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NanoTerasu, a new 3 GeV synchrotron light source in Japan, began user operation in April 2024. It provides high-brilliance soft to tender X-rays and covers a wide spectral range from ultraviolet to tender X-rays. Its compact storage ring with a circumference of 349 m is based on a four-bend achromat lattice to provide two straight sections in each cell for insertion devices with a natural horizontal emittance of 1.14 nm rad, which is small enough for soft X-rays users. The NanoTerasu accelerator incorporates several innovative technologies, including a full-energy injector C-band linear accelerator with a length of 110 m, an in-vacuum off-axis injection system, a four-bend achromat with B-Q combined bending magnets, and a TM020 mode accelerating cavity with built-in higher-order-mode dampers in the storage ring. This paper presents the accelerator machine commissioning over a half-year period and our model-consistent ring optics correction. The first user operation with a stored beam current of 160 mA is also reported. We summarize the storage ring parameters obtained from the commissioning. This is helpful for estimating the effective optical properties of synchrotron radiation at NanoTerasu., Comment: 30 pages, 24 figures, submitted to the journal

Let $H^d$, $00$. In this paper we verify that the sparse operator ${\mathcal A}_{{\mathcal S}}$ maps ${\mathcal L}^p(H^d)$, $1\le p<\infty$, into an associate space of Orlicz-Morrey space ${{\mathcal M}^{p'}_{\Phi_0}(H^d)}'$, $\Phi_0(t)=t\log(e+t)$. We also give another characterizations of those associate spaces using the tiling ${\mathcal T}$ of ${\mathbb R}^n$.

With rectangular doubling weight, a~generalized Hardy-Littlewood-Sobolev inequality for rectangular fractional integral operators is verified. The result is a~nice application of $M$-linear embedding theorem for dyadic rectangles.

It is shown that the fractional integral operator $I_{\alpha}$, $0<\alpha

Early detection and identification of pathogenic bacteria such as Escherichia coli (E. coli) is an essential task for public health. The conventional culture-based methods for bacterial colony detection usually take >24 hours to get the final read-out. Here, we demonstrate a bacterial colony-forming-unit (CFU) detection system exploiting a thin-film-transistor (TFT)-based image sensor array that saves ~12 hours compared to the Environmental Protection Agency (EPA)-approved methods. To demonstrate the efficacy of this CFU detection system, a lensfree imaging modality was built using the TFT image sensor with a sample field-of-view of ~10 cm^2. Time-lapse images of bacterial colonies cultured on chromogenic agar plates were automatically collected at 5-minute intervals. Two deep neural networks were used to detect and count the growing colonies and identify their species. When blindly tested with 265 colonies of E. coli and other coliform bacteria (i.e., Citrobacter and Klebsiella pneumoniae), our system reached an average CFU detection rate of 97.3% at 9 hours of incubation and an average recovery rate of 91.6% at ~12 hours. This TFT-based sensor can be applied to various microbiological detection methods. Due to the large scalability, ultra-large field-of-view, and low cost of the TFT-based image sensors, this platform can be integrated with each agar plate to be tested and disposed of after the automated CFU count. The imaging field-of-view of this platform can be cost-effectively increased to >100 cm^2 to provide a massive throughput for CFU detection using, e.g., roll-to-roll manufacturing of TFTs as used in the flexible display industry., Comment: 18 Pages, 6 Figures

We investigate a simple forced harmonic oscillator with a natural frequency varying with time. It is shown that the time evolution of such a system can be written in a simplified form with Fresnel integrals, as long as the variation of the natural frequency is sufficiently slow compared to the time period of oscillation. Thanks to such a simple formulation, we found, for the first time, that a forced harmonic oscillator with a slowly-varying natural frequency is essentially equivalent to diffraction of light., Comment: 4 pages, 3 figures

