We give necessary and sufficient conditions for the boundedness of generalized fractional integral and maximal operators on Orlicz-Morrey and weak Orlicz-Morrey spaces. To do this we prove the weak-weak type modular inequality of the Hardy-Littlewood maximal operator with respect to the Young function. Orlicz-Morrey spaces contain $L^p$ spaces ($1\le p\le\infty$), Orlicz spaces and generalized Morrey spaces as special cases. Hence we get necessary and sufficient conditions on these function spaces as corollaries.

Ryota Kawasumi Eiichi Nakai Minglei Shi

For the Hardy-Littlewood maximal and Calder\'on-Zygmund operators, the weighted boundedness on the Lebesgue spaces are well known. We extend these to the Orlicz-Morrey spaces. Moreover, we prove the weighted boundedness on the weak Orlicz-Morrey spaces. To do this we show the weak-weak modular inequality. The Orlicz-Morrey space and its weak version contain weighted Orlicz, Morrey and Lebesgue spaces and their weak versions as special cases. Then we also get the boundedness for these function spaces as corollaries.

Ryota Kawasumi Eiichi Nakai

Using data from more than ten-years of observations with the Akeno Giant Air Shower Array (AGASA), we published a result that the energy spectrum of ultra-high energy cosmic rays extends beyond the cutoff energy predicted by Greisen, and Zatsepin and Kuzmin. In this paper, we reevaluate the energy determination method used for AGASA events with respect to the lateral distribution of shower particles, their attenuation with zenith angle, shower front structure, delayed particles observed far from the core and other factors. The currently assigned energies of AGASA events have an accuracy of $\pm$25% in event-reconstruction resolution and $\pm$18% in systematic errors around 10$^{20}$eV. This systematic uncertainty is independent of primary energy above 10$^{19}$eV. Based on the energy spectrum from 10$^{14.5}$eV to a few times 10$^{20}$eV determined at Akeno, there are surely events above 10$^{20}$eV and the energy spectrum extends up to a few times 10$^{20}$eV without a GZK-cutoff.

M. Takeda N. Sakaki K. Honda M. Chikawa M. Fukushima N. Hayashida N. Inoue K. Kadota F. Kakimoto K. Kamata S. Kawaguchi S. Kawakami Y. Kawasaki N. Kawasumi A. M. Mahrous K. Mase S. Mizobuchi Y. Morizane M. Nagano H. Ohoka S. Osone M. Sasaki M. Sasano H. M. Shimizu K. Shinozaki M. Teshima R. Torii I. Tsushima Y. Uchihori T. Yamamoto S. Yoshida H. Yoshii

In this paper, we consider the predual spaces of weak Orlicz spaces. As an application, we provide the Fefferman-Stein vector-valued maximal inequality for the weak Orlicz spaces. In order to prove this statement, we introduced the Orlicz-Lorentz spaces, and showed the boundedness of the Hardy-Littlewood maximal operator on these spaces.

Naoya Hatano Ryota Kawasumi Takahiro Ono

Quadrupole electromagnets have been developed with a hollow coil produced using an improved periodic reverse electroforming. These will be installed in each of the drift tubes of the DTL (324 MHz) as part of the JAERI/KEK Joint Project at the high-intensity proton accelerator facility. Measurements of the magnets' properties were found to be consistent with computer-calculated estimated. The details of the design, the fabrication process, and the measurement results for the quadrupole magnet are described.

K. Yoshino E. Takasaki F. Naito T. Kato Y. Yamazaki K. Tajiri T. Kawasumi Y. Imoto Z. Kabeya

We study the problem of hyperparameter tuning in sparse matrix factorization under Bayesian framework. In the prior work, an analytical solution of sparse matrix factorization with Laplace prior was obtained by variational Bayes method under several approximations. Based on this solution, we propose a novel numerical method of hyperparameter tuning by evaluating the zero point of normalization factor in sparse matrix prior. We also verify that our method shows excellent performance for ground-truth sparse matrix reconstruction by comparing it with the widely-used algorithm of sparse principal component analysis.

Ryota Kawasumi Koujin Takeda

An Alvaretz-type DTL, to accelerate the H- ion beam from 3 to 50 MeV, is being constructed as the injector for the JAERI/KEK Joint Project. The following components of the DTL have been developed: (1) a cylindrical tank, made by copper electroforming; (2) rf contactors; (3) a pulse-excited quadrupole magnet with a hollow coil made by copper electroforming; (4) a switching-regulator-type pulsed-power supply for the quadrupole magnet. High-power tests of the components have been conducted using a short-model tank. Moreover a breakdown experiment of the copper electrodes has been carried out in order to study the properties of several kinds of copper materials.

F. Naito K. Yoshino C. Kubota T. Kato Y. Saito E. Takasaki Y. Yamazaki S. Kobayashi K. Sekikawa M. Shibusawa Z. Kabeya K. Tajiri T. Kawasumi

We derive analytical expression of matrix factorization/completion solution by variational Bayes method, under the assumption that observed matrix is originally the product of low-rank dense and sparse matrices with additive noise. We assume the prior of sparse matrix is Laplace distribution by taking matrix sparsity into consideration. Then we use several approximations for derivation of matrix factorization/completion solution. By our solution, we also numerically evaluate the performance of sparse matrix reconstruction in matrix factorization, and completion of missing matrix element in matrix completion.

Ryota Kawasumi Koujin Takeda

In this paper, we clarify the crucial difference between a deep neural network and the Fourier series. For the multiple Fourier series of periodization of some radial functions on $\mathbb{R}^d$, Kuratsubo (2010) investigated the behavior of the spherical partial sum and discovered the third phenomenon other than the well-known Gibbs-Wilbraham and Pinsky phenomena. In particular, the third one exhibits prevention of pointwise convergence. In contrast to it, we give a specific deep neural network and prove pointwise convergence.

Ryota Kawasumi Tsuyoshi Yoneda

We investigate the robustness of random networks reinforced by adding hidden edges against targeted attacks. This study focuses on two types of reinforcement: uniform reinforcement, where edges are randomly added to all nodes, and selective reinforcement, where edges are randomly added only to the minimum degree nodes of the given network. We use generating functions to derive the giant component size and the critical threshold for the targeted attacks on reinforced networks. Applying our analysis and Monte Carlo simulations to the targeted attacks on scale-free networks, it becomes clear that selective reinforcement significantly improves the robustness of networks against the targeted attacks.

Tomoyo Kawasumi Takehisa Hasegawa