9,624 research outputs found

    Relative commutants of strongly self-absorbing C*-algebras

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    The relative commutant AAUA'\cap A^{\mathcal{U}} of a strongly self-absorbing algebra AA is indistinguishable from its ultrapower AUA^{\mathcal{U}}. This applies both to the case when AA is the hyperfinite II1_1 factor and to the case when it is a strongly self-absorbing C*-algebra. In the latter case we prove analogous results for (A)/c0(A)\ell_\infty(A)/c_0(A) and reduced powers corresponding to other filters on N\bf N. Examples of algebras with approximately inner flip and approximately inner half-flip are provided, showing the optimality of our results. We also prove that strongly self-absorbing algebras are smoothly classifiable, unlike the algebras with approximately inner half-flip.Comment: Some minor correction

    Energy-Efficient Low-Complexity Algorithm in 5G Massive MIMO Systems

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    Energy efficiency (EE) is a critical design when taking into account circuit power consumption (CPC) in fifth-generation cellular networks. These problems arise because of the increasing number of antennas in massive multiple-input multiple-output (MIMO) systems, attributable to inter-cell interference for channel state information. Apart from that, a higher number of radio frequency (RF) chains at the base station and active users consume more power due to the processing activities in digital-to-analogue converters and power amplifiers. Therefore, antenna selection, user selection, optimal transmission power, and pilot reuse power are important aspects in improving energy efficiency in massive MIMO systems. This work aims to investigate joint antenna selection, optimal transmit power and joint user selection based on deriving the closed-form of the maximal EE, with complete knowledge of large-scale fading with maximum ratio transmission. It also accounts for channel estimation and eliminating pilot contamination as antennasM→∞. This formulates the optimization problem of joint optimal antenna selection, transmits power allocation and joint user selection to mitigate inter-cellinterference in downlink multi-cell massiveMIMO systems under minimized reuse of pilot sequences based on a novel iterative low-complexity algorithm (LCA) for Newton’s methods and Lagrange multipliers. To analyze the precise power consumption, a novel power consumption scheme is proposed for each individual antenna, based on the transmit power amplifier and CPC. Simulation results demonstrate that the maximal EE was achieved using the iterative LCA based on reasonable maximum transmit power, in the case the noise power is less than the received power pilot. The maximum EE was achieved with the desired maximum transmit power threshold by minimizing pilot reuse, in the case the transmit power allocation ρd = 40 dBm, and the optimal EE=71.232 Mb/j

    Pembelajaran Matematika Materi Geometri di SD Al Hikmah Surabaya

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    Permasalahan penelitian ini adalah bagaimana proses pembelajaran matematika pada materi geometri agar mudah dipahami, disenangi, dan tidak membuat siswa merasa bosan dengan materi tersebut hingga dapat mengantarkan siswa pada prestasi akademik di taraf nasional maupun Internasional. Tujuan penelitian ini untuk mendeskripsikan perencanaan, pelaksanaan, evaluasi, dan hambatan dalam pembelajaran matematika materi geometri. Metode penelitian menggunakan deskriptif kualitatif. Teknik pengumpulan data dengan wawancara semiterstrukutu, observasi nonpartisipasi, dan studi dokumentasi. Yang menjadi subjek penelitian adalah dosen ahli materi geometri, kepala sekolah, guru matematika kelas 5, dan siswa kelas 5. Hasil penelitian menunjukkan bahwa perencanaan, pelaksanaan, dan evaluasi pembelajaran matematika materi gemoteri kelas 5 berjalan dengan baik, runtut, menyenangkan dan tidak terdapat hambatan yang berarti bagi guru maupun siswa
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