated by the removal of NO at the indoor air level under visible-light irradiation. The band gap and thermal stability of bismuth oxyhalides decreased with increased X atomic numbers. The as-synthesized BiOBr nanoplates exhibited highest photocatalytic activity due to the favorable factors of ultrathin nanoplates, layered structures, relatively high surface area, and suitable band structure, exceeding that of BiOCl and BiOI. The present work could provide new insight into the low-temperature preparation and appropriate selection of visible-light photocatalysts for environmental application

Supplemental Material - Assessment of bidirectional relationships between systemic lupus erythematosus and anxiety disorder: A two-sample Mendelian randomization study

Supplemental Material for Assessment of bidirectional relationships between systemic lupus erythematosus and anxiety disorder: A two-sample Mendelian randomization study by Qin Zhang, Lingxin Zheng, and Kepeng Yang in Lupus</p

ERP waveforms for all experimental conditions in Exp. 1.

<p>Repeated stimuli induced larger negative shift in the N200 time window.</p

Scalp distribution for difference waves.

<p>The upper panel shows topographical distribution in N200 and N400 time windows for Exp. 1, and the lower panel shows topographical distribution in N400 time window for Exp. 2. The N200 time window results are not plotted for Exp. 2 due to absence of effects. Note scale differences in different maps.</p

Stimulus examples for the experimental conditions in Experiment 1, with the first two-character word as the prime and the second word as the target.

<p>The target words in the filler trials were nonsense pseudowords.</p

Stimulus examples for the experimental conditions in Experiment 2, with the first two-character word as the prime and the second word as the target.

<p>All items were real words.</p

Mean response times and error rates for the three experimental conditions (N = 19).

<p>Mean response times and error rates for the three experimental conditions (N = 19).</p