On the H\'enon-Lane-Emden conjecture

We consider Liouville-type theorems for the following H\'{e}non-Lane-Emden system \hfill -\Delta u&=& |x|^{a}v^p \text{in} \mathbb{R}^N, \hfill -\Delta v&=& |x|^{b}u^q \text{in} \mathbb{R}^N, when $pq>1$, $p,q,a,b\ge0$. The main conjecture states that there is no non-trivial non-negative solution whenever $(p,q)$ is under the critical Sobolev hyperbola, i.e. $\frac{N+a}{p+1}+\frac{N+b}{q+1}>{N-2}$. We show that this is indeed the case in dimension N=3 provided the solution is also assumed to be bounded, extending a result established recently by Phan-Souplet in the scalar case. Assuming stability of the solutions, we could then prove Liouville-type theorems in higher dimensions. For the scalar cases, albeit of second order ($a=b$ and $p=q$) or of fourth order ($a\ge 0=b$ and $p>1=q$), we show that for all dimensions $N\ge 3$ in the first case (resp., $N\ge 5$ in the second case), there is no positive solution with a finite Morse index, whenever $p$ is below the corresponding critical exponent, i.e $1<p<\frac{N+2+2a}{N-2}$ (resp., $1<p<\frac{N+4+2a}{N-4}$). Finally, we show that non-negative stable solutions of the full H\'{e}non-Lane-Emden system are trivial provided \label{sysdim00} N<2+2(\frac{p(b+2)+a+2}{pq-1}) (\sqrt{\frac{pq(q+1)}{p+1}}+ \sqrt{\frac{pq(q+1)}{p+1}-\sqrt\frac{pq(q+1)}{p+1}}).Comment: Theorem 4 has been added in the new version. 23 pages, Comments are welcome. Updated version - if any - can be downloaded at http://www.birs.ca/~nassif/ or http://www.math.ubc.ca/~fazly/research.htm

Stealthy Deception Attacks Against SCADA Systems

SCADA protocols for Industrial Control Systems (ICS) are vulnerable to network attacks such as session hijacking. Hence, research focuses on network anomaly detection based on meta--data (message sizes, timing, command sequence), or on the state values of the physical process. In this work we present a class of semantic network-based attacks against SCADA systems that are undetectable by the above mentioned anomaly detection. After hijacking the communication channels between the Human Machine Interface (HMI) and Programmable Logic Controllers (PLCs), our attacks cause the HMI to present a fake view of the industrial process, deceiving the human operator into taking manual actions. Our most advanced attack also manipulates the messages generated by the operator's actions, reversing their semantic meaning while causing the HMI to present a view that is consistent with the attempted human actions. The attacks are totaly stealthy because the message sizes and timing, the command sequences, and the data values of the ICS's state all remain legitimate. We implemented and tested several attack scenarios in the test lab of our local electric company, against a real HMI and real PLCs, separated by a commercial-grade firewall. We developed a real-time security assessment tool, that can simultaneously manipulate the communication to multiple PLCs and cause the HMI to display a coherent system--wide fake view. Our tool is configured with message-manipulating rules written in an ICS Attack Markup Language (IAML) we designed, which may be of independent interest. Our semantic attacks all successfully fooled the operator and brought the system to states of blackout and possible equipment damage

