5,311 research outputs found

    Maximal multihomogeneity of algebraic hypersurface singularities

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    From the degree zero part of logarithmic vector fields along an algebraic hypersurface singularity we indentify the maximal multihomogeneity of a defining equation in form of a maximal algebraic torus in the embedded automorphism group. We show that all such maximal tori are conjugate and in one-to-one correspondence to maxmimal tori in the degree zero jet of the embedded automorphism group. The result is motivated by Kyoji Saito's characterization of quasihomogeneity for isolated hypersurface singularities and extends its formal version and a result of Hauser and Mueller.Comment: 5 page

    Multi-comparisons of rape and rape myth endorsement through analysis of existing modified rape myth items

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    Traditionally, rape has been viewed as a crime perpetrated by men against women. However, it is now recognised that males can also be victims of rape. The current research had several interrelated aims to; (i) provide a profile of both male and female rape victims, (ii) compare the characteristics of rape perpetrated against male and female victims, (iii) estimate the incidence of male and female rape within the general community, (iv) describe the reporting practices of rape victims, and (v) determine the relationship between rape and depression, suicide ideation, and suicide attempts. The community's level of rape myth endorsement was also explored. Rape myths were defined as attitudes and beliefs about rape, rape victims, and rapists that are generally false but are widely and persistently held, and serve to deny and justify sexual aggression against women and men. The present study compared rape myth endorsement levels concerning both male and female victims. However, it was first necessary to construct a rape myth questionnaire, the Rape Attitudinal Scale (RAQ), which minimised the methodological limitations of pre-existing scales. The current research utilised online methodology and, in total, 560 individuals participated in the research. It was found that almost two out of every five participants had been a victim of rape during their lifetime, with males accounting for 8.60% of the raped sample. Rape victims emanated from a variety of demographic backgrounds and the gender differences between the characteristics of the rape were discussed. Approximately one in seven rape victims stated that they had reported the rape to police, with half of those rape victims regretting informing the police of their experience. Almost twice as many female rape victims than male rape victims failed to report their rape to anyone. It was also found that victims of rape are more likely to report rape to authorities when the rape fits the "real rape" stereotype. It was evident that the trauma of rape and its overall negative sequelae can persist long after the rape has occurred. It was found that rape victims were significantly more likely than non-victims to be classified as depressed, experience suicidal thoughts and had attempted suicide. It was concluded that the RAQ was a reliable and valid measure of individual's rape myth endorsement levels. The underlying nature of rape myths did not differ between male and female victims of rape, although certain rape myths seem to be more applicable to each gender. The majority of the current sample did not endorse rape myths, however participants from particular demographic backgrounds were more likely than others to endorse rape myths. A small, yet alarming, proportion of the current sample reported that they would be likely to rape someone if they could get away with it. Implications of the current findings were discussed in terms of future rape education campaigns that could increase public awareness, increase reporting rates and hopefully reduce the incidence of rape within our society

    Computation of a 30750-Bit Binary Field Discrete Logarithm

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    This paper reports on the computation of a discrete logarithm in the finite field F230750\mathbb F_{2^{30750}}, breaking by a large margin the previous record, which was set in January 2014 by a computation in F29234\mathbb F_{2^{9234}}. The present computation made essential use of the elimination step of the quasi-polynomial algorithm due to Granger, Kleinjung and Zumbr\"agel, and is the first large-scale experiment to truly test and successfully demonstrate its potential when applied recursively, which is when it leads to the stated complexity. It required the equivalent of about 2900 core years on a single core of an Intel Xeon Ivy Bridge processor running at 2.6 GHz, which is comparable to the approximately 3100 core years expended for the discrete logarithm record for prime fields, set in a field of bit-length 795, and demonstrates just how much easier the problem is for this level of computational effort. In order to make the computation feasible we introduced several innovative techniques for the elimination of small degree irreducible elements, which meant that we avoided performing any costly Gr\"obner basis computations, in contrast to all previous records since early 2013. While such computations are crucial to the L(14+o(1))L(\frac 1 4 + o(1)) complexity algorithms, they were simply too slow for our purposes. Finally, this computation should serve as a serious deterrent to cryptographers who are still proposing to rely on the discrete logarithm security of such finite fields in applications, despite the existence of two quasi-polynomial algorithms and the prospect of even faster algorithms being developed.Comment: 22 page

    Quasihomogeneity of isolated singularities and logarithmic cohomology

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    We characterize quasihomogeneity of isolated singularities by the injectivity of the map induced by the first differential of the logarithmic differential complex in the top local cohomology supported in the singular point.Comment: 5 page

    Standing and travelling waves in the shallow-water circular hydraulic jump

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    A wave equation for a time-dependent perturbation about the steady shallow-water solution emulates the metric an acoustic white hole, even upon the incorporation of nonlinearity in the lowest order. A standing wave in the sub-critical region of the flow is stabilised by viscosity, and the resulting time scale for the amplitude decay helps in providing a scaling argument for the formation of the hydraulic jump. A standing wave in the super-critical region, on the other hand, displays an unstable character, which, although somewhat mitigated by viscosity, needs nonlinear effects to be saturated. A travelling wave moving upstream from the sub-critical region, destabilises the flow in the vicinity of the jump, for which experimental support has been given.Comment: 9 pages, REVTeX, Additional treatment on travelling waves. Extensively revised in the publised version. Contains a full new section on the role of nonlinearit
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