On the direct indecomposability of infinite irreducible Coxeter groups and the Isomorphism Problem of Coxeter groups

In this paper we prove, without the finite rank assumption, that any irreducible Coxeter group of infinite order is directly indecomposable as an abstract group. The key ingredient of the proof is that we can determine, for an irreducible Coxeter group, the centralizers of the normal subgroups that are generated by involutions. As a consequence, we show that the problem of deciding whether two general Coxeter groups are isomorphic, as abstract groups, is reduced to the case of irreducible Coxeter groups, without assuming the finiteness of the number of the irreducible components or their ranks. We also give a description of the automorphism group of a general Coxeter group in terms of those of its irreducible components.Comment: 30 page

Electric and magnetic Weyl tensors in higher dimensions

Recent results on purely electric (PE) or magnetic (PM) spacetimes in n dimensions are summarized. These include: Weyl types; diagonalizability; conditions under which direct (or warped) products are PE/PM.Comment: 4 pages; short summary of (parts of) arXiv:1203.3563. Proceedings of "Relativity and Gravitation - 100 Years after Einstein in Prague", Prague, June 25-29, 2012 (http://ae100prg.mff.cuni.cz/

The crustacean and molluscan fauna of Tasmanian saltmarshes

The crustaceans and molluscs of 65 saltmarshes and brackish marshes around the coast of Tasmania and the major Bass Strait islands were surveyed. Over 50 species were collected, but only eight (three talitrid amphipods, one crab and four gastropods) were confined to saltmarshes; the typical saltmarsh assemblage consisted of two talitrid amphipods, three oniscoid isopods, two crabs, two prosobranch snails and two pulmonate snails. The greatest species richness was found in marshes from the southeast and the far northwest, where the most extensive saltmarshes have developed. Several undescribed talitrids were collected and the range of two coastal species was extended significantly. The native woodlouse Plymophiloscia ulverstonensis was commonly found on the upper parts of the marshes, as was the introduced slater Porcellio scaber. The burrowing grapsid crab Helograpsus haswellianus was common on the marshes, though it was replaced by the ocypodid Heloecius cordiformis in brackish marshes, and by another grapsid, Paragrapsus gaimardii, in the only marsh examined on King Island. The hymenosomatid crab Amarinus paralacustris was recorded from the state for the first time at Hendersons Lagoon. Amphibolid and ellobiid snails typified the molluscan fauna of the marshes. The introduced ellobiid Phytia myosotis appears to have a major disjunction in its distribution between the southeast and northern sites. Tasmanian saltmarshes have a similar diversity of crustaceans and molluscs to those of New Zealand and South Africa. They are richer in species than saltmarshes of the northeast Atlantic coasts but have fewer crustaceans than the temperate east coast marshes of North America, and fewer molluscs than those of the coasts of the Pacific northwest

Moisture in Molasses as a Factor in the Heating of Feeds.

16 p

Simultaneous Inference of User Representations and Trust

Inferring trust relations between social media users is critical for a number of applications wherein users seek credible information. The fact that available trust relations are scarce and skewed makes trust prediction a challenging task. To the best of our knowledge, this is the first work on exploring representation learning for trust prediction. We propose an approach that uses only a small amount of binary user-user trust relations to simultaneously learn user embeddings and a model to predict trust between user pairs. We empirically demonstrate that for trust prediction, our approach outperforms classifier-based approaches which use state-of-the-art representation learning methods like DeepWalk and LINE as features. We also conduct experiments which use embeddings pre-trained with DeepWalk and LINE each as an input to our model, resulting in further performance improvement. Experiments with a dataset of $\sim$356K user pairs show that the proposed method can obtain an high F-score of 92.65%.Comment: To appear in the proceedings of ASONAM'17. Please cite that versio

Exact Resummations in the Theory of Hydrodynamic Turbulence: I The Ball of Locality and Normal Scaling