IGR J17254-3257, a new bursting neutron star

The study of the observational properties of uncommonly long bursts from low luminosity sources with extended decay times up to several tens of minutes is important when investigating the transition from a hydrogen-rich bursting regime to a pure helium regime and from helium burning to carbon burning as predicted by current burst theories. IGR J17254-3257 is a recently discovered X-ray burster of which only two bursts have been recorded: an ordinary short type I X-ray burst, and a 15 min long burst. An upper limit to its distance is estimated to about 14.5 kpc. The broad-band spectrum of the persistent emission in the 0.3-100 keV energy band obtained using contemporaneous INTEGRAL and XMM-Newton data indicates a bolometric flux of 1.1x10^-10 erg/cm2/s corresponding, at the canonical distance of 8 kpc, to a luminosity about 8.4x10^35 erg/s between 0.1-100 keV, which translates to a mean accretion rate of about 7x10^-11 solar masses per year. The low X-ray persistent luminosity of IGR J17254-3257 seems to indicate the source may be in a state of low accretion rate usually associated with a hard spectrum in the X-ray range. The nuclear burning regime may be intermediate between pure He and mixed H/He burning. The long burst is the result of the accumulation of a thick He layer, while the short one is a prematurate H-triggered He burning burst at a slightly lower accretion rate.Comment: 4 pages, 4 figures, 1 table; accepted for publication in A&A Letters. 1 reference (Cooper & Narayan, 2007) correcte

Transmission Resonance in an Infinite Strip of Phason-Defects of a Penrose Approximant Network

An exact method that analytically provides transfer matrices in finite networks of quasicrystalline approximants of any dimensionality is discussed. We use these matrices in two ways: a) to exactly determine the band structure of an infinite approximant network in analytical form; b) to determine, also analytically, the quantum resistance of a finite strip of a network under appropriate boundary conditions. As a result of a subtle interplay between topology and phase interferences, we find that a strip of phason-defects along a special symmetry direction of a low 2-d Penrose approximant, leads to the rigorous vanishing of the reflection coefficient for certain energies. A similar behavior appears in a low 3-d approximant. This type of ``resonance" is discussed in connection with the gap structure of the corresponding ordered (undefected) system.Comment: 18 pages special macros jnl.tex,reforder.tex, eqnorder.te

Discovery of a large and bright bow shock nebula associated with low mass X-ray binary SAX J1712.6-3739

In a multiwavelength program dedicated to identifying optical counterparts of faint persistent X-ray sources in the Galactic Bulge, we find an accurate X-ray position of SAX J1712.6-3739 through Chandra observations, and discover its faint optical counterpart using our data from EFOSC2 on the ESO 3.6m telescope. We find this source to be a highly extincted neutron star LMXB with blue optical colours. We serendipitously discover a relatively bright and large bow shock shaped nebula in our deep narrowband H alpha imaging, most likely associated with the X-ray binary. A nebula like this has never been observed before in association with a LMXB, and as such provides a unique laboratory to study the energetics of accretion and jets. We put forward different models to explain the possible ways the LMXB may form this nebulosity, and outline how they can be confirmed observationally.Comment: Accepted for publication in MNRAS-Letters; 5 pages, 4 figures, 2 tables. Quality of figure 2 downgraded because of arXiv file size limit

Discovery of the INTEGRAL X/Gamma-ray transient IGR J00291+5934: a Comptonised accreting ms pulsar ?

We report the discovery of a high-energy transient with the IBIS/ISGRI detector on board the INTEGRAL observatory. The source, namely IGR J00291+5934, was first detected on 2nd December 2004 in the routine monitoring of the IBIS/ISGRI 20--60 keV images. The observations were conducted during Galactic Plane Scans, which are a key part of the INTEGRAL Core Programme observations. After verifying the basic source behaviour, the discovery was announced on 3rd December. The transient shows a hard Comptonised spectrum, with peak energy release at about 20 keV and a total luminosity of ~ 0.9E36 erg/s in the 5--100 keV range, assuming a distance of 3 kpc. Following the INTEGRAL announcement of the discovery of IGR J00291+5934, a number of observations were made by other instruments. We summarise the results of those observations and, together with the INTEGRAL data, identifiy IGR J00291+5934 as the 6th member of a class of accreting X-ray millisecond pulsars.Comment: Accepted for publication as an A&A Letter 24/01/2005. 5 pages, 2 figure

A four-year baseline Swift study of enigmatic X-ray transients located near the Galactic center

