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

Inverse approach to Einstein's equations for fluids with vanishing anisotropic stress tensor

We expand previous work on an inverse approach to Einstein Field Equations where we include fluids with energy flux and consider the vanishing of the anisotropic stress tensor. We consider the approach using warped product spacetimes of class $B_1$. Although restricted, these spacetimes include many exact solutions of interest to compact object studies and to cosmological models studies. The question explored here is as follows: given a spacetime metric, what fluid flow (timelike congruence), if any, could generate the spacetime via Einstein's equations. We calculate the flow from the condition of a vanishing anisotropic stress tensor and give results in terms of the metric functions in the three canonical types of coordinates. A condition for perfect fluid sources is also provided. The framework developed is algorithmic and suited for the study and validation of exact solutions using computer algebra systems. The framework can be applied to solutions in comoving and non-comoving frames of reference, and examples in different types of coordinates are worked out.Comment: 15 pages, matches version to appear in Phys.Rev.

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]

On the exactly solvable pairing models for bosons

We propose the new exactly solvable model for bosons corresponding to the attractive pairing interaction. Using the electrostatic analogy, the solution of this model in thermodynamic limit is found. The transition from the superfluid phase with the Bose condensate and the Bogoliubov - type spectrum of excitations in the weak coupling regime to the incompressible phase with the gap in the excitation spectrum in the strong coupling regime is observed.Comment: 19 page

Neuropathy target esterase in mouse whole blood as a biomarker of exposure to neuropathic organophosphorus compounds

The adult hen is the standard animal model for testing organophosphorus (OP) compounds for organophosphorus compound‐induced delayed neurotoxicity (OPIDN). Recently, we developed a mouse model for biochemical assessment of the neuropathic potential of OP compounds based on brain neuropathy target esterase (NTE) and acetylcholinesterase (AChE) inhibition. We carried out the present work to further develop the mouse model by testing the hypothesis that whole blood NTE inhibition could be used as a biochemical marker for exposure to neuropathic OP compounds. Because brain NTE and AChE inhibition are biomarkers of OPIDN and acute cholinergic toxicity, respectively, we compared NTE and AChE 20‐min IC50 values as well as ED50 values 1 h after single intraperitoneal (i.p.) injections of increasing doses of two neuropathic OP compounds that differed in acute toxicity potency. We found good agreement between the brain and blood for in vitro sensitivity of each enzyme as well for the ratios IC50(AChE)/IC50(NTE). Both OP compounds inhibited AChE and NTE in the mouse brain and blood dose‐dependently, and brain and blood inhibitions in vivo were well correlated for each enzyme. For both OP compounds, the ratio ED50(AChE)/ED50(NTE) in blood corresponded to that in the brain despite the somewhat higher sensitivity of blood enzymes. Thus, our results indicate that mouse blood NTE could serve as a biomarker of exposure to neuropathic OP compounds. Moreover, the data suggest that relative inhibition of blood NTE and AChE provide a way to assess the likelihood that OP compound exposure in a susceptible species would produce cholinergic and/or delayed neuropathic effects. Copyright © 2016 John Wiley & Sons, Ltd.The adult hen is the standard animal model for testing organophosphorus (OP) compounds for organophosphorus compound‐induced delayed neurotoxicity (OPIDN). Recently, we developed a mouse model for the biochemical assessment of the neuropathic potential of OP compounds based on brain neuropathy target esterase (NTE) and acetylcholinesterase (AChE) inhibition. The present work represents further development of the mouse model aimed at using whole blood NTE as a biomarker of exposure to neuropathic OP compounds and predicting OPIDN risk in susceptible species by comparing blood NTE and AChE inhibition.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/134102/1/jat3305.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/134102/2/jat3305_am.pd

Some combinatorial identities related to commuting varieties and Hilbert schemes

In this article we explore some of the combinatorial consequences of recent results relating the isospectral commuting variety and the Hilbert scheme of points in the plane

