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It is shown that any subset E of a plane over a finite field Fq, of cardinality |E| > q determines not less than q−1 2 distinct areas of triangles, moreover once can find such triangles sharing a common base.It is also shown that if |E| ≥ 64q log 2 q, then there are more than q 2 distinct areas of triangles sharing a common vertex. The result follows from a finite field version of the Beck theorem for large subsets of F 2 q that we prove. If |E| ≥ 64q log 2 q, there exists a point z ∈ E, such that there are at least q 4 straight lines incident to z, each supporting the number of points of E other than z in the interval between |E| 2q and 2|E| q . This is proved by combining combinatorial and Fourier analytic techniques.We also discuss higher-dimensional implications of these results in light of recent developments.

Abstract-High magnetic field can be trapped in a bulk type-II superconductor through different magnetization methods. In our fully high temperature superconducting (HTS) synchronous motor, the pulsed field magnetization (PFM) method is adopted due to its reduced cost, feasibility, and adaptability on the assembling of our HTS motor system. The HTS rotor was designed with seventy-five YBCO HTS bulks mounted on the surface of the rotor to make two pairs of poles after the PFM. In this paper, we give a PFM circuit used to generate a pulsed magnetic field about 1.5 T at the centre of the magnetizing coil lasting less than 1 s by discharging a capacitor bank. We also investigate the homogeneity of the pulsed magnetic field produced by the coils. The main strategy for magnetizing the superconducting rotor is designed and investigated and the rotor field profile after the whole magnetization procedure is measured and discussed as well.  Index Terms-HTS synchronous motor, HTS rotor, pulsed field magnetization.

In this work, the solution-processed CH3NH3PbI3 perovskite/copper indium disulfide (CuInS2) planar heterojunction solar cells with Al2O3 as a scaffold were fabricated at a temperature as low as 250°C for the first time, in which the indium tin oxide (ITO)-coated glass instead of the fluorine-doped tin oxide (FTO)-coated glass was used as the light-incidence electrode and the solution-processed CuInS2 layer was prepared to replace the commonly used TiO2 layer in previously reported perovskite-based solar cells. The influence of the thickness of the as-prepared CuInS2 film on the performance of the ITO/CuInS2(n)/Al2O3/(CH3NH3)PbI3/Ag cells was investigated. The ITO/CuInS2(2)/Al2O3/(CH3NH3)PbI3/Ag cell showed the best performance and achieved power conversion efficiency up to 5.30%.

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High magnetic fields play a critical role in the development of modern science and technology, breeding many significant scientific discoveries and boosting the generation of new technologies. In the last few years, China has untaken a great deal of work on the application of Ultra-High-Field (UHF) superconducting magnet technology, such as for the Synergetic Extreme Condition User Facility (SECUF) in Beijing, the UHF nuclear magnetic resonance (NMR)/magnetic resonance imaging (MRI), nuclear fusion energy, particle accelerator, and so on. This paper reports the research status of UHF superconducting magnets in China from different perspectives, including design options, technical features, experimental progress, opportunities and challenges.

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