We report on continued monitoring observations of the Galactic center carried out by the X-ray telescope aboard the Swift satellite in 2008 and 2009. This campaign revealed activity of the five known X-ray transients AX J1745.6-2901, CXOGC J174535.5-290124, GRS 1741-2853, XMM J174457-2850.3 and CXOGC J174538.0-290022. All these sources are known to undergo very faint X-ray outbursts with 2-10 keV peak luminosities of Lx,peak~1E34-1E36 erg/s, although the two confirmed neutron star low-mass X-ray binaries AX J1745.6-2901 and GRS 1741-2853 can also become brighter (Lx,peak~1E36-1E37 erg/s). We discuss the observed long-term lightcurves and X-ray spectra of these five enigmatic transients. In 2008, AX J1745.6-2901 returned to quiescence following an unusually long accretion outburst of more than 1.5 years. GRS 1741-2853 was active in 2009 and displayed the brightest outburst ever recorded for this source, reaching up to a 2-10 keV luminosity of Lx~1E37 (D/7.2 kpc)^2 erg/s. This system appears to undergo recurrent accretion outbursts approximately every 2 years. Furthermore, we find that the unclassified transient XMM J174457-2850.3 becomes bright only during short episodes (days) and is often found active in between quiescence (Lx~1E32 erg/s) and its maximum outburst luminosity of Lx~1E36 erg/s. CXOGC J174535.5-290124 and CXOGC J174538.0-290022, as well as three other very-faint X-ray transients that were detected by Swift monitoring observations in 2006, have very low time-averaged mass-accretion rates of ~< 2E-12 Msun/yr. Despite having obtained two years of new data in 2008 and 2009, no new X-ray transients were detected.Comment: Minor textual revisions according to referee report, accepted for publication in A&

Lack of Mutual Respect in Relationship The Endangered Partner

Violence in a relationship and in a family setting has been an issue of concern to various interest groups and professional organizations. Of particular interest in this article is violence against women in a relationship. While there is an abundance of knowledge on violence against women in general, intimate or partner femicide seems to have received less attention. Unfortunately, the incidence of violence against women, and intimate femicide in particular, has been an issue of concern in the African setting. This article examines the trends of intimate femicide in an African setting in general, and in Botswana in particular. The increase in intimate femicide is an issue of concern, which calls for collective effort to address. This article also examines trends offemicide in Botswana, and the antecedents and the precipitating factors. Some studies have implicated societal and cultural dynamics as playing significant roles in intimate femicide in the African setting. It is believed that the patriarchal nature of most African settings and the ideology of male supremacy have relegated women to a subordinate role. Consequently, respect for women in any relationship with men is lopsided in favor of men and has led to abuse of women, including intimate femicide. Other militating factors in intimate femicide ,are examined and the implications for counseling to assist the endangered female partner are discussed

XMM-Newton observations of the INTEGRAL X-ray transient J17544-2619

On 2003 September 17 INTEGRAL discovered a bright transient source 3 degrees from the Galactic Center, IGR J17544-2619. The field containing the transient was observed by XMM-Newton on 2003 March 17 and September 11 and 17. A bright source, at a position consistent with the INTEGRAL location, was detected by the European Photon Imaging Camera (EPIC) during both September observations with mean 0.5-10 keV unabsorbed luminosities of 1.1x10^35 and 5.7x10^35 erg s-1 for an (assumed) distance of 8 kpc. The source was not detected in 2003 March, with a 0.5-10 keV luminosity of < 3.8x10^32 erg s-1. The September 11 and 17 EPIC spectra can be represented by a power-law model with photon indices of 2.25+/-0.15 and 1.42+/-0.17, respectively. Thus, the 0.5-10 keV spectrum hardens with increasing intensity. The low-energy absorption during both September observations is comparable to the interstellar value. The X-ray lightcurves for both September observations show energy dependent flaring which may be modeled by changes in either low-energy absorption or power-law index.Comment: Six pages, five figures; to appear in Astronomy and Astrophysic