Superfluid Phase Transitions in Dense Neutron Matter

The phase transitions in a realistic system with triplet pairing, dense neutron matter, have been investigated. The spectrum of phases of the $^3P_2-^3F_2$ model, which adequately describes pairing in this system, is analytically constructed with the aid of a separation method for solving BCS gap equation in states of arbitrary angular momentum. In addition to solutions involving a single value of the magnetic quantum number (and its negative), there exist ten real multicomponent solutions. Five of the corresponding angle-dependent order parameters have nodes, and five do not. In contrast to the case of superfluid $^3$He, transitions occur between phases with nodeless order parameters. The temperature dependence of the competition between the various phases is studied.Comment: 11 pages, 2 figure

The Reaction Process A+A->O in Sinai Disorder

The single-species reaction-diffusion process $A+A\to O$ is examined in the presence of an uncorrelated, quenched random velocity field. Utilising a field-theoretic approach, we find that in two dimensions and below the density decay is altered from the case of purely diffusing reactants. In two-dimensions the density amplitude is reduced in the presence of weak disorder, yielding the interesting result that Sinai disorder can cause reactions to occur at an {\it increased} rate. This is in contrast to the case of long-range correlated disorder, where it was shown that the reaction becomes sub-diffusion limited. However, when written in terms of the microscopic diffusion constant it is seen that increasing the disorder has the effect of reducing the rate of the reaction. Below two dimensions, the effect of Sinai disorder is much more severe and the reaction is shown to become sub-diffusion limited. Although there is no universal amplitude for the time-dependence of the density, it is universal when expressed in terms of the disorder-averaged diffusion length. The appropriate amplitude is calculated to one-loop order.Comment: 12 pages, 2 figure

Magnetic Flux of EUV Arcade and Dimming Regions as a Relevant Parameter for Early Diagnostics of Solar Eruptions - Sources of Non-Recurrent Geomagnetic Storms and Forbush Decreases

This study aims at the early diagnostics of geoeffectiveness of coronal mass ejections (CMEs) from quantitative parameters of the accompanying EUV dimming and arcade events. We study events of the 23th solar cycle, in which major non-recurrent geomagnetic storms (GMS) with Dst <-100 nT are sufficiently reliably identified with their solar sources in the central part of the disk. Using the SOHO/EIT 195 A images and MDI magnetograms, we select significant dimming and arcade areas and calculate summarized unsigned magnetic fluxes in these regions at the photospheric level. The high relevance of this eruption parameter is displayed by its pronounced correlation with the Forbush decrease (FD) magnitude, which, unlike GMSs, does not depend on the sign of the Bz component but is determined by global characteristics of ICMEs. Correlations with the same magnetic flux in the solar source region are found for the GMS intensity (at the first step, without taking into account factors determining the Bz component near the Earth), as well as for the temporal intervals between the solar eruptions and the GMS onset and peak times. The larger the magnetic flux, the stronger the FD and GMS intensities are and the shorter the ICME transit time is. The revealed correlations indicate that the main quantitative characteristics of major non-recurrent space weather disturbances are largely determined by measurable parameters of solar eruptions, in particular, by the magnetic flux in dimming areas and arcades, and can be tentatively estimated in advance with a lead time from 1 to 4 days. For GMS intensity, the revealed dependencies allow one to estimate a possible value, which can be expected if the Bz component is negative.Comment: 27 pages, 5 figures. Accepted for publication in Solar Physic

Exact correlation functions of the BCS model in the canonical ensemble

We evaluate correlation functions of the BCS model for finite number of particles. The integrability of the Hamiltonian relates it with the Gaudin algebra ${\cal G}[sl(2)]$. Therefore, a theorem that Sklyanin proved for the Gaudin model, can be applied. Several diagonal and off-diagonal correlators are calculated. The finite size scaling behavior of the pairing correlation function is studied.Comment: 4 pages revtex; 2 figures .eps. Revised version to be published in Phys. Rev. Let