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    Regions

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    Conformal mapping of unbounded multiply connected regions onto canonical slit regions

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    We present a boundary integral equation method for conformal mapping of unbounded multiply connected regions onto five types of canonical slit regions. For each canonical region, three linear boundary integral equations are constructed from a boundary relationship satisfied by an analytic function on an unboundedmultiply connected region. The integral equations are uniquely solvable. The kernels involved in these integral equations are the modified Neumann kernels and the adjoint generalized Neumann kernels

    Active regions

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    The following efforts were completed in support of the Solar Maximum Mission (SMM): (1) the evolution of solar vector photospheric magnetic fields in a flare-producing active region was studied; (2) an algorithm was developed to generate maps of force-free magnetic field strengths at varying heights in the solar atmosphere; and (3) the study of the physical state of the material confined along entire magnetic loops was advanced with the use of magnetic field extrapolation

    Overeducation across British regions

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    This paper analyses levels of over-education and wage returns to education for males across eleven regions of the UK using Labour Force Survey data. Significant differences are found in the probability of being over-educated across regions; also, differences are found in the return to the ‘correct’ level of education in each region, in each case associated with flexibility of movement between and into particular regions, which determines the ease of job matching. Furthermore, evidence is found that, after controlling for the level of education acquired, there exists a premium to the ‘correct’ level of education, which varies across UK regions

    Traversing non-convex regions

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    This paper considers a method for dealing with non-convex objective functions in optimization problems. It uses the Hessian matrix and combines features of trust-region techniques and continuous steepest descent trajectory-following in order to construct an algorithm which performs curvilinear searches away from the starting point of each iteration. A prototype implementation yields promising resultsPeer reviewe

    Magnetic structure of solar flare regions producing hard X-ray pulsations

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    We present analysis of the magnetic field in seven solar flare regions accompanied by the pulsations of hard X-ray (HXR) emission. These flares were studied by Kuznetsov et al. (2016) (Paper~I), and chosen here because of the availability of the vector magnetograms for their parent active regions (ARs) obtained with the SDO/HMI data. In Paper~I, based on the observations only, it was suggested that a magnetic flux rope (MFR) might play an important role in the process of generation of the HXR pulsations. The goal of the present paper is to test this hypothesis by using the extrapolation of magnetic field with the non-linear force-free field (NLFFF) method. Having done this, we found that before each flare indeed there was an MFR elongated along and above a magnetic polarity inversion line (MPIL) on the photosphere. In two flare regions the sources of the HXR pulsations were located at the footpoints of different magnetic field lines wrapping around the central axis, and constituting an MFR by themselves. In five other flares the parent field lines of the HXR pulsations were not a part of an MFR, but surrounded it in the form of an arcade of magnetic loops. These results show that, at least in the analyzed cases, the "single flare loop" models do not satisfy the observations and magnetic field modeling, while are consistent with the concept that the HXR pulsations are a consequence of successive episodes of energy release and electron acceleration in different magnetic flux tubes (loops) of a complex AR. An MFR could generate HXR pulsations by triggering episodes of magnetic reconnection in different loops in the course of its non-uniform evolution along an MPIL. However, since three events studied here were confined flares, actual eruptions may not be required to trigger sequential particle acceleration episodes in the magnetic systems containing an MFR.Comment: 33 pages, 5 figures, 2 tables. Accepted for publication in Journal of Atmospheric and Solar-Terrestrial Physics (28 April 2018
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