On the complete classification of extremal log Enriques surfaces

We show that there are exactly, up to isomorphisms, seven extremal log Enriques surfaces Z and construct all of them; among them types D_{19} and A_{19} have been shown of certain uniqueness by M. Reid. We also prove that the (degree 3 or 2) canonical covering of each of these seven Z has either X_3 or X_4 as its minimal resolution. Here X_3 (resp. X_4) is the unique K3 surface with Picard number 20 and discriminant 3 (resp. 4), which are called the most algebraic K3 surfaces by Vinberg and have infinite automorphism groups (by Shioda-Inose and Vinberg).Comment: 22 pages. Math. Z. to appea

Knowledge discovery for friction stir welding via data driven approaches: Part 2 – multiobjective modelling using fuzzy rule based systems

In this final part of this extensive study, a new systematic data-driven fuzzy modelling approach has been developed, taking into account both the modelling accuracy and its interpretability (transparency) as attributes. For the first time, a data-driven modelling framework has been proposed designed and implemented in order to model the intricate FSW behaviours relating to AA5083 aluminium alloy, consisting of the grain size, mechanical properties, as well as internal process properties. As a result, ‘Pareto-optimal’ predictive models have been successfully elicited which, through validations on real data for the aluminium alloy AA5083, have been shown to be accurate, transparent and generic despite the conservative number of data points used for model training and testing. Compared with analytically based methods, the proposed data-driven modelling approach provides a more effective way to construct prediction models for FSW when there is an apparent lack of fundamental process knowledge

An MHD Model For Magnetar Giant Flares

Giant flares on soft gamma-ray repeaters that are thought to take place on magnetars release enormous energy in a short time interval. Their power can be explained by catastrophic instabilities occurring in the magnetic field configuration and the subsequent magnetic reconnection. By analogy with the coronal mass ejection (CME) events on the Sun, we develop a theoretical model via an analytic approach for magnetar giant flares. In this model, the rotation and/or displacement of the crust causes the field to twist and deform, leading to flux rope formation in the magnetosphere and energy accumulation in the related configuration. When the energy and helicity stored in the configuration reach a threshold, the system loses its equilibrium, the flux rope is ejected outward in a catastrophic way, and magnetic reconnection helps the catastrophe develop to a plausible eruption. By taking SGR 1806 - 20 as an example, we calculate the free magnetic energy released in such an eruptive process and find that it is more than $10^{47}$ ergs, which is enough to power a giant flare. The released free magnetic energy is converted into radiative energy, kinetic energy and gravitational energy of the flux rope. We calculated the light curves of the eruptive processes for the giant flares of SGR 1806 - 20, SGR 0526-66 and SGR 1900+14, and compared them with the observational data. The calculated light curves are in good agreement with the observed light curves of giant flares.Comment: Accepted to Ap

Branching Ratio and CP Asymmetry of B_s \to K^*_0(1430)\pi Decays in the PQCD Approach

In the two-quark model supposition for $K_0^{*}(1430)$, the branching ratios and the direct CP-violating asymmetries for decays $\bar B_s^0\to K^{*0}_0(1430)\pi^0, K^{*+}_0(1430)\pi^-$ are studied by employing the perturbative QCD factorization approach. We find that although these two decays are both tree-dominated, the ratio of their penguin to tree contributions are very different: there is only a few percent for the decay $\bar B_s^0\to K^{*+}_0(1430)\pi^-$, while about 37% in scenario I, even 51% in scenario II for the decay $\bar B_s^0\to K^{*0}_0(1430)\pi^0$. It results that these two decays have very different values in the branching ratios and the direct CP asymmetries. The branching ratio of the decay $\bar B_s^0\to K^{*+}_0(1430)\pi^-$ is at the order of $10^{-5}$, and its direct CP asymmetry is about (20-30)%. While for the decay $\bar B_s^0\to K^{*0}_0(1430)\pi^0$, its direct CP-violating asymmetry is very large and about 90%, but it is difficult to measure it, because the branching ratio for this channel is small and only $10^{-7}$ order.Comment: 8pages, 2figure