The 2011 Tohoku tsunami entered the Kitakami river and propagated there as a train of shock waves, recorded with a 1-min interval at water level stations at Fukuchi, Iino, and the weir 17.2 km from the mouth, where the bulk of the wave was reflected back. The records showed that each bore kept its shape and identity as it traveled a 10.9-km-path Fukuchi-Iino-weir-Iino. Shock handling based on the cross-river integrated classical shock conditions was applied to reconstruct the flow velocity time histories at the measurement sites, to estimate inflow into the river at each site, to evaluate the wave heights of incident and reflected tsunami bores near the weir, and to estimate propagation speed of the individual bores. Theoretical predictions are verified against the measurements. We discuss experiences of exercising the shock conditions with actual tsunami measurements in the Kitakami river, and test applicability of the shallow-water approximation for describing tsunami bores with heights ranging from 0.3 m to 4 m in a river segment with a depth of 3-4 m., Comment: 26 pages, 13 figures

Let $n\ge 2$ be the spatial dimension. The purpose of this note is to obtain some weighted estimates for the fractional maximal operator ${\mathfrak M}{\alpha}$ of order $\alpha$, $0\le\alpha

Let $\sg_i$, $i=1,\ldots,n$, denote reverse doubling weights on $\R^d$, let $\cdr(\R^d)$ denote the set of all dyadic rectangles on $\R^d$ (Cartesian products of usual dyadic intervals) and let $K:\,\cdr(\R^d)\to[0,\8)$ be a~map. In this paper we give the $n$-linear embedding theorem for dyadic rectangles. That is, we prove the $n$-linear embedding inequality for dyadic rectangles \[ \sum_{R\in\cdr(\R^d)} K(R)\prod_{i=1}^n\lt|\int_{R}f_i\,{\rm d}\sg_i\rt| \le C \prod_{i=1}^n \|f_i\|_{L^{p_i}(\sg_i)} \] can be characterized by simple testing condition \[ K(R)\prod_{i=1}^n\sg_i(R) \le C \prod_{i=1}^n\sg_i(R)^{\frac{1}{p_i}} \quad R\in\cdr(\R^d), \] in the range $11$. As a~corollary to this theorem, for reverse doubling weights, we verify a~necessary and sufficient condition for which the weighted norm inequality for the multilinear strong positive dyadic operator and for strong fractional integral operator to hold.

A necessary condition and a sufficient condition for one weight norm inequalities on Morrey spaces to hold are given for the fractional maximal operator and the fractional integral operator. We clarify the difference between the behavior of the fractional maximal operator and the one of the fractional integral operator which is originated from the structure of Morrey spaces. Both the necessary condition and the sufficient condition are also verified for the power weights.

The Fefferman-Stein type inequality for strong maximal operator is verified with compositions of some maximal operators in the heigher dimensions. An elementary proof of the endpoint estimate for the strong maximal operator is also given., Comment: I find an error in the proof of Theorem 3.1 and I repair it in this version

The Fefferman-Stein type inequalities for strong maximal operator and directional maximal operator are verified with composition of the Hardy-Littlewood maximal operator in the plane.

In this paper under some growth condition we investigate the connection between RBMO and the Morrey spaces. We do not assume the doubling condition which has been a key property of harmonic analysis. We also obtain another type of equivalent norms., Comment: This is: Yoshihiro Sawano and Hitoshi Tanaka, Equivalent norms for the Morrey spaces with non-doubling measures. Far East J. Math. Sci. (FJMS) 22 (2006), no. 3, 387-404. (14 pages)

Let $\sigma_i$, $i=1,\ldots,n$, denote positive Borel measures on $\mathbb{R}^d$, let $\mathcal{D}$ denote the usual collection of dyadic cubes in $\mathbb{R}^d$ and let $K:\,\mathcal{D}\to[0,\infty)$ be a~map. In this paper we give a~characterization of the $n$ linear embedding theorem. That is, we give a~characterization of the inequality $$ \sum_{Q\in\mathcal{D}} K(Q)\prod_{i=1}^n\left|\int_{Q}f_i\,d\sigma_i\right| \le C \prod_{i=1}^n \|f_i\|_{L^{p_i}(d\sigma_i)} $$ in terms of multilinear Sawyer's checking condition and discrete multinonlinear Wolff's potential, when $1