Hydrodynamic aspects in ship motion problems are described with the linear potential theory. Although nonlinear direct simulations in the time domain are becoming common recently, it is of vital importance to understand the relations among hydrodynamic forces appearing in the ship-motion equations. In this paper, emphasis is placed on the relation between progressive waves generated by a floating body and hydrodynamic forces acting on that body, such as Haskind-Hanaoka-Newman relation for the wave-exciting force. The effects of ship's forward speed on hydrodynamic forces are also described by referring to Tuck's theorem related to the so-called m-term in the pressure integration on the body surface. Timman-Newman relation for the added mass and damping coefficients is explained by introducing the reverse-flow velocity potential.

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Magnetoencephalography is a non-invasive and real time research for the activities of human brains by measuring magnetic fields caused by primary (neuron) currents inside. Those magnetic fields are rather weak, but recent development of the device based on the super-conductivity (SQUID) has made it possible to measure them. First, we describe mathematical analysis to the models of D. B. Geselowitz and F. Grynszpan, particularly non-uniqueness of the full-inverse problem. Next, taking account of the finiteness of observed data, we formulate the discrete inverse problem. Several methods for solving the problem are summarized as over-and under-determined systems. We study their validities in connection with the underlying assumptions on neuron currents. Finally, we propose new algorithms to solve ill-posed problems such as parallel optimizations and so forth.

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This article gives a comprehensive account of quantum theory of statistical inference, whose necessity is recently rising, related to both of applied standpoints and fundamental standpoints. In quantum computation and quantum cryptography, etc, there is a need for extraction of precise information from quantum system, which is to be achieved by quantum statistical inference. Also, the development of the theory is expected to give a new insight to considerations of foundations of quantum mechanics. Centered on the asymptotic aspects of the theory, which is remarkably advanced by Japanese researchers in recent years, the article describe the quantum Stein's lemma in hypothesis testing, and the quantum Cramer-Rao type bound in parameter estimation, which is the minimum of sum of mean square error. For the illustration, the 2-and 3-dimensional-parameter quantum Gaussian state family are analyzed in detail. Historical overview of the theory, and brief review of other important works in recent years are also given. To supply background knowledge, we review asymptotic theory in the classical statistics and quantum measurement theory in the beginning.

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