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We report the discovery of a hyperluminous type 1 quasar (eFEDS J082826.9-013911; eFEDSJ0828-0139) at $z_{\rm spec}$ = 1.622 with a super-Eddington ratio ($\lambda_{\rm Edd}$). We perform the optical spectroscopic observations with KOOLS-IFU on the Seimei Telescope. The black hole mass ($M_{\rm BH}$) based on the single-epoch method with MgII $\lambda$2798 is estimated to be $M_{\rm BH} = (6.2 \pm 1.2) \times 10^8$ $M_{\odot}$. To measure the precise infrared luminosity ($L_{\rm IR}$), we obtain submillimeter data taken by SCUBA-2 on JCMT and conduct the spectral energy distribution analysis with X-ray to submillimeter data. We find that $L_{\rm IR}$ of eFEDSJ0828-0139 is $L_{\rm IR} = (6.8 \pm 1.8) \times 10^{13}$ $L_{\odot}$, confirming the existence of a hypeluminous infrared galaxy (HyLIRG). $\lambda_{\rm Edd}$ is estimated to be $\lambda_{\rm Edd} = 3.6 \pm 0.7$, making it one of the quasars with the highest BH mass accretion rate at cosmic noon., Comment: 9 pages, 3 figures, and 3 tables, accepted for publication in PASJ

Non-thermal components in the intra-cluster medium (ICM) such as turbulence, magnetic field, and cosmic rays imprint the past and current energetic activities of jets from active galactic neuclie (AGN) of member galaxies as well as disturbance caused by galaxy cluster mergers. Meter- and centimeter-radio observations of synchrotron radiation allow us to diagnose the nonthermal component. Here we report on our discovery of an unidentified diffuse radio source, named the Flying Fox, near the center of the Abell 1060 field. The Flying Fox has an elongated ring-like structure and a central bar shape, but there is no obvious host galaxy. The average spectral index of the Flying Fox is -1.4, which is steeper than those for radio sources seen at meter wavelength. We discussed the possibilities of radio lobes, phoenixes, radio halos and relics, and Odd Radio Circle (ORC). In conclusion, the Flying Fox is not clearly explained by known radio sources., Comment: 6 pages, 3 figures, Submitted to PASJ as Letter

We study the maximum number of quads among $\ell$ cards from an EvenQuads deck of size $2^n$. This corresponds to enumerating quadruples of integers in the range $[0,\ell-1]$ such that their bitwise XOR is zero. In this paper, we conjecture a formula that calculates the maximum number of quads among $\ell$ cards., Comment: 13 pages. 2 tables

EvenQuads is a new card game that is a generalization of the SET game, where each card is characterized by three attributes, each taking four possible values. Four cards form a quad when, for each attribute, the values are the same, all different, or half and half. Given $\ell$ cards from the deck of EvenQuads, we can build an error-correcting linear binary code of length $\ell$ and Hamming distance 4. The quads correspond to codewords of weight 4. Error-correcting codes help us calculate the possible number of quads when given up to 8 cards. We also estimate the number of cards that do not contain quads for decks of different sizes. In addition, we discuss properties of error-correcting codes built on semimagic, magic, and strongly magic quad squares., Comment: 20 pages, 8 tables

We study 4-by-4 squares formed by cards from the EvenQuads deck. EvenQuads is a card game with 64 cards where cards have 3 attributes with 4 values in each attribute. A quad is four cards with all attributes the same, all different, or half and half. We define Latin quad squares as squares where the cards in each row and column have different values for each attribute. We define semimagic quad squares as squares where each row and column form a quad. For magic quad squares, we add a requirement that the diagonals have to form a quad. We also define strongly magic quad squares. We analyze types of semimagic and strongly magic quad squares. We also calculate the number of semimagic, magic, and strongly magic quad squares for quad decks of any size. These squares can be described in terms of integers. Four integers form a quad when their bitwise XOR is zero., Comment: 24 pages, 10 figures

We discuss four famous card games that can help learn linear algebra. The games are: SET, Socks, Spot it!, and EvenQuads. We describe the game in the language of vector, affine, and projective spaces. We also show how these games are connected to each other. A separate section is devoted to playing Socks with the EvenQuads deck and vice versa., Comment: 21 pages, 13 figures