This paper is the first in a series of three papers that aim at understanding the scaling behaviour of hydrodynamic turbulence. We present in this paper a perturbative theory for the structure functions and the response functions of the hydrodynamic velocity field in real space and time. Starting from the Navier-Stokes equations (at high Reynolds number Re) we show that the standard perturbative expansions that suffer from infra-red divergences can be exactly resummed using the Belinicher-L'vov transformation. After this exact (partial) resummation it is proven that the resulting perturbation theory is free of divergences, both in large and in small spatial separations. The hydrodynamic response and the correlations have contributions that arise from mediated interactions which take place at some space- time coordinates. It is shown that the main contribution arises when these coordinates lie within a shell of a "ball of locality" that is defined and discussed. We argue that the real space-time formalism developed here offers a clear and intuitive understanding of every diagram in the theory, and of every element in the diagrams. One major consequence of this theory is that none of the familiar perturbative mechanisms may ruin the classical Kolmogorov (K41) scaling solution for the structure functions. Accordingly, corrections to the K41 solutions should be sought in nonperturbative effects. These effects are the subjects of papers II and III in this series, that will propose a mechanism for anomalous scaling in turbulence, which in particular allows multiscaling of the structure functions.Comment: PRE in press, 18 pages + 6 figures, REVTeX. The Eps files of figures will be FTPed by request to [email protected]

Stretched pulse Yb³⁺:silica fibre laser

We report what we believe to be the first results on short-pulse generation in Yb3+:silica fiber. By applying the stretched pulse technique in a unidirectional, polarization-switch Yb3+ fiber laser incorporating a prism-based dispersive delay line, we obtain self-start mode locking and 100pJ pulses that can be compressed to give clean chirp-free <100fs pulses. We believe such sources to have great potential for use not only in all-solid-state high-power femtosecond pulse systems based on Yb3+:silica glass but also as seeds for conventional Nd3+:glass amplifier chains

Iron catalysed assembly of an asymmetric mixed-ligand triple helicate

The 2-pyridinecarbaldehyde isonicotinoyl hydrazone (HPCIH) family of ligands are typically tridentate N,N,O chelators that exhibit very high in vitro activity in mobilizing intracellular Fe and are promising candidates for the treatment of Fe overload diseases. Complexation of ferrous perchlorate with HPCIH in MeCN solution gives the expected six-coordinate complex Fe-II(PCIH)(2). However, complexation of Fe-II with 2-pyridinecarbaldehyde picolinoyl hydrazone (HPCPH, an isomer of HPCIH) under the same conditions leads to spontaneous assembly of an unprecedented asymmetric, mixed-ligand dinuclear triple helical complex Fe-2(II)(PCPH)(2)(PPH), where PPH2- is the dianion of bis(picolinoyl) hydrazine. The X-ray crystal structure of this complex shows that each ligand binds simultaneously to both metal centres in a bidentate fashion. The dinuclear complex exhibits two well separated and totally reversible Fe-III/II redox couples as shown by cyclic voltammetry in MeCN solution

The biologically active iron chelators 2-pyridylcarboxaldehyde isonicotinoylhydrazone, 2-pyridylcarboxaldehyde benzoylhydrazone monohydrate and 2-furaldehyde isonicotinoylhydrazone

In the crystal structures of the respective title compounds, C12H10N4O, C13H11N3O . H2O and C11K9N3O2, variations in the torsion angles of the aromatic pyridyl and benzoyl groups are observed, and the disposition of the heterocyclic aldehyde is shown to be influenced by the ring size of this group

Evidence for Proportionate Partition Between the Magnetic Field and Hot Gas in Turbulent Cassiopeia A

We present a deep X-ray observation of the young Galactic supernova remnant Cas A, acquired with the ROSAT High Resolution Imager. This high dynamic range (232 ks) image reveals low-surface-brightness X-ray structure, which appears qualitatively similar to corresponding radio features. We consider the correlation between the X-ray and radio morphologies and its physical implications. After correcting for the inhomogeneous absorption across the remnant, we performed a point by point (4" resolution) surface brightness comparison between the X-ray and radio images. We find a strong (r = 0.75) log-log correlation, implying an overall relationship of $\log(\Sigma_{_{\rm X-ray}}) \propto (2.21\pm0.05) \times \log(\Sigma_{_{\rm radio}})$. This is consistent with proportionate partition (and possibly equipartition) between the local magnetic field and the hot gas --- implying that Cas A's plasma is fully turbulent and continuously amplifying the magnetic field.Comment: 8 pages with embedded bitmapped figures, Accepted by ApJ Letters 5/1/9